title: Stable localized modes in asymmetric waveguides with gain and loss.
abstract: 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.
authors.forename: Eduard N
authors.initials: EN
authors.lastname: Tsoy
authors.forename: Izzat M
authors.initials: IM
authors.lastname: Allayarov
authors.forename: Fatkhulla Kh
authors.initials: FKh
authors.lastname: Abdullaev