Diffusion-based model of holographic grating formation in photopolymers: generalized non-local material responses

It has recently been shown by Sheridan and Lawrence (Sheridan J T and Lawrence J R 2000 J. Opt. SA A 17 1108-14) that, introducing a Gaussian non-local material response function into the one-dimensional diffusion equation governing holographic grating formation in photopolymers, both high-frequency and low-frequency cut-offs in the spatial frequency response of the materials can be deduced. In this paper generalized non-local responses are examined. These include a Chernov material response, and both the Chernov/Debye and Gaussian responses generalized to include a power-law response. The effects of these responses are examined for various material parameters, including the non-local variance, σ , the power-law degree, k , and the ratio of the rate of diffusion to the rate of polymerization, R . The resulting variations in monomer and polymer concentrations, the cross-sectional grating profiles and the spatial frequency responses predicted are presented and discussed. It is shown that in general, assuming an isotropic even, area-normalized response function, qualitatively acceptable growth curve and spatial frequency response behaviour are observed in all cases.