Fourth-order variational mode solving for anisotropic planar structures

H.P. Uranus; Hugo Hoekstra; Embrecht W.C. van Groesen

doi:10.1142/S0218863503001389

Fourth-order variational mode solving for anisotropic planar structures

H.P. Uranus, Hugo Hoekstra, Embrecht W.C. van Groesen

Research output: Contribution to journal › Article › Academic › peer-review

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Abstract

A variational method that gives 4th-order accuracy by only using linear basis functions within the computational domain is proposed for the mode solving of anisotropic planar stratified waveguides with diagonal permitivity tensor. A non-uniform mesh is used to get rid of the necessity of incorporating interface corrections and higher-order basis functions, while Richardson-like extrapolation is used to obtain 4th-order accuracy. The scheme was derived for both TE and TM mode analysis and completed with infinite elements as transparent boundary conditions. The use of a simple extrapolation technique to further refine the results by using two consecutive calculated results is also demonstrated.

Original language	Undefined
Pages (from-to)	247-261
Number of pages	15
Journal	Journal of nonlinear optical physics & materials
Volume	12
Issue number	2
DOIs	https://doi.org/10.1142/S0218863503001389
Publication status	Published - 2003

Keywords

anisotropic waveguide
Variational method
high accuracy scheme
planar waveguide
IR-45406
EWI-11558
IOMS-MIS: MISCELLANEOUS
METIS-212169
transparent boundary conditions

Access to Document

10.1142/S0218863503001389

http://eprints.eemcs.utwente.nl/secure2/11558/01/UranusJNOPM03(4thOrderVar).pdf

Cite this

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title = "Fourth-order variational mode solving for anisotropic planar structures",

abstract = "A variational method that gives 4th-order accuracy by only using linear basis functions within the computational domain is proposed for the mode solving of anisotropic planar stratified waveguides with diagonal permitivity tensor. A non-uniform mesh is used to get rid of the necessity of incorporating interface corrections and higher-order basis functions, while Richardson-like extrapolation is used to obtain 4th-order accuracy. The scheme was derived for both TE and TM mode analysis and completed with infinite elements as transparent boundary conditions. The use of a simple extrapolation technique to further refine the results by using two consecutive calculated results is also demonstrated.",

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AU - Uranus, H.P.

AU - Hoekstra, Hugo

AU - van Groesen, Embrecht W.C.

PY - 2003

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N2 - A variational method that gives 4th-order accuracy by only using linear basis functions within the computational domain is proposed for the mode solving of anisotropic planar stratified waveguides with diagonal permitivity tensor. A non-uniform mesh is used to get rid of the necessity of incorporating interface corrections and higher-order basis functions, while Richardson-like extrapolation is used to obtain 4th-order accuracy. The scheme was derived for both TE and TM mode analysis and completed with infinite elements as transparent boundary conditions. The use of a simple extrapolation technique to further refine the results by using two consecutive calculated results is also demonstrated.

AB - A variational method that gives 4th-order accuracy by only using linear basis functions within the computational domain is proposed for the mode solving of anisotropic planar stratified waveguides with diagonal permitivity tensor. A non-uniform mesh is used to get rid of the necessity of incorporating interface corrections and higher-order basis functions, while Richardson-like extrapolation is used to obtain 4th-order accuracy. The scheme was derived for both TE and TM mode analysis and completed with infinite elements as transparent boundary conditions. The use of a simple extrapolation technique to further refine the results by using two consecutive calculated results is also demonstrated.

KW - anisotropic waveguide

KW - Variational method

KW - high accuracy scheme

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KW - IR-45406

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KW - IOMS-MIS: MISCELLANEOUS

KW - METIS-212169

KW - transparent boundary conditions

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JO - Journal of nonlinear optical physics & materials

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