  We present analytical results on transport properties of many-mode waveguides
with randomly stratified disorder having long-range correlations. To describe
such systems, the theory of 1D transport recently developed for a correlated
disorder is generalized. The propagation of waves through such waveguides may
reveal a quite unexpected phenomena of a complete transparency for a subset of
propagating modes. We found that with a proper choice of long-range
correlations one can arrange a perfect transparency of waveguides inside a
given frequency window of incoming waves. Thus, mobility edges are shown to be
possible in quasi-1D geometry with correlated disorder. The results may be
important for experimental realizations of a selective transport in application
to both waveguides and electron/optic nanodevices.
