Optical solitons in $\mathcal{P}\mathcal{T}$-symmetric nonlinear couplers with gain and loss

Abstract

We study spatial and temporal solitons in the $\mathcal{P}\mathcal{T}$ symmetric coupler with gain in one waveguide and loss in the other. Stability properties of the high- and low-frequency solitons are found to be completely determined by a single combination of the soliton's amplitude and the gain/loss coefficient of the waveguides. The unstable perturbations of the high-frequency soliton break the symmetry between its active and lossy components which results in a blowup of the soliton or a formation of a long-lived breather state. The unstable perturbations of the low-frequency soliton separate its two components in space blocking the power drainage of the active component and cutting the power supply to the lossy one. Eventually this also leads to the blowup or breathing.

14 pages, 11 figures

References in corpus (8)

• Making Sense of Non-Hermitian Hamiltonians
• Unidirectional Nonlinear PT-symmetric Optical Structures
• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
• Nonlinear suppression of time-reversals in PT-symmetric optical couplers
• Spectral singularities and Bragg scattering in complex crystals
• PT-Symmetric Wave Chaos
• Solitons in a chain of PT-invariant dimers

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