Exact Analytical Equations for Eigenmodes in Varying Refractive-Index Profile’s Waveguides Terminated by Perfectly Matched Layers

Author

Jianxin Zhu ; Yufang Wang

Author_Institution

Dept. of Math., Zhejiang Univ., Hangzhou, China

Volume

33

Issue

2

fYear

2015

fDate

Jan.15, 15 2015

Firstpage

324

Lastpage

332

Abstract

In this paper, the exact analytical equations for both TM and TE cases are presented, when a varying refractive-index profile´s waveguide is terminated by the perfectly matched layers. In the derivation, the differential transfer matrix method and the matrix similarity transformation are mainly used. Moreover, we deduce the asymptotic solutions for Berenger modes in TM case and they can well act as the initial values of Newton´s iteration. Numerical results illustrate that leaky and Berenger modes, from the exact analytical equations, have higher precision than those by the approximate equations.

Keywords

Newton method; eigenvalues and eigenfunctions; optical waveguide theory; refractive index; Berenger modes; Newton iteration; TE mode; TM mode; asymptotic solution; differential transfer matrix method; eigenmodes; exact analytical equations; leaky modes; matrix similarity transformation; perfectly matched layer; varying refractive-index profile waveguides; Approximation methods; Dispersion; Eigenvalues and eigenfunctions; Equations; Optical waveguides; Transmission line matrix methods; Asymptotic solution; asymptotic solution; differential transfer matrix method; eigenmode; exact dispersion equations; perfectly matched layer; similarity transformation; varying refractive-index profile; varying refractiveindex profile;

fLanguage

English

Journal_Title

Lightwave Technology, Journal of

Publisher

ieee

ISSN

0733-8724

Type

jour

DOI

10.1109/JLT.2014.2378775

Filename

6980052