WIAS Preprint No. 1440, (2009)

Comparison of the continuous, semi-discrete and fully-discrete transparent boundary conditions (TBC) for the parabolic wave equation 1. Theory



Authors

  • Sumichrast, Lubomir
  • Ehrhardt, Matthias

2010 Mathematics Subject Classification

  • 65M12 35Q40

2008 Physics and Astronomy Classification Scheme

  • 02.70.Bf 31.15.Fx

Keywords

  • Transparent boundary conditions, beam propagation method, parabolic wave equation

Abstract

For the simulation of the propagation of optical waves in open wave guiding structures of integrated optics the parabolic approximation of the scalar wave equation is commonly used. This approach is commonly termed the beam propagation method (BPM). It is of paramount importance to have well-performing transparent boundary conditions applied on the boundaries of the finite computational window, to enable the superfluous portion of the propagating wave to radiate away from the wave guiding structure. Three different formulations (continuous, semi-discrete and fully-discrete) of the non-local transparent boundary conditions are described and compared here.

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