Breathers inPT-symmetric optical couplers

Abstract

We show that the parity-time (PT ) symmetric coupled optical waveguides with gain and loss support localised oscillatory structures similar to the breathers of the classical φ 4 model. The power carried by the PT -breather oscillates periodically, switching back and forth between the waveguides, so that the gain and loss are compensated on the average. The breathers are found to coexist with solitons and be prevalent in the products of the soliton collisions. We demonstrate that the evolution of the small-amplitude breather's envelope is governed by a system of two coupled nonlinear Schrödinger equations, and employ this Hamiltonian system to show that the smallamplitude PT -breathers are stable.

Nonlinear switching and solitons in PT‐symmetric photonic systems

“…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).…”

“…Generalization of the two-channel dispersive coupler [77] to a PT-symmetric arrangement of 2N dispersive waveguides has been done in [66]. The arrays of waveguides in the form of periodic necklaces with alternating and clustered gain and loss distribution [see Fig.…”

Interaction of sine-Gordon kinks and breathers with a parity-time-symmetric defect

“…These include, among others, unconventional beam refraction [13], Bragg scattering [14], symmetry-breaking transitions [4] and associated ghost states [15][16][17][18], a loss-induced optical transparency [5], conical diffraction [19], a new type of Fano resonance [20], chaos [21], nonlocal boundary effects [22], optical switches [23] and diodes [24,25], phase sensitivity of light dynamics [26][27][28], and the possibility of linear and nonlinear wave amplification and filtering [29][30][31]. Unexpected instabilities were also * saadatmand.d@gmail.com † dmitriev.sergey.v@gmail.com ‡ borisovdi@yandex.ru § kevrekid@math.umass.edu identified at the level of PT -symmetric lattices, and nonlinear modes were identified in few-site oligomers, as well as in full lattice settings both in one dimension [32][33][34][35][36][37] and even in two dimensions [38].…”

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]).…”