Controlled transparency of many-mode waveguides with rough surface

In a unified approach we consider transport properties of 1D and quasi-1D waveguides with rough surfaces. Main attention is paid to the possibility of perfect transmission of waves due to specific long-range correlations in the surface profiles. First, we show how to construct random profiles that lead to a complete transparency of waveguides with one open channel. Then, we present analytical results for many-mode waveguides. It was revealed that by a proper choice of correlations in surface profiles the transmission through such quasi-1D waveguides is described by a coset of non-interacting 1D channels with a perfect transmission along each one. The number of these conducting modes is governed by the control parameter, and can be equal to the total number of channels. Therefore, the waveguides can be completely transparent in some region of frequency of incoming waves. This unexpected phenomenon is discussed in connection with the violation of the single-parameter scaling for surface scattering.