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Optimal design of periodic antireflective structures for the Helmholtz equation

  • David C. Dobson (a1)

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.

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[1]Ono Y., Kimura Y., Ohta Y. & Nishida N. 1987 Antireflection effect in ultrahigh spatial-frequency holographic relief gratings. Appl. Optics 26, 11421146.
[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, 42884304.
[3]Achdou Y. 1991 Numerical optimization of a photocell. Preprint.
[4]Achdou Y. & Pironneau O. 1990 Optimisation d'un capteur d'énergie solaire. Preprint.
[5]Born M. & Wolf E. 1980 Principles of Optics, sixth edition. Pergamon.
[6]Chen X. & Friedman A. 1991 Maxwell's equations in a periodic structure. Trans. Amer. Math. Soc. 323, 465507.
[7]Dobson D. & Friedman A. 1992 The time-harmonic Maxwell equations in a doubly periodic structure. J. Math. Anal. Appl. 166, 507528.
[8]Taylor M. 1981 Pseudodifferential Operators. Princeton University Press.
[9]Engquist B. & Majda A. 1979 Radiation boundary conditions for acoustic and elastic wave calculations. Comm. Pure Appl. Math. 32, 313375.
[10]Givoli D. 1991 Non-reflecting boundary conditions. J. Comp. Phys. 94, 129.
[11]Kohn R. & Strang G., 1986 Optimal design and relaxation of variational problems I, II, and III. Comm. Pure Appl. Math. 39, 113137, 139182, 353377.
[12]Goldstein A. 1967 Constructive Real Analysis. Harper & Row.
[13]Dennis J. E. & Schnabel R. 1983 Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice Hall.
[14]R. Petit (ed.) 1980 Electromagnetic Theory of Gratings, Topics in Current Physics, Vol. 22, Springer-Verlag.
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European Journal of Applied Mathematics
  • ISSN: 0956-7925
  • EISSN: 1469-4425
  • URL: /core/journals/european-journal-of-applied-mathematics
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