High-Frequency Diffraction by an Elliptic Cylinder With a Strongly Elongated Cross-Section

The problem of high-frequency diffraction of the field of a point source on a soft or hard elliptic cylinder is considered. The cross-section of the cylinder is supposed to be strongly elongated and the asymptotic approximations for the field near the surface are derived. These representations are uniform with respect to the rate of elongation and for not too much elongated cross-sections reduce to classical Fock asymptotics.