Replication of dissipative vortices modeled by the complex Ginzburg-Landau equation

Abstract

Dissipative vortices are stable two-dimensional localized structures existing due to balance between gain and loss in nonlinear systems far from equilibrium. Being resistant to the dispersion and nonlinear distortions they are considered as promising information carriers for new optical systems.The key challenge in the development of such systems is getting control over vortex waveforms. In this paper we report on replication of two-dimensional fundamental dissipative solitons and vortices due to their scattering on a locally applied potential in the cubic-quintic complex Ginzburg-Landau equation. It has been found that an appropriate potential non-trivially splits both fundamental solitons and vortices into a few exact copies without losing in their amplitude levels. A remarkably simple potential having a finite supporter along the longitudinal coordinate and a double peaked dependence on a single transverse coordinate is found to be suitable for the replication of the twodimensional localized structures.

Logic gates on stationary dissipative solitons

“…We can imagine a particular waveform transition as an forced displacement of a point in the phase space from a basin of attraction of given attractor to a vicinity of another attractor. Here we further elaborate the ideas of induced waveform transitions [58][59][60][61][62] in the development of controllable interaction between the plain and composite pulses that finally lead us to the implementation of all the logic gates. Below we subsequently demonstrate the most important of them.…”

“…Due to the applied magnetic field the time reversal symmetry is locally broken that leads to significantly different propagation conditions of counter-propagating dissipative optical solitons whose envelops are governed by the cubic-quintic CGLE with a potential term [33,34]. Recently this robust model has successfully been used to perform a selective lateral shift within a group of stable noninteracting fundamental dissipative solitons [58], to replicate dissipative solitons and vortices [59,60], and to induce the waveform transitions between different dissipative solitons [61,62].…”

Compression and stretching of ring vortex in a bulk nonlinear medium

“…They serve as an excellent platform for investigating nonlinear optical dynamics in multiple physical disciplines, including nonlinear optics, fluid dynamics, plasma physics, complex networks, and molecular biology. [1][2][3][4][5][6] Among dissipative solitons, the dissipative vortex [7][8][9] is noteworthy. Dissipative vortex structures with nonzero angular momenta have counterparts in nature, such as tornadoes.…”

Simple harmonic and damped motions of dissipative solitons in two-dimensional complex Ginzburg-Landau equation supported by an external V-shaped potential

“…The CQ CGL equation with potential energy term is a model used to study far-non-equilibrium nonlinear phenomena in physical systems, including mode-locking and fiber laser nonlinear optical waveguide semiconductor devices Bose-Einstein condensate reaction-diffusion system, etc. [12,20,27]. Kochetov et al studied the evolution of dissipative structures to regime with spontaneous transformation of the topological excitations and logic gates on stationary dissipative solitons in the form of the CGL equation with a potential term [28][29].…”