Short wave point source near a unhomogenous halfplane

We consider the diffraction of waves produced by a point source by unhomogenous halfplane. The square of wave-number inside unhomogenous region is supposed to decrease lineary with increasing the distance from the devision boundary. The main aim of the article is to obtain the asymptotic of a whispering gallery waves as $k\to\infty$, where $k$ is the wave-number in a homogenous region.