Dynamical diffraction of guided electromagnetic waves by two-dimensional periodic dielectric gratings

The properties connected to the propagation of electromagnetic waves in rectangular waveguides loaded by periodic dielectric gratings have been treated by extending the theory of dynamical scattering by perfect atomic crystals. The theoretical formulation has been developed for the TE10 excitation of the periodic load, but it remains valid in the same form when a TE(n0) (n > 1) excitation takes place. The analysis was first developed for two-dimensional periodicities, and later the results were applied to one-dimensional periodicities without modifications to the formalism. The generalization of Bragg's law to guided propagation has been obtained, and the conditions and limits of applicability of the theory have been discussed. It has been shown that, when a small permittivity contrast between supporting and loaded material is present, the electromagnetic field can be approximated by either one or two waves only. The expressions of the electromagnetic field supported by the periodic medium and the dispersion relaion have been obtained. The diffraction pattern, the deviation from the generalized Bragg law, the width of the total reflection range, and the extinction length have been evaluated for a regular array of cylindrical holes on a polyethylene support. We have reported the results of an experiment carried out to verify the accuracy of the theory. The comparison between theoretical and experimental results has shown excellent agreement.