We investigate the diffraction modeling of a plane wave by an infinitely thin and deformed perfectly conducting strip. We show that the diffraction pattern in the Fraunhofer domain can be obtained from efficiencies calculated for a periodic surface with an interpolation relationship; the elementary pattern of the periodic surface is identical to the strip. We consider the case where the deformation amplitude of the strip is small compared to its width. In this case, the propagation equation written in a curvilinear coordinate system is solved by a perturbation method inspired from quantum physics and extended to imaginary eigenvalues for evanescent waves. In the Fraunhofer approximation domain where the only waves are the propagative waves, the diffraction pattern obtained for a sinusoidal profile strip shows the phenomenon well known as apodization. Classically this phenomenon is obtained for physical optics with a slot in a screen with a variable transparency function similar to the profile function of the strip.
2. Born, M. and E. Wolf, Principles of Optics, Chap. XI, Cambridge University Press, 1999.
doi:10.1017/CBO9781139644181
3. Bailey, P. B. and G. E. Barr, "Diffraction by a slit or strip," J. Math. Phys., Vol. 10, 1906-1913, 1969.
doi:10.1063/1.1664780
4. Kanaun, S. K., "A numerical method for the solution of electromagnetic wave diffraction problems on perfectly conducting screens," J. Comput. Phys., Vol. 176, 170-195, 2002.
doi:10.1006/jcph.2001.6974
5. Imran, A., Q. A. Naqvi, and K. Hongo, "Diffraction of electromagnetic plane wave by an impedance strip," Progress In Electromagnetics Research, Vol. 75, 303-318, 2007.
doi:10.2528/PIER07053104
6. Imran, A., Q. A. Naqvi, and K. Hongo, "Diffraction of electromagnetic plane wave from a slit in PEMC plane," Progress In Electromagnetics Research M, Vol. 8, 67-77, 2009.
doi:10.2528/PIERM09042207
7. Weinstein, L. A., The Theory of Diffraction and the Factorization Method, Chap. 8, Boulder, Golem, 1969.
8. Jones, D. S., Acoustic and Electromagnetic Waves, Chap. 9, Clarendon, Oxford, 1989.
9. Serdyuk, V. M., "Exact solutions for electromagnetic wave diffraction by a slot and strip," Int. J. Electron. Commun. (AEU), Vol. 65, 182-189, 2011.
doi:10.1016/j.aeue.2010.04.002
10. Cohen-Tannoundji, C., B. Diu, and F. Laloe, Quantum Mechanics, Vol. 2, Chap. XI, WileyInterscience, New York, 1991.
11. Courant, R., Differential and Integral Calculus, Vol. 1, Chap. IX, Blackie & Son Limited, London and Glasgow, 1965.
12. Petit, R., Electromagnetic Theory of Gratings, Chap. 1, Springer-Verlag, Heidelberg, 1980.
doi:10.1007/978-3-642-81500-3
13. Lauberborn, W., T. Kurz, and M. Wiesenfeldt, Coherent Optics, Chap. 9, Springer-Verlag, New York, 1995.
doi:10.1007/978-3-662-03144-5
14. Chandezon, J., D. Maystre, and G. Raoult, "A new theoretical method for diffraction gratings and its numerical application," J. Opt., Vol. 11, 235-241, 1980.
doi:10.1088/0150-536X/11/4/005
15. Chandezon, J., M. T. Dupuis, G. Cornet, and D. Maystre, "Multicoated gratings: A differential formalism applicable in the entire optical region," J. Opt. Soc. Am., Vol. 72, 839-846, 1982.
doi:10.1364/JOSA.72.000839
16. Li, L., J. Chandezon, G. Granet, and J. P. Plumey, "Rigorous and efficient grating-analysis method made easy for the optical engineers," Appl. Opt., Vol. 38, 304-313, 1999.
doi:10.1364/AO.38.000304
17. Gavaix, A. M., G. Granet, and J. Chandezon, "Diffraction of electromagnetic waves by periodic surfaces: Perturbation method," J. Opt., Vol. 12, 115709-115717, 2010.
doi:10.1088/2040-8978/12/11/115709
18. Gavaix, A. M., J. Chandezon, and G. Granet, "Propagative and evanescent waves diffracted by periodic surfaces: Perturbation method," Progress In Electromagnetics Research B, Vol. 34, 283-311, 2011.
doi:10.2528/PIERB11070504
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