Abstract
We analyze electromagnetic scattering of transverse magnetic polarized waves from a diffraction grating consisting of a periodic, anisotropic, and possibly negative index dielectric material. Such scattering problems are important for the modelization of, for example, light propagation in nano‐optical components and metamaterials. The periodic scattering problem can be reformulated as a strongly singular volume integral equation, a technique that attracts continuous interest in the engineering community but has rarely received rigorous theoretic treatment. In this paper, we prove new (generalized) Gårding inequalities in weighted and unweighted Sobolev spaces for the strongly singular integral equation. These inequalities also hold for materials for which the real part of the material parameter takes negative values inside the diffraction grating, independently of the value of the imaginary part. Copyright © 2012 John Wiley & Sons, Ltd.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
