Electromagnetics - Modelling, Simulation, Control and Industrial Applications - Abstract
Bugert, Beatrice
In this talk, we derive and study an integral equation formulation for electromagnetic scattering by a non-selfintersecting surface, which is $2pi$-periodic in both $x_1$- and in $x_2$- direction and separates two different materials of constant electric permittivity and magnetic permeability. The scattering of an incident plane wave on the interface is described by a system of time-harmonic Maxwell's equations in $mathbbR^3$ supplemented by transmission conditions across the interface and the outgoing wave condition, such that the tangential continuity of the electromagnetic fields as well as their boundedness at infinity is ensured. Via potential methods, we then derive a singular integral equation by the combined use of a Stratton-Chu integral representation and a simple electric potential ansatz. The integral formulation is shown to be equivalent to the electromagnetic scattering problem. Moreover, it is possible to deduce Fredholm properties for this equation from Gårding-type inequalities. Under certain conditions on the electric permittivity and the magnetic permeability, we finally obtain existence and uniqueness results for solutions to the integral equation. This generalizes existing work from Gunther Schmidt, who considered the analogous problem for oneperiodic structures. Our model is contained in the class of diffraction problems, which have various applications in micro-optics such as the construction of holographic films, optical storage devices and antireflective coatings.par vspace10pt Acknowledgement: The support from the Berlin Mathematical School at the Technische Universität Berlin is gratefully acknowledged.