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

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.

Inverse scattering for the one-dimensional Helmholtz equation: fast numerical method.

The inverse scattering problem for the one-dimensional Helmholtz wave equation is studied. The equation is reduced to a Fresnel set that describes multiple bulk reflection and is similar to the coupled-wave equations. The inverse scattering problem is equivalent to coupled Gel'fand-Levitan-Marchenko integral equations.