We investigate the formation of collisionless shocks along the spatial profile of a Gaussian laser beam propagating in nonlocal nonlinear media. For defocusing nonlinearity the shock survives the smoothing effect of the nonlocal response, though its dynamics is qualitatively affected by the latter, whereas for focusing nonlinearity it dominates over filamentation. The patterns observed in a thermal defocusing medium are interpreted in the framework of our theory.

Spin-glass theory is one of the leading paradigms of complex physics and describes condensed matter, neural networks and biological systems, ultracold atoms, random photonics and many other research fields. According to this theory, identical systems under identical conditions may reach different states. This effect is known as replica symmetry breaking and is revealed by the shape of the probability distribution function of an order parameter named the Parisi overlap. However, a direct experimental evidence in any field of research is still missing. Here we investigate pulse-to-pulse fluctuations in random lasers, we introduce and measure the analogue of the Parisi overlap in independent experimental realizations of the same disordered sample, and we find that the distribution function yields evidence of a transition to a glassy light phase compatible with a replica symmetry breaking.

We experimentally investigate the interplay between spatial shock waves and the degree of disorder during nonlinear optical propagation in a thermal defocusing medium. We characterize the way the shock point is affected by the amount of disorder and scales with wave amplitude. Evidence for the existence of a phase diagram in terms of nonlinearity and amount of randomness is reported. The results are in quantitative agreement with a theoretical approach based on the hydrodynamic approximation.

Random laser emission is obtained from a fluidic paper-based device realized by conventional soft-lithography techniques on common, flexible, renewable and biocompatible commercial paper. The device is realized exclusively on paper by creating microfluidic porous channels on the cellulose fibres, in which a laser dye (Rhodamine B) can flow by capillarity. The modulation of the random lasing characteristics, in terms of threshold and spectral position, can be tailored by acting on the confinement induced by the lithographic process as well as on the shape and functionalization at the interface of the emitting regions.

We are able to detect the details of spatial optical collisionless wave breaking through the high aperture imaging of a beam suffering shock in a fluorescent nonlinear nonlocal thermal medium. This allows us to directly measure how nonlocality and nonlinearity affect the point of shock formation and compare results with numerical simulations.