Inverse problems for scattering by periodic structures |
| |
| Authors: | Gang Bao Avner Friedman |
| |
| Affiliation: | (1) Department of Mathematics, University of Florida, 32611 Gainesville, Florida;(2) Institute for Mathematics and Its Applications, University of Minnesota, 55455 Minneapolis, Minnesota |
| |
| Abstract: | Suppose the 3-dimensional space is filled with three materials having dielectric constants ? 1 above S 1={x 2=f 1(x 1), x 3 arbitrary}, ? 2 below S 2 = {x 2 =f 2(x 1), x 3 arbitrary} and ? o in {f 2(x 1) <x 2 1(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. |
| |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ |
|
