Complex light: Dynamic phase transitions of a light beam in a nonlinear nonlocal disordered medium

Abstract

The dynamics of several light filaments (spatial optical solitons) propagating in an optically nonlinear and non-local random medium is investigated using the paradigms of the physics of complexity. Cluster formation is interpreted as a dynamic phase transition. A connection with the random matrices approach for explaining the vibrational spectra of an ensemble of solitons is pointed out. General arguments based on a Brownian dynamics model are validated by the numerical simulation of a stochastic partial differential equation system. The results are also relevant for Bose condensed gases and plasma physics.

Mode-locking transitions in nanostructured weakly disordered lasers

“…The PEL, as a manifold in the configurational phase space, has many stationary points (typically minima and saddles) [15], whose distribution strongly affects the thermodynamics (and the dynamics) of the system. Recently this paradigm, developed to investigate the glass transition phenomena, has been applied to the field of photonics, including optical solitons [16,17] and random-lasers [18,19]. In this respect, it is worth to note that the geometrical interpretation of the laser threshold was recognized since the beginning of laser theory, and is considered as one of the successful applications of catastrophe-theory, which classifies the singularities of multi-dimensional manifolds [7,20].…”

Observation of Migrating Transverse Anderson Localizations of Light in Nonlocal Media

“…We observe two effects: (i) the controlled steering of the Anderson localization at 532nm towards the position of the control beam (the "migration"), (ii) a contraction of its spatial extension, that is an all-optically controlled localization length. These To support the previous findings by a theoretical analysis we resort to an approach originally developed for solitons [31]. Specifically, we denote the mean position of any of the exponential localizations by a two dimensional vector r p = (x p , y p ), with p = 1, 2, ..., N and N the number of localizations.…”

Complex dynamics and configurational entropy of spatial optical solitons in nonlocal media

“…20 Hence we are able to control the degree of nonlocality and tune the system through dynamic phases, each of them identified by a peculiar regime of filament propagation. 17 For a small non locality, corresponding to voltages around and above 2.5V, solitons are well separated in the transverse coordinate, exhibit a negligible mutual interaction and propagate almost independently. This is apparent in the last two panels of figure 1 (3.0 and 2.5 V).…”

“…The intensity profile can be taken as a coarselygrained density of filaments/particles and the oblique lines indicate soundlike vibrations in the xz plane, corresponding to an increased interaction range as predicted by the general theory of random matrices. 17,23 In conclusion, we investigated the interplay between non locality and disorder in the propagation of optical spatial solitons in nematic liquid crystals. Dynamic phase transitions of light in such a complex system were demonstrated for the first time.…”

“…Numerical simulations confirm the scenario. 17 Since a PEL is hard to visualize, from the experimental data we can obtain a simple portrait of it by extracting, digitalizing and recording the position of each filament across the transverse coordinate x. A string of binary bits -its length determined by the number of CCD pixels along x can be associated to the transverse distribution of the optical wavefront at a given propagation distance z=Z from the input (we take Z=3.0mm, i.e.…”