Generalized Reciprocity for Gratings of Finite Conductivity

A New Electromagnetic Theory for Scattering from Shallow Rough Surfaces

“…Let us consider two functions u(x, y) and v(x, y) defined in the domain Q of Under these conditions, it can be shown, using the same demonstration as in § 2 .1 for equation (5), that above yM , the functions u and v can be represented by plane wave expansions of U -, U+ , V -, V + . If yM < y < a, where du/dn and dv/dn are the normal derivatives of u and v on S, s being the curvilinear coordinate on S .…”

“…Here, we must consider the asymptotic value of r(a") when a-+ -00 and b->oc . The approximation of r(a") given by equations (17) and (18) Introducing the above formula in (5) shows that the field scattered above the top of the grooves is a sum of plane waves whose directions of propagation are given by the classical grating formula, if y>yM, …”

“…A typical example of this kind of rough surface is the diffraction grating, where the modulation is periodic . The studies of inverse diffraction by gratings [4][5][6] have shown that the solution of this problem requires a prior solution of the corresponding direct problem, that is finding the scattered field when the shape of the grating is known . The direct problem for diffraction gratings has been solved with a great accuracy using rigorous methods [7] .…”

“…The direct problem for diffraction gratings has been solved with a great accuracy using rigorous methods [7] . This permitted the development of a very powerful method of inverse diffraction [4,5] which led to the reconstruction of the shape of holographic diffraction gratings from actual experimental measurements of the diffracted field [8] .…”

Electromagnetic scattering from bounded or infinite subsurface bodies

“…Indeed, the required functional derivative of the diffracted field can be estimated with the solving of a small number of direct problems [Roger, 1983]. The next step consists of combining the forward solver with a conjugate gradient process.…”