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An efficient approach toward guided mode extraction in two-dimensional photonic crystals

Sarrafi, P ; Sharif University of Technology | 2008

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  1. Type of Document: Article
  2. DOI: 10.1016/j.optcom.2008.01.044
  3. Publisher: 2008
  4. Abstract:
  5. A rigorous, fast and efficient method is proposed for analytical extraction of guided defect modes in two-dimensional photonic crystals, where each Bloch spatial harmonic is expanded in terms of Hermite-Gauss functions. This expansion, after being substituted in Maxwell's equations, is analytically projected in the Hilbert space spanned by the Hermite-Gauss basis functions, and then a new set of first order coupled linear ordinary differential equations with non-constant coefficients is obtained. This set of equations is solved by employing successive differential transfer matrices, whereupon defect modes, i.e. the guided modes propagating in the straight line-defect photonic crystal waveguides and coupled resonator optical waveguides, are analytically derived. In this fashion, the governing differential equations are converted into an algebraic and easy to solve matrix eigenvalue problem. Thanks to the analyticity of the proposed approach, the eigenmodes of these structures can be extracted very quickly. The validity of the obtained results is however justified by comparing them to those derived by using the standard finite-difference time-domain method. © 2008 Elsevier B.V. All rights reserved
  6. Keywords:
  7. Crystal defects ; Finite difference time domain method ; Harmonic generation ; Matrix algebra ; Ordinary differential equations ; Photonic crystals ; Waveguides ; Coupled resonator optical waveguides ; Defect modes ; Guided mode extraction ; Photonic crystal waveguides ; Guided electromagnetic wave propagation
  8. Source: Optics Communications ; Volume 281, Issue 10 , 2008 , Pages 2826-2833 ; 00304018 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0030401808000977