The propagation equation, written in a curvilinear coordinate system, is solved by using a perturbation method inspired from quantum physics and extended to imaginary eigenvalues and evanescent waves. The parameter of perturbation is the groove depth which is small compared to the period. The method is expanded up to second order for the non-degenerate problem. In this way the solutions have analytical form compared to a numerical method. They present the advantage to put in evidence the evolution of the energy distribution for different diffraction orders as a function of the magnitude of the perturbation. The efficiencies which are deduced from these analytical solutions are compared of those obtained by the curvilinear coordinate method. The good agreement between the two methods occurs for a groove depth with respect to the wavelength less than or equal to 0.16. Thus, this new approach opens a new range of applications for inverse problems.
2. 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.
3. Li, L., J. Chandezon, G. Granet, and J. P. Plumey, "Rigorous and effcient grating-analysis method made easy for the optical engineers ," Appl. Opt., Vol. 38, 304-313, 1999.
4. Dusseaux, R., C. Faure, J. Chandezon, and F. Molinet, "New perturbation theory of diffraction gratings and its application to the study of ghosts," J. Opt. Soc. Am., Vol. 12, 1271-1282, 1995.
5. Malischewsky, P., Surface Waves and Discontinuities, Elsevier, Amsterdam, 1987.
6. Malischewsky, P. G., "Connections between seismology, waveguide physics and quantum mechanics," Proceedings of the International Conference ``Days on Diffraction", 144-150, 2009.
7. Goldstein, , H., C. Poole, and J. Safko, "Classical Mechanics," Addison Wesley, 2002.
8. Guy, S., A. Bensalah-Ledoux, and A. Stoita, "Sensitivity of chirowaveguides to circular birefringence by first order perturbation theory," Progress In Electromagnetics Research B, Vol. 24, 155-172, 2010.
9. Zheng, J.-P. and K. Kobayashi, "Diffraction by a semi-in¯nite parallel-plate waveguide with sinusoidal wall corrugation: Combined perturbation and Wiener-Hopf analysis ," Progress In Electromagnetics Research B, Vol. 13, 75-110, 2009.
10. Zheng, J.-P. and K. Kobayashi, "Combined Wiener-Hopf and perturbation analysis of the H-polarized plane wave diffraction by a semi-in¯nite parallel-plate waveguide with sinusoidal wall corrugation," Progress In Electromagnetics Research B, Vol. 13, 203-236, 2009.
11. Gavaix, A. M., G. Granet, and J. Chandezon, "Diffraction of electromagnetic waves by periodic surfaces: Perturbation method," J. Opt., Vol. 12, 115709-115717, 2010.
12. Cohen-Tannoudji, , C., B. Diu, and F. Laloe, Quantum Mechanics, Vol. 2, Wiley-Interscience, New York, 1991.