Optical and Quantum Electronics

, Volume 29, Issue 2, pp 179–197 | Cite as

Design of sparse matrix representations for the propagator used in the BPM and directional wave field decomposition

  • M. J. N. VAN Stralen
  • H. Blok
  • M. V. DE Hoop

Abstract

Directional wave field decomposition can be accomplished with the aid of pseudo-differential operators. A fast numerical scheme requires sparse matrix representations of these operators. This paper focuses on designing sparse matrices for the propagator while keeping the accuracy high at the cost of ignoring critical-angle phenomena. The matrix representation follows from a rational approximation for the square root operator and the derivatives. The parameterization thus introduced lends itself to an overall optimization procedure that minimizes the errors for a chosen discretization rate. As such, the approach leads to an accurate propagator up to the (local) critical angle on a coarse numerical grid.

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Copyright information

© Chapman and Hall 1997

Authors and Affiliations

  • M. J. N. VAN Stralen
    • 1
  • H. Blok
    • 1
  • M. V. DE Hoop
    • 2
  1. 1.Laboratory of Electromagnetic Research, Department of Electrical EngineeringDelft University of TechnologyThe Netherlands
  2. 2.Center for Wave PhenomenaColorado School of MinesGoldenUSA

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