Experimental Observation of Speckle Instability in Kerr Random Media

In a disordered nonlinear medium the transmitted speckle pattern was predicted to become unstable as a result of the positive feedback between intensity fluctuations and local variations of the refractive index. We show experimental evidence of speckle instability for light transversally scattered in a liquid crystal cell, where a two-dimensional controlled disorder is imprinted by suitable illumination of a photoconductive wall and nonlinearity is obtained through optical reorientation of the liquid crystal molecules. The speckle pattern spontaneously oscillates at discrete frequencies above a critical threshold, whose dependence on the scattering mean free path confirms the crucial role of disorder in the feedback process.

Figure 1

Sketch of experimental setup. The computer-generated disorder configuration (top-right inset) is projected onto the photoconductive wall ($PH$) of the LC light valve, using a green laser beam ($I_W$) and a spatial-light modulator (not shown). The near-field image of the random distribution of refractive index generated within the LC is shown in the bottom-left inset. The speckle pattern ($I_S$) results from transverse scattering of the beam ($I_S$) as it propagates back and forth through the LC film after reflection at the interface with $PH$ of the red probe beam ($I_P$). The probe field ${\overrightarrow{E}}_p$ is parallel to the LC nematic director $\widehat{e}$ (extraordinary polarization) determined by surface anchoring. The nonlinearity is provided by the molecular reorientation of the liquid crystal under the action of the red laser ($I_P$). ($G=\mathrm{\text{glass cover}}$.)

Figure 2

Temporal modulation of speckle intensity and corresponding power spectrum within an area encompassing a single speckle spot (delineated by the white square shown in the speckle pattern CCD image). Time-averaged intensity in this area is (a) $⟨I(t)⟩=40\mathrm{bits}$ and (b) $⟨I(t)⟩=140\mathrm{bits}$.

Figure 3

Inset: Histograms of oscillation amplitudes measured at positions in the speckle pattern with same time-averaged intensity (top: 20 bits; bottom: 50 bits). Average value of oscillation amplitude plotted vs the time-averaged intensity and for the four frequencies seen in Fig. 2b.

Figure 4

Oscillation amplitude at $f_0=2.39\mathrm{Hz}$ vs the time-averaged intensity and for two different scatterer diameters $D=50$ and $20\mu \mathrm{m}$, corresponding to mean free path $\ell \approx 100$ and $40\mu \mathrm{m}$, respectively. Solid lines are linear best fits of the data. The threshold, which is materialized by the crossing of the lines, decreases with decreasing $\ell$.