Holographic diffraction of complex beams and gratings: theory and simulation

Volume holographic optical elements (HOEs) are of great interest for dense information storage and optical processing such as wavelength division multiplexing (WDM) and angle multiplexing. There are numerous theoretical frameworks that attempt to model and test diffraction from a holographic grating, among the most prominent of which is Kogelnik’s coupled-wave theory, which applies to thick holograms. However, diffraction from grating geometries resulting from interference among more than two wave-vectors is difficult to model mathematically. In particular, gratings formed from converging or diverging beams present curved profiles that vary with the position inside the material. One approach to analyze these types of holographic gratings is to use a finite element method (FEM) to search for a steady-state solution for the wave equation of a beam propagating through, and diffracting from, the grating. Such a method will necessarily be computationally intensive given that the simulation will require a resolution smaller than the reading wavelength but will encompass a large volume, as is required for a thick hologram. Current technology has enabled this approach to be a viable alternative to traditional modeling. Here, we present the results of an FEM analysis using the COMSOL Multiphysics 6.0 computer program to simulate the diffraction of holographic gratings with non-trivial profiles. The results enable us to more accurately design volume HOEs with non-planar profiles such as lenses, WDM, etc., to achieve better Bragg selectivity and overall higher performance.