Rugorous analysis of planar waveguides with two-dimensionally periodic layer

Rigorous analysis of planar waveguides with two-dimensionally periodic (2DP) layer is presented. Characteristic solutions in periodic layer are exactly represented by a double Fourier series known as the Floquet solutions. The vector amplitudes of space harmonics are proved to be governed by five-term recurrence relation in the operator-vector form for sinusoidal modulation. A general transmission-line network representation of two-dimensionally periodic medium and multiport network representation of uniform-periodic-medium interface are introduced. Any layered structures cascading with periodic ones can be analyzed. Numerical results based on the established theory are also presented to illustrate characteristics of 2DP medium and structure.