Asymptotic solutions for the scattered field of plane wave by a cylindrical obstacle buried in a dielectric half-space

Two-dimensional scattering of a plane wave by an embedded conducting strip is formulated rigorously using the concept of Kobayashi potential, in which potential or wave function is expressed in terms of infinite integrals including the Bessel function in the integrand. By imposition of the required boundary conditions at the interface of the dielectric half-space and on the strip, the problem is reduced to a dual integral equation (DIE). Using the discontinuous properties of Weber-Schafheitlin´s integrals, DIE is transformed into a matrix equation with infinite unknowns whose elements are expressed by infinite integrals. Asymptotic solutions for the matrix elements are derived when the separation between the interface of the different media and the obstacle is large compared to the wavelength. Using these results, the expression for the scattered field is derived in a general form which can be applied to an arbitrary cylindrical obstacle. Some numerical results are given for conducting strip and circular cylinder to see the effect of inhomogeneity on the surrounding medium, size of the obstacle, and the angle of incidence on the scattered field.