Selective transparency of single-mode waveguides with surface scattering

Random surface scattering in a one-mode waveguide is studied for a surface profile that has long-range correlations along the waveguide. Analytical treatment of this scattering shows that, with the proper choice of surface, one can arrange any desired combination of transparent and nontransparent frequency windows. We suggest a method for finding such profiles and demonstrate its effectiveness by making use of direct numerical simulations.