Searcharxiv⌕ Search

arXiv subjects

C. Conti

Publications and source records attributed to C. Conti.

33 records · Page 2Linked to original sources
arXiv2008

Phase diagram and complexity of mode-locked lasers: from order to disorder

We investigate mode-locking processes in lasers displaying a variable degree of structural randomness, from standard optical cavities to multiple-scattering media. By employing methods mutuated from spin-glass theory, we analyze the mean-field Hamiltonian and derive a phase-diagram in terms of the pumping rate and the degree of disorder. Three phases are found: i) paramagnetic, corresponding to a noisy continuous wave emission, ii) ferromagnetic, that describes the standard passive mode-locking, and iii) the spin-glass in which the phases of the electromagnetic field are frozen in a exponentially large number of configurations. The way the mode-locking threshold is affected by the amount of disorder is quantified. The results are also relevant for other physical systems displaying a random Hamiltonian, like Bose-Einstein condensates and nonlinear optical beams.

physics.optics↗
arXiv2008

Light-matter interaction in Mie nanolasers

By deriving a three dimensional vector set of Maxwell-Bloch equations, we report on an ab-initio investigation of a spherical Mie nanolaser. Parallel numerical simulations predict a rich physical scenario, ranging from a nontrivial vectorial energy-matter interplay in the initial stage of evolution to mode competition and dynamical frequency pulling effects. Application of these effects could favor the realization of nonlinearly-controlled largely-tunable nanolaser devices.

physics.optics↗
arXiv2007

Tunneling mediated by conical waves in a 1D lattice

The nonlinear propagation of 3D wave-packets in a 1D Bragg-induced band-gap system, shows that tranverse effects (free space diffraction) affect the interplay of periodicity and nonlinearity, leading to the spontaneous formation of fast and slow conical localized waves. Such excitation corresponds to enhanced nonlinear transmission (tunneling) in the gap, with peculiar features which differ on the two edges of the band-gap, as dictated by the full dispersion relationship of the localized waves.

physics.optics↗
arXiv2006

Mode-locking transitions in nano-structured weakly disordered lasers

We report on a statistical approach to mode-locking transitions of nano-structured laser cavities characterized by an enhanced density of states. We show that the equations for the interacting modes can be mapped onto a statistical model exhibiting a first order thermodynamic transition, with the average mode-energy playing the role of inverse temperature. The transition corresponds to a phase-locking of modes. Extended modes lead to a mean-field like model, while in presence of localized modes, as due to a small disorder, the model has short range interactions. We show that simple scaling arguments lead to observable differences between transitions involving extended modes and those involving localized modes. We also show that the dynamics of the light modes can be exactly solved, predicting a jump in the relaxation time of the coherence functions at the transition. Finally, we link the thermodynamic transition to a topological singularity of the phase space, as previously reported for similar models.

cond-mat.stat-mech↗
arXiv2006

Adaptive Frame Methods for Magnetohydrodynamic Flows

In this paper we develop adaptive numerical schemes for certain nonlinear variational problems. The discretization of the variational problems is done by representing the solution as a suitable frame decomposition, i.e., a complete, stable, and redundant expansion. The discretization yields an equivalent nonlinear problem on $\ell_2(\mathcal{N})$, the space of frame coefficients. The discrete problem is then adaptively solved using approximated nested fixed point and Richardson type iterations. We investigate the convergence, stability, and optimal complexity of the scheme. This constitutes a theoretical advantage, for example, with respect to adaptive finite element schemes for which convergence and complexity results are still hard to prove. The use of frames is further motivated by their redundancy, which, at least numerically, has been shown to improve the conditioning of the corresponding discretization matrices. Frames also are usually easier to construct than Riesz bases. Finally, we show how to apply the adaptive scheme we propose for finding an approximation to the solution of the PDEs governing magnetohydrodynamic (MHD) flows, once suitable frame expansions are constructed.

math.NA↗
arXiv2005

Impedance matching in photonic crystal microcavities for Second Harmonic Generation

By numerically integrating the three-dimensional Maxwell equations in the time domain with reference to a dispersive quadratically nonlinear material, we study second harmonic generation in planar photonic crystal microresonators. The proposed scheme allows efficient coupling of the pump radiation to the defect resonant mode. The out-coupled generated second harmonic is maximized by impedance matching the photonic crystal cavity to the output waveguide.

physics.optics↗
arXiv2005

Glassy behavior of light

We study the nonlinear dynamics of a multi-mode random laser using the methods of statistical physics of disordered systems. A replica-symmetry breaking phase transition is predicted as a function of the pump intensity. We thus show that light propagating in a random non-linear medium displays glassy behavior, i.e. the photon gas has a multitude of metastable states and a non vanishing complexity, corresponding to mode-locking processes in random lasers. The present work reveals the existence of new physical phenomena, and demonstrates how nonlinear optics and random lasers can be a benchmark for the modern theory of complex systems and glasses.

cond-mat.dis-nn↗
arXiv2004

Feeding upon negative entropy in a thermal-equilibrium environment

The validity of the Second Law of thermodynamics, indisputable in the macroscopic world, is challenged at the mesoscopic level: a mesoscopic isolated system, possessing spatial dimensions of the order of a few microns, is capable, as shown by a straightforward kinetic analysis, to exhibit a perpetuum mobile behavior associated with large negative variations of the Clausius entropy of the system. This violation of the Second Law is expedient for devising a cyclic process through which an isolated system can extract energy from a surrounding thermal bath.

physics.class-ph↗
arXiv2003

Spontaneously generated X-shaped light bullets

We observe the formation of an intense optical wavepacket fully localized in all dimensions, i.e. both longitudinally (in time) and in the transverse plane, with an extension of a few tens of fsec and microns, respectively. Our measurements show that the self-trapped wave is a X-shaped light bullet spontaneously generated from a standard laser wavepacket via the nonlinear material response (i.e., second-harmonic generation), which extend the soliton concept to a new realm, where the main hump coexists with conical tails which reflect the symmetry of linear dispersion relationship.

physics.optics↗
arXiv2003

X-wave mediated instability of plane waves in Kerr media

Plane waves in Kerr media spontaneously generate paraxial X-waves (i.e. non-dispersive and non-diffractive pulsed beams) that get amplified along propagation. This effect can be considered a form of conical emission (i.e. spatio-temporal modulational instability), and can be used as a key for the interpretation of the out of axis energy emission in the splitting process of focused pulses in normally dispersive materials. A new class of spatio-temporal localized wave patterns is identified. X-waves instability, and nonlinear X-waves, are also expected in periodical Bose condensed gases.

physics.optics↗
arXiv2003

X-waves Generated at Second Harmonic

The process of optical frequency doubling can lead, in the undepleted regime, to the generation of a X-wave envelope with group velocity locked to the pump beam. Its parameters and its angular spectrum, are directly related to the zero- and first-order dispersive features of the nonlinear process. This constitutes a novel mechanism for spatio-temporal localization of light.

physics.optics↗
arXiv2002

The Adiabatic Piston and the Second Law of Thermodynamics

A detailed analysis of the adiabatic-piston problem reveals peculiar dynamical features that challenge the general belief that isolated systems necessarily reach a static equilibrium state. In particular, the fact that the piston behaves like a perpetuum mobile, i.e., it never stops but keeps wandering, undergoing sizable oscillations, around the position corresponding to maximum entropy, has remarkable implications on the entropy variations of the system and on the validity of the second law when dealing with systems of mesoscopic dimensions.

physics.class-ph↗
arXiv2002

Electromagnetic nonlinear X-waves

Nonlinear optical media that are normally dispersive, support a new type of localized (nondiffractive and nondispersive) wavepackets that are X-shaped in space and time and have slower than exponential decay. High-intensity X-waves, unlike linear ones, can be formed spontaneously through a trigger mechanism of conical emission, thus playing an important role in experiments.

physics.optics↗
arXiv2002

Coloured conical emission via second-harmonic generation

We predict that the combination of space and time modulational instabilities occuring via parametric wave-mixing in quadratic media leads to coloured conical emission. This phenomenon should be observed under conditions usually employed in second-harmonic generation experiments.

physics.optics↗