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Journal of Applied & Computational Mathematics

ISSN: 2168-9679

Open Access

An Efficient Solver of Eigenmodes for a Class of Complex Optical Waveguides

Abstract

Jianxin Zhu* and Luying Li

In this paper, for a class of complex optical waveguide, the high-precision computation of the propagation constants β are studied. The corresponding Sturm-Liouville (S-L) problem is represented as image in an open domain (open on one side), where x is a given value. Firstly, a perfectly matched layer is used to terminate the open domain. Secondly, both the equation and the complex coordinate stretching transformations are constructed. Thirdly, the S-L problem is turned to a simplified form such as imagein a bounded domain. Finally, the coefficient function image is approximated by a piecewise polynomial of degree two. Since the simplified equation in each layer can be solved analytically by the Kummer functions, the approximate dispersion equation is established to the TE case. When the coefficient function is continuous, the approximate solutions converge fast to the exact ones, as the maximum value of the subinterval sizes tends to zero. Numerical simulations show that high-precision eigenmodes may be obtained by the Müller's method with suitable initial values.

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