Bragg scattering in a horn with nonperiodic two-dimensional perturbation of the filling permittivity

In the present work a horn filled by a medium with two-dimensional inhomogeneity of permittivity is considered. The permittivity of the filling is assumed to be present in the form of a sum of spatial nonperiodically oscillating harmonics of perturbation. Approximate solutions describing Bragg reflection and mode conversion are found by the modified asymptotic method of Krylov, Bogoliubov and Mitropolsky (KBM). The main distinguishing feature of the proposed approach is using Hankel functions in zeroth-order approximation instead of exponential ones. This has allowed us to overcome the problem of cut-off cross sections