WIAS Preprint No. 758, (2002)

Eigen mode computation of microwave and laser structures including PML


  • Hebermehl, Georg
  • Hübner, Friedrich-Karl
  • Schlundt, Rainer
    ORCID: 0000-0002-4424-4301
  • Tischler, Thorsten
  • Zscheile, Horst
  • Heinrich, Wolfgang

2010 Mathematics Subject Classification

  • 35Q60 65F15 65N22


  • Microwave device, Optoelectronic device, Simulation, Maxwell's equations, PML boundary condition, Eigenvalue problem




The field distribution at the ports of the transmission line structure is computed by applying Maxwell's equations to the structure. Assuming longitudinal homogeneity an eigenvalue problem can be derived, whose solutions correspond to the propagation constants of the modes. The nonsymmetric sparse system matrix is complex in the presence of losses and Perfectly Matched Layer. The propagation constants are found solving a sequence of eigenvalue problems of modified matrices with the aid of the invert mode of the Arnoldi method. Using coarse and fine grids, and a new parallel sparse linear solver, the method, first developed for microwave structures, can be applied also to high dimensional problems of optoelectronics.

Appeared in

  • Scientific Computing in Electrical Engineering, Eds. W. H. A. Schilders, E. J. W. ter Maten, St. H. M. J. Houben, Mathematics in Industry, Springer Verlag, Vol. 4, pp. 196--205, 2004

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