title: Pinned modes in lossy lattices with local gain and nonlinearity.
abstract: We introduce a discrete linear lossy system with an embedded "hot spot" (HS), i.e., a site carrying linear gain and complex cubic nonlinearity. The system can be used to model an array of optical or plasmonic waveguides, where selective excitation of particular cores is possible. Localized modes pinned to the HS are constructed in an implicit analytical form, and their stability is investigated numerically. Stability regions for the modes are obtained in the parameter space of the linear gain and cubic gain or loss. An essential result is that the interaction of the unsaturated cubic gain and self-defocusing nonlinearity can produce stable modes, although they may be destabilized by finite-amplitude perturbations. On the other hand, the interplay of the cubic loss and self-defocusing gives rise to a bistability.
authors.affiliation: Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel.
authors.forename: Boris A
authors.initials: BA
authors.lastname: Malomed
authors.forename: Edwin
authors.initials: E
authors.lastname: Ding
authors.forename: K W
authors.initials: KW
authors.lastname: Chow
authors.forename: S K
authors.initials: SK
authors.lastname: Lai
mesh_terms: D003198:Computer Simulation; D004735:Energy Transfer; D008027:Light; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D012031:Refractometry / Q000379:methods*; D012542:Scattering, Radiation