Grating matrix method to describe a volume transmission diffraction grating

In this work we present a grating matrix method to describe the properties of volume transmission diffraction gratings. The grating matrix will be introduced by using Kogelnik’s coupled wave theory so that the amplitudes of the diffracted and transmitted orders can be obtained at any point of the grating by knowing the values at the input. The use of the grating matrix method will permit predicting the efficiency of the first reflected order which cannot be predicted by only using Kogelnik’s formulation. The results obtained by using this method will be compared to those obtained using the rigorous coupled wave theory and also by the results obtained correcting Kogelnik’s expressions for the transmission and diffraction efficiency to take into account Fresnel losses. As will be seen by using the grating matrix method we will be able to describe the interference pattern created by multiple diffracted waves due to reflections at the boundaries of the diffraction grating, which cannot be predicted using Kogelnik’s coupled wave theory.