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Inverse problems for scattering by periodic structures

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Abstract

Suppose the 3-dimensional space is filled with three materials having dielectric constants ɛ 1 above S 1={x 2=f 1(x 1), x 3 arbitrary}, ɛ 2 below S 2 = {x 2 =f 2(x 1), x 3 arbitrary} and ɛ o in {f 2(x 1) <x 2 <f1(x 1), x 3 arbitrary} where f 1 f 2 are periodic functions. Suppose for a plane wave incident on S 1 from above we can measure the reflected and transmitted waves of the corresponding time-harmonic solution of the Maxwell equations, say at x 2=±b,b large. To what extent can we infer from these measurements the location of the pair (S 1, S 2 ? In this paper, we establish a local stability: If (\(\tilde S_1 ,\tilde S_2\)) is another pair of periodic curves “close” to (S 1, S2), then, for any δ>0, if the measurements for the two pairs are δ-close, then \(\tilde S_1\) and \(\tilde S_2\)are 0(δ)-close to S 1 and S 2, respectively.

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Authors and Affiliations

  1. Department of Mathematics, University of Florida, 32611, Gainesville, Florida

    Gang Bao & Avner Friedman

  2. Institute for Mathematics and Its Applications, University of Minnesota, 55455, Minneapolis, Minnesota

    Gang Bao & Avner Friedman

Authors
  1. Gang Bao
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  2. Avner Friedman
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Communicated by R. Kohn

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Bao, G., Friedman, A. Inverse problems for scattering by periodic structures. Arch. Rational Mech. Anal. 132, 49–72 (1995). https://doi.org/10.1007/BF00390349

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  • DOI: https://doi.org/10.1007/BF00390349

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