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Optimal design of periodic antireflective structures for the Helmholtz equation

Published online by Cambridge University Press:  26 September 2008

David C. Dobson
David C. Dobson
Affiliation:
Institute for Mathematics and its Applications, University of Minnesota, 514 Vincent Hall, Minneapolis, MN 55455-0436, USA
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Abstract

We study the problem of designing a periodic interface between two homogeneous materials with different impedance properties, in such a way that time-harmonic waves incident on the interface over a given range of angles have minimal total reflected energy. It is shown that the problem can be ‘relaxed’ to include continuously varying profiles. A simple gradient descent minimization scheme is proposed and examples from several numerical calculations are given.

Information

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 4 , Issue 4 , December 1993 , pp. 321 - 339
Copyright
Copyright © Cambridge University Press 1993

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References

[1]Ono, Y., Kimura, Y., Ohta, Y. & Nishida, N. 1987 Antireflection effect in ultrahigh spatial-frequency holographic relief gratings. Appl. Optics 26, 1142–1146.Google Scholar
[2]Glytsis, E. N. & Gaylord, T. K. 1988 Antireflection surface structure: dielectric layer(s) over a high spatial-frequency surface-relief grating on a lossy substrate. Appl. Optics 27, 4288–4304.CrossRefGoogle Scholar
[3]Achdou, Y. 1991 Numerical optimization of a photocell. Preprint.CrossRefGoogle Scholar
[4]Achdou, Y. & Pironneau, O. 1990 Optimisation d'un capteur d'énergie solaire. Preprint.Google Scholar
[5]Born, M. & Wolf, E. 1980 Principles of Optics, sixth edition. Pergamon.Google Scholar
[6]Chen, X. & Friedman, A. 1991 Maxwell's equations in a periodic structure. Trans. Amer. Math. Soc. 323, 465–507.Google Scholar
[7]Dobson, D. & Friedman, A. 1992 The time-harmonic Maxwell equations in a doubly periodic structure. J. Math. Anal. Appl. 166, 507–528.CrossRefGoogle Scholar
[8]Taylor, M. 1981 Pseudodifferential Operators. Princeton University Press.CrossRefGoogle Scholar
[9]Engquist, B. & Majda, A. 1979 Radiation boundary conditions for acoustic and elastic wave calculations. Comm. Pure Appl. Math. 32, 313–375.CrossRefGoogle Scholar
[10]Givoli, D. 1991 Non-reflecting boundary conditions. J. Comp. Phys. 94, 1–29.Google Scholar
[11]Kohn, R. & Strang, G., 1986 Optimal design and relaxation of variational problems I, II, and III. Comm. Pure Appl. Math. 39, 113–137, 139–182, 353–377.CrossRefGoogle Scholar
[12]Goldstein, A. 1967 Constructive Real Analysis. Harper & Row.Google Scholar
[13]Dennis, J. E. & Schnabel, R. 1983 Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice Hall.Google Scholar
[14]R., Petit (ed.) 1980 Electromagnetic Theory of Gratings, Topics in Current Physics, Vol. 22, Springer-Verlag.Google Scholar