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      • Department of Electrical and Electronics Engineering
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      Calculation of the scalar diffraction field from curved surfaces by decomposing the three-dimensional field into a sum of Gaussian beams

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      Author(s)
      Şahin, E.
      Onural, L.
      Date
      2013
      Source Title
      Journal of the Optical Society of America A: Optics and Image Science, and Vision
      Print ISSN
      1084-7529
      Publisher
      Optical Society of America
      Volume
      30
      Issue
      3
      Pages
      527 - 536
      Language
      English
      Type
      Article
      Item Usage Stats
      238
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      242
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      Abstract
      We present a local Gaussian beam decomposition method for calculating the scalar diffraction field due to a twodimensional field specified on a curved surface. We write the three-dimensional field as a sum of Gaussian beams that propagate toward different directions and whose waist positions are taken at discrete points on the curved surface. The discrete positions of the beam waists are obtained by sampling the curved surface such that transversal components of the positions form a regular grid. The modulated Gaussian window functions corresponding to Gaussian beams are placed on the transversal planes that pass through the discrete beam-waist position. The coefficients of the Gaussian beams are found by solving the linear system of equations where the columns of the system matrix represent the field patterns that the Gaussian beams produce on the given curved surface. As a result of using local beams in the expansion, we end up with sparse system matrices. The sparsity of the system matrices provides important advantages in terms of computational complexity and memory allocation while solving the system of linear equations.
      Keywords
      Diffraction
      Linear systems
      Surfaces
      Three dimensional
      Curved surfaces
      Decomposition methods
      Discrete points
      Gaussian window
      Linear system of equations
      Scalar diffraction
      System of linear equations
      Transversal planes
      Gaussian beams
      Permalink
      http://hdl.handle.net/11693/21164
      Published Version (Please cite this version)
      https://doi.org/10.1364/JOSAA.30.000527
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      • Department of Electrical and Electronics Engineering 3868
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