Soliton interactions and transformations in colloidal media

We study nonlinear light propagation in colloidal suspensions of spherical dielectric nanoparticles. We analyze the existence and properties of one-dimensional self-trapped beams (spatial optical solitons) in such media and demonstrate the existence of a bistability regime. The solitons corresponding to the two bistable branches have very different properties, and they can be easily distinguished by the measurement of the soliton width. We find that both types of solitons can form spontaneously through spatial modulational instability of continuous wave beams, but the solitons corresponding to the upper branch are more robust. This is also confirmed by the study of soliton collisions, where we describe a number of possible scenarios, including soliton amalgamation, destruction, reflection, deflection, and switching to another branch. We also find that the interaction of two mutually coherent solitons corresponding to different branches is phase independent and always repulsive. We provide a simple physical explanation of this phenomenon.

Figure 1

(Color online) Packing fraction $\eta$ of colloidal particles vs the light intensity (solid line). The dashed line shows the dependence of the exponential model.

Figure 2

(Color online) Modulation instability leading to the formation of solitons from the (a) lower branch for ${\mid u_0\mid }^2=0.05$ and (b) upper branch for ${\mid u_0\mid }^2=1$. The threshold value separating these two scenarios is ${\mid u_0\mid }^2\approx 0.08$.

Figure 3

(Color online) (a) Soliton power and width vs the propagation constant $\kappa$ for ${\eta }_0={10}^{-3}$. Bottom panels show the soliton intensity profile (solid) and colloidal particle packing fraction (dashed) for bistable solitons carrying power $P=40$ from (b) the lower stable branch and (c) the upper stable branch. Notice the difference in the width scale.

Figure 4

(Color online) (a)–(c) Collisions of solitons from the lower stable branch for $P=45$, $k_0=0.05$, and different values of the phase difference $\Delta \phi$. In panels (d), (e), and (f) collisions of solitons from the higher branch are presented for $P=33$ and $k_0=0.1$.

Figure 5

(Color online) Switching from the lower to the upper branch triggered by collision with another soliton for soliton power $P=50$ and (a) $k_0=0.01$ or (b) $k_0=0.03$. Powers of both solitons are equal to $P$.

Figure 6

(Color online) Other scenarios for collision of two solitons from different branches. For high transverse velocities, the solitons pass through each other as shown in (a) for $P=50$ and $k_0=0.5$. For lower velocities, the interaction leads to (b) soliton deflection for $P=35$ and $k_0=0.025$, (c) destruction for $P=40$ and $k_0=0.02$, or (d) reflection for $P=45$ and $k_0=0.01$.

Figure 7

Diagram of collision outcomes for two bistable solitons from different branches. The marked points correspond to numerical data from Figs. 5, 6. The central area corresponds to scenarios where the lower-branch soliton is destructed and the higher-branch soliton changes the propagation direction. The dashed lines determine the bistability region.