WIAS Preprint No. 987, (2004)

Simulation of microwave and semiconductor laser structures including PML: Computation of the eigenmode problem, the boundary value problem, and the scattering matrix


  • Hebermehl, Georg
  • Schefter, Jürgen
  • Schlundt, Rainer
    ORCID: 0000-0002-4424-4301
  • Tischler, Thorsten
  • Zscheile, Horst
  • Heinrich, Wolfgang

2010 Mathematics Subject Classification

  • 35Q60 65N22 65F15 65F10 78M25


  • Microwave device, Semiconductor laser, Simulation, Maxwell's equations, Scattering matrix, Boundary value problem, PML boundary condition, Eigenvalue problem, Linear algebraic equations, Rectangular grids, Tetrahedral nets




The properties of microwave circuits and optical structures can be described in terms of their scattering matrix which is extracted from the orthogonal decomposition of the electric field. We discretize the Maxwell's equations with orthogonal grids using the Finite Integration Technique (FIT). Maxwellian grid equations are formulated for staggered nonequidistant rectangular grids and for tetrahedral nets with corresponding dual Voronoi cells. The surface of the computation domain is assumed to be an electric or a magnetic wall, open-region problems require uniaxial Perfectly Matched Layer (PML) absorbing boundary conditions. Calculating the excitations at the ports, one obtains eigenvalue problems and then systems of linear algebraic equations.

Appeared in

  • Proc. 5th International Workshop Scientific Computing in Electrical Engineering (SCEE), Capo D'Orlando, Italy, September 5--9, 2004, A. Anile, G. Ali, G. Mascali, eds., Scientific Computing in Electrical Engineering, Springer Verlag, 2006, pp. 203--214

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