Pinned modes in two-dimensional lossy lattices with local gain and nonlinearity

Abstract

We introduce a system with one or two amplified nonlinear sites ("hot spots", HSs) embedded into a two-dimensional linear lossy lattice. The system describes an array of evanescently coupled optical or plasmonic waveguides, with gain applied at selected HS cores. The subject of the analysis is discrete solitons pinned to the HSs. The shape of the localized modes is found in quasi-analytical and numerical forms, using a truncated lattice for the analytical consideration. Stability eigenvalues are computed numerically, and the results are supplemented by direct numerical simulations. In the case of self-focusing nonlinearity, the modes pinned to a single HS are stable or unstable when the nonlinearity includes the cubic loss or gain, respectively. If the nonlinearity is self-defocusing, the unsaturated cubic gain acting at the HS supports stable modes in a small parametric area, while weak cubic loss gives rise to a bistability of the discrete solitons. Symmetric and antisymmetric modes pinned to a symmetric set of two HSs are considered too.

arXiv commentPhilosophical Transactions of the Royal Society A, in press (a special issue on "Localized structures in dissipative media")

References in corpus (32)

• Stability of solitons in PT-symmetric couplers
• Optical solitons in $\mathcal{P}\mathcal{T}$-symmetric nonlinear couplers with gain and loss
• Three-Dimensional Light Bullets in Arrays of Waveguides
• Coupled nonlinear Schroedinger field equations for electromagnetic wave propagation in nonlinear left-handed materials
• Plasmon-Soliton
• Exact Solutions of the One-Dimensional Quintic Complex Ginzburg-Landau Equation
• Absolutely stable solitons in two-component active systems
• The variety of stable vortical solitons in Ginzburg-Landau media with radially inhomogeneous losses
• Dissipative periodic waves, solitons and breathers of the nonlinear Schrodinger equation with complex potentials
• Intrinsic localized modes in parametrically-driven arrays of nonlinear resonators
• Nonlinear Schrödinger equation for a PT symmetric delta-functions double well
• Radially symmetric and azimuthally modulated vortex solitons supported by localized gain
• Interaction of a soliton with a localized gain in a fiber Bragg grating
• Solitons in a medium with linear dissipation and localized gain
• Spontaneous symmetry breaking in Schrödinger lattices with two nonlinear sites
• A solvable model for solitons pinned to a PT-symmetric dipole
• Ginzburg-Landau equation bound to the metal-dielectric interface and transverse nonlinear optics with amplified plasmon polaritons
• Symmetry breaking and multi-hump solitons in inhomogeneous gain landscapes
• Resonant Plasmon-Soliton Interaction
• Dissipative surface solitons in periodic structures
• Breathing and randomly walking pulses in a semilinear Ginzburg-Landau system
• Rotating vortex solitons supported by localized gain
• Solitons supported by spatially inhomogeneous nonlinear losses
• A Study of The Formation of Stationary Localized States Due to Nonlinear Impurities Using The Discrete Nonlinear Schrödinger Equation
• Solitary vortices supported by localized parametric gain
• Pinned modes in lossy lattices with local gain and nonlinearity
• Vortex twins and anti-twins supported by multi-ring gain landscapes
• Vortex solitons of the discrete Ginzburg-Landau Equation
• Stable nonlinear amplification of solitons without gain saturation
• Solitons supported by localized parametric gain
• Solitary waves in plasmonic Bragg gratings
• Dissipative vortex solitons in 2D-lattices

Cited by in corpus (7)

• Introduction: Localized Structures in Dissipative Media: From Optics to Plant Ecology
• Discrete solitons in self-defocusing systems with $\mathcal{P}\mathcal{T}$-symmetric defects
• Fundamental and vortex dissipative quadratic solitons supported by spatially localized gain
• Dissipative quadratic solitons supported by a localized gain
• Nonlinear plasmonic amplification via dissipative soliplasmons
• Dissipative localised structures for the complex Discrete Ginzburg-Landau equation
• Dynamics of nonlocal and local discrete Ginzburg-Landau equations: global attractors and their congruence