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Transparent boundary conditions for Maxwell's equations: Numerical concepts beyond the PML method

Please always quote using this URN: urn:nbn:de:kobv:188-fudissthesis000000013994-8
  • Optical technologies are ubiquitously used in hi-tech devices. As a common feature of such devices one finds structures with dimensions in the order of the wavelength of the used light. To design and produce such devices, the wave nature of light must be taken into account. Accordingly, robust simulation tools are required which are based on rigorously solving Maxwell's equations, the governing equations of light propagation within macroscopic media. This thesis contributes to the modeling and the numerical computation of light scattering problems: Light scattering problems are typically posed on the entire space. The Perfectly-Matched -Layer method (PML) is widely used to restrict the simulation problem onto a bounded computational domain. We propose an adaptive PML method which exhibits a good convergence even for critical problems where standard PML implementations fail. Besides the computation of the near field, that is the electromagnetic field within the computational domain, it is of major interest to evaluate the electromagnetic field in the exterior domain and to compute the far field. So far, this was numerically only possible for simple geometries such as homogeneous exterior domains or layered media. To deal with more complicated devices, for example with waveguide inhomogeneities, we develop an evaluation formula based on the PML solution which allows for an exterior domain field evaluation in a half space above the device. Finally, we generalize the PML method to problems with multiply structured exterior domains. The term “multiply structured exterior domain” is defined in this thesis and means that the exterior domain exhibits several half-infinite structures. Mathematically, this gives rise to various complications. For example, no analytical solutions to Maxwell's equations for standard light sources are available in the exterior domain, which are needed to describe the incoming field in a light scattering problem. To tackle this we propose a new light scattering problem formulation which fits well into the PML method framework and which may be regarded as an extension of classical contributions by Sommerfeld, Wiener and Hopf. An exterior domain evaluation formula for multiply structured exterior domains with an extended illumination is derived as well.

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Metadaten
Author:Lin Zschiedrich
Document Type:Doctoral Thesis
Tag:Maxwell's equations; PML; Wiener-Hopf techniques; electromagnetic scattering; perfectly matched layers; transparent boundary conditions
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Qxx Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] / 35Q61 Maxwell equations
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
78-XX OPTICS, ELECTROMAGNETIC THEORY (For quantum optics, see 81V80) / 78Axx General / 78A40 Waves and radiation
78-XX OPTICS, ELECTROMAGNETIC THEORY (For quantum optics, see 81V80) / 78Axx General / 78A45 Diffraction, scattering [See also 34E20 for WKB methods]
PACS-Classification:40.00.00 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS / 42.00.00 Optics (for optical properties of gases, see 51.70.+f; for optical properties of bulk materials and thin films, see 78.20.-e; for x-ray optics, see 41.50.+h) / 42.25.-p Wave optics / 42.25.Bs Wave propagation, transmission and absorption [see also 41.20.Jb-in electromagnetism; for propagation in atmosphere, see 42.68.Ay; see also 52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma and 52.38-r Laser-plasma interactions-in pla
40.00.00 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS / 42.00.00 Optics (for optical properties of gases, see 51.70.+f; for optical properties of bulk materials and thin films, see 78.20.-e; for x-ray optics, see 41.50.+h) / 42.25.-p Wave optics / 42.25.Fx Diffraction and scattering
Granting Institution:Freie Universität Berlin
Advisor:Peter Deuflhard, Ralf Hiptmair
Date of first Publication:2009/11/30
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