Guided Modes in Layered Semiconductor Terahertz Structures

In this paper, we present a simple and robust method for calculating the dispersion relation of guided modes in layered media with conducting interfaces in the terahertz frequency range. The procedure is based on the transfer matrix method and utilizes a Nelder-Mead simplex algorithm for the solution of the resulting transcendental equations. By applying a semi-analytical approach, the algorithm shows very good convergence behavior even for structures containing metallic layers. Analytic forms of the transcendental equations for transverse electric and transverse magnetic polarization for systems with one to four boundaries are presented. Conducting interfaces can, for instance, be used to describe a 2-D electron gas or a planar metamaterial. We demonstrate the performance of this method by examples which are of current technological interest. These include surface waves bound to surface carriers on p-InAs, a parallel plate waveguide and plasma oscillations in a high electron mobility transistor structure.