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End date: 2019 × Start date: 2010 × Type: Text × Subject: Electromagnetic scattering × WGL Institute: WIAS ×

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Now showing 1 - 4 of 4
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    Convergence analysis of the FEM coupled with Fourier-mode expansion for the electromagnetic scattering by biperiodic structures
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Hu, Guanghui; Rathsfeld, Andreas
    Scattering of time-harmonic electromagnetic plane waves by a doubly periodic surface structure in R3 can be simulated by a boundary value problem of the time-harmonic curl-curl equation. For a truncated FEM domain, non-local boundary value conditions are required in order to satisfy the radiation conditions for the upper and lower half spaces. Alternatively to boundary integral formulations, to approximate radiation conditions and absorbing boundary methods, Huber et al. [11] have proposed a coupling method based on an idea of Nitsche. In the case of profile gratings with perfectly conducting substrate, the authors have shown previously that a slightly modified variational equation can be proven to be equivalent to the boundary value problem and to be uniquely solvable. Now it is shown that this result can be used to prove convergence for the FEM coupled by truncated wave mode expansion. This result covers transmission gratings and gratings bounded by additional multi-layer systems.
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    Reflection of plane waves by rough surfaces in the sense of Born approximation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Arnold, Thomas; Rathsfeld, Andreas
    The topic of the present paper is the reflection of electromagnetic plane waves by rough surfaces, i.e., by smooth and bounded perturbations of planar faces. Moreover, the contrast between the cover material and the substrate beneath the rough surface is supposed to be low. In this case, a modification of Stearns' formula based on Born approximation and Fourier techniques is derived for a special class of surfaces. This class contains the graphs of functions if the interface function is a radially modulated almost periodic function. For the Born formula to converge, a sufficient and almost necessary condition is given. A further technical condition is defined, which guarantees the existence of the corresponding far field of the Born approximation. This far field contains plane waves, far-field terms like those for bounded scatterers, and, additionally, a new type of terms. The derived formulas can be used for the fast numerical computations of far fields and for the statistics of random rough
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    Scattering of time harmonic electromagnetic plane waves by perfectly conducting diffraction gratings
    (Berlin: Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Hu, Guanghui; Rathsfeld, Andreas
    Consider scattering of time-harmonic lectromagnetic plane waves by a doubly periodic surface in R^3. The medium above the surface is supposed to be homogeneous and isotropic with a constant dielectric coefficient, while below is a perfectly conducting material. This paper is concerned with the existence of quasiperiodic solutions for any frequency of incidence. Based on an equivalent variational formulation established by the mortar technique of Nitsche, we verify the existence of solutions for a broad class of incident waves including plane waves, under the assumption that the grating profile is a Lipschitz biperiodic surface. Our solvability result covers the resonance case where a Rayleigh frequency is allowed. Non-uniqueness examples are also presented in the resonance case and the TE or TM polarization case for classical gratings.
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    Multiple scattering of electromagnetic waves by a finite number of point-like obstacles
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Challa, Durga Prasad; Hu, Guanghui; Sini, Mourad
    This paper is concerned with the time-harmonic electromagnetic scattering problem for a finite number M of point-like obstacles in R^3. First, we give a rigorous justification of the Foldy method and describe the intermediate levels of scattering between the Born and Foldy models. Second, we study the problem of detecting the scatterers and the scattering strengths from the far-field measurements and discuss the effect of multiple scattering related to each of these models.