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arXiv · 2303.14493

Integrability and trajectory confinement in $\mathcal{PT}$-symmetric waveguide arrays

I V Barashenkov·Frank Smuts·Alexander Chernyavsky
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Abstract

We consider $\mathcal{PT}$-symmetric ring-like arrays of optical waveguides with purely nonlinear gain and loss. Regardless of the value of the gain-loss coefficient, these systems are protected from spontaneous $\mathcal{PT}$-symmetry breaking. If the nonhermitian part of the array matrix has cross-compensating structure, the total power in such a system remains bounded -- or even constant -- at all times. We identify two-, three-, and four-waveguide arrays with cross-compensatory nonlinear gain and loss that constitute completely integrable Hamiltonian systems.

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I V Barashenkov, Frank Smuts, Alexander Chernyavsky. 2023-03-25. Integrability and trajectory confinement in $\mathcal{PT}$-symmetric waveguide arrays. https://doi.org/10.1088/1751-8121/acc3ce

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