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

DOI:
https://doi.org/10.1090/S0002-9939-00-05509-X

Published electronically:
April 7, 2000

MathSciNet review:
1694448

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Abstract | References | Similar Articles | Additional Information

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 .

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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:
https://doi.org/10.1090/S0002-9939-00-05509-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