A Matrix Method for Studying TM Modes of Optical planar Waveguides with Arbitrary Index Profiles

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Title:	A Matrix Method for Studying TM Modes of Optical planar Waveguides with Arbitrary Index Profiles
Authors:	蕭進松;Hsiao, Chin-Sung
Contributors:	光電與通訊學系
Date:	2001-12
Issue Date:	2012-11-26 02:22:53 (UTC+0)
Abstract:	Application of a previously proposed matrix method (which can only be used for TE mode solutions) to studying the wave characteristics of TM modes is described. To derive the matrix equation for TM-mode solutions of slab waveguides, the gradient of a continuous field is defined as the sum of a continuous function and a stepwise function so that boundary conditions are satisfied. By expanding both the index profile and mode field distribution into a truncated Fourier series, a particular matrix equation for determining mode indices and mode field distributions is obtained. Such a matrix equation can be generalized as BX = β2X, where B is a constant matrix, ß is the propagation constant, and the vector X accounts for the mode field distribution. Wave characteristics of TM modes of slab waveguides with arbitrary index profiles can thus be obtained following the solution of a linear algebra problem in a way similar to that for studying TE modes. The matrix B here, however, as indicated by this work, is different from that for TE mode solutions. Also, it is pointed out in this paper that the matrix B for TM-mode solutions has a different form as a different kind of waveguide is considered. Numerical results presented herein show that a sufficiently high accuracy can be obtained by using the proposed method
Relation:	IEEE Journal of Quantum Electronics
Appears in Collections:	[Department of Photonics and Communication Engineering] Journal Article

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