A new type of coupled wave theory is described which is capable, in a very natural way, of analytically describing polychromatic gratings. In contrast to the well known and extremely successful coupled wave theory of Kogelnik, the new theory is based on a differential formulation of the process of Fresnel reflection within the grating. The fundamental coupled wave equations, which are an exact solution of Maxwell’s equations for the case of the unslanted reflection grating, can be analytically solved with minimal approximation. The equations may also be solved in a rotated frame of reference to provide useful formulae for the diffractive efficiency of the general polychromatic slanted grating in three dimensions. The new theory is compared with Kogelnik’s theory where extremely good agreement is found for most cases. The theory has also been compared to a rigorous computational chain matrix simulation of the unslanted grating with excellent agreement for cases typical to display holography. In contrast, Kogelnik’s theory shows small discrepancies away from Bragg resonance. The new coupled wave theory may easily be extended to an N-coupled wave theory for the case of the multiplexed polychromatic grating and indeed for the purposes of analytically describing diffraction in the colour hologram. In the simple case of a monochromatic multiplexed grating at Bragg resonance the theory is in exact agreement with the predictions of conventional N-coupled wave theory.