Bragg phenomena in plane horn with spatially oscillating perturbation of anisotropic surface impedance of wall

In present work plane horns with small inhomogeneous surface impedance of wall is considered. The wall impedance assumes to be presented in the form of a sum of spatial nonperiodically oscillating harmonics of perturbation. Amplitude and wavenumber of each harmonic smoothly vary along radial coordinate. In this case Floquet method cannot be applied because the structure is not periodic even if perturbation is periodic, and traditional coupled-waves method is applicable only far from cut-off cross sections. Approximate solution describing Bragg reflection and mode conversion are found by asymptotic method base on ideas of Krylov, Bogoliubov and Mitropolsky (KBM) method. The main distinguishing feature of proposed approach is using Bessel functions of the third kind in zero-order approximation instead of traditional exponential functions. This modification allows overcoming divergence of asymptotic solution near cut-off cross sections.