Continuous emission of fundamental solitons from vortices in dissipative media by a radial-azimuthal potential

Abstract

We report novel dynamical regimes of dissipative vortices supported by a radial-azimuthal potential (RAP) in the 2D complex Ginzburg-Landau (CGL) equation with the cubic-quintic nonlinearity. First, the stable solutions of vortices with intrinsic vorticity S = 1 and 2 are obtained in the CGL equation without potential. The RAP is a model of an active optical medium with respective expanding anti-waveguiding structures with m (integer) annularly periodic modulation. If the potential is strong enough, m jets fundamental of solitons are continuously emitted from the vortices. The influence of m, diffusivity term (viscosity) β, and cubic-gain coefficient ε on the dynamic region is studied. For a weak potential, the shape of vortices are stretched into the polygon, such as square for m = 4. But for a stronger potential, the vortices will be broke into m fundamental solitons.

Logic gates on stationary dissipative solitons

“…The nonlinear Schrödinger equation with a longitudinal defect [51], an external delta potential [52], and a longitudinal potential barrier [53] appear in optical applications for beam splitters. The complex dynamics of dissipative solitons in active bulk media with spatially modulated refractive indexes in the form of a sharp potential bar-rier [54], umbrella-shaped [55], and radial-azimuthal [56] potentials has been studied on the base of the one-and two-dimensional cubic-quintic CGLEs.…”

Induced waveform transitions of dissipative solitons

“…Various scenarios of the dynamics of dissipative solitons interacting with a sharp potential barrier in the cubic-quintic CGLE are analyzed in [27]. Similarly, the evolution of dissipative solitons in an active bulk medium has been studied in the framework of the two-dimensional CGLE with an umbrella-shaped [28] and a radial-azimuthal [29] potentials.…”

Splitting of Dissipative Vortices

“…The continuous generation of two-dimensional expanding solitons in an active optical medium perturbed by the razor, dagger, and needle potentials has been reported in [19]. The evolution of two-dimensional dissipative solitons in active bulk media upon applied umbrella-shaped and radial-azimuthal potentials has been analyzed in [20] and [21], respectively. On the other hand, an external potential can break the time reversal symmetry as it is in magneto-optic systems [6,7], where an external magnetic field is applied to achieve the non-reciprocal propagation of dissipative optical solitons.…”