We calculated the spectrum of normal scalar waves in a planar waveguide
with absolutely soft randomly rough boundaries. Our approach is beyond perturbation
theories in the roughness heights and slopes and is based instead on the exact
boundary scattering potential. The spectrum is proved to be a nearly real
nonanalytic function of the dispersion of the roughness heights (with square-root singularity) as . The opposite case of large boundary defects is summarized.
© 1998 Optical Society of America
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