Adjusted intensity nonlocal diffusion model of photopolymer grating formation

Diffusion-based models of grating formation in photopolymers have been proposed in which the rate of monomer polymerization (removal) is directly proportional to the illuminating intensity inside the medium. However, based on photochemical considerations, the rate of polymerization is proportional in the steady state to the square root of the interference intensity. Recently it was shown that, by introducing a nonlocal response function into the one-dimensional diffusion equation that governs holographic grating formation in photopolymers, one can deduce both high-frequency and low-frequency cutoffs in the spatial-frequency response of photopolymer materials. Here the first-order nonlocal coupled diffusion equations are derived for the case of a general relationship between the rate of polymerization and the exposing intensity. Assuming a twoharmonic monomer expansion, the resultant analytic solutions are then used to fit experimental growth curves for gratings fabricated with different spatial frequencies. Various material parameters, including monomer diffusion constant D and nonlocal variance s, are estimated.