Quantitative model of volume hologram formation in photopolymers

Abstract

A quantitative model is presented to describe the formation of volume holograms in a polymeric medium containing photopolymerizable acrylate monomers that undergo spatially modulated gelation as a result of exposure to a visible “write” beam. The model refines the simple diffusion model of Zhao and Mouroulis [J. Mod. Opt. 41, 1929 (1994)], by including cure dependence of both the photoreaction kinetics and the monomer diffusivity. These dependences are determined by experimental measurements, using near infrared spectroscopy to quantify the degree of cure and the time dependence of the hologram formation to infer the cure-dependent diffusivity. The cure-dependent diffusion coefficient can be fit by an expression from a free-volume theory, and the cure-dependent reaction rate coefficient is found to be proportional to the diffusivity, showing the reaction rate to be diffusion limited. With the model parameters determined experimentally, predictions are then made of the first, second, and third harmonics of the grating profile, and these are found to be in good agreement with the measured values. The results show the validity of the model and its usefulness in predicting the optimal exposure conditions and performance of a given holographic material.