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Holographic dielectric grating: theory and practice

A holographic dielectric grating is a diffraction grating comprised of a periodic variation of the refractive index of a medium, and is produced by the interference pattern of two monochromatic waves. Emphasis is placed upon photographic emulsion as the medium for recording the pattern, but the treatment is general and includes any material that can have an internal modulation of the refractive index. Three topics are treated: the effective dielectric constant of the emulsion, the diffraction of light by dielectric gratings, and the techniques for producing gratings with high efficiency and good resolution.

The photographic emulsion is treated as an artificially loaded material, i.e. as a suspension of grains in a gelatin base. A Mie scattering theory analysis is used and the effect of adjacent scatterers on the local field is accounted for by the Lorentz-Lorenz relation. The optical density of the emulsion is shown to be proportional to the number of grains present. The effective index variation after bleaching is proportional to the pre-bleached optical density, which implies that the emulsion should have a linear density vs. exposure curve to effect a sinusoidally modulated index of refraction. A relation between the modulation transfer function (MTF) of bleached and unbleached emulsion is derived. Means for improvement of the MTF is also obtained analytically.

The diffraction of light by a dielectric grating is analyzed using the Raman-Nath formalism which is generalized to include loss. Graphs are presented showing the diffraction efficiency versus the index modulation for a wide range of thicknesses and loss. The peak efficiency for arbitrary emulsion thickness can be obtained from measurements at a specific thickness. The conclusion is reached that presently available emulsion should be made thicker, preferably in the 20-30 micron range.

The basic physical processes of various holographic materials are described. The processing techniques of photographic emulsion are emphasized and the merits of various bleaches are evaluated. It is found that resolution can be increased by using a reversal process. The dielectric grains in an emulsion processed this way are round in shape. A desensitizing dye can be used to stabilize the grains. A method of extending the dynamic range of the photographic emulsion using a pre-flashing exposure technique is also described.

Several experiments are proposed, and recommendations are made which may serve as guide-lines for the development of more suitable materials for holographic recording.

Holographic dielectric grating: theory and practice