Low-truncation-error finite difference equations for photonics simulation 1: Beam propagation

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A methodology is presented that allows the derivation of low-truncation-error finite difference equations for photonics simulation. This methodology is applied to the case of wide-angle beam propagation in two dimensions, resulting in finite difference equations for both TE and TM polarization that are quasi-fourth-order accurate even in the presence of interfaces between dissimilar dielectrics. This accuracy is accomplished without an appreciable increase in numerical overhead and is concretely demonstrated for two test problems having known solutions. These finite difference equations facilitate an approach to the ideal of grid-independent computing and should allow the solution of interesting problems on personal computers.

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28 p.

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Hadley, G.R. August 1, 1997.

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  • Sandia National Laboratories
    Publisher Info: Sandia National Labs., Albuquerque, NM (United States)
    Place of Publication: Albuquerque, New Mexico

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Description

A methodology is presented that allows the derivation of low-truncation-error finite difference equations for photonics simulation. This methodology is applied to the case of wide-angle beam propagation in two dimensions, resulting in finite difference equations for both TE and TM polarization that are quasi-fourth-order accurate even in the presence of interfaces between dissimilar dielectrics. This accuracy is accomplished without an appreciable increase in numerical overhead and is concretely demonstrated for two test problems having known solutions. These finite difference equations facilitate an approach to the ideal of grid-independent computing and should allow the solution of interesting problems on personal computers.

Physical Description

28 p.

Notes

OSTI as DE97007801

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  • Progress in electromagnetics research symposium, Cambridge, MA (United States), 7 Jul 1997

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  • Other: DE97007801
  • Report No.: SAND--97-1771C
  • Report No.: CONF-970783--1
  • Grant Number: AC04-94AL85000
  • Office of Scientific & Technical Information Report Number: 515570
  • Archival Resource Key: ark:/67531/metadc689784

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  • August 1, 1997

Added to The UNT Digital Library

  • Aug. 14, 2015, 8:43 a.m.

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  • April 14, 2016, 4:16 p.m.

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Hadley, G.R. Low-truncation-error finite difference equations for photonics simulation 1: Beam propagation, article, August 1, 1997; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc689784/: accessed November 18, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.