Experimental Observation of Modulation Instability and Optical Spatial Soliton Arrays in Soft Condensed Matter

In this Letter we report observations of optically induced self-organization of colloidal arrays in the presence of unpatterned counterpropagating evanescent waves. The colloidal arrays formed along the laser propagation axis are shown to be linked to the breakup of the incident field into optical spatial solitons, the lateral spacing of the arrays being related to modulation instability of the soft condensed matter system.

Figure 1

A schematic diagram outlining the geometry of the experimental setup and a light scattering image of spontaneous ordering of 410 nm polymer colloids seen under typical experimental conditions. The top left diagram indicates the orientation of coupling prism; the propagation direction of the two counterpropagating modes are along the $x$ direction and the observed array formation is aligned along the $x$ direction with a periodic spacing in the $y$ direction (top right). The bottom diagram shows the structure of the nonlinear prism-coupled slab waveguide used for the experiments.

Figure 2

The temporal evolution of the OSS formation for incident powers above the threshold. Each panel is a CCD image of the illuminated region at different times after the light is coupled to the system. Bright field imaging also confirms the presence of ordered colloids in regions of high intensity.

Figure 3

The graph on the left shows in the period of the array spacing as a function of the input power above threshold. The experimental data have been normalized with respect to the threshold array spacing and threshold input power. The period ($L$) is normalized with respect to the period at threshold ($L_{\mathrm{th}}$) and the input coupling power ($P$) is normalized to the power at threshold ($P_{\mathrm{th}}$). The solid line indicates the variation as predicted by the continuum model. The three panels on the right show the array formations for different illumination intensities. Below the threshold the OSS are not observed (top), even after extended periods of illumination; just above threshold stable arrays of OSS are formed.