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## Replica Symmetry Breaking in Random Lasers
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 and provide different values for observable quantities. 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 atransition to a glassy light phase compatible with a replica symmetry breaking.
## Solitonized Anderson localized states moveThe conventional wisdom is that transport is absent in the presence of Anderson localization. However, nonlinearity changes things. In a paper published in Physical Review Letters (arXiv:1407.7990), Marco Leonetti, Salman Karbasi, Arash Mafi, and Claudio Conti, report experimental evidence that disorder induced two-dimensional states in an optical fiber display collective motion and action at a distance. It is also shown that the trend of the localization length with power is compatible with that of a spatial optical soliton, giving support to the fact that two mechanicsms, disorder and nonlinearity, may cohexist. The pictures below show the profile of one localized state versus power and the collective motion of several localizations, they exhibit a mutual attraction because of the nonlocal nonlinearity. ## Nonlocality and Bose Einstein condensation of lightIn arXiv:1406.6250, Marcello Calvanese Strinati and Claudio Conti consider a microcavity made by a graded-index (GRIN) glass, doped by dye molecules, placed within two planar mirrors and study Bose-Einstein condensation (BEC) of photons. The presence of the mirrors leads to an effective photon mass, and the index grading provides an effective trapping frequency; the photon gas becomes formally equivalent to a two dimensional Bose gas trapped in an isotropic harmonic potential. The inclusion of nonlinear effects provides an effective interaction between photons.Thermal lensing effects and the resulting nonlocal nonlinearity are considered, and quantitatively compared with the reported experimental data (courtesy of Jan Klaers and Martin Weitz) ## Rogue waves and the landscapeNon-deterministic giant waves, denoted as rogue, killer, monster or freak waves, have been reported in many different branches of physics. Their origin is however still unknown: despite the massive numerical and experimental evidence, the ultimate reason for their spontaneous formation has not been identified yet. In arXiv:1406.5966, Andrea Armaroli, Claudio Conti, and Fabio Biancalana, show that rogue waves in optical fibres actually result from a complex dynamic process very similar to well known mechanisms such as glass transitions and protein folding. They describe the way the interaction among optical solitons produces an energy landscape in a highly-dimensional parameter space with multiple quasi-equilibrium points. These configurations have the same statistical distribution of the observed rogue events and are explored during the light dynamics due to soliton collisions, with inelastic mechanisms enhancing the process. Slightly different initial conditions lead to very different dynamics in this complex geometry; a rogue soliton turns out to stem from one particular deep quasi-equilibrium point of the energy landscape in which the system may be transiently trapped during evolution. This explanation will prove fruitful to the wide community interested in freak waves. ## Quantum Gravity and Nonlinear Optics: the Generalized Uncertainty PrincipleQuantum gravity is one of the most intriguing fields of physics, people is working a lot for finding an experimental framework. It is apparently impossible to reach in the laboratory the required energies, many consider the scale of the Universe, looking for high energy particles. Perhaps we can play the quantum gravity game in the laboratory by using nonlinear optics. It is really interesting that the equations that describe some of the modifications of quantum mechanics, which are supposed to hold true at the Planck scale (as the famous KMM proposal), are also valid for the propagation of nonparaxial nonlocal optical beams. This is treated in a recent work in Phys. Rev. A (ArXiv:1406.6677) One of the simplest and beautiful predictions of the quantum gravity literature is the possibility of a generalized uncertainty principle, which reads as that implies that the spatial uncertainity cannot be smaller than a minimal quantity. The states that satistfy this condition are named the maximally localized states. In Phys. Rev. A (ArXiv:1406.6677) we show that in nonlinear optics these states can be excited by an ultrafocused laser beam, this provides fascinating analogs of supposed quantum gravity effects. ## Nonlinear Optomechanical Pressure and GrapheneThe mechanical effect of light has been the subject of the investigations of many scientists for more than three centuries but many questions are still open. In a recent manuscript (arXiv.org:1403.1948, Physical Review A 89, 033934, Editors' Suggestion), C. Conti and Robert W. Boyd predict that high energy ultrashort laser pulses may mechanically attract an object. The effect is due to the fact that the velocity of a photon depends on the laser intensity. Because of the momentum conservation, also the velocity of an optically pushed object depends on the light intensity; hence the mechanical action of light can be all-optically controlled. This may be denoted to as By using this nonlinear optical effect it may be possible to design experiments in which objects are attracted or accelerated by short pulses by an amount determined by pulse energy, temporal duration and spectral content. This nonlinear mechanical action is due to a property common to any sufficiently transparent material, the optical Kerr effect, that is, an intensity dependent refractive index. Conti and Boyd consider the specific case of a thin membrane of graphene, which has a very pronounced optical Kerr effect, and predict that is may be deformed as an optical sail by light. This may have a variety of applications for laser propulsion, and for laser controlled shaping of surfaces. The authors report a theoretical analysis, which is validated by first principles simulations of the 3D+1 nonlinear Maxwell equations by using High Performance Computing (HPC) facilities within the CINECA-ISCRA initiative.
## Nonlocality and dissipation due to non-paraxialityThe investigation of nonlinear optical propagation in extreme regimes is one of the frontiers of modern research. Generally speaking, beyond the usual approximations, one could expect just small perturbations to known effects, as diffraction, solitons, and self-phase modulation; however, in specific cases, novel phenomena arise. One relevant example is given by the breaking of the paraxial approximation. In a paper published in the Physical Review A, (arXiv:1402.1161) Nicola Bulso and Claudio Conti theoretically and numerically show that non-paraxial propagation in a simple local Kerr medium may produce effective dissipation and nonlocality even if no loss mechanism is present. This radically affects well known processes as modulational instability and soliton propagation. The picture below shows the evolution of an higher order soliton when including non-paraxiality in different theoretical models. ## Dissipative Shock Waves in Normal Dispersion Fiber LaserIn a paper published in Optics Letters, C. Lecaplain, J. M. Soto-Crespo, Ph. Grelu, and C. Conti, report on a theoretical analysis revealing that the routinely observed spectral features in fibre lasers in the normal dispersion regime can be explained in terms of the generation of a stable shock profile of the electromagnetic pulse inside the laser cavity. This mechanism is described by an analytic solution of the relevant Haus master equation, and seems to be are origin of the well-known M-shape of the laser spectrum. The following is the Burgers-like equation derived for the shock wave in the fiber laser ## Optical Shock Waves in Silica AreogelSilica Areogel is a material that is mostly composed by air. A tiny silica scaffold forms samples that have unique physical properties with an enormous amount of applications. Also the nonlinear optical properties and, in particular, the thermally driven features, are very surprising and in several respects are unknown. In a paper published in Optics Express, S. Gentilini, F. Ghajeri, N. Ghofraniha, A. Di Falco, and C. Conti, report on the experimental observation of wave-breaking phenomena in these materials, very promising because they can sustain high power continuous wave irradiation without boiling and melting. The samples have been realized by A. Di Falco and F. Ghajeri. This is another remarkable example of shock waves in disordered media. The picture below shows the areogel sample. ## Anderson localization with a purely nonlinear originAnderson localization concerns the transition to a regime in which all the modes of a disordered system are exponentially localized. It also often and generically refers to wave-localizations in a disordered potential. In general the potential that induces these states is linear; but one may argue if, in a linearly homogeneous medium, localizations may arise from a random modulation of the nonlinear response. This is what Viola Folli, Katia Gallo and Claudio Conti investigate in a paper published in Optics Letters. It turns out that disorder-induced localized states may have a purely nonlinear origin, but this is accompanied by instability processes that amplify the Anderson states and lead to complicated nonlinear dynamics, still un-explored. An example is given in the process of parametric down-conversion in periodically poled crystals for optical second harmonic generation (picture below). A notable property of purely nonlinear Anderson states is the fact that their localization length is determined by the input power.
## Dynamics of Phase-Locking in Random LasersIn a paper published in the Physical Review A, Marco Leonetti, Claudio Conti, and Cefe Lopez report on experimental investigations of the random laser emission from micron-sized clusters of TiO2 particles by using pump pulses with different pulse durations. It is found that the spectral properties depend on the pulse duration, and this is explained in terms of phase-locking processes in random lasers that is enhanced for nano-second pump pulses and limited in the pico-second (or shorter) regime. This furnishes further evidence of the mode-locking processes in random lasers. The results also supported by numerical solutions of the coupled mode theory equations (CMT). The picture below shows that the spectral width of the random laser depends on the pump pulse duration, and the following shows the corresponding numerical simulations of the CMT.
## Random Laser in Paper!In two papers published in Optics Letters (arXiv:1407.7376) and in Journal of Materials Chemistry C, N. Ghofraniha, I. Viola, A. Zacheo, V. Arima, G. Gigli, and C. Conti, demonstrate and investigate the physical properties of Random Lasers fabricated in simple paper. ## More on the random walk of solitons and shock wavesThe inteplay of disorder and coherent nonlinear waves, as solitons and shocks, sustains several interesting and complex phenomena that touch many branches of fundamental and theoretical physics. In a manuscript published in New Journal of Physics, Viola Folli and Claudio Conti report on further results about the random walk of solitons and shock waves, also following some experimental investigations. ## Nonlocality and condensation in Random LasersIn a paper published in Light: Science & Applications, Marco Leonetti, Claudio Conti and Cefe Lopez report on the experimental evidence of a collective emission from a disordered laser resonators realized by a self-assembled cluster of dielectric particles. Evidences are given of a transition from a "Bose-Glass like" lasing regime sustained by a fragmented distribution of intensity, made by nearly independent localized states, to a "condensed nonlocal" regime in which the spectral emission is identical in any point of the system and the intensity profile is smooth The transition is interpreted by resorting to a Ginzburg-Landau (imaginary time, or dissipative, Gross-Pitaevskii) equation that gives the wave profile in the system and links Random Lasers with Dissipative Solitons
In the following figure we compare the spatial profile of the intensity with the numerical solution of the Ginzburg-Landau equation ## Nonlinear Anderson localization in curved potentialsDisorder, nonlinearity, and curvature, cooperate to localize energy. In a manuscript (arXiv:1305.3232) published in The results include an analytical theory for such a complicated problem, and the fact that the three localizing effects can be described all-together by a single scaling parameter including radius of curvature, strength of nonlinearity and amount of disorder. The picture below shows the appearance of Anderson states when some amount of disorder is included in a bended potential |