Stability and nesting of dissipative vortex solitons with high vorticity

Using the variational method extended to dissipative systems and numerical simulations, an analytical stability criterion is established allowing the determination of stability domains of parameters for vortices with high topological charge S. Parameters from these domains are used as inputs for numerical self-generation of previously unexplored coexisting stable vortex solitons with topological charge ranging from $S=3$ to $S=20$. The nesting of low-vorticity solitons within those of higher vorticity is discovered. Such a self-organized structuring of light allows for selective dynamic nanophotonic tweezing.

Figure 1

Stability domains produced by the VA-generated fixed points, in the plane of the nonlinear-gain strength, $\varepsilon$, and the nonlinear-loss strength, $\mu$ (both dimensionless). In the darker region fixed points are only radially stable, while in the brighter one they are also azimuthally stable. This is confirmed by direct simulations of Eq. (1) for parameters inside elliptic areas, delimited by dashed lines.

Figure 2

Initial vortices ($z=0$) for charges $S=3$ (a) and $S=5$ (d) correspond to the input parameters $\beta =0.25$, $\delta =0.01$, $\mu =0.4$, and $\varepsilon =0.45$ from stability region. Vortex solitons are self-generated after respectively $z=300$ (b) and $z=500$ (e) steps. They both remain stable after $z=20000$ [see (c) and (f)].

Figure 3

For the same parameters, vortices for $S=10$ (a) and $S=20$ (d) become solitons respectively at $z=1000$ (b) and at $z=2000$ (e) remaining stable at least till $z=50000$ (c) and $z=80000$ (f).

Figure 4

(a) The nesting of $S=3$ vortex within those of vorticity $S=10$ and $S=20$. (b) Propagation distance $z=100S=2000$ is necessary for achieving structured self-organization of solitons. (c) Their robustness verified till $z=50000$ allows selective optical tweezing and precise manipulation [20].