Linear and nonlinear parity-time-symmetric oligomers: a dynamical systems analysis

Linear and nonlinear parity-time-symmetric oligomers: a dynamical systems analysis.

In the present work, we focus on the cases of two-site (dimer) and three-site (trimer) configurations, i.e. oligomers, respecting the parity-time (PT) symmetry, i.e. with a spatially odd gain-loss profile. We examine different types of solutions of such configurations with linear and nonlinear gain/loss profiles. Solutions beyond the linear PT-symmetry critical point as well as solutions with a...

Linear Symmetric Dynamical Systems

The problem of characterizing those linear systems that exhibit a symmetric behavior was completely solved in the 1D case, ten years ago, in a few papers by F. Fagnani and J. C. Willems. Unfortunately, that theory could not be extended in its full generality to multidimensional systems: the techniques used in the proofs limited the results to systems of independent equations and to a restricted...

Locally Parity-Time Symmetric and globally Parity-Symmetric systems

We introduce a new class of systems holding Parity Time (PT)-symmetry locally whereas being globally Psymmetric. The potential is globally symmetric, U=U(|r|), and fulfills PT-symmetry with respect to periodically distributed points r0: U(|r0+r|)=U*(|r0-r|) being r0∫ 0. We show that such systems hold novel properties arising from the merging of the two different symmetries, leading to a strong ...

Integrable nonlinear parity-time-symmetric optical oscillator.

The nonlinear dynamics of a balanced parity-time-symmetric optical microring arrangement are analytically investigated. By considering gain and loss saturation effects, the pertinent conservation laws are explicitly obtained in the Stokes domain, thus establishing integrability. Our analysis indicates the existence of two regimes of oscillatory dynamics and frequency locking, both of which are ...

Discrete Parity-Time Symmetric Nonlinear Schrodinger Lattices