Propagation of electromagnetic waves in two dimensionally periodic media
Abstract
The propagation of electromagnetic waves in two dimensionally periodic structure is systematically investigated, to provide the basic theory for two dimensionally modulated dielectric waveguide. A canonical two dimensionally periodic medium of infinite extent, whose dielectic constant varies sinusoidally in two orthogonal directions, is first examined. The charact solutions are represented exactly by a double Fourier series which is known as the Floquet solution. The harmonic amplitudes of the Floquet solution are determined by a fiveterm recurrence relation in the vector form, properly taking into account the hybridmode nature of the propagation problem. The fiveterm recurrence relation is then treated by different approaches so that clear physical pictures and practical numerical methods can be obtained. The characteristic solutions for two dimensionally periodic medium are then applied to the boundaryvalue problem of multilayer dielectric waveguides containing a finite layer of periodic medium. As an example, the guidance characteristics are then carried out. Besides the canonical medium as a model, more general two dimensionally periodic medium are also discussed.
 Publication:

Ph.D. Thesis
 Pub Date:
 December 1985
 Bibcode:
 1985PhDT........19D
 Keywords:

 Dielectrics;
 Electromagnetic Radiation;
 Wave Propagation;
 Waveguides;
 Amplitudes;
 Boundary Value Problems;
 Floquet Theorem;
 Fourier Series;
 Mathematical Models;
 Communications and Radar