Fabrizio Antenucci

General phase diagram of multimodal ordered and disordered lasers in closed and open cavities.

We present a unified approach to the theory of multimodal laser cavities including a variable amount of structural disorder. A general mean-field theory is studied for waves in media with variable nonlinearity and randomness. Phase diagrams are reported in terms of optical power, degree of disorder, and degree of nonlinearity, tuning between closed and open cavity scenarios. In the thermodynamic limit of infinitely many modes, the theory predicts four distinct regimes: a continuous wave behavior for low power, a standard mode-locking laser regime for high power and weak disorder, a random laser for high pumped power and large disorder, and a novel intermediate regime of phase locking occurring in the presence of disorder but below the lasing threshold.

The glassy random laser: replica symmetry breaking in the intensity fluctuations of emission spectra

The behavior of a newly introduced overlap parameter, measuring the correlation between intensity fluctuations of waves in random media, is analyzed in different physical regimes, with varying amount of disorder and non-linearity. This order parameter allows to identify the laser transition in random media and describes its possible glassy nature in terms of emission spectra data, the only data so far accessible in random laser measurements. The theoretical analysis is performed in terms of the complex spherical spin-glass model, a statistical mechanical model describing the onset and the behavior of random lasers in open cavities. Replica Symmetry Breaking theory allows to discern different kinds of randomness in the high pumping regime, including the most complex and intriguing glassy randomness. The outcome of the theoretical study is, eventually, compared to recent intensity fluctuation overlap measurements demonstrating the validity of the theory and providing a straightforward interpretation of qualitatively different spectral behaviors in different random lasers.

Complex spherical 2 + 4 spin glass: A model for nonlinear optics in random media

A disordered mean field model for multimode laser in open and irregular cavities is proposed and discussed within the replica analysis. The model includes the dynamics of the mode intensity and accounts also for the possible presence of a linear coupling between the modes, due, e.g., to the leakages from an open cavity. The complete phase diagram, in terms of disorder strength, source pumping and non-linearity, consists of four different optical regimes: incoherent fluorescence, standard mode locking, random lasing and the novel spontaneous phase locking. A replica symmetry breaking phase transition is predicted at the random lasing threshold. For a high enough strength of non-linearity, a whole region with nonvanishing complexity anticipates the transition, and the light modes in the disordered medium display typical discontinuous glassy behavior, i.e., the photonic glass has a multitude of metastable states that corresponds to different mode-locking processes in random lasers. The lasing regime is still present for very open cavities, though the transition becomes continuous at the lasing threshold.

Statistical physics of nonlinear wave interaction

The thermodynamic properties of vector (O(2) and Complex Spherical) models with four-body interactions are analyzed. When defined in dense topologies, these are effective models for the nonlinear interaction of scalar fields in the presence of a stochastic noise, as has been well established for the case of the mode locking laser formation in a closed cavity. With the help of a novel efficient Monte Carlo algorithm we show how beyond the fully connected case novel and rich phenomenology emerges. Below a certain dilution threshold, the spherical model condensates in a non-equipartite way, while in the XY model the transition becomes continuous and the O(2) symmetry remains unbroken, we attribute this fact to the invariance under local gauge transformations. The introduction of topological inhomogeneities in the network of quadruplets induces novel features: again symmetry conservation; the vanishing of two-point correlators; and a dynamical correlation function presenting two timescales, the large one being related to the transition between different degenerated configurations, connected by nonlocal gauge transformations. We discuss possible experimental implications of these results in the context of nonlinear optics.

Statistical physical theory of mode-locking laser generation with a frequency comb

A study of the Mode-locking lasing pulse formation in closed cavities is presented within a statistical mechanical framework where the onset of laser coincides with a thermodynamic phase transition driven by the optical power pumped into the system. Electromagnetic modes are represented by classical degrees of freedom of a Hamiltonian model at equilibrium in an effective ensemble corresponding to the stationary laser regime. By means of optimized Monte Carlo numerical simulations, the system properties are analyzed varying mode interaction dilution, gain profile and number of modes. Novel properties of the resulting mode-locking laser phase are presented, not observable by previous mean-field approaches. For strong dilution of the nonlinear interaction network, power condensation occurs as the whole optical intensity is taken by a few electromagnetic modes, whose number does not depend on the size of the system. For all reported cases laser thresholds, intensity spectra, and ultra-fast electromagnetic pulses are computed.

Regularization and decimation pseudolikelihood approaches to statistical inference inXYspin models

We implement a pseudolikelihood approach with l1 and l2 regularizations as well as the recently introduced pseudolikelihood with decimation procedure to the inverse problem in continuous spin models on arbitrary networks, with arbitrarily disordered couplings. Performances of the approaches are tested against data produced by Monte Carlo numerical simulations and compared also to previously studied fully connected mean-field-based inference techniques. The results clearly show that the best network reconstruction is obtained through the decimation scheme, which also allows us to make the inference down to lower temperature regimes. Possible applications to phasor models for light propagation in random media are proposed and discussed

Inverse problem for multi-body interaction of nonlinear waves

The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we test two methods based on pseudolikelihood, respectively with regularization and with decimation, to determine the coupling constants from sets of measured configurations. We test statistical inference predictions for increasing number of sampled configurations and for an externally tunable temperature-like parameter mimicing real data noise and helping minimization procedures. Analyzed models with phasors and rotors are generalizations of problems of real-valued spherical problems (e.g., density fluctuations), discrete spins (Ising and vectorial Potts) or finite number of states (standard Potts): inference methods presented here can, then, be straightforward applied to a large class of inverse problems. The high versatility of the exposed techniques also concerns the number of expected interactions: results are presented for different graph topologies, ranging from sparse to dense graphs.