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Register a new userStable and oscillating solitons of $mathcal{PT}$-symmetric couplers with gain and loss in fractional dimension
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Families of coupled solitons of $mathcal{PT}$-symmetric physical models with gain and loss in fractional dimension and in settings with and without cross-interactions modulation (CIM), are reported. Profiles, powers, stability areas, and propagation dynamics of the obtained $mathcal{PT}$-symmetric coupled solitons are investigated. By comparing the results of the models with and without CIM, we find that the stability area of the model with CIM is much broader than the one without CIM. Remarkably, oscillating $mathcal{PT}$-symmetric coupled solitons can also exist in the model of CIM with the same coefficients of the self- and cross-interactions modulations. In addition, the period of these oscillating coupled solitons can be controlled by the linear coupling coefficient.
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Following the concept of $mathcal{PT}$-symmetric couplers, we propose a linearly coupled system of nonlinear waveguides, made of positive- and negative-index materials, which carry, respectively, gain and loss. We report novel bi- and multi-stability states pertaining to transmitted and reflective intensities, which are controlled by the ratio of the gain and loss coefficients, and phase mismatch between the waveguides. These states offer transmission regimes with extremely low threshold intensities for transitions between coexisting states, and very large amplification ratio between the input and output intensities leading to an efficient way of controlling light with light.
We report the role of $mathcal{PT}$-symmetry in switching characteristics of a highly nonlinear fiber Bragg grating (FBG) with cubic-quintic-septic nonlinearities. We demonstrate that the device shows novel bi-(multi-) stable states in the broken regime as a direct consequence of the shift in the photonic band gap influenced by both $mathcal{PT}$-symmetry and higher-order nonlinearities. We also numerically depict that such FBGs provide a productive test bed where the broken $mathcal{PT}$-symmetric regime can be exploited to set up all-optical applications such as binary switches, multi-level signal processing and optical computing. Unlike optical bistability (OB) in the traditional and unbroken $mathcal{PT}$-symmetric FBG, it exhibits many peculiar features such as flat-top stable states and ramp like input-output characteristics before the onset of OB phenomenon in the broken regime. The gain/loss parameter plays a dual role in controlling the switching intensities between the stable states which is facilitated by reversing the direction of light incidence. We also find that the gain/loss parameter tailors the formation of gap solitons pertaining to transmission resonances which clearly indicates that it can be employed to set up optical storage devices. Moreover, the interplay between gain/loss and higher order nonlinearities brings notable changes in the nonlinear reflection spectra of the system under constant pump powers. The influence of each control parameters on the switching operation is also presented in a nutshell to validate that FBG offers more degrees of freedom in controlling light with light.
We investigate vortex excitations in dilute Bose-Einstein condensates in the presence of complex $mathcal{PT}$-symmetric potentials. These complex potentials are used to describe a balanced gain and loss of particles and allow for an easier calculation of stationary states in open systems than in a full dynamical calculation including the whole environment. We examine the conditions under which stationary vortex states can exist and consider transitions from vortex to non-vortex states. In addition, we study the influences of $mathcal{PT}$ symmetry on the dynamics of non-stationary vortex states placed at off-center positions.
A Parity-Time (PT)-symmetric system with periodically varying-in-time gain and loss modeled by two coupled Schrodinger equations (dimer) is studied. It is shown that the problem can be reduced to a perturbed pendulum-like equation. This is done by finding two constants of motion. Firstly, a generalized problem using Melnikov type analysis and topological degree arguments is studied for showing the existence of periodic (libration), shift periodic (rotation), and chaotic solutions. Then these general results are applied to the PT-symmetric dimer. It is interestingly shown that if a sufficient condition is satisfied, then rotation modes, which do not exist in the dimer with constant gain-loss, will persist. An approximate threshold for PT-broken phase corresponding to the disappearance of bounded solutions is also presented. Numerical study is presented accompanying the analytical results.
Families of analytical solutions are found for symmetric and antisymmetric solitons in the dual-core system with the Kerr nonlinearity and PT-balanced gain and loss. The crucial issue is stability of the solitons. A stability region is obtained in an analytical form, and verified by simulations, for the PT-symmetric solitons. For the antisymmetric ones, the stability border is found in a numerical form. Moving solitons of both types collide elastically. The two soliton species merge into one in the supersymmetric case, with equal coefficients of the gain, loss and inter-core coupling. These solitons feature a subexponential instability, which may be suppressed by periodic switching (management).
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