http://dx.doi.org/10.1364/OE.23.011952">
 

Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Efficient approximations of dispersion relations in optical waveguides with varying refractive-index profiles

Language

English

Abstract

© 2015 Optical Society of America. In this paper we consider the problem of computing the eigenmodes for the varying refractive-index profile in an open waveguide. We first approximate the refractive-index by a piecewise polynomial of degree two, and the corresponding Sturm-Liouville problem (eigenvalue problem) of the Helmholtz operator in each layer can be solved analytically by the Kummer functions. Then, analytical approximate dispersion equations are established for both TE and TM cases. Furthermore, the approximate dispersion equations converge fast to the exact ones for the continuous refractive-index function as the maximum value of the subinterval sizes tends to zero. Suitable numerical methods, such as Müller's method or the chord secant method, may be applied to the dispersion relations to compute the eigenmodes. Numerical simulations show that our method is very practical and efficient for computing eigenmodes.

Publication Date

2015

Source Publication Title

Optics Express

Volume

23

Issue

9

Start Page

11952

End Page

11964

Publisher

Optical Society of America

ISSN (print)

10944087

ISSN (electronic)

10944087

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