Chaotic self-trapped optical beams in strongly nonlocal nonlinear media

The self-trapped optical beams possessing both chaotic and solitonlike properties, which are termed as chaoticons, were predicted by us [Sci. Rep. 7, 41438 (2017)] in the strongly nonlocal nonlinear media. We reveal that any random input beam, which has random initial transverse distribution and arbitrary input power, propagating in the strongly nonlocal nonlinear media with the exponential-decay response, will evolve into a chaoticon. The chaotic properties are signified by the positive Lyapunov exponents and spatial decoherence, while the solitonlike properties are demonstrated by the invariance of the beam width and the interaction of quasielastic collisions. Distinctively, the propagations of random inputs are always periodic in the strongly nonlocal media with the Gaussian response.

Figure 1

The evolution of a random initial input with $P_i=P_9$ in the ERF model. (a) The initial input $r\left(x\right)$ (blue solid curve) with a random profile holding the same power and beam width with the nine-humped HGSS (black dotted curve). (b), (c) The contour plots of $\left|q\right(x,z\left)\right|$, (d), (e) the corresponding statistic beam widths $w\left(z\right)$. (c), (e)The enlargements of (b), (d) in the region of $z\in [100,105]$, respectively.

Figure 2

The evolutions of random initial inputs with $P_i=0.7P_9$ (left) and $P_i=1.3P_9$ (right) in the ERF model. (a), (b)The contour plots of $\left|q\right(x,z\left)\right|$, (c), (d) the beam widths corresponding to (a), (b), respectively.

Figure 3

The periodic evolutions of random initial inputs for the unphysical GRF model. (a) The contour plot of $\left|q\right(x,z\left)\right|$ for $P_i=P_9$, (b) the beam widths corresponding to (a). (c) The beam widths for $P_i=0.7P_9$ (the upper red solid curve) and $P_i=1.3P_9$ (the lower green dashed curve), respectively.

Figure 4

The maximal Lyapunov exponents for several cases. The four curves from top to bottom are corresponding to the evolutions show in Fig. 2, Fig. 1, Fig. 2, and Fig. 3, respectively.

Figure 5

The modulus of the spatial cross correlation function for the evolution of the random input $r\left(x\right)$.

Figure 6

The interaction of quasielastic collisions between the two identical beans shown in Fig. 1. (a) The contour plot of $\left|q\right(x,z\left)\right|$, (b) the partially enlarged detail of (a) in box.