Detailed comparison of two approximate methods for the solution of the scalar wave equation for a rectangular optical waveguide

Thomas Rasmussen; Jørn Hedegaard Povlsen; Anders Overgaard Bjarklev; Ole Lumholt; Bo Pedersen; Karsten Rottwitt

doi:10.1109/50.219576

Detailed comparison of two approximate methods for the solution of the scalar wave equation for a rectangular optical waveguide

Thomas Rasmussen, Jørn Hedegaard Povlsen, Anders Overgaard Bjarklev, Ole Lumholt, Bo Pedersen, Karsten Rottwitt

Technical University of Denmark

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Abstract

Two approximate methods for the determination of the fundamental mode of an optical waveguide with rectangular core cross section and step refractive-index profiles are presented and analyzed thoroughly. Both methods are based on Galerkin's method. The first method uses Hermite-Gauss basis functions and the second uses the guided and nonguided slab waveguide solutions as basis functions. The results are compared with results from an accurate circular harmonic analysis. Both methods provide values of the normalized propagation constant with errors less than 0.1% for practical rectangular single-mode waveguides. The slab waveguide method is the fastest, and even when only one slab waveguide mode is used the propagation constant for the fundamental mode can be calculated with an error of less than 1%. The slab waveguide method also gives very accurate results for the propagation constant for higher order modes.

Original language	English
Journal	Journal of Lightwave Technology
Volume	11
Issue number	3
Pages (from-to)	429-433
ISSN	0733-8724
DOIs	https://doi.org/10.1109/50.219576
Publication status	Published - 1993

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Copyright: 1993 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE

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title = "Detailed comparison of two approximate methods for the solution of the scalar wave equation for a rectangular optical waveguide",

abstract = "Two approximate methods for the determination of the fundamental mode of an optical waveguide with rectangular core cross section and step refractive-index profiles are presented and analyzed thoroughly. Both methods are based on Galerkin's method. The first method uses Hermite-Gauss basis functions and the second uses the guided and nonguided slab waveguide solutions as basis functions. The results are compared with results from an accurate circular harmonic analysis. Both methods provide values of the normalized propagation constant with errors less than 0.1% for practical rectangular single-mode waveguides. The slab waveguide method is the fastest, and even when only one slab waveguide mode is used the propagation constant for the fundamental mode can be calculated with an error of less than 1%. The slab waveguide method also gives very accurate results for the propagation constant for higher order modes.",

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note = "Copyright: 1993 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE",

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AU - Rasmussen, Thomas

AU - Povlsen, Jørn Hedegaard

AU - Bjarklev, Anders Overgaard

AU - Lumholt, Ole

AU - Pedersen, Bo

AU - Rottwitt, Karsten

N1 - Copyright: 1993 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE

PY - 1993

Y1 - 1993

N2 - Two approximate methods for the determination of the fundamental mode of an optical waveguide with rectangular core cross section and step refractive-index profiles are presented and analyzed thoroughly. Both methods are based on Galerkin's method. The first method uses Hermite-Gauss basis functions and the second uses the guided and nonguided slab waveguide solutions as basis functions. The results are compared with results from an accurate circular harmonic analysis. Both methods provide values of the normalized propagation constant with errors less than 0.1% for practical rectangular single-mode waveguides. The slab waveguide method is the fastest, and even when only one slab waveguide mode is used the propagation constant for the fundamental mode can be calculated with an error of less than 1%. The slab waveguide method also gives very accurate results for the propagation constant for higher order modes.

AB - Two approximate methods for the determination of the fundamental mode of an optical waveguide with rectangular core cross section and step refractive-index profiles are presented and analyzed thoroughly. Both methods are based on Galerkin's method. The first method uses Hermite-Gauss basis functions and the second uses the guided and nonguided slab waveguide solutions as basis functions. The results are compared with results from an accurate circular harmonic analysis. Both methods provide values of the normalized propagation constant with errors less than 0.1% for practical rectangular single-mode waveguides. The slab waveguide method is the fastest, and even when only one slab waveguide mode is used the propagation constant for the fundamental mode can be calculated with an error of less than 1%. The slab waveguide method also gives very accurate results for the propagation constant for higher order modes.

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DO - 10.1109/50.219576

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ER -

Detailed comparison of two approximate methods for the solution of the scalar wave equation for a rectangular optical waveguide

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