Solving the Helmholtz equation in conformal mapped ARROWstructures using homotopy perturbation method

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    Abstract

    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.
    Original languageEnglish
    JournalOptics Express
    Volume19
    Issue number3
    Pages (from-to)1808-1823
    ISSN1094-4087
    DOIs
    Publication statusPublished - 2011

    Keywords

    • Optical design and fabrication
    • Instrumentation, measurement and metrology
    • Optomechanics
    • Pressure measurement

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