On the scattering by a biperiodic structure
HTML articles powered by AMS MathViewer
- by Gang Bao and David C. Dobson PDF
- Proc. Amer. Math. Soc. 128 (2000), 2715-2723 Request permission
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 $W^{1,2}$.References
- Toufic Abboud, Formulation variationnelle des équations de Maxwell dans un réseau bipériodique de $\textbf {R}^3$, C. R. Acad. Sci. Paris Sér. I Math. 317 (1993), no. 3, 245–248 (French, with English and French summaries). MR 1233420
- T. Abboud, Electromagnetic waves in periodic media, Second International Conference on Mathematical and Numerical Aspects of Wave Propagation (Newark, DE, 1993) SIAM, Philadelphia, PA, 1993, pp. 1–9. MR 1227824
- Toufic Abboud and Jean-Claude Nédélec, Electromagnetic waves in an inhomogeneous medium, J. Math. Anal. Appl. 164 (1992), no. 1, 40–58. MR 1146575, DOI 10.1016/0022-247X(92)90144-3
- Gang Bao, Variational approximation of Maxwell’s equations in biperiodic structures, SIAM J. Appl. Math. 57 (1997), no. 2, 364–381. MR 1438758, DOI 10.1137/S0036139995279408
- D. C. Dobson, A variational method for electromagnetic diffraction in biperiodic structures, RAIRO Modél. Math. Anal. Numér. 28 (1994), no. 4, 419–439. MR 1288506, DOI 10.1051/m2an/1994280404191
- David Dobson and Avner Friedman, The time-harmonic Maxwell equations in a doubly periodic structure, J. Math. Anal. Appl. 166 (1992), no. 2, 507–528. MR 1160941, DOI 10.1016/0022-247X(92)90312-2
- Avner Friedman, Mathematics in industrial problems. Part 3, The IMA Volumes in Mathematics and its Applications, vol. 31, Springer-Verlag, New York, 1990. MR 1074003, DOI 10.1007/978-1-4613-9098-5
- Roger Petit (ed.), Electromagnetic theory of gratings, Topics in Current Physics, vol. 22, Springer-Verlag, Berlin-New York, 1980. MR 609533
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
- 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
- © Copyright 2000 American Mathematical Society
- 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
- MathSciNet review: 1694448