WIAS Preprint No. 3059, (2023)

Solving a spectral problem for large-area photonic crystal surface-emitting lasers


Authors

  • Radziunas, Mindaugas
    ORCID: 0000-0003-0306-1266
  • Kuhn, Eduard
    ORCID: 0000-0001-8868-6497
  • Wenzel, Hans
    ORCID: 0000-0003-1726-0223

2020 Mathematics Subject Classification

  • 78M20 78A60 78-04 35L02 65N25 65Y04

Keywords

  • Modeling, finite difference, spectral problem, Green's function, exponential growth, simulations, semiconductor laser, photonic crystal

DOI

10.20347/WIAS.PREPRINT.3059

Abstract

We present algorithms for constructing and resolving spectral problems for novel photonic crystal surface-emitting lasers with large emission areas, given by first-order PDEs with two spatial dimensions. These algorithms include methods to overcome computer-arithmetic-related challenges when dealing with huge and small numbers. We show that the finite difference schemes, constructed using relatively coarse numerical meshes enable accurate estimation of several major, optical modes, which are essential in practical applications.

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