| Summary: | A rigorous analysis based upon the extinction theorem is presented to study anomalous resonance effects from single- 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. Both the traditional characteristic matrix technique and a recursive or R-matrix propagation technique are presented. The R-matrix propagation algorithm was found to be stable numerically, and computational results agree favorably with both experimental and other theoretical work. Numerical results are presented in order 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 this analysis, a wavelength of 0.6328 μm and grating period of 0.7 μm were chosen so that only a -1 diffracted order other than the specular is 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. Investigated in this work is the effect of nonreplication of the grating profile at film interfaces on anomalous diffraction; a transition from trapezoidal profile at the grating substrate to a rounded relief at the top surface of the multilayer structure is assumed. For the cases studied, it was found that nonreplication has the effect of reducing the strength of the resonance outcoupling. Finally, experimental results on anomalous resonance effects for multilayer-coated gratings are presented. Good agreement with computational results was attained.
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