Diffraction by a highly contrast transparent wedge

The problem of a plane wave diffraction by a highly contrast transparent wedge of an arbitrary opening is studied. With the aid of the Sommerfeld integrals it is reduced to a system of coupled Maliuzhinets' equations. By use of the theory of S-integrals the system of functional equations is transformed to a system of linear equations in a Banach space. In the case of the high contrast of a material inside the wedge in comparison with that in the wedge's exterior the linear equations are solved by means of perturbation theory. Convergence of the corresponding Neumann series is proved. Singularities of the integrands in the Sommerfeld integrals are investigated. Application of the steepest descent method leads to the determination of the reflected, transmitted and diffracted waves. Expressions for the diffraction coefficients are also represented.