Index Modulation and Spatial Harmonic Generation in Dichromated Gelatin Films

A model for volume hologram formation in thick dichromated gelatin fih-ns is given. Using the model and a few basic film measurements, we can quantify the index modulation vs. exposure curve. The effects of saturation and dynamic absorption increase during exposure are considered in the generation of spatial harmonics. The effects of exposure with non-unity beam-ratio and multiple incoherent exposures are predicted and experimentally verified. The thick transmission grating diffraction efficiencies resulting from firstand higher-order index modulations are calculated and compared to experiments. The methods and conclusions are applicable to other phase materials. Index Codes: 42.65, 42.30 Hardened dichromated gelatin is a holographic phase material that is essentially lossless after development and can be made to yield volume holograms of very high index modulation. It is the purpose of this paper to develop a model for dichromated gelatin which, together with a minimum number of measured parameters, will quantify the dependence of index modulation on exposure under various exposure conditions. Because some of the film properties we report can also be seen in tests of other materials, it is expected that many of the predicted effects and our analytic methods will apply in general to a large class of holographic films. The model presented is both a mathematical and physical one. The form of the equations chosen to represent various film quantities is based on our macroscopic observation that the absorption vs. exposure curve and the first-order index modulation vs. exposure curve both have the form of saturating exponential functions (which saturate at different rates depending on the film preparation conditions). It is these functional forms that prompt us to give a mathematical treatment to the numerical values of the index curves. Results of past [1, 21 and present investigations, and knowledge of the chemistry of dichromated colloids also lead us to postulate as to the origin of the index variation in these films. 1. Chemistry and Hologram Formation Mechanism The chemistry of the photo-induced hardening process in dichromated gelatin films was treated extensively by Kosar [3] and is shown in Figure 1. Briefly, a gelatin film is sensitized in an ammonium dichromate solution and then allowed to dry. During exposure, light is absorbed to reduce the Cr +6 ion to Cr +3 which tbrms several intermediate chromium compounds. During development, the chromic ion, Cr § acts to form a crosslink bond between the carboxylate groups of neighboring gelatin strands. This bond gives rigidity (hardness) to the gelatin. For hologram formation, the exposure of the film is not uniform, as in a sinusoidal exposure resulting from the interference of two incident plane waves (Fig. 2). Highly exposed and relatively unexposed regions will be hardened to different degrees during development, causing periodic strain within the gelatin. When the firm is rapidly dehydrated with isopropanol 42 S. K. Case and R. Alferness