Incoherent solitons in instantaneous nonlocal nonlinear media

We predict random-phase spatial solitons in instantaneous nonlocal nonlinear media. The key mechanism responsible for self-trapping of such incoherent wave packets is played by the nonlocal (rather than the traditional noninstantaneous) nature of the nonlinearity. This kind of incoherent soliton has profoundly different features than other incoherent solitons.

Figure 1

(Color online) Propagation of a random-phase beam comprising of Gauss-Hermite waves 0 and 1. Single frame self-trapped propagation when (a) $\varphi =0$, and (b) $\varphi =\pi ∕2$. Insets show the induced waveguides. Propagation of time-averaged intensity with nonlinearity “on” demonstrating statistical nonlinear diffraction (c), and with nonlinearity “off” showing linear diffraction (d). Note that the $x$ scale in (d) is 2.5 times larger than in (a)–(c). (e) Normalized time-averaged intensity profiles at the input face (dotted), and at the output face with (dashed) and without (solid) nonlinearity. (f) Calculated power spectrum of the beam (solid) and probability distribution of the transverse momentum (dashed).

Figure 2

(Color online). Propagation of random-phase beams consisting of Gauss-Hermite waves 0 and 2. Single frame beam propagation when (a) $\varphi =0$, and (b) $\varphi =\pi ∕2$. Propagation of the time-averaged intensity when the incident waves coincide (c) [do not coincide (d)] with the guided modes of the waveguide demonstrating a soliton [breather]. (e) Propagation of the time-averaged intensity of an incoherent beam demonstrating an incoherent soliton. (f) Propagation of the time-averaged intensity with nonlinearity “off” showing linear diffraction. The $x$ scale in (f) is five times larger than in (a)–(e).

Figure 3

(Color online). Propagation of an incoherent beam from a quasithermal source. (a) and (b) propagation of individual frames. Propagation of the time-averaged intensity with nonlinearity on demonstrating self-trapping with a small statistical nonlinear diffraction (c), and with nonlinearity off showing linear diffraction (d). The $x$ scale in (d) is 4.5 times larger than in (a)–(c). (e) Normalized profiles of the time-averaged intensity at the input face (dotted), and output face with (dashed) and without (solid) the nonlinearity. (f) Time-averaged power spectrum of the beam (solid) probability distribution of the transverse momentum (dashed).