Nonlinearly PT-symmetric systems: Spontaneous symmetry breaking and transmission resonances

By Andrey Miroshnichenko, Boris A. Malomed, Yuri Kivshar. 2011

164 citations recorded by the source corpus.

We consider a class of $\mathcal{PT}$-symmetric systems which include mutually matched nonlinear loss and gain (in other words, a class of $\mathcal{PT}$-invariant Hamiltonians in which both the harmonic and anharmonic parts are non-Hermitian). For a basic system in the form of a dimer, symmetric and asymmetric eigenstates, including multistable ones, are found analytically. We demonstrate that, if coupled to a linear chain, such a nonlinear $\mathcal{PT}$-symmetric dimer generates previously unexplored types of nonlinear Fano resonances, with completely suppressed or greatly amplified transmission, as well as a regime similar to the electromagnetically induced transparency. The implementation of the systems is possible in various media admitting controllable linear and nonlinear amplification of waves.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/72b414e427a60ecad6a10fef713e5ecebacc43e0

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

Nonlinear waves in PT -symmetric systems (2016, background): “Looking for stationary nonlinear modes in the form of q0,1 = A0,1e iφ0,1e−iEz, one can classify possible solutions into three groups (Chen et al., 2015; Duanmu et al., 2013; Miroshnichenko, Malomed, and Kivshar, 2011): a. Continuous families of PT -symmetric solutions.”
Nonlinear switching and solitons in PT‐symmetric photonic systems (2015, background): “where the overdot stands for the time derivative, γ0 > 0 accounts for the linear gain and loss acting on complex variables ψA and ψB , respectively, E is a frequency shift, γ2 accounts for the PT-symmetric nonlinear loss and gain (as shown in [35], stable eigenstates are obtained with γ2 > 0, i.”