Stable localized modes in asymmetric waveguides with gain and loss
  It is shown that asymmetric waveguides with gain and loss can support a stable propagation of optical beams. This means that the propagation constants of modes of the corresponding complex optical potential are real. A class of such waveguides is found from a relation between two spectral problems. A particular example of an asymmetric waveguide, described by the hyperbolic functions, is analyzed. The existence and stability of linear modes and of continuous families of nonlinear modes are demonstrated. 
Eduard N. Tsoy, Izzat M. Allayarov, and Fatkhulla Kh. Abdullaev
nlin.PS physics.optics