Master class with Ursula Keller
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00:00
Audio frequencyLaserQuantum opticsSolidShort circuitAngeregter ZustandJanuaryCombProzessleittechnikControl systemChemical substanceModel buildingReaction (physics)LadungstransferDumpy levelEveningShip classAngeregter ZustandYearAudio frequencyLaserAutomobileHull (watercraft)MeasurementSolid-state laserScale (map)CaliberNoise figureCircuit diagramAmplitudeSwitchAtomismNegativer WiderstandIntegrated circuitMovement (clockwork)SemiconductorAerodynamicsElectronOctober: Ten Days That Shook the WorldLecture/ConferenceMeeting/InterviewComputer animation
02:24
Plane waveEnvelopeUniverseNuclear physicsNatürliche RadioaktivitätLaserScale (map)FirearmUltraMast (sailing)Rolling (metalworking)Orbital periodGroup delay and phase delayYearAerodynamicsTypesettingSensorAtomismBrake shoeElectronic componentDirect currentNegativer WiderstandLecture/ConferenceComputer animation
04:37
LightLaserNegativer WiderstandWind waveEnvelopeLimiterAmplitudeOrbital periodShort circuitDisc brakeLightSpeed of lightMicrometerOrder and disorder (physics)Cosmic distance ladderNatürliche RadioaktivitätOpticsScale (map)AutomobileSensorSpectroscopyPump (skateboarding)Space probeLecture/ConferenceComputer animationDiagram
06:47
Short circuitSensorLaserIntensity (physics)AmplitudeBroadbandElectromagnetic spectrumOpticsCommunications satelliteProzessleittechnikMaterialNuclear fusionCombAudio frequencyAudio frequencyClockMeasurementAerodynamicsColor chargeTransfer functionElectronWire bondingWeather frontAtomismDampfbügeleisenLaserMeasurementGroup delay and phase delayWorkshopShort circuitSensorFlashtubeIntensity (physics)Communications satelliteAmplitudeProzessleittechnikNonlinear opticsMaterialMachineKeramikSolar cellLightLastHose couplingAudio frequencyYearComputer animationLecture/ConferenceMeeting/Interview
08:56
Crystal structureSynchrotronSource (album)LightPhotonWavelengthCrystal structureCylinder blockTrockendockWavelengthSynchrotronDiffractionSource (album)Energy levelSynchrotron radiationList of light sourcesSensorKilogramPhotonX-raySauerstoff-16ProzessleittechnikRelative datingHot workingWire bondingFullingComputer animationLecture/ConferenceMeeting/Interview
11:35
Crystal structureToolProzessleittechnikProzessleittechnikToolFuelSensorMicrometerDirect currentFlashlightPressure vesselHose couplingPhotographyRailroad carHandwagenVideoRegentropfenCrown (headgear)Computer animationLecture/Conference
13:34
Gas balloonProzessleittechnikPressure vesselAschenwolkePhotographyGunBlack holeLaserStörlichtbogenAerodynamicsCrown (headgear)Model buildingLightFlashtubePhotographySensorFlashlightAnalog signalLaserGas balloonAtmosphere of EarthPressure vesselLocherBallpoint penDayProzessleittechnikCartridge (firearms)Space probeKoerzitivfeldstärkeLecture/ConferenceComputer animationMeeting/Interview
15:44
LaserStörlichtbogenPump (skateboarding)Beam splitterProzessleittechnikLaserWoodFlightCosmic distance ladderController (control theory)FlashlightSpace probeSunriseAnalog signalGas balloonRoll formingWire bondingCrystal structurePhotodissoziationDiffractionWavelengthFuelX-rayKette <Zugmittel>Lecture/ConferenceComputer animationDiagram
17:46
Chemical substanceReaction (physics)MagnetismPhotonWavelengthAtomMovement (clockwork)DiffractionHot workingStandard cellPump (skateboarding)Space probeSurgical sutureSpaceportYearEffects unitEuropean Train Control SystemProzessleittechnikElektrooptischer EffektKüchenmaschineRoman calendarSunriseCrystal structureMint-made errorsSizingWavelengthX-raySensorFree-electron laserAerodynamicsHose couplingVideoLecture/ConferenceMeeting/InterviewComputer animationDiagram
19:47
DiffractionMovement (clockwork)Chemical substanceReaction (physics)Swimming (sport)Electromagnetic spectrumLaserVisibilityOrbitFree-electron laserWavelengthUniverseLaserActive laser mediumDiffractionMeasurementAerodynamicsYearNonlinear opticsInfraredSource (album)Optical tableAtmosphere of EarthVakuumphysikComputer animationLecture/Conference
21:49
Containment buildingVakuumphysikFlexibility (anatomy)Space probeLaserOptical tablePump (skateboarding)FullingYearClockHot workingMorningProzessleittechnikCommitteeKüchenmaschineSensorBallpoint penTypesettingDayVisible spectrumMeasurementElectromagnetic spectrumVideoDomäne <Kristallographie>AutomobilePlatingCogenerationLecture/ConferenceComputer animation
24:51
Short circuitOpticsCommunications satelliteAutumnCogenerationPlatingLaceDelay line memoryInterferometrySubwooferSensorMeasurementCommunications satelliteLaserClockCamera lensRulerBandwidth (signal processing)IndustrieelektronikCombined cycleNuclear power plantCableElectronOpticsPulp (paper)LightOptoelectronicsPhotonicsComputer animationLecture/ConferenceMeeting/Interview
27:25
OpticsCardboard (paper product)Short circuitSensorLaserCommunications satelliteIntensity (physics)AmplitudeElectromagnetic spectrumBroadbandProzessleittechnikMaterialNuclear fusionAudio frequencyAudio frequencyCombClockGlassSuperheterodyne receiverMeasurementPrintingElectricityGentlemanCableOpticsElectronCommunications satelliteProzessleittechnikSeries and parallel circuitsAmplitudeIntensity (physics)LocherMaterialPulse-width modulationTypesettingCut (gems)HeatQuality (business)SpitzenlastwerkKeramikFocus (optics)ForceLaserMicrometerUltraShort circuitWater vaporPrintingGlassComputer animationLecture/ConferenceMeeting/Interview
30:14
SensorSuperheterodyne receiverSharpeningLaserTransverse modeTrainElectromagnetic spectrumPrintingLaserLocherWeather frontShort circuitElectromagnetic spectrumInterferometrySensorCoherence (signal processing)SapphireVisible spectrumProzessleittechnikMode of transportVideoLecture/ConferenceComputer animation
32:21
Audio frequencyRulerElectromagnetic spectrumVideoTransverse modeLaserCrystallizationOpticsClockInterval (mathematics)Global Positioning SystemPiezoelectricityShort circuitSensorIntensity (physics)AmplitudeBroadbandCommunications satelliteProzessleittechnikMaterialQuartz clockNuclear fusionAudio frequencyCombMeasurementMechanical watchLaserVideoCrystal structureElectromagnetic spectrumMode of transportAudio frequencyRulerClockAtomic clockAngeregter ZustandMovement (clockwork)Mint-made errorsHot workingCrystal oscillatorHourglassDayHourWatchProgressive lensNegativer WiderstandLecture/ConferenceComputer animation
34:22
ClockQuartz clockNegativer WiderstandOpticsMeasurementCombSensorAudio frequencySignal (electrical engineering)AmplitudeIntensity (physics)BroadbandElectromagnetic spectrumCommunications satelliteLaserVideoAudio frequencyProzessleittechnikMaterialNuclear fusionClockAtomic clockGlobal Positioning SystemCylinder blockHot workingSatelliteMeasurementOpticsVideoNuclear powerAudio frequencyLightEngineTape recorderUniverseFrequency combNegativer WiderstandAudio frequencyElectronVisible spectrumElectromagnetic spectrumPhotodetectorComputer animationLecture/Conference
36:33
LaserYearOrbitCork (material)Frequency combWind waveScoutingSignal (electrical engineering)OpticsClockAudio frequencyAudio frequencyRulerMeasurementSensorStock (firearms)Data conversionLecture/ConferenceMeeting/InterviewComputer animationDiagram
38:37
Domäne <Kristallographie>Near field communicationOpticsIntensity (physics)ProzessleittechnikHarmonicYearGenerationAudio frequencyLaserChandrasekhar limitLaserAutomobileEffects unitNegativer WiderstandDomäne <Kristallographie>Audio frequencySensorNonlinear opticsProzessleittechnikOrbital periodVisible spectrumShort circuitLimiterLecture/ConferenceComputer animationDiagram
40:46
Rad (unit)KoerzitivfeldstärkePhotonWavelengthGenerationHarmonicLaserIntensity (physics)Order and disorder (physics)AtomGasActive laser mediumTARGET2Airbus A300Orbital periodNonlinear opticsAudio frequencyAmplitudeIntensity (physics)Near field communicationProzessleittechnikHarmonicInfraredFocus (optics)PaperVolkswagen GolfYearLaserMicrometerSapphireJet (brand)GasNeon lampOrder and disorder (physics)Perturbation theoryFrequency-shift keyingCombCoherence (signal processing)Frequency combGenerationMeasurementBird vocalizationEveningMolding (process)Computer animationLecture/Conference
43:18
Cork (material)AccelerationPhotodissoziationGround (electricity)Angeregter ZustandLaserLuftionisationPhase (matter)LappingModel buildingWater vaporX-rayMachineDiffractionPhotonicsProzessleittechnikIntensity (physics)LaserNoble gasElectronCoulomb's lawNegativer WiderstandNeon lampMembrane potentialLecture/ConferenceComputer animationDiagram
45:17
GenerationCombAudio frequencyContinuum mechanicsSingle (music)CollisionFullingOrbital periodElectronBallpoint penProzessleittechnikCombAudio frequencyFrequency combPhotonPhotographyMolding (process)Bird vocalizationElectromagnetic spectrumMode of transportHull (watercraft)Hall effectOpticsMeasurementPump (skateboarding)Homogeneous isotropic turbulenceMonthLecture/ConferenceComputer animation
47:50
YearKerr-EffektMechanismus <Maschinendynamik>LuftionisationSchwellenspannungProzessleittechnikGenerationOpticsIntensity (physics)LaserFarbstofflaserAerodynamicsSpace probePump (skateboarding)SapphireHot workingSolid-state laserShip breakingMorningCardinal directionPower (physics)Bandwidth (signal processing)Railroad carOctober: Ten Days That Shook the WorldComputer animationLecture/ConferenceDiagramMeeting/InterviewEngineering drawing
49:58
AmplitudePIN diodeCork (material)OrbitDomäne <Kristallographie>Power (physics)Source (album)PhotonTiefdruckgebietPlain bearingYearIntensity (physics)Ship breakingToolYearSpitzenlastwerkHall effectMachineLocherSharpeningValve amplifierSolar prominenceAir compressorFender (vehicle)Hot workingElectromagnetic spectrumGasFACTS (newspaper)Domäne <Kristallographie>MeasurementSignal-to-noise ratioPower (physics)Noise (electronics)Signal (electrical engineering)PhotonLecture/ConferenceComputer animationEngineering drawing
51:59
Negativer WiderstandLaserDomäne <Kristallographie>Valve amplifierTiefdruckgebietIntensity (physics)Roman calendarDomäne <Kristallographie>Intensity (physics)KeelPower (physics)Natürliche RadioaktivitätMeasurementApparent magnitudeSignal (electrical engineering)LaserSpace probePump (skateboarding)ProzessleittechnikHot workingSensorAtmosphere of EarthValve amplifierMachineGroup delay and phase delayNegativer WiderstandYearLecture/ConferenceComputer animation
53:59
Phase (matter)MeasurementPolarisierte StrahlungLinear motorElectronElectricityReference workQuantumMechanicCrystallographic defectPump (skateboarding)Space probeBird vocalizationInfraredMeasurementOrbital periodTrainElectronLuftionisationMultiplexed Analogue ComponentsClockLightOpticsRotationDayStopwatchClock faceMinuteLecture/ConferenceComputer animation
56:01
Quantum opticsAudio frequencyLaserCombJanuaryShort circuitSolidAngeregter ZustandMeasurementWavelengthSensorClockAudio frequencyLaserEnvelopePulse shapingShip breakingFlavour (particle physics)Apparent magnitudePlane (tool)AerodynamicsEngineOrbital periodIntensity (physics)Lecture/ConferenceComputer animation
59:20
Audio frequencyEnvelopeLaserBird vocalizationFullingRailroad carRadarmeteorologieGamma rayMusical ensembleGaussian beamIntensity (physics)Domäne <Kristallographie>TiefdruckgebietClockAcousticsToolNear field communicationModel buildingShip classOrder and disorder (physics)TurningLecture/Conference
01:02:33
Audio frequencyCosmic distance ladderOrbital periodNegativer WiderstandGamma rayNetztransformatorBird vocalizationElectromagnetic spectrumLaserFullingBasis (linear algebra)BrightnessHyperbelnavigationVoltaic pileEnvelopePair productionCartridge (firearms)Die proof (philately)Visible spectrumGround (electricity)Roll formingComputer animationLecture/Conference
01:04:32
GentlemanGemstoneParabolic antennaCell (biology)Electromagnetic spectrumVisible spectrumIntensity (physics)FullingTiefdruckgebietEnvelopeBird vocalizationRoll formingNegativer WiderstandContrast (vision)Selectivity (electronic)Audio frequencyPulse shapingSolidNanotechnologyVolkswagen GolfWeekBallpoint penBand gapBe starFender (vehicle)Bandwidth (signal processing)Lecture/ConferenceComputer animationMeeting/Interview
01:07:17
Anomale DispersionHull (watercraft)Active laser mediumLaserNanotechnologyActive laser mediumBandwidth (signal processing)MaterialAbsorption (electromagnetic radiation)Refractive indexSteckverbinderSpectral lineAudio frequencyAudio frequencyX-rayVisible spectrumDrehmasseElectronPhononYachtAnomale DispersionGlassGas turbineDispersionskurveRedshiftConstellationPulse shapingMassElectronic componentCosmic distance ladderElectromagnetic spectrumLimiterPhase (matter)Negativer WiderstandLecture/ConferenceComputer animation
01:10:20
Electronic componentBloomeryAnomale DispersionThin filmLaserWearElectromagnetic spectrumTypesettingRoll formingPlane (tool)NetztransformatorDirect currentElectric motorBook designMinerDisplay deviceRailroad carLecture/ConferenceComputer animation
01:12:29
Audio frequencyOrder and disorder (physics)FirearmWind waveDouglas A-20 HavocCartridge (firearms)Lambda baryonWavelengthSwitcherEnvelopeNetztransformatorCosmic distance ladderMaterialGroup delay and phase delayRadioactive decayComputer animationLecture/Conference
01:14:39
Phase (matter)FahrgeschwindigkeitEnvelopeFahrgeschwindigkeitSunriseGentlemanTurningBird vocalizationHose couplingPagerRefractive indexHot workingWeather frontPhase (matter)Wind waveEnvelopeNegativer WiderstandMorningMeasurementStonewareCylinder blockFood packagingMountainBiasingGroup delay and phase delayOncotic pressureMaterialAtmosphere of EarthGround stationLocherStar catalogueCell (biology)Computer animationLecture/Conference
01:16:44
Order and disorder (physics)Group delay and phase delayDIN 72552FahrgeschwindigkeitMassBrechungWavelengthRefractive indexEffects unitTurningFahrgeschwindigkeitGas turbineGroup delay and phase delayCosmic distance ladderTypesettingLambda baryonOrder and disorder (physics)Relative datingAudio frequencyElectronic componentCoherence (signal processing)Electromagnetic spectrumNoise (electronics)Interface (chemistry)Computer animationLecture/Conference
01:19:18
Active laser mediumElectromagnetic spectrumDomäne <Kristallographie>Linear motorLoudspeakerFuelLaserCamera lensSpace probeLightFiberPump (skateboarding)TARGET2Initiator <Steuerungstechnik>Visible spectrumShip breakingProzessleittechnikLinear motorElectromagnetic spectrumWeather frontVideoProgressive lensPhase (matter)Electronic componentCoherence (signal processing)Intensity (physics)Bird vocalizationAnomale DispersionSingle (music)Computer animationLecture/Conference
01:22:04
Intensity (physics)Quartz clockOrder and disorder (physics)Cash registerGroup delay and phase delaySawFiberElectromagnetic spectrumQuartz clockYearCamera lensMaterialNissan SunnyGlassOrder and disorder (physics)Linear motorLaserCartridge (firearms)Refractive indexCosmic distance ladderWavelengthCell (biology)Natürliche RadioaktivitätVideoGas turbineMicrometerApparent magnitudeKühlkörperFused quartzMetreGround stationComputer animationEngineering drawingDiagram
01:24:27
Camera lensHose couplingLaserMetreQuartz clockSensorPlant (control theory)Ballpoint penFused quartzActive laser mediumPotentiometerRoll formingLimiterAnomale DispersionNetztransformatorElectromagnetic spectrumComputer animationLecture/Conference
01:26:26
YearKerr-EffektCamera lensBelt (mechanical)Mechanismus <Maschinendynamik>YearElectromagnetic spectrumQuartz clockFused quartzLimiterMaterialAnomale DispersionLaserOceanic climateCamera lensGlassMode of transportLecture/ConferenceComputer animationDiagram
01:28:28
Phase (matter)Mode of transportLaserElectromagnetic spectrumFuse (electrical)Periodic acid-Schiff stainIntensity (physics)Optical cavityReflection (mathematics)Railway couplingMode of transportWorkshopLaserBallpoint penMolding (process)Electric power distributionTurningIntensity (physics)Band gapRoll formingBandwidth (signal processing)NanotechnologyPhase (matter)Noise (electronics)Short circuitModulationGameSaturdayAstronomisches FensterStandard cellCartridge (firearms)Solid-state laserWeightLecture/ConferenceComputer animationDiagramProgram flowchart
01:30:25
Periodic acid-Schiff stainPhase (matter)Electromagnetic spectrumMode of transportLaserIonDomäne <Kristallographie>Audio frequencyMode of transportBusModulationGentlemanAudio frequencyHull (watercraft)Domäne <Kristallographie>MultiplizitätMolding (process)Band gapModel buildingProzessleittechnikLaserCoherence (signal processing)SunlightCartridge (firearms)Electromagnetic spectrumBroadbandSEEDScoutingFrequency combDayQ-switchingShort circuitOptical cavityInterface (chemistry)Lecture/ConferenceComputer animationMeeting/Interview
01:33:10
Swimming (sport)Domäne <Kristallographie>Audio frequencyLaserCartridge (firearms)Audio frequencyMode of transportModulationYearPhase (matter)EngineProzessleittechnikFrequency combDigging stickEveningEffects unitTurningGameDayBelt (mechanical)Tire balanceElectromagnetic spectrumGate (airport)Quantum fluctuationShort circuitTransmission (mechanics)Domäne <Kristallographie>Fender (vehicle)Narrow gauge railwayAmplitudeComputer animationLecture/Conference
01:35:37
Optical cavityReflection (mathematics)Railway couplingIntensity (physics)Domäne <Kristallographie>Audio frequencyLaserModel buildingMode of transportMechanicAngeregter ZustandSpare partModulationSolid-state laserOpticsAcousticsLaceMagnetic susceptibilityWeightAbsorption (electromagnetic radiation)Astronomisches FensterShort circuitCell (biology)Tire balanceAmplitudeAmplitude modulationKey (engineering)NeutronenaktivierungStock (firearms)Noise (electronics)ProzessleittechnikLecture/ConferenceComputer animationDiagram
01:38:54
Band gapElectronAngeregter ZustandDensityElectrical conductorCarriagePhotodissoziationValence bandBulk modulusLaserMissileMeasurementPower (physics)MechanicHot workingAngeregter ZustandForceAbsorption (electromagnetic radiation)BahnelementMultiplizitätCartridge (firearms)SemiconductorAstronomisches FensterSemiconductorFuelLocherAbsorption (electromagnetic radiation)Station wagonTheodoliteBand gapWire bondingConduction bandElectronElectromagnetic spectrumValence bandLecture/ConferenceMeeting/InterviewDiagram
01:41:08
Angeregter ZustandDensityBand gapIntensity (physics)ElectronScatteringElektronenstreuungDirect currentVideoMonthThermalBand gapSemiconductorOrder and disorder (physics)Conduction bandCommand-line interfaceAbsorption (electromagnetic radiation)Noise reductionPhotodissoziationSelectivity (electronic)ModulationAmplitudeCombined cycleAnimal trappingSiliconMaterialMolekularstrahlepitaxieLecture/ConferenceDiagram
01:43:07
Domäne <Kristallographie>Audio frequencyElectronAbsorption (electromagnetic radiation)Conduction bandMaterialModulationAbsorption (electromagnetic radiation)SemiconductorSemiconductorAbsorbanceTrainMode of transportBird vocalizationCartridge (firearms)Angeregter ZustandSolid-state laserElectromagnetic spectrumYearAudio frequencyFrequency combSundialCombLaserSeasonDiagramLecture/ConferenceComputer animationMeeting/Interview
01:45:19
Domäne <Kristallographie>Audio frequencyAtmosphere of EarthAudio frequencyCombElectromagnetic spectrumTransverse modeVertical stabilizerLaserTrainJitter-EffektMeasurementNoise (electronics)BloomeryVisible spectrumPulse shapingCartridge (firearms)Electromagnetic spectrumLaserCardinal directionLimiterNetztransformatorTurningPhase (matter)Book designFrequency combLine segmentAmplitudeAmateur radio repeaterCoalMultiplizitätElectric power distributionRing strainTrainCombPolsterungVideoGreen politicsFaltenbildungComaSingle (music)Audio frequencyDomäne <Kristallographie>Bird vocalizationComputer animationDiagramLecture/Conference
01:48:34
Transverse modeAudio frequencyCombPhase (matter)FahrgeschwindigkeitGroup delay and phase delayAudio frequencyCartridge (firearms)Frequency combEnvelopeYearHot workingTrainCombElectromagnetic spectrumBird vocalizationRulerDomäne <Kristallographie>LaserGamePhase (matter)Mode of transportGroup delay and phase delayLecture/ConferenceComputer animation
01:50:54
RedshiftAudio frequencyAircraft carrierFeldelektronenmikroskopEnvelopeAudio frequencyGameMultiplizitätCartridge (firearms)SwitcherWavelengthOptical cavityMode of transportLaserLambda baryonGas turbineElectromagnetic spectrumRedshiftDirect currentModel buildingAudio frequencyFahrgeschwindigkeitFrequency combCombTrainLecture/ConferenceComputer animation
01:53:07
Audio frequencyCombFeldelektronenmikroskopAircraft carrierAudio frequencyEnvelopeAprilRedshiftTrainQuantum fluctuationRing strainCombSpieltisch <Möbel>Offset (film)Audio frequencyLaserTiefdruckgebietRSD-10 PioneerMechanicOptical cavityMolding (process)Cartridge (firearms)Counter (furniture)Mode of transportAbsolute zeroElectronic componentRedshiftMultiplizitätFrequency combEnvelopeRemotely operated underwater vehicleAircraft carrierLecture/ConferenceComputer animationMeeting/Interview
01:55:59
EnvelopeTrainMode of transportElectricityQuantumElectronMoonAudio frequencyOpticsCommunications satelliteAircraft carrierAudio frequencyOffset (film)EnvelopeTurningGas turbinePhase (matter)Frequency combRelative datingLaserNonlinear opticsProzessleittechnikSpare partString theoryLecture/ConferenceComputer animationDiagram
01:58:02
Phase (matter)FahrgeschwindigkeitGroup delay and phase delayLaserNegativer WiderstandGenerationNoise (electronics)Field strengthElectric generatorElectricityNonlinear opticsLaserAudio frequencyReference workMode of transportEnvelopeController (control theory)Aircraft carrierAudio frequencyTurningMonthGroup delay and phase delayFahrgeschwindigkeitHeatDiagramLecture/ConferenceComputer animation
02:00:00
Audio frequencyGunReference workAudio frequencySignal (electrical engineering)LaserFrequency combElectromagnetic spectrumInterferometryPaperVideoRep (fabric)Hall effectTelevisionNightSpare partToolAngeregter ZustandNonlinear opticsAirlinerMorningPhotodetectorMicrowaveComputer animationLecture/Conference
02:01:58
FeldelektronenmikroskopTransverse modeMeasurementAudio frequencyCombHarmonicMicrowaveInterference (wave propagation)SensorElectromagnetic spectrumElectromagnetic spectrumSignal (electrical engineering)Audio frequencyMicrowaveSpectrum analyzerFoot (unit)Nonlinear opticsPhotodetectorSolid-state laserPower (physics)TurningSpare partPotentiometerNyquist stability criterionYearKette <Zugmittel>Group delay and phase delayMechanicFahrgeschwindigkeitElectric motorOptical cavityPump (skateboarding)LaserPaperDayAtmosphere of EarthComputer animationLecture/Conference
02:05:24
EnvelopeSecond-harmonic generationDirect currentTransfer functionGenerationContinuum mechanicsAprilSensorChandrasekhar limitTransverse modeAudio frequencyCombHarmonicMeasurementElectromagnetic spectrumMicrowaveInterference (wave propagation)FeldelektronenmikroskopMinuteFiat 500 (2007)Organic solar cellJuneTransmission lineLuggerOpticsPhase (matter)PelzwareAbsolute zeroControl systemAircraft carrierVoyager programDuty cycleLaserWeightMicrophoneTiefdruckgebietÜberschallstaustrahltriebwerkFiberAudio frequencyTape recorderFiling (metalworking)LaserSapphireElectromagnetic spectrumInterferometrySignal (electrical engineering)MechanicNyquist stability criterionNoise (electronics)ButtonNonlinear opticsMonthTelevisionPaperAudio frequencyNarrow gauge railwayGroup delay and phase delayMultiplexed Analogue ComponentsFiberProzessleittechnikContinuum mechanicsData conversionHall effectIntensity (physics)Phase noiseWhiteShort circuitComputer animationDiagramLecture/Conference
02:07:30
FahrgeschwindigkeitSchwellenspannungNoise (electronics)Valve amplifierNegativer WiderstandLaserPhase (matter)Group delay and phase delayTrainOptische WeglängeNoise (electronics)WhiteGravitational singularityHot workingEnvelopeFighter aircraftValve amplifierTurningQuantum fluctuationAir compressorRulerGroup delay and phase delayFrequency combInterferometryTrainAmpouleSingle (music)Electromagnetic spectrumBroadbandBird vocalizationAudio frequencyRailroad carNonlinear opticsPhase (matter)Mode of transportAircraft carrierInterference (wave propagation)Fender (vehicle)Computer animationLecture/Conference
02:09:28
Interference (wave propagation)FahrgeschwindigkeitGroup delay and phase delayNegativer WiderstandLaserEnvelopeMode of transportTrainElectricityPhase (matter)ElectronQuantumSchwellenspannungNoise (electronics)Valve amplifierOpticsOptical cavityInterference (wave propagation)Electromagnetic spectrumFender (vehicle)YearSteelAudio frequencySpantFrequency combHose couplingTurningStaple (fastener)Nyquist stability criterionPhase (matter)VideoLaserHarmonicRelative datingGenerationCoherence (signal processing)ProzessleittechnikPaperBook designModulationElectronic mediaFiberMondayLinear motorPhase modulationContinuum mechanicsMinuteComputer animationLecture/ConferenceDiagramMeeting/Interview
02:12:42
Mode of transportLaserContinuous waveMolding (process)Rail transport operationsWind waveNoise (electronics)Transmission (mechanics)SwitchQ-switchingNyquist stability criterionCartridge (firearms)Optical cavityFundamental frequencyRailway couplingMultiplizitätHarmonicSubwooferLecture/ConferenceComputer animation
02:14:52
ElektronentheorieRailway couplingOpticsRear-view mirrorSemiconductorDiodeAngeregter ZustandSolidLaserBallpoint penMolding (process)Fundamental frequencyQ-switchingAbsorption (electromagnetic radiation)Single (music)Model buildingNyquist stability criterionMachineSolid-state laserCartridge (firearms)Mode of transportLaserDiaphragm (optics)SeasonSemiconductorOptical cavityOrder and disorder (physics)TypesettingController (control theory)SemiconductorAccess networkHot workingDyeingPump (skateboarding)ClockForgingComputer animationLecture/Conference
02:17:20
Pump (skateboarding)Space probeSignal (electrical engineering)MarsOpticsMeasurementHailColorfulnessModulationToolMicrowaveLaserDoorbellParticle physicsAngeregter ZustandAccess networkSemiconductorMaterialSemiconductorToolCartridge (firearms)Measuring instrumentAbsorption (electromagnetic radiation)ModulationAbsorption (electromagnetic radiation)ReflexionskoeffizientRear-view mirrorActive laser mediumAerodynamicsFluenceMode of transportHull (watercraft)SeasonWavelengthWeather frontMeasurementHot workingValve amplifierElectric motorCompact CassetteGroup delay and phase delayLock-in-VerstärkerComputer animationLecture/ConferenceDiagramMeeting/Interview
02:19:42
Transverse modeAcousticsOpticsAir coolingWater vaporPower (physics)Electric motorSignal (electrical engineering)SeasonPower (physics)MicrowaveMeasurementMeasuring instrumentNoise (electronics)Ship classMode of transportWater vaporModulationAcousticsKosmischer StaubYearLecture/ConferenceMeeting/InterviewComputer animation
02:21:47
LaserPaperTransverse modeOptical cavityEffects unitMode of transportOpticsMaterialLaserFinger protocolHot workingRail transport operationsMorningCrystallizationDayLiquidTypesettingFarbstofflaserJet (brand)PhotographyDyeingPaperAbsorption (electromagnetic radiation)Cell (biology)ModulationModel buildingVisibilityMode of transportOrbital periodYearSapphireOptical cavityGroup delay and phase delayFaxPhotocopierHose couplingLecture/ConferenceComputer animation
02:24:52
OpticsCPALaserSapphireGameDrehmasseAbsorption (electromagnetic radiation)Fender (boating)ModulationTire balanceFarbstofflaserAnomaly (physics)DyeingMode of transportWeightAstronomisches FensterHot workingCamera lensFlavour (particle physics)Fundamental frequencySeasonEffects unitOptical cavityMolding (process)Transverse modeHose couplingTransfer functionMultiplizitätLecture/ConferenceComputer animation
02:26:52
GentlemanMode of transportAvalanche diodeMinuteLaserGas compressorOptical cavityAnomale DispersionUran-238DoorbellMultiplexed Analogue ComponentsDimmerHull (watercraft)FirearmEffects unitRedshiftPhase (matter)Intensity (physics)Scanning probe microscopyInsect wingInterference (wave propagation)AmplitudeTransverse modeColor codeFiberPaperMode of transportPickup truckTypesettingSolid-state laserHot workingLaserMolding (process)SnowOptical cavityHose couplingColorfulnessFiberEffects unitAir compressorAbsorption (electromagnetic radiation)ModulationNoise (electronics)Atmosphere of EarthTire balanceModel buildingMorningMagic (cryptography)Book designNegationGroup delay and phase delayComputer animationLecture/Conference
02:29:21
Optischer HalbleiterverstärkerVanEffects unitProzessleittechnikIntensity (physics)ToolMode of transportPhase modulationHose couplingInterference (wave propagation)NegationWindAmplitudeOptical cavityFender (vehicle)WorkshopPaperKette <Zugmittel>Hot workingSemiconductorFiberSemiconductorSummer (George Winston album)DoorbellRear-view mirrorSwitchLaserModel buildingProgrammable Array LogicOrbital periodMolding (process)Lecture/ConferenceComputer animationMeeting/Interview
02:31:30
ResonanceBird vocalizationSemiconductorOptical cavityGas compressorUnterseebootÜberschallstaustrahltriebwerkRear-view mirrorSeasonHot workingOptical cavityCupboardCogenerationSemiconductorAbsorption (electromagnetic radiation)ViseReflection (mathematics)Atmosphere of EarthRailway couplingTemperatureFuse (electrical)Multiple birthScatteringLaserMultiplizitätQuantumWeatherCartridge (firearms)Order and disorder (physics)Energy levelPaperScoutingElectromagnetic spectrumProtectionSwitchDomäne <Kristallographie>SensorAnomale DispersionPower (physics)Computer animationLecture/Conference
02:34:58
MeasurementSignal (electrical engineering)Electric motorMicrowaveNoise (electronics)Measuring instrumentVisibilityCrystal habitComputer animationLecture/Conference
Transcript: English(auto-generated)
00:04
Good evening everybody. It's a pleasure to you here in my class. So we have a full program and I hope you will enjoy it. I mean The talk title is pretty long and I hope I can get you some of the excitement
00:22
That I have had during the last 30 years of my life and share it with you So it's a exciting journey from ultrafast laser physics to frequency metrology And of the second science and when I started this journey I never even thought I go into frequency metrology nor did I think I ever going to get into the auto second so
00:47
As an outline I would like to first give you a little bit of a taste an introduction a little bit of a feeling I mean I cannot go too much into the depths here and just a little bit of an idea how the measurement technique goes and
01:02
Evolves and then we go a little bit in more depth in the into lecture two and three about laser pulse and frequency cone and The ultrafast solid-state lasers. Okay, and so let me just jump in and basically give you a little bit of a calibration about the time and
01:24
Time scale and length scale in comparison So we are starting here with a second and the meter which is our daily life experience and then we go always About a factor of a thousand so from a second to a millisecond
01:40
Which is relevant for ski racing another thousand to a microsecond people still normally can kind of figure think what this is all about a nanosecond the typical switching time of Integrated circuits to a picosecond which is the oscillation of atoms in in lattices or on
02:02
molecules and then to femtosecond where you get into into really small molecule movement already in femtosecond dynamics in for example semiconductors and then you go not a Thousand which is then the up to second which is actually the movement of the electron on an atomic scale
02:24
So we are talking here 18 orders of magnitude that you can cover in your laser lab at a university Facility which you could not do if you would do that in space, right? If you go from a meter to a centimeter you are nuclear physics and then you know down here is something bigger in
02:45
terms of the equipment that you need to look at and then up to second basically means that's 10 to minus 18 second the femtosecond time 10 to minus 15 second and Sometimes people think gee, it doesn't really matter but there is actually a real application
03:02
that actually matter for the femtosecond and you can and An important V in Switzerland. We just started a long-term research pro program That is looking at ultra fast processes on an atomic and Fento and up to second time scale and
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This is actually entity our mast it involves 16 professor group all over Switzerland and has a Period over 12 years to address those fundamental questions because it is really the first time we can actually resolve the dynamics on the Atomic scale with femto and after second time resolution
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so if you are more interested if you type in entity our mast mast stands for Molecular ultra fast science and technology you can keep sure what is going on in Switzerland on this subject so when you go and
04:02
go into this kind of femto and after second the only way you get there in terms of Time resolution is with laser pulses and Normally, did you describe the laser pulse as follows? So All of you know how to write a plane wave that is propagating in set direction right with the fast
04:25
oscillating frequency component Omega zero and if you go to a fixed position you have the time dependent oscillation of Expanded in time Infinitely, right and the only thing you do then if you describe a laser pulses you multiply
04:44
these plane wave with a time dependent envelope instead of having a constant amplitude and This time dependent envelope is the so-called pulse envelope and that limits these fast plane wave oscillation
05:00
Over a certain time period right and you can make this one Very very short. I mean this is for example a very short pulse because it is comparable to the oscillation period so at 800 nanometer one oscillation period is basically a 2.7 femtosecond so
05:23
So when you look at it when you have a 5 femtosecond pulse, for example Then you have a light disk which is extended in space of over only 1.5 Micrometer that is moving at speed of light through the space right a flash of light Which is expanded over 1.5 micrometer
05:43
It's worthwhile to kind of imagine that you know Because the speed of light means that the light propagates in one femtosecond over the distance of point three micrometer, right? And it helps to keep a little bit the order of magnitude that at 800 nanometer one Optical cycle is 2.7 femtosecond, right?
06:04
so So on this time scale of basically going from a microsecond nanosecond Then Pico femto auto second the first time the femtosecond has been
06:21
Resolved this with ultrafast short pulsed Laser physics and I will explain to you how the techniques typically work. It's based on the so-called pump probe Spectroscopy and that actually allowed to resolve Chemistry chemical reaction of small molecules for the first time which was rewarded with a Nobel Prize in
06:45
1999 and now we actually got into this other second regime which allows us to actually resolve the dynamics of the
07:02
Chemical reaction ultimately the chemical reaction is moving of atoms but the electrons are responsible for the bonding the electrons are responsible for the transfer of charge of Transfer of energy and that's why if we really want to understand how it works It is helpful to really resolve the electronic dynamics
07:25
independent of the iron dynamics So when you look at the application of ultrafast lasers you have basically You can group the application based on the properties of the short pulses So the short pulses have a short time resolution. So it's a short flash of light which give you a
07:46
Good time resolution in measurement then you can have these flashes of light coming at really high repetition rate Which you can use for optical communication Clocking then you can concentrate the energy into a really short time duration, which
08:02
Which then pushes up the peak intensity? And you can use that for nonlinear optics or material processing. This is one of the Fastest growing market actually, you know lasers have been used in material processing for a long time But with the short pulsed lasers now we can do much more precise
08:23
Machining and also machine materials that normally would fall apart like ceramics or or Solar cells and so on and a short flash of light means We have a very broad spectrum and that gives a whole bunch of Application one of them which has been very popular over the last couple of years is the frequency metrology
08:45
So let me go a little bit more in details of all of that So when you look at first in the time resolution, you know when you go back to Francis Crick who said 1962 if you want to understand function study structure, so he's a chemist
09:03
So normally as a physicist, what do you really mean? that basically means If you know the structure of molecules, you know, for example a molecule who has kind of a docking end like this You know that this molecule if this one is fitting into this docking end It can dock in and have a function block a certain chemical reaction have a certain
09:25
healing whatever for pharmaceutical application, so this structure actually allows people to develop new medicine and to know this structure you need to have the
09:41
Wavelengths that actually resolves the structure over the diffraction. So therefore people have been building synchrotron light sources to provide the The wavelength's range in the ray in the regime of the structure that you want to resolve. So typically 20 nanometer to
10:02
To angstrom level the dimension of the molecule of the of the things But the synchrotron light sources have not really provided too much time resolution So it's really static structure But they have been booked out and have been extremely successful and just that you know where where this is going when you're talking about 20 nanometer to point one nanometer that you get a
10:26
little bit of feeling this corresponds to to A photon energy from the EV regime to the kilo EV So you really move into the heart x-ray regime in terms of your sources
10:44
Now what you would like to do actually and what people also discovered is that actually the static structure alone is not Always giving the full picture certain things only work For example how oxygen is bonding to the hemoglobin is only working as in a dynamical process
11:03
The static picture would not explain how the oxygen gets bonded and so in principle what you really want to ask is If you want to understand function study time dependent structure, but of course at that time In 1962 it was impossible to address the time dependence, right?
11:23
But today we can do that Okay, and the question is how do we do this? We basically use ultrafast science and technology now I explained in a little bit what this really means But generally you can say that if you develop new tools that allows you to see
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Processes which you normally cannot see you will discover something new which is beyond your imagination Because sometimes you can theoretically predict something But if you don't really have taken all the parameters into account you might not really predict the right outcome
12:05
Now to visualize that one give me I want to give you some example even in the one micrometer Time resolution you will encounter surprises. So normally if you shoot with a With a bullet through an apple you normally it makes bang and then you have Apple moose on the floor, right?
12:26
But you don't know how the Apple is actually falling apart, right? Normally, you would think oh well It's you know, the Apple moose goes in all direction as far as you can tell right no matter where you stand you get Get dirty, but actually if you can time resolve it, you know, if you get the flashlight
12:43
You know synchronized to the bullet correctly you can take this beautiful photograph and you can see that the bullet goes through the Apple and Actually, it explodes not only forward as you may think but also backwards After you see this picture. It actually makes sense. You can explain it. You can model it and
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Understand it perfectly. Well, what is going on? Right, and then another one like the cart when you should when you actually manage to hit the cart from the side and Actually shoot through it who would have thought you end up with this snake line here or
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Another one a blip into a milk right a drop into the milk It goes in blip and then actually something comes back and on the certain condition you create this crown Who would have predicted that this crown gets created now if this Now that you see it you can actually model it you could understand it and now imagine it would be a chemical reaction and
13:47
You never even put enough parameters into your model You never would have theoretically predicted that something like this occurs in in the dynamics and maybe Exactly. The crown is important to make it work at the end, right?
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So even in the mic one microsecond time exposure surprises are there Then what do you think is going to happen if you move? Into the femto into the other second in the other second where we don't even know what is going to happen, right? So, how do we now address the timescale which is going much faster than a microsecond the microsecond you can do with flash
14:26
Light flash photography, right? Did you have a dark room? You take a picture with the camera and The time resolution is given by the Duration of the flashlight right which is triggered at a certain time
14:42
now How do we do it with a laser? So let me take the analogy of flash Photography again where the bullet goes through an air balloon So I have an air balloon here Sitting here and the bullet went through this air balloon and you see it's already huge hole
15:02
in the air balloon, but you know, the balloon is still in pretty good condition, right and You know, how do you do this one now with the with the laser light? so normally you have a short pulsed laser a femtosecond or octosecond or picosecond and One pulse out of this laser is starting
15:24
Ultrafast process So in this case now if you take the analogy to this picture This first pulse is the bullet right is basically triggering the explosion of the balloon and then you take a
15:41
Soft a weaker a so-called probe So the strong pulse you call the pump right because it starts the process and then you take Through a beam splitter a weaker pulse and delay just through The flight time of flight, right, you know Distance here of a one micron gives you two times three point three femtosecond mechanically
16:06
You can step a fraction of a micron very well controlled stepping through right so you can control With a fraction of a femtosecond the delay of this second pulse This is the probe which is the flashlight that is looking how this
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Device on the test is Behaving so at this point now if I take this analogy with the flashlight This would be my flashlight right now if I then step through the delay Here and take a later delay
16:43
then The balloon is already You know falling apart a little bit more, but you can see it's still together and then a Little bit later the balloon is pretty much into pieces But the amazing thing when you look at this one the form of the balloon is still maintained
17:03
And now you can imagine if this would be a molecule of course a molecule falling apart You cannot you can basically Dissociate the molecule with a laser pulse right to make it fall apart But you cannot see it anymore with flashlight, so you need another
17:22
Visualization of this structure and one way to do it is through for example diffraction So if you do this pump and probe so the first pulse has the right wavelengths to dissociate for example this molecule and with the second pulse which is an x-ray pulse
17:43
It can resolve the structure of the molecule and you can actually then step through How this molecule is falling apart and you can model it right so this is basically the Standard technique that is being used for ultrafast spectroscopy It's called the pump and probe and you can then have any variation how you measure this one
18:06
using different Different Visualization of what of the device on the test that you want to look at and there is huge amount of Opportunities and a lot of things have been measured over the years
18:22
Okay, so you can actually look at chemical reaction. You can look at magnetic properties You can you get nanostructures. You can look at the higher molecules. It's it's a huge variety any any Surfaces catalysis process anything it doesn't have to be just diffraction. It can be an
18:42
Electro-optic effect it can be a magneto optical effect etc So it's a huge variety of Techniques that can be used but normally if you want to do do it on this Structure to resolve the structure then of course you need to have a wavelengths which is comparable to the size of the atoms and
19:06
The only way to get to that is into the soft and hard x-ray regime And that's why to get the time resolution of these dynamics People build all over the world the so-called free electron lasers because they
19:22
in addition to getting the Softened hard x-ray regime. They also get you the time resolution Okay, and for example in Switzerland we're also building one the one that is operating right now is at Stanford and more will come online in the next couple of years and
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As I said the resolution will be of these free electron lasers typically in the femtosecond and the Wavelength regime and the spatial resolution will be in the soft and hard x-ray regime
20:00
basically a wavelength of 20 nanometer to 0.1 nanometer basically an angstrom So what can we do at the university lab? I mean a free electron laser is not something you can have in your university lab So typically at the university lab we can have ultrafast lasers in the UV in the visible in
20:22
Infrared in the mid-infrared in the terahertz regime. This is all things that we can get readily can have in the lab We can get them down into the few cycle regime so that we only have one to a few cycle per pulse But the wavelength is of course not sufficient for diffraction measurement to resolve
20:46
molecules and so on so you need to resolve different optical properties To get the dynamics out of these measurements over the years basically people have
21:01
Discovered the so-called high harmonic generation and with the high harmonic generation Using for example the infrared of these ultrafast lasers amplified infrared pulses we can actually get up to a hundred EV and And potentially into the hundred octosecond regime and these are you know
21:24
this is for example a source that we build up at ETH that allows you to to get pulses in this Hundred octosecond regime in that regime the pulse of will become Will be absorbed in air and that's why everything has to happen in vacuum
21:43
So you reduce your laser table space into the space that you have here on the vacuum So to have these Containers here is just you know Having some flexibility when the laser goes in here to set up your experiments to do these pump probe Experiments because they have to be in vacuum so you can arrange it over the full laser table because we
22:07
We cannot obviously not really work in vacuum, right? so and then through all this work we discovered more recently the technique which we referred to as the other clock technique and with the other clock technique
22:22
We've been able to actually resolve the fastest processes in quantum mechanics such as for example the tunneling delay time and The other clock technique will be a topic of the plenary talk to talk tomorrow morning So after this master course, you should be then able to understand
22:42
That those experiments better tomorrow So let me go now a little bit more into the application So it's clear good time resolution the shorter your laser pulse the better is your time resolution And that's why it was clear for all these years We just try to get shorter and shorter and shorter pulses, right because every time we had shorter pulses
23:05
We got better time resolution in the measurement, right? Yeah. Yeah. Yeah just interrupt The spectrum becomes larger
23:21
You know, you always have to be The optical spectrum becomes larger right and then it depends on your measurement what are your Observables and how do you define the time resolution and the other clock is for example something where you can actually get very good time resolution without auto second time resolution without actually having a problem with the
23:45
With the Heisenberg on certain principles. So come tomorrow morning So it's always a question right what you measure in quantum mechanics What are your uncertainties right? What are your observables? I only gave you now a very simple group of type of experiments
24:03
which is this pump probe type of experiments, but there is different variation of Experiments where you also can get time resolution and one of them is the autoclop for example Where you actually work even with femtosecond pulses, which is amazing, too Yeah, how to get the pulses really short
24:32
Aha to do Okay, I mean normally I mean for example the autosecond you really have to be very careful
24:41
But in the autosecond domain you're in vacuum anyway And when you look at the picture of the auto line look at this here It's on a laser table and we actually put the on top of a laser table a plate Which is thermal thermalized so that you really have to in interferometric delay line
25:02
Which is in the sub femtosecond regime and with this one We have a hundred of the second time resolution and you can get it that accurately But you have to take care of it Right because the average at a certain delay for a long time depending on the measurement and you have to keep it stable Otherwise your time resolution is washing out. That's that's clear. Yeah
25:24
Absolutely Good So so good time resolution the short pulses, but there is of course a lot of other possibilities I mean in principle It's your creativity that allows you to come up with new measurement technique how to get
25:41
Good time resolution and it's actually funny the other clock we could have done Long long long time ago, but we simply didn't have the idea and it's actually only through You know detours that we came up and basically Created the other clock but more of that tomorrow
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So the other one is what you can also get out of these lasers is Pulses at a really high repetition rate and this is basically being used today so I mean you couldn't go onto your internet without actually any lasers and You know when you look at how the optical communication is going
26:21
I mean everything is growing more and more bandwidth is going I mean This is still growing exponentially and it's clear that that we will go up in Repetition rate from the gigahertz towards the terahertz in terms of the optical communication So we use it in long haul and you know, normally you lose you use
26:43
photons light for communication and electrons for switching why Light is not interacting very strongly So it's great for communication electrons are strongly interacting. So they're good for switching So that's why I think it's it's a good combination
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It's it's moving, you know optics is moving into the optoelectronic devices. So we already Replacing electrical cables. So this is in a in a data center, you know The data center becomes more and more you need to have a nuclear power station next to the data center
27:21
Right, and that makes them not so popular after all and you know when you look at the electrical electronic cables here It's a mess and already just replacing this electronic cable with optical cables You already get much better much cleaner
27:42
Interconnects and it's also clear I mean today already optics is down on this level, but in the future Optics will move in inside the computer as a communication between the boards and between the chips I mean already today we have multi-core
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Microprocessors and if we want to use and they will move to hundreds Thousands of course and if you want to use this course for parallel processing they need to process in Synchronizing synchronization, right and one way to do this is with optics between the two and so I think this is clear that the optics is also moving into into the
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Computer into the personal computer from all of us So the high peak intensity, of course, you know if you have such a high intensity you ultimately burn a hole
28:40
drill a hole into any kind of material and There has been a lot of studies done and you can do actually more precise material processing when you get into the shorter pulse width regime and the reason I mean The idea is called ablation Basically means when you come with the long pulses you have a tendency to melt the material and it is
29:04
It melts it gets injected like a volcano type of thing. You have to push put in more energy Whereas in in when you work with short pulses you can work with less Energy and you evaporate the material at each shot. And so it's a much cleaner less heat
29:24
Load on the device and so you can actually cut through glass through ceramics and Any kind of critical material? I mean, there is no iPhone that has not been touched by an ultra fast laser today right
29:41
so you can do a lot of extra things with additional things with With ultra short pulses you can be more precise. You can get better high surface quality You you can get functional surfaces that either, you know make the water
30:03
Attracted or rejected or you can have Material processing inside the material given by the focus and only at the peak power something happens 3d printing in the micrometer regime So not just macroscopic so there is infinite possibilities with this kind of laser and this is one of the
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Fastest growing market out there in industry and you can just think I mean you're getting very close to the holodeck Where you say what you want and it gets produced in front of your eyes, right? So we're getting closer and then of course the other things is
30:43
That the short laser pulses produce a very broad spectrum and the broad spectrum has a short coherence lengths for interferon in interferometry and that can be used for OCT so you can actually look into your eyes and just to get you a feeling
31:03
This is basically the resolution of the retina looked with Tie sapphire laser pulse 30 femtosecond and be and the optical spectrum of a 30 femtosecond laser pulse that goes penetrates a little bit into the material and and gets partially reflected and this is the spatial resolution that you get and
31:28
With a 10 femtosecond pulse you already get a much better resolution. And so you can actually resolve if if actually you're any Retina gets detached at a much earlier
31:40
position and time The Spectrum that you could get from a mode locked laser can be extremely broad through nonlinear processes You can make it cover the whole visible spectrum So the light becomes white if you go through a nonlinear process
32:00
But but the amazing thing is if you look very closely Actually when it comes from mode locked laser Then it is not continuous Averaged over all the pulses and I will explain that afterwards in the next lecture. It's not continuous It actually has a line
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structure and the line structure is equidistant Even if you have dispersion in the laser, which is actually also maybe something not so obvious, right? And So a mode locked laser Actually produces a ruler for the frequency
32:42
Because you have over the full spectrum you have each individual lines They are equally spaced and they're equally spaced which an extremely high accuracy and This spacing can be used to actually then build optical clocks so let me just very quickly give you an idea why an optical clock is
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More accurate than for example for example an atomic clock so how our clocks defined a clock is basically using an Repeted a periodic motion and you define how many?
33:22
repetition of this motion Happens per second. So in the slowest say one This is a second right? So and of course and then you just count this movement and This is how you define the time. So the faster this is swinging the smaller is the error on
33:46
A fraction of the count right on on say you make an error of one count over an hour or over a day Right. So the faster this is oscillating the smaller is the error So when we went from the sand clock to the mechanical clock to the quartz oscillator
34:05
We made a huge progress in the accuracy of the of the our watches I mean the quartz oscillator basically oscillates at 10 megahertz and we just count this 10 megahertz oscillation in which we can easily do and
34:20
Then the progress was then to go to the atomic clock, which is actually oscillating at 9 gigahertz 9 gigahertz we still can count Today at gigahertz, right? And that's why these atomic clocks are so accurate and all the satellites actually use atomic clocks in space And the GPS would not work if we wouldn't have these accurate clocks up there and we would have not
34:46
GPS also wouldn't work if Albert Einstein's prediction in general relativity theory We would have discovered general relativity theory with GPS if Einstein wouldn't have done it for us Earlier, right because then our measurements always would have been off and we would have tried to figure out why is it off?
35:06
And then we would have discovered the general relativity as well, right but The engineers would have discovered it, right? But Einstein was actually a little bit ahead of the engineers and and but but it was part, you know
35:20
It is out that the atomic the GPS wouldn't work so accurately So what is the optical clock the optical clock is basically that we take optical light Optical light what is the frequency of the optical light? It's in the heart. It's in the hundreds of terahertz Hundreds of terahertz we cannot count anymore
35:43
There is no electronics that can count hundreds of terahertz Right the fastest electronics are in the terahertz regime, you know, really good good University records, right but nobody can count in the hundred terahertz, so basically, you cannot use the optical frequencies as a fast oscillating to define the time and
36:08
With the frequency comb basically you can count because you have this frequency comb over the full visible Spectrum and then you take this unknown frequency that you want to count right and you just do it as a beating
36:22
Right. I mean if you have done a photo detector And to have this unknown frequency beating with the frequency comb. It gives you a measurable signal at Basically the beat signal which is the spacing of the frequency comb So if the spacing of the frequency comb is in the gigahertz you can count
36:42
Right as long as you know the the ruler Really well, and this is how do you know it and how do you stabilize this frequency comb? I will explain that in the next section But this is basically why the optical clocks going to be so much more accurate
37:01
And the hope is that with so with the optical clocks you can actually hear you can actually measure the wave that hit the UK beaches because they have a very specific Frequency and the gravitational waves from these waves You can hear I mean you can measure
37:22
within Paris with an optical clock Okay So and the idea is that hopefully maybe with the optical clock we can actually measure at one point if the Or our natural constant are actually constant over time and we do a measurement where we stay
37:45
Still alive during the measurement right if the natural constants are constant I mean, why should that be constant? We don't even understand them Where they coming from right? So then moving to up a second so moving to up a second really
38:07
Changed life for a long time, you know We were stuck in the few femtosecond regime in terms of the fastest time resolution That we could achieve with any means so in the mid 80s
38:22
The shortest pulses were produced six femtoseconds in Chuck Shanks lab at Bell Labs And that pretty much remained the technology improved We got the six femtoseconds easier and easier and easier over time, but we didn't get much shorter the breakthrough really came with the auto seconds and as so often in
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Laser physics is that it came as a total. I mean it was not. Oh tomorrow. I'm gonna discover up the second No it was kind of again by having lasers having tools available and just shooting into something and see
39:01
What is going on and the people who actually have all their eyes open and also look for the unexpected? are gonna see something and hopefully can explain it and And that's how the up the second science actually started so in the femtosecond and
39:22
Pico second time domain we can today easily produce these pulses from laser oscillators I mean you can get into the few cycle regime. You can buy these lasers You don't even need to build them anymore And there is even industrial applications of this time domain that are now
39:41
emerging and are becoming very strong and Then the next frontier is this other second time domain to really support this short time resolution you have to move up into the VUV X UV regime you need to increase your frequency
40:02
you need in intense femtosecond pulses to get there and You generate it through this Highly nonlinear process, which is the so-called high harmonic generation So, you know, I remember I told you a short laser pulse Is shown here at 800 nanometer the optical period is 2.75 seconds
40:23
So you cannot go much shorter than an optical period because then your optical spectrum goes You know DC at DC it stops because DC doesn't propagate Right, so so you have a finite optical spectrum and That basically limits your pulse duration to the femtosecond regime if you want to go to up to second
40:44
the only way to do that is to move up in frequency to shorten this period right and The way it was done is basically is high harmonic generation The first person who really saw the so-called plateau in this high harmonic generation was
41:04
Ann Lillie in 1988 in her paper, so Basically today what we are doing we are taking an intense infrared laser pulse Which is typically based on the Thai sapphire laser that produces five to thirty femtosecond pulses
41:22
We see enough intensity so that when we focus it into a gas jet like neon argon xenon With a peak intensity of about 10 to the 13 to 10 to the 15 watt per square centimeter The nonlinear process is so strong that we not only produce second harmonics third harmonic and so on
41:45
No, we producing many many harmonics and we're going up to actually Hundreds of the original harmonics, so we are going for we're going from the infrared 800 nanometer 1 micrometer and we move all so in the 1 e V regime and we're moving all the way up to
42:06
100 e 100 e V And you know what was surprising is normally when you do nonlinear optics the efficiency goes down Because it's a nonlinear process you do a Taylor expansion Perturbation theory and you expect that the efficiency goes down right every or higher order will have a lower efficiency
42:26
but the surprise was in the experiment is that the plot suddenly was a plateau and This plateau was basically first discovered by on on Lillie and this plateau was an equally spaced
42:40
Frequency comb that went Over time old all the way to 100 e V and then of course anybody who knows about mode-locked laser if you have an equally spaced Frequency comb if you take the Fourier transform you actually and if this is a coherent
43:02
Frequency comb you produce Autosecond pulses so early on it was predicted that there should be something Autosecond in there, but you know for the longest time you couldn't measure it I Mean the generation was kind of there but there was no way to measure it and actually
43:21
measuring out the second pulses was the first experiment that had to be built up and and actually designed and the concept had to be Made and so what you can easily get in the lab today is this plateau all the way to 100 e V People are moving of trying to push it further into the into the heart x-ray regime because of the diffraction, right?
43:46
I mean that I talked about in terms of the motivation But the efficiency just goes down more and more I mean the typical efficiency from what you're getting in here. This is at about 10 to minus 6
44:00
Right, but you start with so much that you still have enough photons to do experiments and How is the over time people learn to explain how it works and it was then on? until 1993 so you see the first Plateau was basically 1988 people said why is this possible?
44:24
Why is there a plateau people did not understand and over time came an explanation and The three-step model is the simplest way to explain this process so you have an electron in a in an atom like
44:41
neon argon Right noble gas and you bring in these really intense laser pulse So the electric field of your laser pulse bends the coulomb potential, you know every time You know going through the oscillation So it bends the coulomb potential and because the electric field is so strong in the short pulse
45:03
That that the electric that the coulomb potential is so strong event that the electron can tunnel out and As soon as the electron is out it gets accelerated and then stopped at the turning point when the electric field is turning around and then gets accelerated over the full half period
45:22
Slamped back into the atom and if the timing is right for this electron coming out here it can Get a lot of energy It's kind of like the slam shot where you lay the ball land and then you and you yank it back So not all electrons come back. So depending on when the electron comes here you get different
45:46
Final energy and so averaged over many of these processes You can cover the whole energy regime and you have a comb because this is a periodic process Every half a cycle the electron gets driven back the next half a cycle
46:02
So the spacing of this frequency comb is basically two omega Right half an optical cycle So it gets back then you have the overlap spatial overlap and the electron can recombine and they meet in XUV photon So it basically means when you have a longer pulse
46:24
You can actually get then a pulse out every half cycle So and if you fully turn if you assume that this one this frequency comb is coherent and you would fully transform it It's very similar to mode locking and you get a short pulse depending on how broad your spectrum is
46:42
And so you can easily get an octosecond pulse easily Conceptually if you can then deal with it then measure it and use it. That's a different thing, right? So assuming you have now a long strong infrared pulse This half cycle is happening many many times and so you get in the time domain
47:03
many of the second pulses repeated at half the optical cycle so at 800 nanometer optical cycle is 2.7 femtoseconds so every 1.35 femtoseconds there is a pulse coming and For pump probe, this is really fast, right?
47:22
There's not too many experiments that you can measure where you can just hit the device that you want to measure You know with a certain delay so fast with the next pulse because normally you want to hit the Hit the at the process a fast process and the fast process takes some time to evolve and then comes the next pulse
47:44
So 1.4 is very often too fast And so that's why for many application you would like to have just one Octosecond pulse and then last then for a long time nothing and then again up the second pulses and so if you actually take the pulse and make it shorter and shorter and shorter and
48:04
Then you only reach the threshold for the tunnel ionization and going back actually only during one Optical cycle then you can actually restrict this Recollision process and the single of the second pulse generation to one per of the sec per
48:23
femtosecond pulse right and then the repetition rate of this octosecond pulse is Given by the repetition rate of the strong Ventosecond pulse right and so for many experiments you actually would like to have that one But this requires that you have these really high intensities of the laser pulses
48:45
With really short pulses, which is not easy So normally the short pulses when you look at how how it evolved over time the first time you know The femtosecond pulses were produced were with so-called dye lasers and the whole time, you know the first
49:07
chemical Reaction dynamics and older original Pump probe experiments and so on were done in the 70s and 80s with these Dye lasers which was very hard to work with right and the breakthrough really came with the Thai sapphire laser
49:25
Because with the Thai sapphire laser We finally had a solid-state laser available that could produce that hadn't necessarily bandwidth and that could produce your Short pulses which much more power and much more ease So in the morning, you can just switch on this laser and then go on and do this experiment
49:43
Whereas in the in the car in this dye laser area, it was much harder to work with So for the octosecond, however, you need to then amplify these laser pulses out of a laser You don't have enough power at this point. I mean we're working on it of getting this done
50:01
so normally when you amplify you know the breakthrough to really high intensity to the millet tool regime or even much more of course is the sharp pulse amplification So you take the femtosecond pulse and first broaden the pulse so that the peak power is not so large that you start
50:21
Making a hole into your ear that you don't micromachine your amplifier, right? So you reduce your peak power Amplify and then push it together again and get your short pulses and we will discuss that in the lecture too how exactly this is being done, but then of course you have a
50:42
normally much longer pulses than you started off with because any Amplification you have gained nano wing and you have a much broader pulse afterwards and then you have to again May find ways how to compress it and there have been different techniques that
51:01
Have been developed. I mean one easy way is through filament compressor. So you just go through Some gases again and produce a broader spectrum that you can then compress again But you know, I cannot go too much into the details, but you can get now with different techniques
51:21
Back to the five femtoseconds through an additional compression so you can't just Amplify and then hope that you stay at the five femtoseconds You have to compress it again because the amplification unfortunately is broadening your pulse So these infrared pulses are then used to get the other second pulses
51:43
So that basically means in comparison to the femtosecond domain in the femtosecond domain, you know You have basically nanotube pulses at a hundred megahertz Which is a hundred milliwatt of average power and when you do measurements You're always a signal to noise is limited by average photon flux
52:03
when you take a One nanotube pulse in the other second domain it typically because you need this really high intensity to create the other second pulse These pulses come at the kilohertz So your average power is a micro watt so you have already five order of magnitude less signal to noise and
52:25
That's why there is hardly any measurements done in the other second domain Which is pump and probe so that you take an other second pulse to start a process and probe at other second time resolution so the first other second time Measurements have been done actually with some kind of streaking technique
52:44
But you know right now there's a huge amount of laser work going on to push the Power the average power up so that we can get the nanotube of the second pulses at a megahertz
53:00
But that of course requires high average power. So there is work going with amplifiers the Normally traditionally the amplifier. This is the pulse energy as a function of repetition rate Typically amplifiers are at a kilohertz or lower pulse repetition rate and You know, there is a lot of work going to push the amplifiers into the megahertz regime, but if you push
53:26
Every the repetition rate then you go into the average power you go into hundreds of watt of even thousand watt of average power right This is where where the money comes in and at the same time, you know, for example in my group we are pushing
53:46
the average We are starting with laser oscillator and we are pushing the average power of laser oscillators into the hundreds of watt kilowatt regime so that the short pulses directly come out of a laser and
54:02
I mean And and because of that we then can ultimately do it hopefully this octosecond pump and probe But meanwhile, you know, we do this streaking. So because these octosecond pulses have one advantage They have their synchronized to the infrared pulse, right? And so the first
54:22
Measurements have been done by using the octosecond pulse, which is much shorter than an optical period Remember, this is 2.7 femtosecond You have an synchronized to the octosecond pulse and infrared pulse And the infrared pulse is very well defined. So depending on
54:43
the timing when the electron comes out of whatever you're going to look at It will be amplified by the electric field of this infrared pulse. So you map ionization time to final energy
55:01
Right, so it's a streaking of this electrical field Depending on when the electron comes out. So you map time to energy This is the so-called streaking technique in the other clock. I'm using actually circular polarized light
55:20
And we know in a circular polarized light the electric field rotates in one optical cycle All around 360 degrees c so in one optical cycle Which is in the range of a femtosecond the electric field goes in full rotation And we know we can do time
55:41
Like a stopwatch we can do time measurements when we have this rotating electric field The time accuracy is better the faster the hand of the clock is moving So, you know the hour hand the minute hand the second hand and you make more and more accurate measurement
56:02
and for example if you work at a Center wavelengths of 735 nanometer as i've been using it in the other clock, you know one degree Equals to seven octosecond. So you have a perfect octosecond time resolution if you
56:20
anglery resolve your dynamics And this was the principle of the other clock how we resolve then the tunneling delay Which will be the topic tomorrow in more details? This is just to give you a little bit of flavor why we care about short pulses And what we can measure and the nice thing what I think what makes actually ultrafast laser physics
56:46
So exciting is that it's a very interdisciplinary approach So you learn the technology then you can apply it to engineering to biology to chemistry to physics You can go anywhere you want with this if you know the technology and this is what makes it so
57:06
Absolutely interesting. It's never going to get boring because there is always some open question in In some kind of a field that needs to be resolved and you can use the same kind of techniques, right? And that's why I think
57:21
ultrafast science, you know when you do a phd and then you move on and You can do a phd in physics and then move on to biology or whatever, right? That makes it actually so interesting and so rich So now let me go into the more detail
57:40
Basically the lecture two, where are we time wise? Okay We are now at basically So, um, yeah, I can keep going a little bit more and then we'll take a break so It's important that you understand
58:00
Some of the basics so so far i've been pretty general. Was it? Okay. Was it all known or was it? Was it? Okay, so you have a feeling right? Now of course we need to start understanding the pulses better So the topic of this second lecture in a little bit more details is about the laser pulse and the frequency cone
58:21
Okay So I want to go a little bit in more details about this laser pulse. So you already got used to the idea That you can describe this laser pulse With a fast oscillating electrical field, which is the same electrical field like in a plane wave, right? Which has this optical period and you just have a pulse envelope that limits the flash of light
58:45
the laser pulse into right duration So mathematically you can write it in a fixed position as a pulse envelope a of t times i e omega naught t, right? Okay, a can be complex doesn't need to be real
59:04
So normally very often you normalize a of t such so that the magnitude squared gives you the pulse intensity, right? So Let's take an example a gaussian pulse shape
59:22
Because you know from any experiments it matters what exactly the pulse envelope it looks like, right? So out of a mode lock laser Um, you either get typically a gaussian or a secant hyperbolic square, but i'll come back to it Gaussian is very often a good approximation People do all kind of approximation of pulse shapes
59:43
In in their calculus, but it makes it makes a difference sometimes so When we when we talk about the gauss pulse then the envelope is given by a gauss function e to the minus gamma t squared right and
01:00:00
the gamma can be complex so if if you have a complex gamma the real part of that one gives you you can do that easy this calculation and gives you the pulse duration and normally in a laser pulse the pulse duration if nothing is said the pulse duration is always full with half maximum
01:00:23
that's a convention and people sometimes are a little bit sloppy don't say it any more full base half maximum is the pulse duration so basically it is the intensity from the intensity full base half maximum this is the pulse
01:00:48
duration tau P when people talking about it right this isn't the convention like you have on a Gaussian beam that the radius is the e to the minus 2 right this is our conventions and then the complex term the complex term will have
01:01:07
here then an additional time dependent phase shift here on your laser pulse and that gives you a time dependent frequency right because if you have a
01:01:20
time dependent phase shift you can define a momentum frequency if you take the first derivative if you don't if gamma 2 is 0 then you will just end up with omega naught and if gamma 2 has a certain value then you get a time dependent frequency people always say oh time dependent frequency either
01:01:40
you're in the time domain or a frequency domain what about the time dependent frequency oh I'm blacking out right you know take a car on a road coming by me it makes you that's a pulse an acoustic pulse with a time dependent frequency it's not a linear chirp because it much easier you know
01:02:06
that's the Doppler shift right by by the car going by that's a time dependent frequency a bird that goes time dependent frequency music time dependent
01:02:20
frequency okay so it's actually everywhere everywhere so just relax right it happens and so so what does this mean to the laser pulse what does this mean now is this time dependent frequency the time dependent frequency means that the oscillations here that are equally spaced when gamma 2 is is 0 so that
01:02:48
you don't have a time dependence in the frequency then each period each distance of these oscillations is the same so every position inside the pulse you have the same spectrum the same center frequency but if you have a chirp
01:03:04
of time dependent frequency basically means that this period is changing over time right so when you look at the laser pulse these on what is the spectrum of the laser pulse because we need to know about the spectrum so we
01:03:24
know you can do the Fourier transformation to get the spectrum the Fourier transformation is clear so you take that the electric field as a function of T is basically the superposition of the different waves at
01:03:42
the specific frequency added over the full spectrum right E of Omega this is tilde here is my spectrum of this laser pulse so we how what's the spectrum of the pulse envelope mathematically you can show that the spectrum of the
01:04:03
envelope is can be described by this expression where Delta Omega is the difference to the center frequency so if you look at the this you can easily show if you do this equation it's a one-line proof that this is the case
01:04:21
so if you have the optical spectrum of your of your pulse it's centered around Omega or not in a Gaussian pulse you have a Gaussian spectrum because the Fourier transform of a Gaussian is Gaussian right so you have a Gaussian spectrum with a with a certain width normally the full width have maximum of an optical spectrum is again defined with the intensity of the
01:04:44
spectrum the spectral intensity full width have maximum and you can easily show now when you look at this equation here you can write it as Omega naught plus Delta Omega then pull out here the Omega naught then you
01:05:01
have here the spectrum of your of your pulse envelope so you can easily see that the spectrum of the end a pulse envelope is the same as the spectrum from the electric field pulse but shifted to zero so the whole
01:05:24
information about the pulse form the slowly varying in pulse form in contrast to the fast oscillation here is actually given by the form of the spectrum and it's basically in the pulse envelope right it's very easy so this is something you really need to remember the spectrum of the pulse
01:05:44
envelope the same as the electric field just shifted to DC by the center frequency Omega zero right so you can then easily go through the mathematic mathematics so we looked at the Gaussian pulse shape but you but
01:06:01
you can also get other pulse shape like secant hyperbolic square which is basically the so-called Soliton pulse in comparison to the Gauss pulse it's very similar to the Gauss pulse it's just a little bit and it's normally has more wings so if this is the Gauss you know the Soliton
01:06:21
pulse is a little bit has a little bit more wings okay not so nice but what is interesting when you then look at the full width half maximum of the optical spectrum on the full width maximum half maximum of the of the pulse you have a so-called time bandwidth product right this depends on
01:06:45
the pulse shape so for a Gaussian pulse you have a time bandwidth product of 0.44 for a hyperbolic secant it's 0.31 okay so meaning the the spectrum
01:07:04
here the spectral width is basically the product is 0.44 if you look at a spectrum for a given pulse duration it it depends a little bit how with how wide the spectrum is right so these are number for anybody who is working in
01:07:20
laser physics we know these numbers by heart right secant hyperbolic what this time bandwidth product is so what happens now when I sent this pulse through dispersion through a medium what happens you have dispersion so normally in a in a material so in a material you have certain absorption
01:07:43
and the if you look at the refractive index over kramers kronig you have a connection to the refractive index right so at lower frequency normally your refractive index is larger and then if you move above and above and above all absorption lines you ultimately go to one right refractive index one so in the
01:08:05
hard x-ray you asymptotically slowly but surely moving to one with actually a refractive index slightly below one right slowly slowly moving to one and we are normally with our infrared and optical spectrum we're somewhere in
01:08:21
between these absorption lines so normally you know we have the terahertz absorption these are the phonons and then we have the electron absorption which are in the UV and we are in the infrared and in the visible we are in in between and when we use glass we are in the
01:08:43
transparent regime and typically in this regime we have both so-called positive dispersion which is also called as normal dispersion and basically means the curvature of the refractive index as a function of frequency the second derivative the curvature is positive so the positive dispersion regime is
01:09:04
defined by this expression it's the second derivative why do you care about the second derivative and not the first derivative it's because for the pulse broadening how the pulse shape is changing the first derivative is
01:09:21
irrelevant the first derivative is only giving you a pulse delay but never a broadening and that's something which is intuitively when you ask people that's not obvious but you can go through the mass and show it and for a Gaussian pulse you can actually go through the mass very carefully so what
01:09:43
happens if you take a so-called transform limit limit the pulse a transform limit the pulse means you have the shortest pulse for a given spectrum when you have the shortest pulse for a given spectrum then you have an un-chirped pulse that means that you have nicely equal distance
01:10:04
between all the oscillations and then if you sent this transform limit the pulse through a dispersive medium then the different frequency components of this pulse will get different phase shift right and what
01:10:22
actually happens is you get a chirped pulse coming out different components in in your pulse will get different delays here and in the normal dispersion regime it is so that the blue comes first and the red comes
01:10:41
later in the positive dispersion regime and so when you do how do you calculate the propagation of a pulse you take you take the e of t you make a Fourier transform and how is the then this spectrum propagating it's very
01:11:03
easy it's e of omega times e to the minus car n of omega times set right it's a plane it's because each plane wave component is propagating like a plane wave because remember the notation in laser physics if you go to
01:11:22
quantum mechanics you have a different notation but in laser physics you use the electrical engineering notation for plane wave right so you have plus i omega naught propagating in positive set direction that means you know if you
01:11:41
take an equation out of the laser physics books you have to be aware that they normally use this notation if you take an equation out of the quantum mechanics book they use the other matters sometimes right it's just a sign so if you if you take the Fourier transform you let it propagate with
01:12:02
this phase shift and then you make a Fourier back transformation and it gives you then the pulse this is the input pulse and then you make a Fourier back transformation and then you have the pulse that is coming out and you can easily numerically calculate if you want to do it
01:12:24
analytically you basically do a Taylor expansion of the dispersion so you take your KN so the KN is the wave vector 2 pi over lambda right which is perpendicular on the wavefronts and is basically KN in the notation
01:12:45
always is K times N and this is the 2 pi over lambda where lambda is the vacuum wavelengths right so you then make a Taylor expansion of this one the
01:13:04
first derivative KN d omega times them then and so on and so you take the first or the dispersion is the first derivative second or dispersion is the second and so on that's the typical notation that people use right and so if
01:13:22
you then do this Taylor expansion you can actually go through analytically go through this Fourier back transformation in the slowly varying envelope approximation which I not have the time to explain but you can actually analytically derive what the pulse looks like so you put in a Gaussian
01:13:43
pulse at the distance set equal zero and let it propagate do all this Fourier transformation analytically this Taylor expansion up to the second order and this is what comes out and you can see then that that basically the
01:14:02
pulse envelope is propagating with the so called group velocity and out of this calculation comes that the group velocity is given by d omega derivative d KN and because normally in materials people give the dispersion N as a
01:14:30
function of omega or N as a function of lambda it is easier to calculate the group velocity as 1 over d KN d omega which is this first derivative of
01:14:46
the refractive index right so this is the group velocity and you can see here the phase fronts here from the electric field they are propagating with the so-called phase velocity and the phase velocity coming out of this
01:15:05
calculation which is a couple of pages right you have to go through all this math is omega over KN and it's clear this is not the same in a dispersive medium right so the phase velocity that's the speed at which this
01:15:23
fast oscillating electric fields are propagating is different than the pulse envelope you know that also in in waves on lakes right if you go very early on in the morning on a lake and throw a stone in it you can
01:15:43
actually see how the wave fronts come faster towards you then the whole wave mountain right the block of wave the wave packet the wave packet as a whole moves slower than the wave front so even on on border you have this difference
01:16:02
in the in phase velocity and the group velocity so this is very very important okay so that you have these two different velocities and I think from a notation point of view it's easy this is the group it's the wave
01:16:20
packet is the pulse envelope it's the whole group the energy is propagating with the group velocity so normally the material properties are given by the so-called cell Meyer fits you there is whole short catalogs I mean it's by
01:16:41
now it's all on the web you get the refractive index as a function of wavelengths and you can actually show this is a very useful table you can calculate basically the phase velocity as a function of the wavelength dependent refract the wavelength dependent refractive index is C over n the group
01:17:01
velocity it takes a little bit of mass to prove these two things but it's nothing miraculous you know you have to take into account that K is also omega dependent and n is omega dependent so you have to go through this properly and then you can show that this is the same right as a
01:17:23
function of the lambda definite so and then the group delay is the time it takes for the pulse to propagate over the distance set with the group velocity set over VG is the group delay and you can see here this is the
01:17:41
second is the first derivative of the face that you accumulate the face is always K and Z right so this is the dispersion first order is the group delay and then you have all the other terms the second and third order where are they coming in you can show that they actually coming in in the
01:18:04
pulse lengths so you get this regrouping of the frequency component in the pulse and the pulse lengths after certain distance is given by the second dispersion so the only the second order of dispersion gives you
01:18:22
a pulse change and higher of course right the third the fourth and so on the short the broader your spectrum right yeah yeah so far everything is coherent we are not destroying the coherence because all the spectral components are in face we don't create any additional noise you know if I would
01:18:44
create additional face noise here which would be a not a coherent superposition of all this spectrum then I would just create noise right so no no no everything is coherent at this point right everything because it's the superposition of ill each spectral campaign component and they are all have
01:19:06
a defined face and then while they're propagating they have only the face difference because of the propagation and then you can actually show a good value to know if you because in the lab you need to say is so you're
01:19:24
working with picosecond pulses you're working with femtosecond pulses can you send a 10 femtosecond pulse through a focusing lens if you want to do an experiment and ultimately want to focus you need to quickly check in the lab do can I send it through a lens do I need to take actually this pulse
01:19:44
broadening into account so now I work so much invested so much money got a 10 femtosecond laser in my lab and I now want to do an experiment the pump probe experiment and focus the light into my target can I use a lens or can I send it through a fiber what happens with the pulse so I quickly need
01:20:04
to check if this is okay and you know you can easily show that this more complicated dependence here can be actually in the regime if this pulse broadening becomes important meaning that the dispersion second order is much larger than the pulse the initial pulse duration then the final
01:20:24
pulse duration is at the dispersion second order times the optical spectrum now let me give you an example okay and but you know one more important thing and then we'll take a break I think let me see yeah then it's time
01:20:41
and unique and during the break you need to think about it please remember dispersion is a linear process is a linear pulse propagation meaning only the pulse in the time domain gets broadened the spectrum remains the
01:21:03
same the spectrum is unchanged you can prove that with a single line with things that are standing here in front of you and you think about it during your coffee and you know it's very easy to explain why the spectrum is
01:21:24
not changing in dispersive pulse propagation and therefore dispersion pulse propagation is linear which means when it's linear you can always regroup right you broaden this is the whole idea about chirp pulse amplification you broaden your pulse and then you bring it together
01:21:41
coherence is always maintained right so you always just regroup the different components right because you know you only get a phase shift right and the intensity of the spectrum will not change it's only a phase shift you know
01:22:05
it's also you know when you actually send the pulse through a fiber and the input spectrum and the output spectrum after the fiber is the same you actually pretty much know you are in a linear pulse propagation regime except
01:22:22
if things just compensate each other so it's a good check right okay now let's get a little bit of numbers because it always helps certain numbers you need to have in the lab to get a feeling right so let's look at for example fused quartz so this is a typical material fibers a focusing lens you know
01:22:44
a glass you know everything is kind of in the order of the same order of magnitude so a few squares refractive index at 0.8 micrometer thi-sapphire laser wavelength is 1.45 when I look at the first and the
01:23:00
second derivative I can calculate this out of the cell my equation and then calculate the first and the second dispersion order with this table that I showed you right this gives you then the first and the second order of
01:23:22
dispersion over a certain distance set right so you can easily calculate that so for a few squirts at 800 nanometer you have the second dispersion or there is 36 femtosecond square per millimeter okay now assuming you go
01:23:46
through one millimeter of few squirts your second order dispersion is 36 femtosecond that means if your input pulse is 6 femtosecond squared is 36 femtosecond you are kind of just getting into the regime where dispersion
01:24:05
pulse broadening becomes important right you want to have that this strong pulse broadening occurs when the dispersion second order is much larger than the input pulse duration squared so what happens if you send it
01:24:21
through more than a millimeter of few squirts you know until you get normally on the D under your device on the test on your experiment you may use a couple of focusing lenses and the focusing lenses are thicker than a millimeter right so assuming you invested a lot of money into a 10
01:24:41
femtosecond pulse laser system and you go through a couple of one centimeter of fused quartz couple of lenses then you're actually at the end after all these lenses after one centimeter so you get a pulse broadening
01:25:01
of a factor of 10 so at the end at your experiment you actually have a hundred femtosecond pulse so your whole time resolution is gone right if you actually would have gotten a cheaper hundred femtosecond pulse to begin with and send it through one centimeter of fused quartz nothing
01:25:23
would have happened you will still have the hundred femtosecond right no pulse broadening for the hundred femtosecond so an easy way an easy estimate does it matter when I go through stuff is this number fused
01:25:42
quartz 800 nanometers 36 femtosecond square per millimeter and you have strong pulse broadening if you're going through materials so that basically the the 36 times the lengths of all your dispersive medium is much larger than
01:26:03
the input pulse duration squared it's important to realize that this formula is only valid for an input transform limit pulse right a dispersive pulse broadening does not change anything on the spectrum that doesn't mean that if you
01:26:21
go through a few one centimeter confused quartz then your pulse is hundred femtosecond then you say oh yeah and now it doesn't matter I keep sending it through everything nothing happens it is the spectrum that does your pulse broadening right this formula is valid for an input
01:26:41
transform limit the pulse because the pulse broadening is given by your spectrum you understand what I'm saying so if you send it your 10 femtosecond pulse through one centimeter fuse quartz you say okay pulse broadening to a hundred femtosecond okay now I have a hundred
01:27:00
femtosecond now send it again through one centimeter of fuse quartz nothing happens so it remains hundred femtosecond no no no no because you know if you go through 10 centimeter at the end you have basically a picosecond it's the spectrum is the same right so the pulse broadening is
01:27:20
given by the dispersion second order which is becoming more and more and more the true material you go times the spectrum which remains the same for a 10 femtosecond pulse if you go to a hundred femtosecond pulse your spectrum is much narrower a transform limited on the femtosecond pulse right
01:27:43
but it but you get a chirped one through dispersion right so this gives you a little bit of a feeling how strong pulse dispersive pulse broadening is and you know you can easily get now commercial laser on the
01:28:00
table very tiny where we had to work very hard you know and you get your five femtosecond pulse in the laser and you need to know that you need to be careful and that's why you normally never use glass lenses you use reflective lenses so that you don't have this pulse broadening in the
01:28:20
focusing okay now how do you produce the short pulses let me give you a little bit of an introduction into mode locking the short pulses are produced with lasers and the technique is called mode locking and it goes back to the simple argument that if you in a laser I hope you all had your basic
01:28:42
laser already right this is a graduate course so I assume you had laser physics and you know that the laser has axial modes assuming the laser else lasers in many axial modes with arbitrary intensity distribution arbitrary phase if you Fourier transform that you just have noise right it's not coherent
01:29:04
and if you however take all your axial modes and give it a reasonable intensity distribution and a constant phase and if you Fourier transform that you get a short pulse right basically one over the spectral with the time
01:29:22
bandwidth product of the pulse now how do you do that normally you you do it through either active or passive mode locking so the time domain picture is very easy to understand right so you have a laser with a resonator you have
01:29:42
an amplification and the loss and you assume now you have a loss modulation the losses all the way actually in principle at the end of the standing wave and per round trip you go through the sinusoidal loss modulation and so the loss modulation you only get over gain saturate the game for a short time
01:30:04
window and so you obviously only get lasing for a short time window so if you have this loss modulation and you saturate this gain which is pretty low so you have just this up to rate the gain in a solid-state laser and the net gain window that gives you the short pulses now how is that fitting why is
01:30:25
this called mode locking how is this now connected to the mode you know what the sinusoidal loss modulator does right a sinusoidal loss modulator you can write this mathematically as a modulation depth times one minus
01:30:44
cosine omega MT the modulation frequency so if you send the pulse through this loss modulator you multiply it with this loss modulation in the time domain if you do go into the frequency domain a multiplication goes
01:31:02
into a convolution okay and the Fourier transform of for example just one axial mode which is a plane wave gives you a delta the Fourier transform of one minus cosine news gives you two side bands at the modulation frequency
01:31:23
if you convolve a convoluted you produce side bands around the center frequency so you push energy from your CW sent the frequency to the side bands at minus omega M and plus omega M and if this difference is exactly the
01:31:44
axial mode spacing you basically with this loss modulator push energy into the other axial modes so you push coherent this is a coherent process so you push coherent laser light into this axial modes and it's like in
01:32:02
section seeding and you you build up this whole frequency comb every time this one goes then through the loss modulator you again push side bands and that's how you build up over many round trip this this broad spectrum and that's why it's mode locking because it's a coherent process they're in phase
01:32:24
and it gives you the short pulse yeah yes it's different from Q switching I will come back to this one Q switching is definitely totally different this is a totally coherent process from pulse to pulse you know
01:32:45
each analysis I'll discuss in the next lecture a little bit the differences to the Q switching normally you don't get the short pulses with Q switching because Q switch pulses are always longer than the cavity round trip pulse around trip time and here you know in the laser the cavity round trip
01:33:04
time is in the nanoseconds yeah here you basically you to get a short pulse you modulate at the round trip frequency of your laser so you always modulate so that this modulation frequency is covering the axial mode
01:33:25
spacing right which is one over the round trip time of the laser okay so you modulate at one over the round trip and you build up this whole frequency comb and the whole process is is coherent this is kind of a quick
01:33:41
simple picture now you know when you then go through this build-up phase I mean of course you can show this all mathematical but it's good if you could build up a feeling for it before you go dig into the mathematics and you know and my lecture normally goes over a whole semester and not just one evening so all I want to get to you is right now a feeling right for this
01:34:04
whole process so basically when this pulse goes through the gain and the loss the loss is the sinusoidal modulation so as during the build-up time in the time domain your pulse becomes shorter because you have this loss modulation
01:34:21
which basically keeps makes the pulse shorter right you have this transmission through the pulse it basically drives the pulse to become shorter and then it goes through the gain the gain has a finite spectrum in
01:34:40
the frequency domain and your short pulse has a finite spectral width but you the peak of your of your spectrum will get more gain than the wings therefore when you go through the gain you get gain narrowing what does gain narrowing mean the pulse could be wider again then it goes through the loss the loss modulator push it together the gain pushes it
01:35:04
out and at the end you have a steady state and normally at steady state this fluctuation in the pulse is very minor it's small effects at the end or in the belt a build-up phase things are stronger
01:35:21
it's breathing heavier and then and at the end you have a balance right at the end is that the pulse shortening through the loss is compensated by the pulse broadening in the game and that's your steady-state solution right yeah
01:35:41
build-up time the build-up time in it depends on the on the laser but for example in solid-state lasers the mode locking build-up time can be even I mean normally would like to keep it below a microsecond because otherwise it's not self-starting so lasers tend to be less stable when the build-up
01:36:01
time takes too long so normally when you switch on a laser just to go into CW lacing is nanoseconds but the mode locking build-up time takes longer because you have this breathing and then you ultimately go into steady state so normally faster than a microsecond when it gets longer it becomes hard so
01:36:25
and now you understand when I do passive mode locking when I do passive mode locking I can actually get a loss mechanism which is much faster than the sinusoidal loss modulation that I normally do in active active mode
01:36:40
locking active mode locking I use like an acoustic optic loss modulator that goes at the round-trip time so it's a sinusoidal loss modulation but with a subtle absorber and I will give you an example afterwards you can get much faster curvatures I mean much stronger curvatures here and so from the
01:37:02
time domain it's very clear that you have a net gain window that is shorter that gives you shorter pulses but with this simple picture of the pulse shortening the stronger this curvature is the stronger the loss modulation pushes the pulse shorter right then this balance will come at a
01:37:26
shorter pulse so if I have a subtle absorber which is producing a self amplitude modulation then you can get shorter pulses and then the question is how does it start starts from noise because a laser you always have a
01:37:45
bit of noise and then one noise spike starts this process and builds up yes it's a subtle thing and that's why passive mode locking on solid-state laser hasn't happened for a long time and people for a long time were
01:38:03
thinking it's not possible exactly because of this thing at one point you want to get it started out of noise but you don't want to have it too noisy that the whole thing explodes it's a nonlinear process and it's only a window over which it's actually self starting and stable and that's exactly
01:38:23
the key and that's why for a long time actually this diopam solid-state laser have not been passively mode lock that was even the prediction that it can't be done when I was a graduate student right so ah okay so
01:38:51
normally when you have an active mode locker you have a sinusoidal active most so we only force it to one and here you need to adjust your
01:39:02
nonlinearity such that it only happens one a pulse because for a given average power if you have only one pulse per round trip you have the most energy and so you have to adjust your nonlinearity such that it is favorable that the laser has the lowest losses with only one pulse and
01:39:23
if we can get lower losses with two pulses it will go into pulses that's exactly the point the laser will always go into the state of lowest loss and if this nonlinear element allows it to have lower loss with multiple pulses it will go into multiple pulses and you need to prevent that also these are all
01:39:44
these in nonlinear mechanism that you need to prevent and that's why when you go into a passive mechanism you need to adjust all the parameters correctly to prevent that from happening that it explodes that itself you need to have itself starting not going into into instabilities Q switching
01:40:03
instabilities and multiple pulsing instabilities there's a golden window so give me I give you one example of such a subtle absorber most of you had basic semiconductor physics right as a physicist you had it so you know
01:40:20
energy and the density of state so in a bulk semiconductor you have the valence band with the holes and the conduction band with the electrons so if you have laser light which is basically allowing a direct transition from an electron from the valence band to go into the conduction band then
01:40:42
you push electrons from the valence band into the conduction band over the full spectrum of the pulse these electrons in the conduction band and that and if you do this very strongly it fills up all the states up here that means if all the states are occupied band filling you will have no more
01:41:04
absorption so the absorption goes down because you fill up the states and then these electrons here will scatter electron electron scatter will thermalize through phonons and we'll get a nice D rock party rocks
01:41:24
statistic which lowers the number of electrons this is the intra band thermalization this has been studied nicely in the 70s and 80s in semiconductor this intra band thermalization depending on where you go how far you go in the conduction band and and the curvature and so on is
01:41:45
in the order of a hundred tenth a second and then so it gives you initially a reduction of your absorption which can be very fast and then you ultimately have recombination removing the electrons again and in a
01:42:03
good semiconductor the electrons live for a nanosecond really long right so if you so this will will give you a long long tail but very often you know this is so fast because this is already happening if you for example if you
01:42:20
have a picosecond pulse this thermalization will already happening when you pump this up so this is will not give you a very strong modulation so everything is given by actually the recombination but the nanosecond is too slow this is a really slow modulation but you want to have a fast modulation to get the short pulses how do you make it fast if you
01:42:44
introduce mid gap traps for example low temperature grown gallium arsenide are being used for for electronics you know they don't have the oxide like in silicon electronics they have the oxide as an insulating material so the low temperature grown MBE grown material in gallium arsenide have been
01:43:03
used as isolating materials and they actually have mid gap traps and and they make the electron disappear from the conduction band and therefore make this this recovery so that the absorption much much faster and so by
01:43:25
actually doing material growth growth parameter how you grow it what material you take you can actually design your modulation you can actually design your response here how the subtle absorber is working and if you
01:43:44
know semiconductor physics you can dial it in and you know that's why the semiconductor subtle absorbers have been so successful and I will then in the lectures in the third lecture to go a little bit more into the detail of
01:44:00
that one you know that was actually then the semiconductor subtle absorber mirror the season that then mode locked the dial pumped solid state laser for the first time stably without any instability and self starting because we could dial in all these parameters very carefully and that's why they have been so successful now let me go before we go
01:44:23
into the detail of these subtle absorber let me go into the frequency comb because this is also another one we're a people so when I say to you a single pulse has a continuous spectrum but the pulse train has a frequency comb spectrum does this make sense to you let me repeat again a single optical
01:44:49
pulse has a continuous spectrum you saw it the Fourier transform of a Gaussian gives the Gaussian right continues but a pulse train gives you a
01:45:02
comb now let me show that mathematically and in a picture right now so when I talk about a pulse train means that because out of a mode locked laser every round trip a pulse comes out right so I have basically a pulse e of t repeated at every round trip time coming out of this laser the round trip
01:45:27
time t are one over the pulse repetition rate coming this short pulse okay and the pulse duration of the short pulse is given by the optical spectrum you know one you know depending on the pulse shape the Delta spectrum
01:45:45
west times the pulse duration is 0.44 or 0.31 or whatever right so assuming this is a transform limited pulse constant phase over the pulse duration but repeated at every round trip time how do I write this mathematically I can
01:46:06
very nicely write this by this following notation this is actually in Sigmunds book that's how I learned it when I was a graduate student actually before frequency combs with that notation have been invented so you have
01:46:21
actually you know what the Delta function is right it's one peak infinitely high infinitely narrow at Delta function it's a distribution but you know we call it function so if we have now a pulse train repeated so it's a infinitely narrow this is a Delta comb right you add a Delta peak at
01:46:47
multiples of the round trip time right so this is your pulse train but this pulse with the Delta peak is infinitely narrow and infinitely white so if you then can convoluted this with the with a pulse the way we discussed
01:47:07
it then you get actually a pulse repeated at every round trip right can you follow this so this is how you write mathematically a pulse train this
01:47:20
is actually some of the most useful thing because that's how you can actually so easily describe how frequency coma stabilized and so on everything the whole Nobel Prize how you do it is one line okay also let's go through this one so the Fourier transform of a frequency comb is not a
01:47:44
continuous spectrum because of single pulse it would be the green line right but because we are repeating this pulse we end up with the frequency comb but why the Fourier transform goes with a convolution goes into a
01:48:07
multiplication the Delta comb Fourier transforms you can takes a little bit more effort but it actually goes in also in the frequency domain into a Delta comb you can prove this one nicely takes a little bit more so I'm
01:48:21
not going to do this but you can look it up in basic Fourier transform books a Delta comb in the time domain or in the frequency dome goes over in a delta comb in the in the Fourier transformation and the spacing is then when here the spacing is the round trip time then this is the frequency
01:48:44
comb with the spacing with the repetition rate 1 over R is the repetition rate and then multiplied so you have here basically the envelope of a infinitely frequency comb therefore a pulse train produces you a spectrum
01:49:03
which is not continuous but has a comb easy right mathematically clear it has to be like this right so that explains why when we look at the full
01:49:23
spectrum from a mode-locked laser you actually have the comb the ruler in the frequency domain is it even constant when you have dispersion so in a laser you have a gain like an amplification so is this comb even constant if you
01:49:44
have to take you know if you get this pulse shorter and shorter and you have a really broad spectrum is it equally spaced what about the dispersion what determines the mode spacing is it the phase velocity the
01:50:01
group velocity so let's do a vote what determines the spacing of the frequency comb from a mode-locked laser is it the phase velocity hands up why is it the group velocity hands up why you know you have a 50% chance
01:50:30
when you guess right yeah it's a pulse but could you show it mathematically what about the axial mode spacing you can actually show mathematically it's
01:50:45
the group velocity so you know you know at steady state you know the axial mode spacing you know is you sent the pulse through one round trip and the gain minus loss so gain equal loss and you have a phase shift for
01:51:03
the pulse which must be a multiple of 2 pi the phase shift is this again the phase shift is 2 times KN at the ax at whatever wavelengths times L the lengths of the laser resonator and that means it's a standing wave laser
01:51:24
resonator you go twice through the laser lengths right so this is the phase shift so this should be multiple of 2 pi and then the spacing would be PI right so Delta lambda lambda and plus 1 minus V lambda M normally the
01:51:42
axial mode spacing is pretty narrow right in the big laser like this it's very narrow so you can look at this as a first derivative times the spectral width and if you take the first derivative of this phase shift here you
01:52:00
have to derivative of KN in here and that gives you the group velocity and not the phase velocity right so the the spacing on this mode lock laser and visually it is like this otherwise you know your your laser would not be stable either right the pulse would not be a steady-state solution going through
01:52:23
a dispersive medium so it's the group velocity so you can even show it nicely mathematically so it's a group velocity now the frequency comb has basically the repetition rate is given by the round trip time coming out right
01:52:42
of this pulse train and does it go to zero normally not normally you know a frequency comb has two things what happens if it doesn't go to zero let me first maybe show you look so normally if you have a laser that is not
01:53:08
stabilized your pulse train has fluctuation in arrival time which is breathing of your comb and you can have translation these are the two degrees of
01:53:21
freedom right breathing and translation translation is by this offset and this one is the breathing right so how to stabilize the repetition rate was actually already done in the 80s actually what my professor where I did
01:53:42
my PhD he was one of the pioneer to stabilize the mode locked pulse train with really low timing chitter and how do you do that you just put the out one of the mirrors in the laser resonator on a piezo and make sure that that you adjust the cavity length such that the pulse repetition rate
01:54:03
which is just a round trip time one over the counter is constant right so that's easy adjusting that one but how do you do the translation what physical mechanism is the translation you could stabilize it to an absolute frequency
01:54:22
right but what is actually doing the translation so let me go back what is the translation so assuming there is an offset fco I called it but you know why I called it like this it's not because it's the chief executive officer
01:54:46
has another reason which which comes out just in a little bit so let's just say there is an offset in comparison to zero of this whole frequency comb which otherwise is equally spaced n times the f right so I can then write this
01:55:04
pulse train with an additional offset instead of so I take F now for frequency right F minus M repetition rate minus an offset if I Fourier transform this one with an offset I can actually take the shift theorem of the Fourier
01:55:22
transform what is the shift theorem of a Fourier transform it gives you an exponential multiplication here so this shift the thing will give an exponential component here and of course multiplication goes into
01:55:40
convolution so you have an additional time dependent phase shift here of your pulse which is the pulse envelope this is normally your center frequency Omega zero so this is the carrier which Omega zero I call now the
01:56:01
carrier which is the center frequency is the carrier in optical communication and so on carrier because you modulate information onto the center the carrier frequency so Omega C is the carrier and then I have a time dependent so I have a time dependent additional phase shift of this pulse through that right
01:56:24
through this offset so what does this mean it means that I have the electric field has a different variation assuming here it's at maximum the electric field with the pulse envelope but if I have a time dependent phase
01:56:43
shift the electric field will not be all the time at the maximum with the envelope that's why and this one is the derivative here to this phase shift but
01:57:01
it's not continuous it's per pulse so it's there basically the change of the phase from one pulse to over the time TR gives you the offset and that's why we called it the carrier envelope offset frequency so if I stabilize the
01:57:28
translation of the frequency comb I stabilize the electric field underneath the pulse envelope which was actually the problem that I tried to solve at that time in the 80s I wasn't in the frequency metrology I
01:57:42
wanted to solve that problem because we got shorter and shorter pulses and we wanted to do you know think about it if you have a laser pulse that goes with electric fields fluctuating every pulse when you have this five femtosecond pulse and you want to do high harmonic generation right it's a very highly nonlinear process it matters if you have an electric field
01:58:02
of this strengths or of this strengths otherwise it's a noise generator right each pulse is another maximum electric field it's total noise generation in nonlinear optics extreme nonlinear optics so we want to stabilize this one so we've realized oh this offset is actually related to this offset to this
01:58:25
translation but then we still had the question how do I measure this offset so of course if you have a very stabilized laser somewhere as a reference you can do the meat beating and stabilize it to an external
01:58:40
frequency but then you need an additional laser you lock your mode locked laser to which cost money there's a cheaper way and there and actually and also something also important when you do the mode locking you only you
01:59:01
you normally only have control over the pulse envelope nothing on the electric field the electric field is not stabilized in mode locking only the pulse envelope so normally out of a laser each pulse has a different carrier envelope offset frequency if you have it running so but you can actually
01:59:22
control this one inside the laser and it's actually any difference in the laser any knob which is a different between the face and the group velocity can control the position of this one right because this one is propagating with the face velocity and this one is the group velocity so if I have a knob that
01:59:43
allows me to adjust the group velocity and the face velocity I can make them always coming exactly the same way as long as I can measure the carrier the carrier envelope offset frequency but how can I measure the carrier envelope
02:00:00
frequency here without an additional reference it's this one down here I don't have any normally I don't have any signal down here and I don't want to bring up another stabilized laser which is really expensive how do you do that and the really clever way that we proposed actually in collaboration with
02:00:24
tele was basically this F to 2f interferometer before henshman hall published 99 that's the paper I gave you to read so basically if you have a very short pulse which is covering more than an octave then the frequency doubled
02:00:45
spectrum of this pulse will have an overlap with this fundamental spectrum so what is this overlap doing because this overlap is not perfectly overlapping with the fundamental when the CEO is not zero and you can show that with one
02:01:04
line and there is the whole invention one line let me go you through the math right so this is your frequency comb f1 co plus n times f rep is the fundamental pulse the new frequency double the pulse so it's 2f12 is the
02:01:24
blue one right each stick now when you look at then if this is a more than an octave and you take the higher frequency part of your fundamental pulse which is at 2n f rep so the f2 is the higher frequency part of your
02:01:43
fundamental pulse is co plus 2n f rep is this f2 and you beat it with the lower frequency part of your frequency double spectrum you actually get a beat signal if you just look at here on a photo detector put it on a microwave
02:02:01
spectrum analyzer you see huge signal this is the pulse repetition rate and this is the CEO frequency so and you can see that this is the beat because the if you take basically the 2f1 minus the f2 the 2f1 minus the f2 gives you
02:02:24
the CEO frequency so as long as you have a spectrum that is covering more than an octave so that the frequency double spectrum has an overlap with your fundamental you can see it on a photo detector and spectrum analyzer and if
02:02:42
you can see it you can stabilize it it's kind of like you know if he bleeds you can kill it right so there is some fundamental because you know as an experimentalist if you see if you measure something then you just turn knobs and try to understand what makes things change right and you
02:03:06
know anything that changes the face and the group velocity differently will change the CEO right so actually what it turns out when you actually modulate the pump laser a little bit it will shift the CEO so you can actually watch
02:03:26
on your RF spectrum analyzer when you change things how this is jumping all over the place and if it moves you just figure it out you know always have to have a stabilization mechanism you know I told you for the repetition rate
02:03:41
you change the cavity lengths right but that also changes the CEO because in air you still have a little bit of dispersion may be negligible difference between group and phase velocity in air still a little bit also changes the CEO but then with the power you can actually show that if you
02:04:04
modulate the pump power for example on your laser it changes the group and phase velocity differently than when you do the cavity links so they are not independent knobs but as it turns out actually you know sometimes life is very nice to you actually as it turned out for the solid-state lasers I mean
02:04:24
many years later after we understand and so on actually it even helps you so that there are not independent knobs and at the end you can get it even more stable than if you would have had in independent knobs you know it's
02:04:40
complicated but you know believe me sometimes sometimes you know life is just good for you you know there are days where basically no matter what you do it always gets worse but there are days no matter what you do it always gets better and you just enjoy it when it happens right this is one of them
02:05:02
first you think this is oh it's a problem actually it turns out if you do it right it actually can be good most of the time if you understand it you can most of the time find an application that you actually even can use it to make it better electrical engineers feedback loops they're very
02:05:22
clever they can do it okay so this is what we published in this paper at that time actually we we had the world record in Thi sapphire laser and we didn't had an octave spanning spectrum so we didn't have enough spectrum enough signal to do this directly F to 2F as it was later on this was then
02:05:46
called as the F to 2F interferometer you know F to 2F interferometer technique basically we didn't have enough signal to get enough beat signal to noise on the beat signal because you need about 30 DB to do a good
02:06:02
feedback loop and stabilization mechanism and so we came up with a whole bunch of different techniques how you can do it you know if you actually do frequency doubling and frequency tripling you can actually work with narrow spectrum for example once you understand this equation you can come up with a whole bunch of other ones right once you understand this so that's what
02:06:24
we actually showed in this paper a whole bunch of different techniques where you only you needed different spectral widths now what tele and hench group did they actually used the microstructure fiber so what they realized is you don't really need the shortest pulses from the Thi sapphire
02:06:44
laser you can create a very broad super continuum with this microstructure fiber you get white light out of this but normally normally you always think when you have an extreme nonlinear process you have a lot of AM to PM conversion basically meaning intensity noise producing a lot of phase noise so
02:07:05
these whole white light might not be continue not not coherent and it's true you know not all white light that you produce which is your pulse is coherent but with the reasonably short Thi sapphire pulse it is coherent and
02:07:24
actually then you can use this one then you have more than an octave of spectrum and can do this f to 2f beating and get this stabilization what what's amazing is actually that even so you produce this white light how coherent it is there is a little bit of noise this is true but it is amazing how
02:07:46
little noise you produce again something which you normally would think poof shouldn't work but it works this is the amazing things so so this whole you know what you can do today you can actually stabilize the electric field
02:08:05
underneath the pulse envelope you need to do that there are commercial products out there you can even amplify these pulses compress them and they're still stable which is pretty much amazing when you think about it because any any difference between group and phase velocity so if you have
02:08:24
fluctuation in the path lengths or if you go through amplifier on compressors you have to be a little bit careful how you do it that it that you don't introduce differences noise in this otherwise it creates noise so in the amp so this basically this f to 2f interferometer uses basically pulse
02:08:46
train because you it's built on this frequency comb idea but in amplified pulses very often your repetition rate is really low so you deal with individual pulses and not miss a lot of pulses coming an individual pulse has a
02:09:01
continuous spectrum so how do you do it then so if you have a very broad spectrum a single has a continuous spectrum you frequency double it and if they are overlapping and the CEO face is not arbitrarily going in fluctuation mode you actually because the CEO face gives you an additional phase
02:09:22
shift right in the carrier then you can actually resolve the spectrum I mean the interference at the wings of the spectrum if you know remember in the pulse the CEO goes don't you know I know it gets a little bit late but you
02:09:41
know remember ah here you see here if you have this one is related to this CEO phrase so if you have not the stabilized frequency comb you have an arbitrary face and if you do an interference with an arbitrary noisy
02:10:00
face in there you don't see interference right so that's why if you then do the frequency double and and you have a staple you only see interference if you actually have the CEO phase stabilize and so if you have single pulses you
02:10:21
see the interference at the overlap of the spectrum if you have arbitrary free running laser you normally don't see interference and so you can see nicely the interference fringes on each pulse stabilized or not right and
02:10:41
that's how you use today these lasers to oh my god and we are only a lecture to basically to do the high harmonics so you need those co stabilized pulses to do the high harmonics and the other second pulses now are you ready for until 12 o'clock or what yeah this is a very good
02:11:13
question under what condition is the super continuum generation coherent there's a whole book written about this one because you know in these in
02:11:24
these in these microstructure fibers there is a whole bunch of nonlinear processes starting there is self phase modulation self steepening among you name it there is so many nonlinearities and the amazing thing is
02:11:42
that it's actually much longer coherent than you think that's the amazing thing but to really predict the coherence on this super continuum you need to run the numerics so John Dudley has one of these review paper written
02:12:00
about that one which I would encourage you to read it's nonlinear pulse propagation so far we only did linear pulse propagation so there's a whole lecture you know on nonlinear pulse propagation which we haven't really touched so we would be here for a long time okay lecture three so we're
02:12:27
getting let me oh you know how long can you hold how long can you go yeah I know five minutes let me just give you a little bit of because there was an
02:12:43
earlier question about Q switching versus mode locking and so on so you know when you look at the different mode of operation in a laser you can have it CW running ideally in one axial mode right continuous wave one axial mode or then you can have it running in Q switched one axial mode Q
02:13:07
switched multi axial mode Q switch which normally causes a lot of noise or Q switched mode locked or mode locked so we looked at this one now CW mode locked right so the Q switching normally I cannot I don't have the time
02:13:25
to explain it to you how Q switching is done but the Q switching is defined you can get stable pulses but if they're Q switch the pulse duration is always longer than the cavity round trip time because as soon as it is shorter
02:13:41
it is repeated at the round trip and then it goes into the Delta calm and the whole thing right so the pulse duration is always longer than the than the cavity round trip time so you know either you make the laser really really short or otherwise forget about the short pulses I mean femtosecond is very hard to get with Q switching and then mode locking fundamental mode
02:14:04
locking you want to have one pulse per cavity round trip right and then the pulses are repeated at every round trip going through the output coupler you can have situation this is also stable that you can have multiple pulses
02:14:22
per cavity round trip but most of the time you don't really want it because then you need to make make sure that then the pulses are really stable in fundamental mode locking it's stable either it stops mode locking or then it's it's really only one pulse in in harmonic mode locking you need to then stabilize this sub harmonic pulses against each other and you can
02:14:44
you otherwise they introduce noise they will mix with each other and this is not such a healthy situation so normally you want to run your laser in fundamental mode locking but you know depending on if you have a subtle absorber inside the laser it can also go into Q switched mode locking and
02:15:03
that's normally if you are lucky you have pulses mode lock pulses which are then strongly modulated like in a Q switching regime slower than the round trip time but this is normally also not something you want because then each pulse is modulated not each of them are the same so for many application
02:15:24
that is not desirable so normally you either want to go into single stable axial Q switching but long pulses or then CW mode locking and the breakthrough for diaphragm solid-state laser was really by introducing the season where I could adjust all the parameters correctly to
02:15:47
make itself starting to prevent Q switching to make only one pulse per cavity round trip and this is because with the semiconductor I could change a lot of things all the parameter is it's you had the full control of all all the
02:16:03
things and you know and traditionally people knew about I pumped solid-state laser or they knew about semiconductor physics and I was lucky at Bell Labs after my PhD I had access to semiconductors and diaphragm solid-state laser and it was as usual when you can you make a breakthrough when you
02:16:25
actually have an interdisciplinary effort but I could now stand here and you know it has been a success story so I invented the first device I did 1992 and I could say oh I was so smart and I knew everything but the
02:16:40
reality is you know the most important breakthroughs are coming because you nearly stumble onto it and by trying to understand something that maybe didn't even work out then what you wanted to do so don't get too upset if your experiment doesn't work maybe you are at the edge of a major invention right
02:17:05
so you need to understand why your experiment doesn't work because that gives you normally a lot of ideas I mean this is actually how we invented the other clock the experiment didn't work so so I could give you now a
02:17:21
large lecture how smart I was with this one but you know I was lucky I was in a lab with a lot of tools I had a lot of equipment and the measurement tool and I just stumbled on and was smart enough when I actually stumbled on to and something I knew that this is maybe good okay and so I followed up on
02:17:46
it so I explained to you how we semiconductor suitable absorber you can get a custom-designed recovery time so you can actually custom design your your modulation your self-amplitude but another important thing was you know when you know when when you put this this
02:18:05
semiconductor suitable absorber on a mirror right then as soon as you saturate the absorption the reflectivity goes up and it will ultimately saturate and when at what pulse fluence this reflectivity starts
02:18:23
to saturate how strongly it saturates which is the modulation depth and how much residual losses you have this all plays a role in in your mode locking dynamics and you need to adjust that right to make it work and if it
02:18:43
happened the semiconductor was an ideal situation and and you know you can get the semiconductor basically a season at any length any wavelengths but now let me give you a little bit of an idea how I stumbled onto it how the
02:19:02
idea evolved because you know it was really it was really as a PhD student I actually I actually did a master's degree in physics so when I nearly became a theoretical physicist and then I went for my PhD to Stanford and you
02:19:20
know at the beginning I didn't even know what a lock-in amplifier was you know I mean I had no idea about measurement technique and I ended up being with an electrical engineer as a professor and when I joined his group I didn't understand a single word they talked about DB and you know the other PC student of course said oh take the HP 8566 you know they knew all the
02:19:45
instruments by the number of the manufacturer and I kind of was thinking oh my god I'm in nerd country to the power of 10 okay but I stuck it out okay I learned DB DBC and all this stuff and actually what I've learned
02:20:03
with my miss an electrical engineer as a PhD advice I learned measurement technique I learned microwave technique and that actually these whole measurement tools and noise characterization helped me afterwards for every measurement I did afterwards in the lab where physicists didn't see a
02:20:22
signal I could see the signal and if you see a signal you can optimize it and stabilize it no no it's true when you see a signal you can improve it if you don't see a signal you can turn whatever you're blind right what I have learned with this with actually learning good electrical engineering
02:20:44
education in experimental physics I can tell you this helps take some like classes in electrical engineering because that basically made it for me to make a difference and so you know basically when I invented the season you
02:21:01
know it replaced all this active mode locking so this was a typical active mode locker that I used for my PhD in the lab with an acoustic loss modulator needed RF power water cooling and it was replaced by a season you know and it did it all and even better and that's you know the picture before and
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after and that's why it was a success because it basically nobody does this anymore everybody does this and that's why it was successful it was much simpler but the whole complexity went into the design of the season and over the years I developed pretty simple guys guidelines you know how to
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design the season so that it works okay so how did I invent it when I became a P basically went to Bell Labs the Thi-sophi laser became it became a new material and the new material is always good put your finger on new
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material because that actually changes something and certain things people do certain things and keep repeating it without thinking why but with a new material their normal way of operation maybe just doesn't work anymore and then you need to think why doesn't it work not or maybe it
02:22:23
works better so everybody started to work on this Thi-sophi laser because this Thi-sophi laser was finally replacing these dye lasers that produced before all these femtoseconds and the dye laser was a liquid laser who wants to work with a liquid laser that photo degraded and if if the jet
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was clogged up you know you know you got the dye all over you so it was a messy situation because you know everybody tells you clean up the jet right before you go home but you know like every graduate student or a young person you forget it and the next morning you switch it on and then you
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have it all over you so anyway Thi-sophir is a solid-state crystal much easier to use was a great laser and then they happened two experiments that actually should not have worked and they worked they were not mine okay so the first one was a post deadline paper by Siebert where he he
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demonstrated the post deadline paper with a mode lock Thi-sophi laser without an absorber now I told you it for mode locking you need a loss modulation it had no visible loss modulation and produced 60 femtosecond
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pulses nobody knew how it worked when we went to the post deadline session basically you know it was submitted as a post deadline paper it was afterwards on every fax machine in the world and everybody had a copy of it and we all went to the post deadline session it was standing room only to watch what is going on nobody knew what was going on and it
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was called magic mode locking because there was no satrop absorber people said oh there is a satrop absorber in the sapphire oh there is something this and oh this is this wild speculation actually Siebert explained it in the in this paper with coupled cavity mode locking and I explained to
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you why he came up with couple it wasn't the right explanation the other one was an other post deadline paper which also should not have worked it was done by a Japanese group they presented it as a post deadline paper at
02:24:40
ultrafast phenomena in the same year and they basically built a so-called CPM that tie sapphire laser so all the femtosecond laser in the dye laser period were CPM dye lasers and if you understand how they work you never would build a CPM tie sapphire laser because they don't work because if you
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actually understand it you don't build it they obviously didn't understand it oh now I'm on YouTube on this statement okay okay anyway so they didn't understand it because they build it anyway right but it worked it worked but it should not have worked because you know when you know the CPM
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dye laser was a critical balance between the loss and the gain and the loss mode was a very slow dye satrop absorber that recovered in nanoseconds how can you get femtosecond pulses with a loss modulation in nanoseconds slow no way it was actually an open net gain window in the tie sapphire laser
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how could it work both were actually later on explained by care lens mode locking both work fast satrop absorber and it was actually care lens mode locking right and the care lens mode locking most of you understand by now
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I don't have the time anymore to explain that one because I want to go a little bit to give you a flavor why I came to the season so couple mode locking right I mean Sipit explained actually his result with coupled molding he said because the the student had to slightly misalign the
02:26:21
laser and then suddenly boom it went into mode locking and so he they assumed it was a coupled cavity effect between the fundamental transverse mode and the higher-order transverse mode by the misalignment you had a super position of multiple transverse modes that were beating against each other
02:26:40
because at that time the big thing for solid-state mode locking was coupled cavity mode locking because at that time remember it was said you cannot passively mode lock type on solid-state laser without making them unstable there was even in paper written by Hermann Haus who said it doesn't work
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but there was this coupled cavity mode locking Lynn Mollenauer became very famous 1984 for mode locking a color center laser with a nonlinear coupled cavity basically he had a fiber inside a coupled cavity so you have your
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normal laser no subtle absorber and and you get here an effective nonlinear nonlinearity that actually produces mode locking because assuming you have a pulse here out of noise and this pulse fulfills the soliton compression
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the pulse gets shorter through the soliton effect comes back and gets a pulse shortening so by going through this negative dispersive fiber you actually the pulse that comes out here comes back get soliton compression gets
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sent back to the main cavity it's kind of like a subtle absorber it produces a shorter pulse like the loss modulation produces a shorter pulse that gets this balance right that ultimately makes this mode locking so what actually Sippet did before he discovered this magic mode locking
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actually one of his students took the wrong fiber one morning instead of a negative dispersion a positive dispersion it still worked so instead of actually being a stupid student and actually saying whoops I took the one on replacing it real quick and put the right one in actually this
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student realized oops this might be important right because it still works I have no clue why it works but it works so now think about it now that you had a very simple explanation so the this negative dispersion I have soliton compression with positive dispersion you know the pulse gets
02:29:01
broader coming back so why should that make it mode lock doesn't make any sense right but it worked anyway that's why we do experiments right so it was actually not really explained at by by the Sippet group and actually it was that the group of Ippen and House who came up with a very simple
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explanation they say and they then introduced a new acronym and called it additive pulse mode locking because you still have self phase modulation I explained that to you this is a nonlinear process basically it takes the care
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effect n n2 times the intensity right so you take a self phase modulation so mean basically if everything is adjusted right you have a phase shift so that at the peak of the pulse you have positive interference of the pulse
02:30:04
coming back from the couple cavity and negative interference destructive interference in the wings without this one and so the superposition gives you a shorter pulse that means you have to actively stabilize the cavity lengths
02:30:25
here because otherwise it wouldn't work right otherwise you get arbitrary phase shift and you don't have this interference pulse shortening effect and this is really true this additive pulse mode locking only worked when you actually stabilize the cavity lengths so and then there was actually a theory
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paper that said any nonlinearity in a couple cavities would actually more look a numerical study right no you know numerics you can show a lot of things without getting a feeling but they showed any nonlinearity and here I was a Bell Labs I had semiconductors so instead of fiber I put in semiconductor
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I put in a semiconductor so I took borrow the semiconductor mirror from a neighbor who used it for all optical switching plucked it into the laser and it worked it worked even better than additive pulse model again
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because I didn't have to stabilize the cavity lengths because I used an amplitude nonlinearity and so by trying to understand why this thing actually works so well and so easily I then came up with the season the first season device and actually the idea was after I understood how it all works you
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can take this cupboard cavity and spatially move it on top of your other cavity because this is the same length and you put us that the same subtle absorber but put that output coupler which was I had like a 5% output
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coupler so put a 95% top reflector on top of this subtle of this of this semiconductor absorber and I designed the device got it grown and it worked and with this I had a semiconductor sot-trouble absorber mirror the first
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design and after that when it works then you change parameters right change this to this to this and then you understand more and more how it all works and that's how the season was invented right yeah so yes yes yes
02:32:47
because you know the funny thing is I had when I moved this one to one micron I had actually when I was growing it at normal temperature the subtle absorber which means a slow recovery then because it was done at
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one micron the semiconductor multiple quantum well section had surface roughness and so it introduced scattering losses and I had to and resolve these scattering losses by moving to low temperature growth and the low temperature growth removed the scattering losses but also made the
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absorber faster and it all worked better on multiple levels solving one problem actually helped me on other ones and then afterwards I realized oops that was actually good and again if you you know if you change parameters so once you have an experiment going change parameters and
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try to understand you know change things and then you understand and make it better and that's how it all evolved over the so that kept me busy for 20 years and we're still publishing paper on season design because now we have seasons even you know at the beginning people were saying oh well that's complicated or then somebody said oh it will burn now we have it in
02:34:04
laser with over 300 watt of average output power inside the laser 3 kilowatt with femtosecond and it's not burning actually the dispersive dielectric mirrors burn before the semiconductor so this is the story so I
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mean all I can say to you I mean I'm a hardcore experimentalist I really like experiments because we do experiments because we go beyond theory theory is always based on some assumption and if you limit your assumption you will
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always limit your results if you go into the lab you discover new things because you're not limiting your assumption you just have to make sure that you keep all your eyes open when you go into the lab switch on all your detection spectrum time domain the more you look the more you see the more you
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discover and learn good measurement technique know what you are actually dealing with with the instrument go a little bit over and learn something from electrical engineers RF microwave signal to noise noise generally good habit to know that you can make signals visible that normally other
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people don't see okay with this I want to conclude I hope you had a little bit of fun and I hope I could get you excited for this field and you know thanks for your patience and you know see you tomorrow okay thanks a lot