Coexistence of collapse and stable spatiotemporal solitons in multimode fibers

We analyze spatiotemporal solitons in multimode optical fibers and demonstrate the existence of stable solitons, in a sharp contrast to earlier predictions of collapse of multidimensional solitons in three-dimensional media. We discuss the coexistence of blow-up solutions and collapse stabilization by a low-dimensional external potential in graded-index media, and also predict the existence of stable higher-order nonlinear waves such as dipole-mode spatiotemporal solitons. To support the main conclusions of our numerical studies we employ a variational approach and derive analytically the stability criterion for input powers for the collapse stabilization.

Figure 1

Schematic illustration of stable spatiotemporal solitons propagating in a graded-index optical fiber. Two types of spatial cross-section profiles are shown on the right, namely, fundamental and dipole-mode solitons, respectively.

Figure 2

Families of multidimensional solitons presented through the key dependencies: (a) Hamiltonian $H$ vs power $P$ and (b) power $P$ vs propagation constant $\lambda$. Red bars in (b) show the analytical estimate of the critical power. Gray curves in (a) depict analytical solutions for the fundamental solitons for both stable and unstable branches.

Figure 3

Examples of three-dimensional solitons, shown for (a.1–a.3) power ${\left|A\right|}^2(x,y,t)$ in the plane $(x,y)$ for different $\mu$ and $\lambda =-0.25\sqrt{\mu }$, and power profiles as cross sections in $t$ and $x$.

Figure 4

Families of the dipole-mode spatiotemporal solitons, shown for (a) Hamiltonian $H$ vs propagation constant $\lambda$ and (b) power $P$ vs propagation constant $\lambda$.

Figure 5

Power plots and spatial profiles (top) of the dipole-mode multidimensional solitons for different parameters $\mu$ and $\lambda$.

Figure 6

Two-dimensional Hamiltonian $H(a,b)$ for different values of the parameter $\mu$: $\mu =1$ (left) and $\mu =0$ (right). Here $\sigma =1$ and $P_0=1$. The areas bounded by purple curves correspond to collapse. Blue curves correspond to the dynamics of an input Gaussian pulse corresponding to the fundamental soliton.

Figure 7

Results of the direct numerical three-dimensional modeling: ${\left|A\right|}^2(x,0,t,z)$ isosurfaces present (a) the light bullet regime with solitonlike dynamics and (b) the spatiotemporal dynamics with temporal compression.