Optical pattern formation with a two-level nonlinearity

We present an experimental and theoretical investigation of spontaneous pattern formation in the transverse section of a single retroreflected laser beam passing through a cloud of cold rubidium atoms. In contrast to previously investigated systems, the nonlinearity at work here is that of a two-level atom, which realizes the paradigmatic situation considered in many theoretical studies of optical pattern formation. In particular, we are able to observe the disappearance of the patterns at high intensity due to the intrinsic saturable character of two-level atomic transitions.

Figure 1

Observation of patterns. (a) Experimental scheme. (b) Typical single-shot light distributions observed in the transverse instability regime, in the near (left) and far (right) field. The pump parameters are $I=0.47$ W/${\mathrm{cm}}^2$ and $\delta =+6.5\mathrm{\Gamma }$.

Figure 2

Saturation of the instability. We show the evolution of the patterns as the pump intensity is increased : (a) $I=0.24$, (b) $I=0.47$, (c) $I=1.41$, and (d) $I=4.24$ W/${\mathrm{cm}}^2$. The detuning is $\delta =+6.5\mathrm{\Gamma }$.

Figure 3

(a) Two-level instability domain $\left(\delta >0\right)$. We measure $P_d$ (see text) as a function of $\delta$ and $I$, and plot the data as isolines. Note the logarithmic horizontal scale. The dots indicate the theoretical threshold for the instability (see text). (b), (c) Cuts through the 2D chart of (a) as indicated by the dashed lines.

Figure 4

Talbot effect and pattern size $\left(\delta >0\right)$. We measure $\mathrm{\Lambda }$ (see text) as the feedback mirror distance $d$ is varied (dots: lowest $q$ mode; circles: higher $q$ mode). The line is the prediction of a thick-medium model. Inset: The measured $d$ period as a function of the pattern size (stars), together with the Talbot effect prediction (line).