The full optical response of multilayer gratings containing anisotropic layers until now has been the domain of the experimentalist with no suitable theoretical model available to investigate such systems. The introduction of such a model would clearly benefit this relatively unexplored area of diffractive optics. To this end we present a differential theory based on the work of Chandezon et al. [ J. Opt. Soc. Am. A 72, 839 ( 1982)], extending our previous analysis to explore not only the in-plane diffraction with anisotropic layers but also the twisted grating, or conical diffraction, case. In this case there are now two possible mechanisms for transverse magnetic to transverse electric conversion, those being the twisted grating and the anisotropic, uniaxial layer. To illustrate the modeling, results of the new theory are compared with experimental data for a twisted grating anisotropic liquid-crystal system. Resonance mode position and intensity are in good agreement, showing the validity of the new mathematical procedure.
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