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Longitudinal legendre polynomial expansion of electromagnetic fields for analysis of arbitrary-shaped gratings

Khavasi, A ; Sharif University of Technology | 2008

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  1. Type of Document: Article
  2. DOI: 10.1364/JOSAA.25.001564
  3. Publisher: OSA - The Optical Society , 2008
  4. Abstract:
  5. The Legendre polynomial expansion method (LPEM), which has been successfully applied to homogenous and longitudinally inhomogeneous gratings [J. Opt. Soc. Am. B 24, 2676 (2007)], is now generalized for the efficient analysis of arbitrary-shaped surface relief gratings. The modulated region is cut into a few sufficiently thin arbitrary-shaped subgratings of equal spatial period, where electromagnetic field dependence is now smooth enough to be approximated by keeping fewer Legendre basis functions. The R-matrix propagation algorithm is then employed to match the Legendre polynomial expansions of the transverse electric and magnetic fields across the upper and lower interfaces of every slice. The proposed strategy then enhances the overall computational efficiency, reduces the required memory size, and permits the efficient study of arbitrary-shaped gratings. Here the rigorous approach is followed, and analytical formulas of the involved matrices are given. © 2008 Optical Society of America
  6. Keywords:
  7. Demodulation ; Electric fields ; Electromagnetic field measurement ; Electromagnetic field theory ; Electromagnetic fields ; Electromagnetic waves ; Magnetic fields ; Magnetic materials ; Matrix algebra ; Polynomial approximation ; Polynomials ; Analytical formulas ; Efficient analysis ; Field dependences ; Legendre basis functions ; Legendre polynomial expansion ; Legendre polynomials ; Memory size ; R matrices ; Rigorous approach ; Shaped gratings ; Surface relief gratings ; Transverse electric ; Electromagnetism
  8. Source: Journal of the Optical Society of America A: Optics and Image Science, and Vision ; Volume 25, Issue 7 , 2008 , Pages 1564-1573 ; 10847529 (ISSN)
  9. URL: https://www.osapublishing.org/josaa/abstract.cfm?uri=josaa-25-7-1564