Dynamic power balance for nonlinear waves in unbalanced gain and loss landscapes

Abstract

The presence of losses in nonlinear photonic structures is a crucial issue for modern applications. Active parts are introduced for wave power compensation resulting in unbalanced gain and loss landscapes where localized beam propagation is, in general, dynamically unstable. Here we provide generic sufficient conditions for the relation between the gain-loss and the refractive index profiles in order to ensure efficient wave trapping and stable propagation for a wide range of beam launching conditions such as initial power, angle of incidence and position. The stability is a consequence of an underlying dynamic power balance mechanism related to a conserved quantity of wave dynamics.

14 pages, 4 figures

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• Continuous families of solitary waves in non-symmetric complex potentials: A Melnikov theory approach
• Edge and bulk dissipative solitons in modulated PT-symmetric waveguide arrays
• Bistable soliton switching dynamics in a $\mathcal{P}\mathcal{T}$-symmetric coupler with saturable nonlinearity
• Loss compensation symmetry in dimers made of gain and lossy nanoparticles
• Superpositions of bright and dark solitons supporting the creation of balanced gain and loss optical potentials
• Robust PT symmetry of two-dimensional fundamental and vortex solitons supported by spatially modulated nonlinearity
• Floquet topological properties in the Non-Hermitian long-range system with complex hopping amplitudes
• On non-existence of continuous families of stationary nonlinear modes for a class of complex potentials