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

Journal of Applied & Computational Mathematics

article

Jianxin Zhu¹  Luying Li¹ 

[1] Department of Mathematics, Jinan University

关键词: Eigenmode;    Helmholtz equation;    Optical waveguide;    Numerical method;    Kummer functions;   

DOI  :  10.37421/2168-9679.2020.9.449

来源: Hilaris Publisher

【 摘 要 】

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 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 in a bounded domain. Finally, the coefficient function 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.

【 授权许可】

Unknown