Through flattening-boundaries method to new square-gradient mechanism of surface scattering

We develop the flattening-boundaries method to the problem of wave scattering in quasi-one-dimensional guiding systems with rough boundaries. This method allows one to reduce the problem to that describing the waveguide with flat boundaries and an effective scattering potential of a special structure. A detailed analysis of the potential reveals that apart from terms associated with well-known mechanisms of surface scattering, it contains important terms describing the square-gradient mechanism of scattering. These terms depend on the square of the derivative of the waveguide boundaries and in spite of their apparent smallness, they prevail in a physically important region of roughness parameters.