Extracting parameters from slanted non-uniform gratings recorded in photopolymer. Part I: Theoretical derivations

Despite the practical significance of slanted volume holographic gratings, most research presented in the photopolymer literature involves the use of unslanted reflection or transmission geometry gratings. A physically accurate electromagnetic model of the slanted holographic non-uniform gratings recorded in photopolymers is necessary in order to extract key volume grating parameters. In this paper we present a model, based on a set of two coupled differential equations, which include the effects of: (i) an exponential decay of refractive index modulation in the direction of the beam propagation due for example to the effects of dye absorption with depth; (ii) Gaussian profile of refractive index modulation due to recording by finite Gaussian beams, and (iii) a quadratic variation in the spatial period of the grating (chirp) arising due to non-uniform average index and thickness changes, i.e., shrinkage and swelling. Analytic results and numerical simulation are presented. In Part II the model developed in Part I is applied to fit experimental data, i.e., angular scans, of slanted gratings recorded in a polyvinylalcohol/acrylamide based material for different slant angles in order to extract key volume grating parameters.