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)], which assumes short polymer chains are free to diffuse, and generalizes a similar model presented in [J. Opt. Soc. Am. B 27, 197 (2010)] 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. (C) 2016 Optical Society of America
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机译:本文介绍了一种用于丙烯酰胺基光敏聚合物中全息光栅形成的改进数学模型,该模型由物理定律导出的偏微分方程组成。该模型基于[Appl.Am.选择。 43,2900(2004)],它假设聚合物短链可以自由扩散,并推广了一个类似的模型[J.选择。 Soc。上午。 B 27,197(2010)],介绍了由链增长和交联决定的固定化率。为了研究光聚合物体系在短时间和长时间曝光下的行为,进行了数值模拟,尤其着重于记录参数(例如照明频率和强度)以及材料磁导率对折射率调制的影响,折射率分布和光栅畸变。该模型重现了许多众所周知的实验观察结果,例如当扩散速率远低于聚合速率时,在高空间频率下折射率调制的降低和在折射率分布图中出现高次谐波。这些性质得到了理论研究的支持,该研究使用微扰技术在各种时间范围内近似求解。 (C)2016美国眼镜学会
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