Extinction theorem analysis of diffraction anomalies in overcoated gratings

A rigorous analysis based on the extinction theorem is presented to study anomalous resonant effects from single-layer- and multilayer-overcoated, low-efficiency diffraction gratings. Anomalously high diffraction efficiency at resonance results from the coupling of the incident beam into guided waves that can be propagated within the composite structure. This analysis incorporates a recursive or R-matrix propagation algorithm that is numerically stable, and the results agree favorably with both experimental and other theoretical research. Numerical results are presented to investigate the influence of certain parameters (i.e., groove depth and shape and the number of high- and low-index overlayers) on the diffraction efficiency at resonance. In the analysis a wavelength of 0.6328 μm and a grating period of 0.7 μm were chosen so that only a −1 diffracted order and the specular beam are reflected from the gratings. Perfect transfer of the grating relief to the film boundaries does not occur in all instances; it depends on the grating and film characteristics, together with the conditions during deposition. We investigate the effect of nonreplication of the grating profile at film interfaces on anomalous diffraction. For the cases studied, it is found that nonreplication has the effect of reducing the strength of the resonant outcoupling. Incident beams with a Gaussian intensity profile are also considered. This effect is accomplished by having multiple incident beams weighted such that their superposition forms a Gaussian envelope. Numerical results show the effect of guided-wave resonances for which distortion of the reflected envelopes is seen.

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