Fig. 4
Simulation of the topological control for a small waist. a Numerical simulation of the control of the final state after a propagation distance \(L=2.5\) mm for an initial beam waist \({W}_{0}=10\,\upmu\)m (\({I}_{0}=\frac{P}{{U}_{0}{W}_{0}}=5.33\times 1{0}^{5}\) W/m2). Axis \(t\) expresses time of detection, while \(x\) is the beam transverse coordinate. b Initial beam intensity: a super-Gaussian wave centered at \(x=150{\,}\upmu\)m. c–e Peregrine soliton generation: beam intensity (c) at \(t=12\) s, and (d) at \(t=64\) s, during the formation of the Peregrine soliton, while (e) exhibits the Peregrine soliton profile at \(t=70\) s. f, g Higher-order Peregrine soliton generation: beam intensity at f \(t=85\) s, and g \(t=100\) s, where the Peregrine soliton is alternately destroyed and reformed
