Boundary integral methods for periodic scattering problems. (English) Zbl 1189.78026

Laptev, Ari (ed.), Around the research of Vladimir Maz’ya. II. Partial differential equations. Dordrecht: Springer; Novosibirsk: Tamara Rozhkovskaya Publisher (ISBN 978-1-4419-1342-5/hbk; 978-1-4419-1343-2/ebook; 978-5-9018-7342-7/hbk). International Mathematical Series (New York) 12, 337-363 (2010).
This paper deals with the scattering of time-harmonic plane waves by a surface, which in Cartesian coordinates \((x, y, z)\) is periodic in \(x\) and invariant in \(z\)-direction and separates two different materials. This model has several applications in micro-optics, where tools from the semiconductor industry are used to fabricate optical devices with complicated structural features within the length-scale of optical waves. In the present paper, by means of related boundary integral techniques, the author studies the equivalence of these equations to the electromagnetic formulation. It is also established the existence and uniqueness of solutions under adequate hypotheses on the permittivity and permeability of the materials. The author is also concerned with materials having negative permittivity or permeability.
For the entire collection see [Zbl 1180.47002].


78A45 Diffraction, scattering
78M15 Boundary element methods applied to problems in optics and electromagnetic theory
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