Tsoy E.N., Allayarov I.M., Abdullaev F.Kh. Stable localized modes in asymmetric waveguides with gain and loss. // OPTICS LETTERS. July 15, 2014 / V. 39. No.14.

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.