Diffraction of electromagnetic waves by periodic surfaces: perturbation method

Abstract

The propagation equation, written in a curvilinear coordinate system, is solved by using a perturbation method inspired by quantum physics. 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 of providing evidence for the evolution of the energy distribution for different diffraction orders as a function of the magnitude of the perturbation. The results that are deduced from these analytical solutions are within less than 5 × 10 − 3 of those obtained by the curvilinear coordinate method. Thus, this new approach opens a new range of applications for inverse problems.

Fraunhofer Diffraction by a Strip: Perturbation Method

“…(10) and 14on the one hand and from Eqs. (17) and (20) on the other hand), -the continuity of the tangential components of H for y = ±0 and any x (from Eqs. (11) and 15on the one hand and from Eqs.…”

“…Then the calculation of the amplitude A + d (α) given in relation (34) requires the calculation of the amplitudes A + m = A + (α m ) of the diffracted fields by the periodic surface associated to the strip. It is the object of next sections where we give the essential steps of the calculation largely developed in [17,18] in the case of a strip weakly deformed with respect to its width.…”

“…Section 5 presents the essential steps of the perturbation method [17,18]. They lead to eigenvalues and eigenvectors according to expansions up to the second order in series of powers of the amplitude of the perturbation.…”

Propagative and Evanescent Waves Diffracted by Periodic Surfaces: Perturbation Method

“…From the periodicity of the rough surface we have shown in [11] the quantification of diffracted beam directions. Let U p = {m/|α m | < 1}, then it is possible to define the angles θ m so that:…”

“…In a first paper [11] we have combined the theory of perturbation with the method of curvilinear coordinates. However, this work was inspired by text book [12] widely used in quantum mechanics.…”