Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

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 $W^{1,2}$.

References [Enhancements On Off] (What's this?)

  • 1. T. Abboud, Formulation variationnelle des équations de Maxwell dans un réseau bipéiodique de $\mathbf{R}^3$, 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

David C. Dobson
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843

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

American Mathematical Society