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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the scattering by a biperiodic structure


Authors: Gang Bao and David C. Dobson
Journal: Proc. Amer. Math. Soc. 128 (2000), 2715-2723
MSC (2000): Primary 35J50, 78A45; Secondary 35Q60
Published electronically: April 7, 2000
MathSciNet review: 1694448
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Abstract:

Consider scattering of electromagnetic waves by a nonmagnetic biperiodic structure. The structure separates the whole space into three regions: above and below the structure the medium is assumed to be homogeneous. Inside the structure, the medium is assumed to be defined by a bounded measurable dielectric coefficient. Given the structure and a time-harmonic electromagnetic plane wave incident on the structure, the scattering (diffraction) problem is to predict the field distributions away from the structure. In this note, the problem is reduced to a bounded domain and solved by a variational method. The main result establishes existence and uniqueness of the weak solutions in $W^{1,2}$.


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Additional Information

Gang Bao
Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
Address at time of publication: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027
Email: bao@math.msu.edu

David C. Dobson
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: dobson@math.tamu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05509-X
PII: S 0002-9939(00)05509-X
Keywords: Diffraction, scattering, periodic structure
Received by editor(s): November 1, 1998
Published electronically: April 7, 2000
Additional Notes: The first author was supported by the NSF Applied Mathematics Program grant DMS 98-03604 and the NSF University-Industry Cooperative Research Program grant DMS 98-03809.
The second author was supported by AFOSR grant number F49620-98-1-0005 and Alfred P. Sloan Research Fellowship.
Communicated by: Suncica Canic
Article copyright: © Copyright 2000 American Mathematical Society