Optical wall dynamics induced by coexistence of monostable and bistable spatial regions

Abstract

When nonequilibrium extended homogeneous systems exhibit multistability, it leads to the presence of domain walls between the existing equilibria. Depending on the stability of the steady states, the dynamics differs. Here, we consider the interface dynamics in the case of a spatially inhomogeneous system, namely, an optical system where the control parameter is spatially Gaussian. Then interfaces connect the monostable and the bistable nonuniform states that are associated with two distinct spatial regions. The coexistence of these two regions of different stability induces relaxation dynamics and the propagation of a wall with a time-dependent speed. We emphasize analytically these two dynamical behaviors using a generic bistable model. Experimentally, an inhomogeneous Gaussian light beam traveling through either a dye-doped liquid crystal cell or a Kerr cavity depicts these behaviors, in agreement with the theoretical predictions.

Dissipative structures induced by photoisomerization in a dye-doped nematic liquid crystal layer

“…The previous dynamical behaviour can be described universally by means of a bistable model with inhomogeneous parameters [17,18]. In order to reconcile our description with this universal one, we consider the limit for which the light beam varies slowly (w 1) and the decay rate related to the transition from cis to trans state is much faster than the variation rate of the order parameter (λ A).…”

“…Indeed, in the illuminated area, the dyes photoisomerization induces a phase transition to the isotropic state. Theoretically, based on nascent of bistability model with inhomogeneous coefficients allows quantitatively and qualitatively explain this adaptive front dynamics [17,18]. However, this description was not derived from the physics of liquid crystals and concentration of dopants, which are fundamental elements in the phenomenon under study.…”

“…where the bifurcation parameter A + C 0 (x, y, I 0 , w) is controlled by the light intensity. By means of a simple variable translation with the objective of eliminating the quadratic term, one retrieves the universal model used to describe the front propagation in inhomogeneous media [17,18]. Note that by means of pulsed light, one can induce molecular disorder and molecular reorientation of pure liquid crystals [21].…”

Basins of attraction of the bistable region of time-delayed cutting dynamics

“…Bistability or multistability has been universally found in almost all areas of science and engineering, including neuronal systems [1], optics [2], electronics [3], epidemics [4], and mechanical systems [5]. This discovery has been an exciting development for the dynamical systems research community as it offers an opportunity to control the system dynamics without the need to vary the system parameters [6].…”

Control of traveling localized spots

“…In a photosensitive Belousov-Zhabotinsky (BZ) medium, periodic variation of the applied light intensity can force a spiral wave tip to describe a wide range of hypocycloidal and epicycloidal trajectories [30,31]. In optical bistable media like dye-doped liquid crystals and Kerr cavities, interface dynamics can be controlled by spatially inhomogeneous forcing [32]. Position control of traveling wave patterns can be tackled by feedback control as well.…”