Document Type

Article

Rights

This item is available under a Creative Commons License for non-commercial use only

Disciplines

Applied mathematics, Optics

Publication Details

Journal of the Optical Society of America A

Vol 33, No 5, May 2016

p920-929

Abstract

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 \cite{izabela}, which assumes short polymer chains are free to diffuse, and generalizes a similar model presented in \cite{josab} by introducing an immobilization rate governed by chain growth and cross-linking. Numerical simulations were carried out in order to investigate the behaviour 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 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 polymerization rate. These properties are supported by a theoretical investigation which uses perturbation techniques to approximate the solution over various time scales.

DOI

https://doi.org/10.1364/JOSAA.33.000920

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