Dispersion relations of the modes for open nonhomogeneous waveguides terminated by perfectly matched layers

• DOI: 10.1364/josab.29.002524
• Publication Date: 2012-08-30T16:36:28Z
• Authors: Jianxin Zhu; Zheqi Shen; Zengsi Chen
• Keywords: Perfectly Matched Layer; Dispersion relation; Waveguide; Transfer matrix; Transfer-matrix method (optics); Algebraic equation

The perfectly matched layer (PML) is a widely used tool to truncate the infinite domain in modal analysis for optical waveguides. Since PML mimics unbounded domain, propagation modes and leaky of original waveguide can be derived. However, presence will introduce series new modes, which depend on parameters PML, they are named as Berenger modes. For two-dimensional step-index waveguides, eigenmode problem usually transformed into an algebraic equation by transfer matrix method (TMM). When nonhomogeneous, refractive index core varied, TMM not available. In this paper, we use differential derive dispersion relation. We also deduced asymptotic formulas separately, accurate large