Scattering of evanescent electromagnetic waves by a cylinder near the flat boundary: the Green function and fast numerical method

Abstract

The scattering of plane evanescent waves by a cylinder is studied. The Green function for the Helmholtz equation for two dielectrics with flat interface is found and applied for the numerical calculation of the scattered field by the boundary elements method. The Green function keeps close track of scattering, including multiple reflections. The result may be applicable for the data analysis in near-field optical microscopy.

Plasmons excited by an evanescent wave in a periodic array of nanowires

“…A general approach has been built, based on integral equation, to study the field scattered by an object near two-media interface, for excitation by homogeneous [21] and evanescent [6,7] light wave.…”

“…The numerical methods allows one to solve the problem for one elliptic cylinder [5]. The numerical solution for two different dielectric half spaces are found recently for one [6] and two [7] cylinders. The scattering by few cylinders has very small cross-section and then is difficult to observe.…”

Frustration of total internal reflection by a hidden nanowire

“…That is why its scattering should be considered along with its source, in our problem the dielectric half-space with incident and reflecting waves. For calculation we exploit the modified boundary elements method (BEM) [7]. The feature of modified BEM is the special Green function exactly taking into account the layered medium (free and dielectric half-spaces).…”

“…In previous work [7,8] the object is located on the substrate. In present paper the scatterer hidden inside the dielectric is considered.…”

“…BEM reduces the problem to calculation of field at the boundary, then decrements, in fact, the dimension of problem. In our case two-dimension problem reduces to one-dimension boundary integral equations.In previous work [7,8] the object is located on the substrate. In present paper the scatterer hidden inside the dielectric is considered.…”