O'Reilly logo

Periodic Structures: Mode-Matching Approach and Applications in Electromagnetic Engineering by Ruey-Bing Hwang

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

Chapter 4

Two-and Three-Dimensional Periodic Structures

Wave propagating characteristics in periodic structures (gratings) have been intensively studied for several decades; most of the research results were focused on those of 1D periodic structures employed as diffraction gratings or grating waveguides. In the previous chapters the phase and dispersion relations of waves supported in a 1D periodic medium have been studied using the Fourier and modal transmission-line approaches, respectively. Moreover, the scattering of a plane wave by a 1D periodic structure (or grating) and the guiding characteristics of a dielectric waveguide incorporating 1D periodic structures have also been investigated. In this chapter we will extend the 1D periodic structure to two dimensions: one that is periodic in two directions and homogeneous in the third direction. Furthermore, the 3D periodic structure, which can be considered as a stack of 2D periodic layers, is also taken into account for evaluating the eigenwave and scattering characteristics. The rigorous mode-matching method will be employed for solving the electromagnetic boundary-value problem of the two types of periodic structures including the metallic and dielectric cylinders. Specifically, the Brillouin and phase diagrams will be exploited to understand the physical picture of the wave process involved in the structure under consideration.

4.1 Modal Transmission-Line Approach for a 2D Periodic Metallic Medium: In-Plane Propagation ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required