Optical Nonlinearities and Enhanced Light Transmission in Soft-Matter Systems with Tunable Polarizabilities

We demonstrate a new class of synthetic colloidal suspensions capable of exhibiting negative polarizabilities, and observe for the first time robust propagation and enhanced transmission of self-trapped light over long distances that would have been otherwise impossible in conventional suspensions with positive polarizabilities. Such light penetration through the strong scattering environment is attributed to the interplay between optical forces and self-activated transparency effects while no thermal effect is involved. By judiciously mixing colloidal particles of both negative and positive polarizabilities, we show that the resulting nonlinear response of these systems can be fine-tuned. Our experimental observations are in agreement with theoretical analysis based on a thermodynamic model that takes into account particle-particle interactions. These results may open up new opportunities in developing soft-matter systems with engineered optical nonlinearities.

Figure 1

Schematic illustrations (a)–(c) and experimental demonstrations (d)–(f) of light-particle interactions in colloidal suspensions. (a),(d) Positive-polarizability particles ($2\mu \mathrm{m}$ polystyrene beads suspended in water) are attracted by an optical beam. (b),(e) Repulsion of negative-polarizability particles (hollow glass spheres with estimated average diameter of $7\mu \mathrm{m}$ and refractive-index of 1.2 in aqueous suspension). (c),(f) Collective motion of PP and NP particles, when both species are present. Movies of the three cases can be found in the Supplemental Material S1 [20].

Figure 2

Experimental observation of a light beam propagating through 10-mm-long colloidal suspensions of different polarizabilities. (a) Catastrophic self-focusing collapse occurs in the PP suspension. (b) Enhanced transmission against scattering is observed in the NP suspension over several diffraction lengths. In both (a) and (b), the initial volume filling factor is 0.3%. (c) The same beam diffracts linearly even at high power in a refractive index matched (zero-polarizability) suspension. In (c) the image contrast has been enhanced to improve visibility despite the much weaker scattering.

Figure 3

Observation of stable optical self trapping in an NP colloidal suspension with $f_0=0.3\%$. (a) Input beam profile. (b) Linear output intensity after a propagation distance of 2 mm at a low input power of 0.1 W. (c) Nonlinear output corresponding to a stable soliton at a high input power of 3.0 W. The side-view photograph (d) shows the propagation of such a self-trapped beam over a distance of 5 mm.

Figure 4

(a) Normalized nonlinear response of a mixed-polarizability suspension. The collective nonlinearity arises from a superposition of the two components for a fixed overall volume filling factor. The pure NP dispersion corresponds to a mixing ratio of $c=0$, while a ratio of $c=1$ indicates a pure PP system. The transition between saturable NP and supercritical PP behaviors is indicated by the Kerr plane (gray). (b) Measured output beam size after 2 mm of propagation as a function of the input power for mixed colloidal suspensions containing 0.7% of NP and varying amounts of PP particles. (The input beam width was $11\mu \mathrm{m}$.) (c) Measured intensity-dependent transmission for different suspensions [pure NP ($c=0$, $f_0=0.7\%$), pure PP ($c=1.0$, $f_0=0.22\%$), and two mixtures thereof] after 2 mm of propagation. All mixtures were appropriately diluted to exhibit the same linear transmission of 18% at the lowest input power. In (b) and (c) the error ranges are indicated by the shaded regions surrounding the respective graphs.