This paper introduces an improved mathematical model for holographic grating formation in an acrylamide-based photopolymer, which consists of partial differential equations derived from physical laws. The model is based on the two-way diffusion theory of [Appl. Opt.43, 2900 (2004)10.1364/AO.43.002900APOPAI1559-128X], which assumes short polymer chains are free to diffuse, and generalizes a similar model presented in [J. Opt. Soc. Am. B27, 197 (2010)10.1364/JOSAB.27.000197JOBPDE0740-3224] by introducing an immobilization rate governed by chain growth and cross-linking. Numerical simulations were carried out in order to investigate the behavior of the photopolymer system for short and long exposures, with particular emphasis on the effect of recording parameters (such as illumination frequency and intensity), as well as material permeability, on refractive index modulation, refractive index profile, and grating distortion. The model reproduces many well-known experimental observations, such as the decrease of refractive index modulation at high spatial frequencies and appearance of higher harmonics in the refractive index profile when the diffusion rate is much slower than the polymerization rate. These properties are supported by a theoretical investigation which uses perturbation techniques to approximate the solution over various time scales.
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