Our research ...
The Optimal Disorder for the Anderson Localization of Light
Many authors investigated the onset of light localization in the regime of strong-disorder.
But how much strong?
Determining how much strong the disorder has to be to give rise to localized states (in three-dimensions) is an extremely difficult enterprise, as it depends on the specific kind of sample that is considered. One has to demonstrate that an optimal region for localization exists, once a parameter that quantifies the strength of the disorder has been identified. This is a very tricky problem, even more tricky if one wants to be far from a perturbative regime as the case of weakly disordered Photonic Crystals, considered here and here.
In a recent article (http://arxiv.org/abs/1003.2555), authored by Silvia Gentilini, Andrea Fratalocchi and Claudio Conti, a specific case has been considered by resorting to parallel large-scale Finite Difference Time-Domain simulations. A molecular dynamics code has been used to generate some disorder realizations of a colloidal solution composed by spherical particles. By varying the filling fraction of the resulting sample, the response of the material to an ultra-wide band (Frequency Comb) optical excitation has been spectrally analyzed.
It has been shown that the maximum spectral delay of the various frequencies in the transmitted spectrum displays a sharp peak in correspondence of a narrow region in the filling fraction for high-index contrast particles (figure below, delay expressed in picoseconds); this also being the first ab-initio numerical investigation of a Frequency Comb in a disordered material. Such a result shows that an optimal disorder for light localization can be indeed identified even for completely randomized samples.
The Page Rank Equation
In a recent article in Europhysics Letters, authored by N. Perra, V. Zlatic, A. Chessa, C. Conti, D. Donato and G. Caldarelli an equation for the page-rank in the WWW and in several other kinds of networks has been derived. The equation strongly resembles other famous ones in physics, like the Schroedinger or the Helmotz equations, and it enables to make fascinating connections between theoretical physics and the science of scale-free networks. The arXiv version of this paper has been formerly commented in the New Scientist issue of August 2008.
The picture shows a localized solution of the Page Rank equation, corresponding to the formation of an HUB node.
Nonlinear light diffusion, ab-initio results
In this manuscript we report on the numerical simulation of ultra-short intense laser pulse propagating in a random medium.
With Alessandro Ciattoni, we developed a general theory of Quantum X-waves and we have shown that classical X-waves may have different quantum counterparts (which share the classical expectation field profile) encoding different degree of entanglement. See arXiv:0704.0442.
A proposed experimental setup for generating the "progessive undistorted squeezed vacuum" (see quant-ph/0409130)
More on Nonlinear X-waves
People coming from soliton theory (especially nonlinear optics) are used to associate self-localization to a nonlinear self-action. Actually, self-localized waves do even exist for linear systems, and, surprisingly, they have been mostly studied in recent years, AFTER solitons and bullets.
The typical argument against localized waves (to be intended as the linear waves) is that they carry infinite enegy. However, this holds true for many nonlinear waves, as for example dark solitons and vortices. Finite energy realizations of localized waves have been observed, as it has been for darks and vortices.
The situation is even more intricate when localized waves propagate in the presence of a nonlinear self-action. The result are the NONLINEAR X-WAVES. They aresolutions to 3D+1 nonlinear evolution equations carrying infinite energy and have been investigated both experimentally and theoretically. [see Conti C., Phys. Rev. E 70, 046613 (2004) and the book chapter NonlinearXwaves (.pdf, 1.2MB) in the book Localized Waves (ISBN 0-470-10885-1) for an introduction]
In other words:
1D nonlinear waves with infinite energy = dark solitons
2D nonlinear waves with infinite energy = vortex solitons
3D nonlinear waves with infinite energy = nonlinear X waves (or X solitons)
The world of nonlinear X waves is still mainly unexplored; not only it is fascinating because it deals with 3D waves, which have a counterpart in Bose Einstein condensates, but also because they are expected to play a role in ultrafast laser propagation. Indeed, contrary to light bullets, X-waves are sustained by normal dispersion, which is always the case in the relevant experiments.
Soliton experimental setup
This picture shows our experimental setup for observing optical spatial solitons. The microscope is used for imaging the light scattered from the top of the sample, which is illuminated by a laser beam through the input inverted microscope.
The ab-investigation of the 3D Anderson localization
In a recent paper in the arXiv (http://arxiv.org/abs/0810.1690 ), Claudio Conti and Andrea Fratalocchi reported on the first ab-initio investigation in 3D and time-resolved of the Anderson localization of light in a colloid.
Femtosecond propagation in disordered matter
The theoretical analysis of ultra-fast laser propagation in disordered matter is enormously complicated by the need to account for a 3D enviroment (Anderson localization and related phenomena are indeed a trivial issue in reduced dimensionality), material dispersion, multiple-scattering processes, polidispersivity and many other phenomena.
Thermodynamics of soliton gases
In a recent article in Physical Review Letters, in collaboration with Andrea Fratalocchi, Giancarlo Ruocco and Stefano Trillo, we have shown that within a purely integrable model solitons undergoes non canonical phase transitions. For the nonlinear Schroedinger equation, many solitons should behave as a gas of free particles. In this respect, phase transitions are not expected. However by employing non canonical phase-space measures, mutuated from the so-called thermostatistics of chaotic systems, it is possible to show that a suitably defined free energy undergoes a methamorphosis as the number of solitons grows.
A notable issue is that this mathematical circumstance has a clear physical signature, i.e. the development of a dispersive shock wave, which is the result of the cooperative evolution of the solitons. This theoretical result fixes a link between chaotic and integrable systems, which is fairly not trivial and can be experimentally tested. The experiments are now being performed in our group.
Random Lasers (intro)
In a nutshell, a random laser is the coherent emission from active stochastic resonators.
In a series of articles around 1966, a Russian scientist V. S. Letokhov, of the Lebedev Physics Institute in Dubna considered the generation of light in the interstellar medium. In the presence of scatterers, as for example dust particles, photons diffuse like neutrons and, if some mechanism (following Letokhov a “negative absorption”) is able to increase their number, a sort of photonic reactor can be realized. At a threshold value for the amplification, a quantum generator of light, not properly a laser, is realized. Nowadays the process is known as RANDOM LASER.
The Letokhov’s basic idea is that of a stochastic resonator: a scattering medium with a large number of modes (roughly, waves with different directions) which are strongly coupled and display radiation losses. If the number of modes is sufficiently large their overlapping resonances merge and the result is a nonresonant feedback sustaining a laser-like action; its properties are today largely investigated, while, in many respects, they are still unknown. There are several analogies with neutrons in a reactor.
Letokhov’s analysis was not limited to the interstellar medium, but also included particles dispersed in a host medium able to amplify light, like a liquid dye. Indeed, the first demonstration of a random laser, in 1994, was done in the laboratory using such a kind of medium; since then the amount of related literature has grown steadily.
Examples of Random Lasers and Stochastic Resonators include granular systems, bio-logical tissue, nano-structured devices and many others.
Fundamental thermodynamics at a mesoscopic level
The MD-FDTD technique (intro)
Theoretical modelling of light driven self-organization and nonlinear processes in soft-matter
C. Conti, G. Ruocco, S. Trillo "Optical Spatial Solitons in Soft Matter" Phys. Rev. Lett. 95, 183902 (2005); C. Conti, N. Ghofraniha, G. Ruocco, S. Trillo "Laser beam filamentation in soft matter" Phys. Rev. Lett. 97, 123903 (2006) References added by Claudio Conti
Random lasers and spin-glasses
There are two basic ingredients for complexity: randomness and nonlinearity. Random Lasers display both of them.
In order to assess the complexity of a given physical systems, one has to make reference to some paradimatic approaches; these typically furnish the basic ideas in a clear and well defined way. In the science of complexity, Spin Glass Theory is the most fundamental paradigm.
However Spin Glass Theory is an abstract and largely idealized approach to the thermodynamics and the dynamics of complex systems; a major difficulty is finding a specific physical system that is described by Spin Glass Theory within a reasonable accuracy. The common situation is that Spin Glass Theory only furnishes a qualitative description of the physical process.
Random Lasers seem to be an important exception. As detailed in two articles in Physical Review Letters and Physical Review B, we derived a model for multimode Random Lasers that is based on Spin Glass Theory. This approach enables to predict mode-locking transitions of these devices and the fact that these are glassy transitions.