Optical solitons inPT-symmetric nonlinear couplers with gain and loss

Abstract

We study spatial and temporal solitons in the PT symmetric coupler with gain in one waveguide and loss in the other. Stability properties of the high-and low-frequency solitons are found to be completely determined by a single combination of the soliton's amplitude and the gain/loss coefficient of the waveguides. The unstable perturbations of the high-frequency soliton break the symmetry between its active and lossy components which results in a blowup of the soliton or a formation of a long-lived breather state. The unstable perturbations of the low-frequency soliton separate its two components in space blocking the power drainage of the active component and cutting the power supply to the lossy one. Eventually this also leads to the blowup or breathing.

Nonlinear switching and solitons in PT‐symmetric photonic systems

“…System (29) supports two types of soliton solutions: symmetric and antisymmetric [82,83], termed by analogy with conservative systems (when γ = 0) [17]. These two solitons can be presented in the following form:…”

“…First, we consider a planar PT-symmetric coupler where light experiences diffraction in the x direction and propagates along the z coordinate [77,[82][83][84]. Figure 13(a) shows a schematic presentation of the coupler where the red plane (b)), while blue color indicates loss (white circles, respectively).…”

A PT -Symmetric Dual-Core System with the Sine-Gordon Nonlinearity and Derivative Coupling

“…It includes the swap of ψ and φ as the P transformation in the direction transverse to x, as in usual P T -symmetric couplers [42][43][44][45][46][47]. Obviously, the system is invariant with respect to the transformation defined by Equation (4).…”

“…Note that the expansion of Equation (17) for small leads to the same condition, illustrating the consistency of the analysis. The system of coupled NLS Equations (19) and (20) with β = 0 is identical to the above-mentioned model of the P T -symmetric coupler, which may be realized in terms of nonlinear fiber optics, admitting an exact analytical solution for solitons and their stability [42][43][44][45]. The additional terms ∼ β in the coupler model may represent the temporal dispersion of the coupling strength in fiber optics [94,95] (in that case, t and x are replaced, respectively, by the propagation distance and reduced time [13,14]).…”

Multisoliton Newton's cradles and supersolitons in regular and parity-time-symmetric nonlinear couplers

“…Recently, a PT -symmetric extension of the concept of solitons in nonlinear couplers was introduced, assuming, as it should be in diverse realizations of such systems [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48], the balance between the gain and loss in the two cores of the coupler [49][50][51][52][53] (in the abovementioned earlier studied models, the loss acting in the passive core was stronger than the gain in the active one, to secure the stability margin for the resulting dissipative solitons [25,26,29]). …”