A method for calculating the propagation constants of allowed guided and leaky modes in multilayer planar waveguides is presented. We develop a two-way graph model to describe the tangential fields propagating in the waveguides. According to the special structure of the graph model, it is convenient to employ a topology scheme to derive analytical and closed-form dispersion equations for TE and TM modes. By comparing the dispersion equations formulated by series-expansion methods, approximation methods, and transfer-matrix methods, we find that the use of these equations for finding the eigenmodes has some benefits. First, this method can be easily employed to solve eigenmodes accurately in numerical computation without using series truncation. Second, the dispersion equations are exact. Moreover, all the eigenmodes can be determined according to the formulas without losing roots or causing numerical instability even for a waveguide with thick layers.
© 2007 Optical Society of America
Original Manuscript: May 23, 2006
Revised Manuscript: July 31, 2006
Manuscript Accepted: August 21, 2006
Published: February 14, 2007
Wen-Jeng Hsueh and Jhih-Chang Lin, "Stable and accurate method for modal analysis of multilayer waveguides using a graph approach," J. Opt. Soc. Am. A 24, 825-830 (2007)