Photorefractive grating formulation with any light modulation and excitation: exact and approximate steady-state analytic solutions

Abstract

A hologram generally is formed in a photorefractive crystal by the interaction of the grating formulation that is due to the space-charge field that grows from the beam interference pattern and of the beam energy exchange that results from two-beam coupling in the grating. Analytic expressions for the grating recording formed by this interaction can be obtained only by simultaneous solution of the material equations and the coupled-wave equations. Using Moharam’s space-charge field function, we deduce both the exact steady-state analytic solution for two-beam coupling under any boundary-light modulation and constant-light excitation and the approximate analytic solutions with distance-dependent light excitation. Based on Kukhtarev’s idea of three-step calculation, the formulation of a hologram under any light modulation and excitation is further solved analytically. These steady-state analytic solutions understanding are useful in arriving at a clearer and more exact understanding of photorefractive two-beam coupling and holographic recording.