Bistability Controlled by Convection in a Pattern-Forming System

We analyze the transition from convective to absolute dynamical instabilities in a nonlinear optical system forming patterns, i.e., a photorefractive crystal in a single feedback configuration. We demonstrate that the convective regime is directly related to the bistability area in which the homogeneous steady state coexists with a pattern solution. Outside this domain, the system exhibits either a homogeneous steady state or an absolute dynamical regime. We evidence that the bistability area can be greatly increased by adjusting the mirror tilt angle and/or by applying an external background illumination on the photorefractive crystal.

Figure 1

Schematic of our photorefractive single feedback system. The forward ($F$) and backward ($B$) beams are responsible for the pattern formation. Lens ($L$2) and different beam splitters ($BS$) are used to monitor the transverse patterns arising onto the backward beam trajectory. $L$: distance between the mirror and the crystal, $\beta$: mirror tilt angle, $H=L.\sin (\beta )$: transverse shift (in $\mu \mathrm{m}$).

Figure 2

Normalized intensity of the hexagons as a function of the input power obtained experimentally (EXP.) in (a),(c), and (e) and numerically (NUM.) in (b),(d),(f) as function of the photorefractive coupling strength $\gamma$. Crosses and circles are obtained when increasing and decreasing the input power (and corresponding $\gamma$), respectively. Three cases are studied: no advection effect (a),(b), weak (c),(d) and strong advection (e),(f) corresponding to a drift of the otherwise stable pattern towards the left on the different pictures. The areas between the dashed lines correspond to the bistability regimes where the homogeneous solution coexists with the hexagonal pattern state. Insets correspond to experimental near-field intensity patterns obtained for different input powers.

Figure 3

Evolution of near-field pattern size versus the pump power for a strong advectionlike effect [Figs. 2]. Orange dashed lines correspond to the pattern occupation inside the total available space represented by the solid orange lines. The black dotted lines represent the different thresholds for convective and absolute regimes. Crosses and circles are obtained when increasing and decreasing the input power, respectively.

Figure 4

Plots similar to Figs. 2 with a background illumination switched on. (a) Experimental results and (b) numerical simulation.