Spectral theory of a surface-corrugated electron waveguide: The exact scattering-operator approach

We apply the exact surface scattering operator to solve the problem of scalar (electron or sound) wave propagation through a strip with absolutely soft randomly rough boundaries. This approach is nonperturbative in either roughness heights or slopes. We analyzed the roughness-induced dephasing and attenuation of waves both asymptotically and numerically. The analysis proves that the signal is always scattered most effectively into the "resonant" waveguide modes, whose transverse wavelength is comparable to the rms roughness height zeta and whose total number is proportional to zeta(-1). According to this integral resonance rule, the dephasing dominates over the attenuation and shows a nonanalytic (square-root) dependence on the dispersion zeta(2) when (k zeta)(2) much greater than 1 (k is the wave number). In the case (k zeta)(2)much greater than 1 the dephasing and attenuation may well compete. We predict another two surprising effects: reentrant transparency and increase of the phase velocity of the wave. [S0163-1829(99)01525-8].