The resonance expansion method in surface scattering problems: transmittance of narrow rough-boundary 2D strips

The influence of inhomogeneities and defects on the transmission properties of waveguides for both quantum and classical waves is a subject of increasing research. We address the interference localization of waves in narrow two-dimensional (2D) surface-corrugated waveguides. The problem stated generally consists of two different rather complicated ones. The first lies in the correct description of the wave interaction with randomly rough surfaces, and the other consists in due consideration of multiple scattering of waveguide modes in searching their localization. The approach most frequently used for taking into account the effect of roughness of the underlying surface on wave propagation is reduced, for the most part, to expansion of the boundary conditions in terms of the power series of the asperity height, and subsequently solving an impedance-type boundary-value statistical problem. We argue that such an approach is unsuitable as applied to wave transfer through narrow surface-corrugated waveguides. We propose an alternative method, derived conformably to the electron transport in rough-bounded quantum wires that eliminates this problem