Application of Extended Taylor Series based Finite Difference Method in photonics

Author

Sujecki, S.

Author_Institution

George Green Inst., Univ. of Nottingham, Nottingham, UK

fYear

2013

fDate

23-27 June 2013

Firstpage

1

Lastpage

3

Abstract

The Finite Difference Method (FDM) has numerous applications in the modelling and design of photonic devices. One of the main limitations to the accuracy and computational efficiency of FDM comes from the presence of discontinuities in the functions describing the unknown physical quantities, e.g. the normal component of the electric field vector field is discontinuous across a step change in the value of the refractive index. The presentation will focus on introducing the concept of the Extended Taylor Series and its application to an elegant and consistent derivation of the Finite Difference approximations to discontinuous functions. Selected illustrating examples will show the significance of the technique for the numerical modelling in photonics.

Keywords

approximation theory; finite difference methods; optical waveguides; refractive index; discontinuous functions; electric field vector field; extended Taylor series; finite difference approximations; photonic devices; refractive index; unknown physical quantity; Adaptive optics; Approximation methods; Finite difference methods; Optical refraction; Optical waveguides; Taylor series; Taylor series; finite difference method; optical waveguides;

fLanguage

English

Publisher

ieee

Conference_Titel

Transparent Optical Networks (ICTON), 2013 15th International Conference on

Conference_Location

Cartagena

ISSN

2161-2056

Type

conf

DOI

10.1109/ICTON.2013.6603003

Filename

6603003