Dynamical control of solitons in a parity-time-symmetric coupler by periodic management

Abstract

We consider a dual-core nonlinear waveguide with the parity-time (PT ) symmetry, realized in the form of equal gain and loss terms carried by the coupled cores. To expand a previously found stability region for solitons in this system, and explore possibilities for the development of dynamical control of the solitons, we introduce "management" in the form of periodic sinusoidal variation of the loss-gain (LG) coefficients, along with synchronous variation of the inter-core coupling (ICC) constant. This system, which can be realized in optics (in the temporal and spatial domains alike), features strong robustness when amplitudes of the variation of the LG and ICC coefficients keep a ratio equal to that of their constant counterparts, allowing one to find exact solutions for PTsymmetric solitons. A stability region for the solitons is identified in terms of the management amplitude and period, as well as the soliton's amplitude. In the long-period regime, the solitons evolve adiabatically, making it possible to predict their stability boundaries in an analytical form. The system keeping the Galilean invariance, collisions between moving solitons are considered too. Slowly moving solitons undergo multiple collisions, but eventually separate.

Discrete solitons dynamics in $$\mathscr {PT}$$-symmetric oligomers with complex-valued couplings

“…The existence and stability of localized mode solutions to nonlinear dynamical lattices of the DNLS type of equations with two-component settings have been considered and a general framework has been provided in [64]. A dual-core nonlinear waveguide with the PT -symmetry has been expanded by including a periodic sinusoidal variation of the loss-gain coefficients and synchronous variation of the inter-core coupling constant [65]. The system leads to multiple-collision interactions among stable solitons.…”

Collapse Dynamics of Vector Vortex Beams in Kerr Medium with Parity–Time-Symmetric Lattice Modulation

“…Many novel applications in linear and nonlinear PT symmetry optics systems have been demonstrated, such as the localization of light, unidirectional transmission, and information encryption [36][37][38][39][40]. The nonlinear collapse and evolution of different types of beams in PT-symmetrically modulated nonlinear media have recently been studied [10,[41][42][43]. The PT-symmetric potential mainly affects the collapse of light beams through two mechanisms.…”