| Title:
|
Conical diffraction by multilayer gratings: A recursive integral equation approach (English) |
| Author:
|
Schmidt, Gunther |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
58 |
| Issue:
|
3 |
| Year:
|
2013 |
| Pages:
|
279-307 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper is devoted to an integral equation algorithm for studying the scattering of plane waves by multilayer diffraction gratings under oblique incidence. The scattering problem is described by a system of Helmholtz equations with piecewise constant coefficients in $\mathbb R^2$ coupled by special transmission conditions at the interfaces between different layers. Boundary integral methods lead to a system of singular integral equations, containing at least two equations for each interface. To deal with an arbitrary number of material layers we present the extension of a recursive procedure developed by Maystre for normal incidence, which transforms the problem to a sequence of equations with $2 \times 2$ operator matrices on each interface. Necessary and sufficient conditions for the applicability of the algorithm are derived. (English) |
| Keyword:
|
diffraction |
| Keyword:
|
periodic structure |
| Keyword:
|
multilayer grating |
| Keyword:
|
singular integral formulation |
| Keyword:
|
recursive algorithm |
| MSC:
|
35J05 |
| MSC:
|
45E05 |
| MSC:
|
78A45 |
| MSC:
|
78M15 |
| idZBL:
|
Zbl 06221232 |
| idMR:
|
MR3066822 |
| DOI:
|
10.1007/s10492-013-0014-6 |
| . |
| Date available:
|
2013-05-17T10:43:18Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143279 |
| . |
| Reference:
|
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| Reference:
|
[2] Elschner, J., Hinder, R., Penzel, F., Schmidt, G.: Existence, uniqueness and regularity for solutions of the conical diffraction problem.Math. Models Methods Appl. Sci. 10 (2000), 317-341. Zbl 1010.78008, MR 1753114, 10.1142/S0218202500000197 |
| Reference:
|
[3] Elschner, J., Yamamoto, M.: An inverse problem in periodic diffractive optics: Reconstruction of Lipschitz grating profiles.Appl. Anal. 81 (2002), 1307-1328. Zbl 1028.78008, MR 1956063, 10.1080/0003681021000035551 |
| Reference:
|
[4] Goray, L. I., Schmidt, G.: Solving conical diffraction with integral equations.J. Opt. Soc. Am. A 27 (2010), 585-597. 10.1364/JOSAA.27.000585 |
| Reference:
|
[5] Goray, L. I., Seely, J. F., Sadov, S. Yu.: Spectral separation of the efficiencies of the inside and outside orders of soft-x-ray-extreme-ultraviolet gratings at near normal incidence.J. Appl. Physics 100 (2006). 10.1063/1.2359224 |
| Reference:
|
[6] Gotlib, V. Yu.: On solutions of the Helmholtz equation that are concentrated near a plane periodic boundary.J. Math. Sci., New York 102 4188-4194; Zap. Nauchn. Semin. POMI 250 (1998), 83-96 Russian. Zbl 1071.35512, MR 1701861, 10.1007/BF02673850 |
| Reference:
|
[7] Maystre, D.: A new general integral theory for dielectric coated gratings.J. Opt. Soc. Am. 68 (1978), 490-495. 10.1364/JOSA.68.000490 |
| Reference:
|
[8] Maystre, D.: Electromagnetic study of photonic band gaps.Pure Appl. Opt. 3 (1994), 975-993. 10.1088/0963-9659/3/6/005 |
| Reference:
|
[9] Petit, R.: Electromagnetic theory of gratings.Topics in Current Physics, 22 Springer: Berlin (1980). MR 0609533, 10.1007/978-3-642-81500-3 |
| Reference:
|
[10] Schmidt, G.: Integral equations for conical diffraction by coated grating.J. Integral Equations Appl. 23 (2011), 71-112. Zbl 1241.78015, MR 2781138, 10.1216/JIE-2011-23-1-71 |
| Reference:
|
[11] Schmidt, G.: Boundary integral methods for periodic scattering problems.In: Around the Research of Vladimir Maz'ya II. Partial Differential Equations International Mathematical Series 12 Dordrecht: Springer A. Laptev (2010), 337-363. Zbl 1189.78026, MR 2676182 |
| Reference:
|
[12] Schmidt, G., Kleemann, B. H.: Integral equation methods from grating theory to photonics: An overview and new approaches for conical diffraction.J. Mod. Opt 58 (2011), 407-423. Zbl 1221.78050, 10.1080/09500340.2010.538734 |
| . |
