Mutual transitions between stationary and moving dissipative solitons

Abstract

Application of stable localized dissipative solitons as basic carriers of information promises the significant progress in the development of new optical communication networks. The success development of such systems requires getting the full control over soliton waveforms. In this paper we use the fundamental model of dissipative solitons in the form of the complex Ginzburg-Landau equation with a potential term to demonstrate controllable transitions between different types of coexisted waveforms of stationary and moving dissipative solitons. Namely, we consider mutual transitions between so-called plain (fundamental soliton), composite, and moving pulses. We found necessary features of transverse spatial distributions of locally applied (along the propagation distance) attractive potentials to perform those waveform transitions. We revealed that a one-peaked symmetric potential transits the input pulses to the plain pulse, while a two-peaked symmetric (asymmetric) potential performs the transitions of the input pulses to the composite (moving) pulse.

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.…”

“…2(a)] can only be performed by a weak attractive potential, which slowly shifts the composite pulse without considerable squeezing of its waveform. Otherwise, being attracted by a strong potential the composite pulse can collapse to the plain pulse [62].…”

“…5(e). First of all, we apply q 1 (x) to transit four different pairs of input pulses to so-called moving pulses [14,62]. The asymmetrical profile of q 1 (x) is properly chosen to transit two input plain pulses to the moving pulse with a transverse drift along the negative direction of the x axis [ Fig.…”

“…On the other hand, having applied the external potential (2) one can get control over the soliton waveforms, for example, to transit the plain pulse to the composite pulse and to return its waveform back [62]. In general, such transitions induced by an external potential can be possible between an arbitrary pair of stable coexisting dissipative solitons if an appropriate control potential is applied [61,62]. 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.…”

“…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].…”