## Abstract

The dynamic properties of dichromated gelatin plates are investigated during exposure by illuminating them first by a single plane wave and second by two interfering plane waves produced from an argon-ion laser at 514.5 nm. The grating recorded is shown to be a pure absorption grating. The experimental results obtained for the output beam intensities as a function of time are compared with the predictions of a theoretical model, and reasonable agreement is found. It is further shown that owing to the effect of a humid atmosphere, the recorded grating may self-develop into a phase grating of much higher efficiency.

© 1985 Optical Society of America

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### Equations (15)

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(1)
$${N}_{1}\left(x,t\right)+{N}_{2}\left(x,t\right)={N}_{10}.$$
(2)
$$\begin{array}{r}\begin{array}{rr}{\alpha}_{i}=g{N}_{10}{\sigma}_{1},& {\alpha}_{f}=g{N}_{10}{\sigma}_{2},\end{array}\\ \alpha \left(x,t\right)=g\left[{N}_{1}\left(x,t\right){\sigma}_{1}+{N}_{2}\left(x,t\right){\sigma}_{2}\right],\end{array}\}$$
(3)
$$\frac{\partial {N}_{2}}{\partial t}=-\frac{\partial {N}_{1}}{\partial t}=\gamma I\left(x,t\right)\left[{N}_{10}-{N}_{2}\left(x,t\right)\right],$$
(4)
$$\frac{\partial \alpha \left(x,t\right)}{\partial t}=\gamma I\left(x,t\right)\left[{\alpha}_{f}-\alpha \left(x,t\right)\right],$$
(5)
$$\frac{\partial I\left(x,t\right)}{\partial x}=-\frac{2\alpha \left(x,t\right)}{\text{cos}\theta}I\left(x,t\right),$$
(6)
$$\begin{array}{ccc}\alpha \left(x,0\right)={\alpha}_{i}& \text{and}& I\left(0,t\right)={I}_{0}\end{array},$$
(7)
$$I\left(x,0\right)={I}_{0}\phantom{\rule{0.2em}{0ex}}\text{exp}\left[-\frac{2{\alpha}_{i}x}{\text{cos}\theta}\right].$$
(8)
$$\begin{array}{ccc}R\phantom{\rule{0.2em}{0ex}}\text{exp}j\left(\rho \xb7r\right)& \text{and}& S\phantom{\rule{0.2em}{0ex}}\text{exp}j\left(\sigma \xb7r\right)\end{array},$$
(9)
$$I={R}^{2}+{S}^{2}+2RS\phantom{\rule{0.2em}{0ex}}\text{cos}\left(K\xb7r\right),$$
(10)
$$\text{cos}\theta \frac{\partial R}{\partial x}+{\alpha}_{0}R=-\frac{{\alpha}_{1}}{2}S,$$
(11)
$$\text{cos}\theta \frac{\partial S}{\partial x}+{\alpha}_{0}S=-\frac{{\alpha}_{1}}{2}R,$$
(12)
$$\alpha ={\alpha}_{0}+{\alpha}_{1}\phantom{\rule{0.2em}{0ex}}\text{cos}\left(K\xb7r\right).$$
(13)
$$\begin{array}{ccc}\alpha \left(x,y,0\right)={\alpha}_{i},& R\left(0,t\right)=\sqrt{{I}_{1}},& S\left(0,t\right)=\sqrt{{I}_{2}},\end{array}$$
(14)
$$\begin{array}{cc}R={I}_{1}\phantom{\rule{0.2em}{0ex}}\text{exp}\left(-\frac{{\alpha}_{i}x}{\text{cos}\theta}\right),& S={I}_{2}\phantom{\rule{0.2em}{0ex}}\text{exp}\left(-\frac{{\alpha}_{i}x}{\text{cos}\theta}\right),\end{array}$$
(15)
$$\begin{array}{ccc}R\left(0,{t}_{b}\right)=\sqrt{{I}_{1}}& \text{and}& S\left(0,{t}_{b}\right)=0\end{array}.$$