Asymmetric Wave Propagation Through Nonlinear PT-symmetric Oligomers

Abstract

In the present paper, we consider nonlinear PT-symmetric dimers and trimers (more generally, oligomers) embedded within a linear Schr{ö}dinger lattice. We examine the stationary states of such chains in the form of plane waves, and analytically compute their reflection and transmission coefficients through the nonlinear PT symmetric oligomer, as well as the corresponding rectification factors which clearly illustrate the asymmetry between left and right propagation in such systems. We examine not only the existence but also the dynamical stability of the plane wave states and interestingly find them to be generically unstable. Lastly, we generalize our numerical considerations to the more physically relevant case of Gaussian initial wavepackets and confirm that the asymmetry in the transmission properties persists in the case of such wavepackets, as well.

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• Stability boundaries and collisions of two-dimensional solitons in PT-symmetric couplers with the cubic-quintic nonlinearity
• A solvable model for solitons pinned to a PT-symmetric dipole
• Nonlinear dynamics in PT-symmetric lattices
• Nonreciprocal wave scattering on nonlinear string-coupled oscillators
• Nonreciprocal Elasticity
• Solitons in PT-symmetric ladders of optical waveguides
• Controllable unidirectional transport and photon storage in an one-dimensional lattice with complex hopping rates
• Interaction of sine-Gordon kinks and breathers with a $\mathcal{P}\mathcal{T}$-symmetric defect
• $\mathcal{P}\mathcal{T}$ symmetry breaking in waveguide arrays with competing loss/gain pairs
• Interactions of bright and dark solitons with localized $\mathcal{P}\mathcal{T}$-symmetric potentials
• $\mathcal{P}\mathcal{T}$-symmetric coupler with ${\chi }^{(2)}$ nonlinearity
• $\mathcal{P}\mathcal{T}$ symmetric phase transition and single-photon transmission in an optical trimmer system
• Asymmetric Acoustic Energy Transport in Non-Hermitian Metamaterials
• Exceptional points in oligomer chains
• Staggered $\mathcal{P}\mathcal{T}$-symmetric ladders with cubic nonlinearity
• Symmetry breaking and restoring wave transmission in diode-antidiode double chains
• Quasi-energies, parametric resonances, and stability limits in ac-driven $\mathcal{P}\mathcal{T}$-symmetric systems
• Unidirectional transport of wave packets through tilted discrete breathers in nonlinear lattices with asymmetric defects
• Asymmetric Nonlinear System is Not sufficient for Non-Reciprocal Quantum Wave Diode
• $\mathcal{P}\mathcal{T}-$Symmetric Dimers with Time-Periodic Gain/Loss Function
• Asymmetric Wave Propagation Through Saturable Nonlinear Oligomers
• Eigenstates and instabilities of chains with embedded defects
• Multi-soliton states under triangular spatial modulation of the quadratic nonlinearity
• Asymmetric wave transmission through one dimensional lattices with cubic-quintic nonlinearity
• $\mathcal{P}\mathcal{T}$-symmetric ladders with a scattering core
• Self trapping transition for a nonlinear impurity within a linear chain
• Optical trimer: A theoretical physics approach to waveguide couplers