Nonlinear multi-core waveguiding structures with balanced gain and loss

Abstract

We study existence, stability, and dynamics of linear and nonlinear stationary modes propagating in radially symmetric multi-core waveguides with balanced gain and loss. We demonstrate that, in general, the system can be reduced to an effective $\mathcal{P}\mathcal{T}$-symmetric dimer with asymmetric coupling. In the linear case, we find that there exist two modes with real propagation constants before an onset of the $\mathcal{P}\mathcal{T}$-symmetry breaking while other modes have always the propagation constants with nonzero imaginary parts. This leads to a stable (unstable) propagation of the modes when gain is localized in the core (ring) of the waveguiding structure. In the case of nonlinear response, we show that an interplay between nonlinearity, gain, and loss induces a high degree of instability, with only small windows in the parameter space where quasi-stable propagation is observed. We propose a novel stabilization mechanism based on a periodic modulation of both gain and loss along the propagation direction that allows bounded light propagation in the multi-core waveguiding structures.

9 pages, 13 figures

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Cited by in corpus (12)

• Nonlinear switching and solitons in PT-symmetric photonic systems
• Integrable nonlocal vector nonlinear Schrödinger equation with self-induced parity-time-symmetric Potential
• Dimer with gain and loss: Integrability and $\mathcal{P}\mathcal{T}$-symmetry restoration
• Revisiting the optical $PT$-symmetric dimer
• $\mathcal{P}\mathcal{T}$ phase control in circular multicore fibers
• Solitons in PT-symmetric ladders of optical waveguides
• Gyrating solitons in a necklace of optical waveguides
• Integrable Local and Non-local Vector Non-linear Schrodinger Equation with Balanced loss and Gain
• Controllable multiple beam splitting in Hermitian and non-Hermitian symmetric coupled waveguide systems
• Integrability and trajectory confinement in $\mathcal{P}\mathcal{T}$-symmetric waveguide arrays
• Angular Momentum Supercontinuum from Fibre Rings
• Vortex ring beams in nonlinear $\mathcal{P}\mathcal{T}$-symmetric systems