arXiv subjects

Giovanni Giacomelli

Publications and source records attributed to Giovanni Giacomelli.

15 recordsLinked to original sources

arXiv2026

A mean field approach to multiple, long-delayed systems

The concept of multiple, long-delayed feedback systems is introduced and discussed with reference to a paradigmatic model. We analyse how the resulting chaotic dynamics is affected by the delay distribution. Via a mean-field approach, we show that a spatio-temporal representation equivalent to the one developed for the single-delay can be extended to this wider class of dynamical systems. Numerical simulations are complemented by a theoretical study based on a multiple-scale analysis, which, in the vicinity of a Hopf bifurcation, allows mapping the initial model onto a complex Ginzburg Landau equation. As a result, we find that the only relevant feature influenced by the multiple delays is the size of the coherent spatio-temporal structures which, in turn, depends exclusively on a generalized {\it variance} of the delay distribution.

nlin.CD↗

arXiv2023

Ultra-slow dynamics of free-running ring lasers: towards a minimal model

The dynamics of a resonant, free-running ring laser, in the common case of a fast relaxation of the atomic polarization, is unexpectedly highly singular. As shown in [Phys. Rev. Research, {\bf 5}, 023059 (2023)], this is due to the closeness to a pure Hamiltonian dynamics ruled by a nonlinear wave equation, herein named Klein-Gordon-Toda model. In this paper, we derive a quasi-Hamiltonian model which allows describing realistic systems. In particular, we identify two nearly conserved, energy-like quantities, which ``naturally" exhibit an ultra-slow dynamics confirmed and highlighted by numerical simulations. A minimal version of the quasi-Hamiltonian model is finally derived, which does not only reproduce the laser thresholds, but also helps understanding the origin of the nearly integrable character of the laser dynamics.

physics.optics↗

arXiv2023

Nearly Hamiltonian dynamics of laser systems

The Arecchi-Bonifacio (or Maxwell-Bloch) model is the benchmark for the description of active optical media. However, in the presence of a fast relaxation of the atomic polarization, its implementation is a challenging task even in the simple ring-laser configuration, due to the presence of multiple time scales. In this Article we show that the dynamics is nearly Hamiltonian over time scales much longer than those of the cavity losses. More precisely, we prove that it can be represented as a pseudo spatio-temporal pattern generated by a nonlinear wave equation equipped with a Toda potential. The existence of two constants of motion (identified as pseudo energies), thereby, elucidates the reason why it is so hard to simplify the original model: the adiabatic elimination of the polarization must be accurate enough to describe the dynamics correctly over unexpectedly long time scales. Finally, since the nonlinear wave equation with Toda potential can be simulated on much longer times than the previous models, this opens up the route to the numerical (and theoretical) investigation of realistic setups.

physics.optics↗

arXiv2022

Spatio-temporal phenomena in complex systems with time delays

Real-world systems can be strongly influenced by time delays occurring in self-coupling interactions, due to unavoidable finite signal propagation velocities. When the delays become significantly long, complicated high-dimensional phenomena appear and a simple extension of the methods employed in low-dimensional dynamical systems is not feasible. We review the general theory developed in this case, describing the main destabilization mechanisms, the use of visualization tools, and commenting on the most important and effective dynamical indicators as well as their properties in different regimes. We show how a suitable approach, based on a comparison with spatio-temporal systems, represents a powerful instrument for disclosing the very basic mechanism of long-delay systems. Various examples from different models and a series of recent experiments are reported.

nlin.CD↗

arXiv2021

Spaceless description of active optical media

The acclaimed Maxwell-Bloch (or Arecchi-Bonifacio) equations are a valid dynamical model, effectively describing wave propagation in nonlinear optical media: from the amplification in input-output devices to multimode instabilities arising in laser systems. However, the inherent spatial variability of the physical observables represents an obstacle to fast simulations and analysis, especially whenever networks of active elements have to be considered. In this paper, we propose an approach which, stripping the spatial dependence of its role as a generator of dynamical richness, allows for a compelling simple portrait. It leads to (a few) ordinary differential equations in input-output configurations, complemented by a time-delayed feedback in closed-loop setups. Such scheme reproduces accurately the dynamics, paving the way to a plain treatment of the wealth of phenomena described by the Maxwell-Bloch equations.

physics.optics↗

arXiv2020

Spatio-temporal representation of long-delayed systems: an alternative approach

Dynamical systems with long delay feedback can exhibit complicated temporal phenomena, which once re-organized in a two-dimensional space are reminiscent of spatio-temporal behavior. In this framework, normal forms description have been developed to reproduce the dynamics and the opportunity to treat the corresponding variables as true space and time has been since established. However, recently an alternative approach has been proposed in Ref. \cite{Marino2018} with a different interpretation of the variables involved, which takes better into account their physical character and allows for an easier determination of the normal forms. In this paper, we extend such idea and apply it to a number of paradigmatic examples, paving the way to a re-thinking of the concept of spatio-temporal representation of long-delayed systems.

nlin.PS↗

arXiv2020

Modeling active optical networks

The recently introduced complex active optical network (LANER) generalizes the concept of laser system to a collection of links, building a bridge with random-laser physics and quantum-graphs theory. So far, LANERs have been studied with a linear approach. Here, we develop a nonlinear formalism in the perspective of describing realistic experimental devices. The propagation along active links is treated via suitable rate equations, which require the inclusion of an auxiliary variable: the population inversion. Altogether, the resulting mathematical model can be viewed as an abstract network, its nodes corresponding to the (directed) fields in the physical links. The dynamical equations differ from standard network models in that, they are a mixture of differential delay (for the active links) and algebraic equations (for the passive links). The stationary states of a generic setup with a single active medium are thoroughly discussed, showing that the role of the passive components can be combined into a single transfer function that takes into account the corresponding resonances.

nlin.AO↗

arXiv2019

Excitable wave patterns in temporal systems with two long delays

Excitable waves arise in many spatially-extended systems of either biological, chemical, or physical nature due to the interplay between local reaction and diffusion processes. Here we demonstrate that similar phenomena are encoded in the time-dynamics of an excitable system with two, hierarchically long delays. The transition from 1D localized structures to curved wave-segments is experimentally observed in an excitable semiconductor laser with two feedback loops and reproduced by numerical simulations of a prototypical model. While closely related to those found in 2D excitable media, wave patterns in delayed systems exhibit unobserved features originating from causality-related constraints. An appropriate dynamical representation of the data uncovers these phenomena and permits to interpret them as the result of an effective 2D advection-reaction-diffusion process.

nlin.PS↗

arXiv2018

A new spatio-temporal description of long-delayed systems: ruling the dynamics

The data generated by long-delayed dynamical systems can be organized in patterns by means of the so-called spatio-temporal representation, uncovering the role of multiple time-scales as independent degrees of freedom. However, their identification as equivalent space and time variables does not lead to a correct dynamical rule. We introduce a new framework for a proper description of the dynamics in the thermodynamic limit, providing a general avenue for the treatment of long-delayed systems in terms of partial differential equations. Such scheme is generic and does not depend on the vicinity of a super-critical bifurcation as required in previous approaches. We discuss the general validity and limit of this method and consider the exemplary cases of long-delayed excitable, bistable and Landau systems.

nlin.CD↗

arXiv2018

The LANER: optical networks as complex lasers

We discuss the main features of a new optical system capable of laser action: the active complex optical network, or lasing network (LANER). The system is experimentally realized with optical fibers linked each other with suitable optical couplers and with one or more coherent optical amplifying sections. The LANER displays a standard laser behavior: when the gain provided by the active sections is high enough to overcome the losses a coherent emission is produced, with a complicated intensity spectrum reflecting the structure of the network. A simple linear theoretical description is introduced and discussed, showing how the LANER can be considered as a generalization of the laser for a complicated cavity represented by the network itself. The system can be mapped to directed graphs and permits to disclosure the analogies with the problem of quantum chaos on graphs. In the case the links are all integer multiples of the same length, it is shown that the LANER framework corresponds to a lattice problem, with the equivalence of the Brillouin zone with the cavity Free Spectral Range. Experimental realizations of different configurations are presented and examples of spectra are reported, in a phenomenological agreement with the numerical findings of the theory.

physics.optics↗

arXiv2018

Evidence of a critical phase transition in a purely temporal dynamics with long-delayed feedback

Experimental evidence of an absorbing phase transition, so far associated with spatio-temporal dynamics is provided in a purely temporal optical system. A bistable semiconductor laser, with long-delayed opto-electronic feedback and multiplicative noise shows the peculiar features of a critical phenomenon belonging to the directed percolation universality class. The numerical study of a simple, effective model provides accurate estimates of the transition critical exponents, in agreement with both theory and our experiment. This result pushes forward an hard equivalence of non-trivial stochastic, long-delayed systems with spatio-temporal ones and opens a new avenue for studying out-of-equilibrium universality classes in purely temporal dynamics.

cond-mat.stat-mech↗

arXiv2017

Complex active optical networks as a new laser concept

Complex optical networks containing one or more gain sections are investigated and the evidence of lasing action is reported; the emission spectrum reflects the topological disorder induced by the connections. A theoretical description well compares with the measurements, mapping the networks to directed graphs and showing the analogies with the problem of quantum chaos on graphs. We show that the interplay of chaotic diffusion and amplification leads to an emission statistics with characteristic heavy-tails: for different topologies, an unprecedented experimental demonstration of Levy statistics expected for random lasers is here provided for a continuous-wave pumped system. This result is also supported by a Monte-Carlo simulation based on ray random walk on the graph.

physics.optics↗

arXiv2014

Pattern formation in systems with multiple delayed feedbacks

Dynamical systems with complex delayed interactions arise commonly when propagation times are significant, yielding complicated oscillatory instabilities. In this Letter, we introduce a class of systems with multiple, hierarchically long time delays, and using a suitable space-time representation we uncover features otherwise hidden in their temporal dynamics. The behaviour in the case of two delays is shown to ''encode'' two-dimensional spiral defects and defects turbulence. A multiple scale analysis sets the equivalence to a complex Ginzburg-Landau equation, and a novel criterium for the attainment of the long-delay regime is introduced. We also demonstrate this phenomenon for a semiconductor laser with two delayed optical feedbacks.

nlin.PS↗

arXiv2007

Resonant activation in bistable semiconductor lasers

We theoretically investigate the possibility of observing resonant activation in the hopping dynamics of two-mode semiconductor lasers. We present a series of simulations of a rate-equations model under random and periodic modulation of the bias current. In both cases, for an optimal choice of the modulation time-scale, the hopping times between the stable lasing modes attain a minimum. The simulation data are understood by means of an effective one-dimensional Langevin equation with multiplicative fluctuations. Our conclusions apply to both Edge Emitting and Vertical Cavity Lasers, thus opening the way to several experimental tests in such optical systems.

physics.optics↗

arXiv2006

Low frequency fluctuations in a Vertical Cavity Lasers: experiments versus Lang-Kobayashi dynamics

The limits of applicability of the Lang-Kobayashi (LK) model for a semiconductor laser with optical feedback are analyzed. The model equations, equipped with realistic values of the parameters, are investigated below solitary laser threshold where Low Frequency Fluctuations (LFF) are usually observed. The numerical findings are compared with experimental data obtained for the selected polarization mode from a Vertical Cavity Surface Laser (VCSEL) subject to polarization selective external feedback. The comparison reveals the bounds within which the dynamics of the LK can be considered as realistic. In particular, it clearly demonstrates that the deterministic LK, for realistic values of the linewidth enhancement factor $α$, reproduces the LFF only as a transient dynamics towards one of the stationary modes with maximal gain. A reasonable reproduction of real data from VCSEL can be obtained only by considering noisy LK or alternatively deterministic LK for extremely high $α$-values.

physics.optics↗