|
On the scattering by a biperiodic structure
Author(s):
Gang
Bao;
David
C.
Dobson
Journal:
Proc. Amer. Math. Soc.
128
(2000),
2715-2723.
MSC (2000):
Primary 35J50, 78A45;
Secondary 35Q60
Posted:
April 7, 2000
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
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  .
References:
-
- 1.
- T. Abboud, Formulation variationnelle des équations de Maxwell dans un réseau bipéiodique de
 , C. R. Acad. Sci. Paris, t. 317, Série I (1993), 245-248. MR 94f:78002 - 2.
- T. Abboud, Electromagnetic waves in periodic media, in Second International Conference on Mathematical and Numerical Aspects of Wave Propagation, ed. by R. Kleinman et al, SIAM, Philadelphia, 1993, 1-9. MR 95a:78010
- 3.
- T. Abboud and J. C. Nédélec, Electromagnetic waves in an inhomogeneous medium, J. Math. Anal. Appl. 164 (1992), 40-58. MR 93a:78005
- 4.
- G. Bao, Variational approximation of Maxwell's equations in biperiodic structures, SIAM J. Appl. Math. 57 (1997), 364-381. MR 97m:65199
- 5.
- D. Dobson, A variational method for electromagnetic diffraction in biperiodic structures, Modél. Math. Anal. Numér. 28 (1994), 419-439. MR 95m:78017
- 6.
- D. Dobson and A. Friedman, The time-harmonic Maxwell equations in a doubly periodic structure, J. Math. Anal. Appl. 166 (1992), 507-528. MR 92m:78015
- 7.
- A. Friedman, Mathematics in Industrial Problems, Part 3, Springer-Verlag, Heidelberg, 1990. MR 92e:00007
- 8.
- Electromagnetic Theory of Gratings, Topics in Current Physics, Vol. 22, edited by R. Petit, Springer-Verlag, Heidelberg, 1980. MR 82a:78001
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
35J50, 78A45,
35Q60
Retrieve articles in all Journals with MSC
(2000):
35J50, 78A45,
35Q60
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:
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
Posted:
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
Copyright of article:
Copyright
2000,
American Mathematical Society
|
Comments: webmaster@ams.org