Light-matter interaction induces a shadow vortex

Abstract

By sending a light beam on a homeotropic nematic liquid-crystal cell subjected to a voltage with a photosensitive wall, a stable matter vortex can be induced at the center of the beam. When the applied voltage is decreased, the vortex disappears from the illuminated region; however, the system shows a stationary molecular texture. Based on a forced Ginzburg-Landau amplitude equation, we show that the vortex with a core of exponentially suppressed amplitude always remains in a shadow region below instability threshold and that the observed texture is induced by its phase distribution. This is a different type of vortex phase singularity solution. Numerical simulations and experimental observations show a quite fair agreement.

Symmetry Breaking and Restoration in the Ginzburg–Landau Model of Nematic Liquid Crystals

“…We show that when a = 0 the global minimizer is radially symmetric and unique and that its symmetry is instantly broken as a > 0 and then restored for sufficiently large values of a. Symmetry breaking is associated with the presence of a new type of topological defect which we named the shadow vortex. The symmetry breaking scenario is a rigorous confirmation of experimental and numerical results obtained earlier in [7].…”

The connecting solution of the Painlevé phase transition model

“…, and µ rad (ρ) = 0 for a unique ρ > 0, In the physical context described in [8] the function µ is specific…”

Gradient theory of domain walls in thin, nematic liquid crystals films

“…For this purpose we will restrict our attention to the time independent solutions, the idea being that the system quickly relaxes to its stationary state. If one ignores the dependence on the transversal x 2 coordinate, the system exhibits two type of walls that separate domains that evanesce asymptotically [1,4]. One corresponds to the extension of Ising wall, standard kink, in this inhomogeneous system, which is a symmetric solution and centered in the region of the maximal illumination i.e.…”

“…x = 0 (since µ(x) attains its maximum in the origin). The other corresponds to a wall centered in the non-illuminated part, shadow kink [1,4]. To understand the latter one can expand the solution around the point where µ(x) = 0.…”

“…Let ω n be the open set bounded by Γ n , let ν n (z) be the outer unit normal vector at z ∈ Γ n , and let us define the open set Ω n = {x ∈ R 2 : d(x, ω n ) < λǫ n }, where d stands for the Euclidean distance, and λ is the constant defined in Lemma 3.1. As previously we setD 1…”