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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 3 — Jan. 31, 2011
  • pp: 1808–1823

Solving the Helmholtz equation in conformal mapped ARROW structures using homotopy perturbation method

Kasper Reck, Erik V. Thomsen, and Ole Hansen  »View Author Affiliations

Optics Express, Vol. 19, Issue 3, pp. 1808-1823 (2011)

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The scalar wave equation, or Helmholtz equation, describes within a certain approximation the electromagnetic field distribution in a given system. In this paper we show how to solve the Helmholtz equation in complex geometries using conformal mapping and the homotopy perturbation method. The solution of the mapped Helmholtz equation is found by solving an infinite series of Poisson equations using two dimensional Fourier series. The solution is entirely based on analytical expressions and is not mesh dependent. The analytical results are compared to a numerical (finite element method) solution.

© 2011 Optical Society of America

OCIS Codes
(220.4880) Optical design and fabrication : Optomechanics
(120.5475) Instrumentation, measurement, and metrology : Pressure measurement

ToC Category:
Physical Optics

Original Manuscript: December 6, 2010
Revised Manuscript: January 12, 2011
Manuscript Accepted: January 12, 2011
Published: January 14, 2011

Kasper Reck, Erik V. Thomsen, and Ole Hansen, "Solving the Helmholtz equation in conformal mapped ARROW structures using homotopy perturbation method," Opt. Express 19, 1808-1823 (2011)

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