Engineering optical soliton bistability in colloidal media

We consider a mixture consisting of two species of spherical nanoparticles dispersed in a liquid medium. We show that with an appropriate choice of refractive indices and particle diameters, it is possible to observe the phenomenon of optical soliton bistability in two spatial dimensions in a broad beam power range. Previously, this possibility was ruled out in the case of a single-species colloid. As a particular example, we consider the system of hydrophilic silica particles and gas bubbles generated in the process of electrolysis in water. The interaction of two soliton beams can lead to switching of the lower branch solitons to the upper branch, and the interaction of solitons from different branches is phase independent and always repulsive.

Figure 1

(a) Packing fractions of silica particles (dashed) and bubbles (dash-dotted), and the total induced refractive index change (solid) vs. the light intensity. The inset presents the dependence in the low intensities range. (b) The same presented in a bilogarithmic scale. Thanks to the appropriate choice of particle sizes and concentrations (see text), the refractive index dependence has a form of two “steps” and supports two-dimensional soliton bistability. See text for values of parameters.

Figure 2

(a) Soliton power (solid) and width (dash-dotted) vs. the propagation constant $\kappa$. Two stable branches with $\mathrm{d}P/\mathrm{d}\kappa >0$ exist. The dashed lines depict power dependence in the cases when one of the colloidal components (particles or bubbles) is removed from the system. Bottom panels show the soliton intensity profiles (solid) and colloidal particle (dashed) and bubble (dash-dotted) packing fractions for two bistable solitons carrying power $P=10\hspace{0.5em}$W from (b) the lower stable branch and (c) the upper stable branch. In (c), the bubble packing fraction is negligible. Notice the difference in the width scale.

Figure 3

Collision of two identical out-of-phase solitons ($\Delta \phi =\pi$) from the lower branch (left column) and of two solitons from different branches (right column). The power in each of the beams is equal to $P=15\hspace{0.5em}$W (left) and $P=12\hspace{0.5em}$W (right), and the angle between the beams is $5^{°}$ and $2.5^{°}$, respectively. The consecutive frames correspond to propagation distances $z=0$ (top row), $z=165\hspace{0.5em}\mu$m (middle row), and $z=425\hspace{0.5em}\mu$m (bottom row), In the first case, repulsive interaction leads to switching of the solitons from the lower (a) to the upper branch (c). In the second case, the interaction is also repulsive, independently of the relative phase between the solitons, and leads to destruction of the wider but weaker soliton.