Breathers in PT-symmetric optical couplers

Abstract

We show that the parity-time (PT) symmetric coupled optical waveguides with gain and loss support localised oscillatory structures similar to the breathers of the classical ${\varphi }^4$ model. The power carried by the PT-breather oscillates periodically, switching back and forth between the waveguides, so that the gain and loss are compensated on the average. The breathers are found to coexist with solitons and be prevalent in the products of the soliton collisions. We demonstrate that the evolution of the small-amplitude breather's envelope is governed by a system of two coupled nonlinear Schrödinger equations, and employ this Hamiltonian system to show that the small-amplitude PT-breathers are stable.

14 pages; 11 figures

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• PT-Symmetric Nonlinear Metamaterials and Zero-Dimensional Systems
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• PT-symmetric coupler with a coupling defect: soliton interaction with exceptional point
• Interaction of sine-Gordon kinks and breathers with a $\mathcal{P}\mathcal{T}$-symmetric defect
• Stationary modes and integrals of motion in nonlinear lattices with PT-symmetric linear part
• Spinor solitons and their $\mathcal{P}\mathcal{T}$-symmetric offspring
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• $\mathcal{P}\mathcal{T}-$Symmetric Dimers with Time-Periodic Gain/Loss Function
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• Integrable Local and Non-local Vector Non-linear Schrodinger Equation with Balanced loss and Gain
• Solvable Limits of a class of generalized Vector Nonlocal Nonlinear Schrödinger equation with balanced loss-gain
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• Classical Hamiltonian Systems with Balanced loss and gain
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• Discrete solitons dynamics in $\mathcal{P}\mathcal{T}$-symmetric oligomers with complex-valued couplings