Filter Function of a Holographic Grating With Non-Negligible Absorption

Abstract

We present a theoretical model for the filter function of a holographic grating when the absorption coefficient of the photomaterial is nonnegligable. In this case there is also modulation in the conductivity, which leads to a cosinusoidal function for the dielectric permittivity. The filter function of a holographic grating registered in this photographic material appears to be a complex function in which additional terms that are due to nonzero conductivity are present. The intensity response contains coupling terms that do not appear in the purely dielectric case. We introduce a new relative-diffraction-efficiency coefficient, which depends on the degree of modulation of the conductivity. Numerical calculations have been carried out for different values of the coupling constant of the conductivity β = ∆σ/σ_0 when: β ≃ α(α ≃ ∆ε/ε_0), β<α, or β>α. A generalization of this model is also calculated in which the wave fronts used in the register are Gaussian.