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.
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