Papers by Hugo L D S Cavalcante
Physical Review A, 2005
We consider the dynamics of a single atom submitted to periodic pulses of a far-detuned standing ... more We consider the dynamics of a single atom submitted to periodic pulses of a far-detuned standing wave generated by a high-finesse optical cavity, which is an atomic version of the well-known "kicked rotor". We show that the classical phase-space map can be "reconstructed" by monitoring the transmission of the cavity. We also studied the effect of spontaneous emission on the reconstruction, and put limits to the maximum acceptable spontaneous emission rate.
Physical Review A, 2015
The propagation of light in a resonant atomic vapor can a priori be thought of as a multiple scat... more The propagation of light in a resonant atomic vapor can a priori be thought of as a multiple scattering process, in which each scattering event redistributes both the direction and the frequency of the photons. Particularly, the frequency redistribution may result in Lévy flights of photons, directly affecting the transport properties of light in a resonant atomic vapor and turning this propagation into a superdifusion process. Here, we report on a Monte-Carlo simulation developed to study the evolution of the spectrum of the light in a resonant thermal vapor. We observe the gradual change of the spectrum and its convergence towards a regime of Complete Frequency Redistribution as the number of scattering events increases. We also analyse the probability density function of the step length of photons between emissions and reabsorptions in the vapor, which governs the statistics of the light diffusion. We observe two different regime in the light transport: superdiffusive when the vapor is excited near the line center and normal diffusion for excitation far from the line center. The regime of Complete Frequency Redistribution is not reached for excitation far from resonance even after many absorption/reemission cycles due to correlations between emitted and absorbed frequencies.
Optics Communications, 2019
Mode-locked fiber lasers are rich dynamical systems that may present several different types of p... more Mode-locked fiber lasers are rich dynamical systems that may present several different types of pulsed operating modes, depending on external control parameters such as pump power. A systematic experimental characterization of such regimes is a challenging problem. Here single pulse regimes of ytterbium mode-locked fiber laser are explored and related to the nonlinear amplitude modulation affecting the pulses inside the laser cavity. To understand the full dynamics of this system, average power measurements (slow time scale) have been performed and compared to simultaneous time-resolved measurements (fast time scale). The average nonlinear transmission resulting from the amplitude modulation is measured, allowing to relate the transitions between dynamical regimes to the system's nonlinearity.
We demonstrate a position-sensing technique that relies on the inherent sensitivity of chaos, whe... more We demonstrate a position-sensing technique that relies on the inherent sensitivity of chaos, where we illuminate a subwavelength object with a complex structured radio-frequency field generated using wave chaos and a nonlinear feedback loop. We operate the system in a quasi-periodic state and analyze changes in the frequency content of the scalar voltage signal in the feedback loop. This allows us to extract the object's position with a one-dimensional resolution of ~\lambda/10,000 and a two-dimensional resolution of ~\lambda/300, where \lambda\ is the shortest wavelength of the illuminating source.
We observe deterministic chaos in a simple network of electronic logic gates that are not regulat... more We observe deterministic chaos in a simple network of electronic logic gates that are not regulated by a clocking signal. The resulting power spectrum is ultra-wide-band, extending from dc to beyond 2 GHz. The observed behavior is reproduced qualitatively using an autonomously updating Boolean model with signal propagation times that depend on the recent history of the gates and filtering of pulses of short duration, whose presence is confirmed experimentally. Electronic Boolean chaos may find application as an ultra-wide-band source of radio waves
The critical relations for statistical properties on saddle-node bifurcations are shown to displa... more The critical relations for statistical properties on saddle-node bifurcations are shown to display undulating fine structure, in addition to their known smooth dependence on the control parameter. A piecewise linear map with the type-I intermittency is studied and a log-periodic dependence is numerically obtained for the average time between laminar events, the Lyapunov exponent and attractor moments. The origin of the oscillations is built in the natural probabilistic measure of the map and can be traced back to the existence of logarithmically distributed discrete values of the control parameter giving Markov partition. Reinjection and noise effect dependences are discussed and indications are given on how the oscillations are potentially applicable to complement predictions made with the usual critical exponents, taken from data in critical phenomena.
Physical review. E, Jun 1, 2016
For a long time, extreme events happening in complex systems, such as financial markets, earthqua... more For a long time, extreme events happening in complex systems, such as financial markets, earthquakes, and neurological networks, were thought to follow power-law size distributions. More recently, evidence suggests that in many systems the largest and rarest events differ from the other ones. They are dragon kings, outliers that make the distribution deviate from a power law in the tail. Understanding the processes of formation of extreme events and what circumstances lead to dragon kings or to a power-law distribution is an open question and it is a very important one to assess whether extreme events will occur too often in a specific system. In the particular system studied in this paper, we show that the rate of occurrence of dragon kings is controlled by the value of a parameter. The system under study here is composed of two nearly identical chaotic oscillators which fail to remain in a permanently synchronized state when coupled. We analyze the statistics of the desynchronizat...
Journal of the Optical Society of America B, 2016
Optical feedback with orthogonal polarization enables frequency sweep of semiconductor lasers and... more Optical feedback with orthogonal polarization enables frequency sweep of semiconductor lasers and leads to frequency bistability when a resonant medium is used to filter the reinjected radiation. Here, we explore a configuration with two lasers coupled through mutual injection. Each laser injects and receives light with a polarization orthogonal to the plane of emission. Both injections are independently filtered by a resonant atomic vapor. We show that this more versatile version also exhibits bistable states, and that it is possible to reduce the laser frequency jitter as well as to invert its frequency hysteresis cycle on demand (from counterclockwise to clockwise and vice versa). Experimental demonstration is done with diode lasers emitting around 780 nm, using Rb thermal vapors as nonlinear filters.
Journal of Physics B: Atomic, Molecular and Optical Physics, 2016
Physica A: Statistical Mechanics and its Applications, 2016
Many man-made and natural processes involve the diffusion of microscopic particles subject to ran... more Many man-made and natural processes involve the diffusion of microscopic particles subject to random or chaotic, random-like movements. Besides the normal diffusion characterized by a Gaussian probability density function, whose variance increases linearly in time, so-called anomalous-diffusion regimes can also take place. They are characterized by a variance growing slower (subdiffusive) or faster (superdiffusive) than normal. In fact, many different underlying processes can lead to anomalous diffusion, with qualitative differences between mechanisms producing subdiffusion and mechanisms resulting in superdiffusion. Thus, a general description, encompassing all three regimes and where the specific mechanisms of each system are not explicit, is desirable. Here, our goal is to present a simple method of data analysis that enables one to characterize a model-less diffusion process from data observation, by observing the temporal evolution of the particle spread. To generate diffusive processes in different regimes, we use a Monte-Carlo routine in which both the step-size and the time-delay of the diffusing particles follow Pareto (inverse-power law) distributions, with either finite or diverging statistical momenta. We discuss on the application of this method to real systems.
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2015
Complex systems, such as financial markets, earthquakes, and neurological networks, exhibit extre... more Complex systems, such as financial markets, earthquakes, and neurological networks, exhibit extreme events whose mechanisms of formation are not still completely understood. These mechanisms may be identified and better studied in simpler systems with dynamical features similar to the ones encountered in the complex system of interest. For instance, sudden and brief departures from the synchronized state observed in coupled chaotic systems were shown to display non-normal statistical distributions similar to events observed in the complex systems cited above. The current hypothesis accepted is that these desynchronization events are influenced by the presence of unstable object(s) in the phase space of the system. Here, we present further evidence that the occurrence of large events is triggered by the visitation of the system's phase-space trajectory to the vicinity of these unstable objects. In the system studied here, this visitation is controlled by a single parameter, and we exploit this feature to observe the effect of the visitation rate in the overall instability of the synchronized state. We find that the probability of escapes from the synchronized state and the size of those desynchronization events are enhanced in attractors whose shapes permit the chaotic trajectories to approach the region of strong instability. This result shows that the occurrence of large events requires not only a large local instability to amplify noise, or to amplify the effect of parameter mismatch between the coupled subsystems, but also that the trajectories of the system wander close to this local instability.
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2009
We undertake a systematic study of the dynamics of Boolean networks to determine the origin of ch... more We undertake a systematic study of the dynamics of Boolean networks to determine the origin of chaos observed in recent experiments. Networks with nodes consisting of ideal logic gates are known to display either steady states, periodic behaviour or an ultraviolet catastrophe where the number of logic-transition events circulating in the network per unit time grows as a power law. In an experiment, the non-ideal behaviour of the logic gates prevents the ultraviolet catastrophe and may lead to deterministic chaos. We identify certain non-ideal features of real logic gates that enable chaos in experimental networks. We find that short-pulse rejection and asymmetry between the logic states tend to engender periodic behaviour, at least for the simplest networks. On the other hand, we find that a memory effect termed ‘degradation’ can generate chaos. Our results strongly suggest that deterministic chaos can be expected in a large class of experimental Boolean-like networks. Such devices ...
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2014
The synchronization of chaotic lasers was studied considering the coupling scheme with the intens... more The synchronization of chaotic lasers was studied considering the coupling scheme with the intensity of light pulses from one laser saturating the other one. The experimental synchronization of two single mode CO2 lasers with saturable absorber is reviewed. Numerical simulations are presented for diode lasers made chaotic by optical feedback. Optical intensity saturation coupling was introduced in Lang-Kobayashi equations. Parameters were chosen such that both lasers were uncorrelated and chaotic before coupling and partially synchronize after coupling. Correlation functions for the numerical solutions were used to characterize the properties of the synchronism. They show partial in-phase and antiphase synchronism for the pulse intensities, depending on the coupling mechanism. These synchronisms are independent of optical interferometric effects and so, relevant for communication applications.
Bulletin of the American Physical Society, 2010
Networks with nodes consisting of ideal Boolean logic gates are known to display either steady st... more Networks with nodes consisting of ideal Boolean logic gates are known to display either steady states, periodic behavior, or an ultraviolet catastrophe where the number of logic-transition events circulating in the network per unit time grows as a power-law. In an experiment, non-ideal ...
Latin America Optics and Photonics Conference, 2016
Latin America Optics and Photonics Conference, 2016
Coupling two lasers through mutual orthogonal optical injection we observe frequency bistability ... more Coupling two lasers through mutual orthogonal optical injection we observe frequency bistability when the injections are spectrally filtered. The hysteresis chirality may be changed on demand. We use diode lasers and rubidium vapors as filters
Latin America Optics and Photonics Conference, 2016
A few statistical aspects of photons propagation in resonant atomic vapors are investigated, from... more A few statistical aspects of photons propagation in resonant atomic vapors are investigated, from Lévy flights and frequency redistribution to nonlinearity-mediated interactions between photons and their effect on the intensity distribution and correlation.
Resumo Biestabilidade na frequência de emissão de um laser semicondutor sujeito a realimentação ... more Resumo Biestabilidade na frequência de emissão de um laser semicondutor sujeito a realimentação ótica com polarização ortogonal foi observada experimentalmente por Farias et al. em 2005. Um modelo de equações de taxa para esse sistema dinâmico, apresentado posteriormente por Masoller et al. em 2007, que leva em conta os efeitos térmicos e ganho de saturação, prevê uma variação linear da frequência do laser com a intensidade do campo de realimentação. Nesse trabalho, usando o mesmo modelo, estudamos o processo de biestabilidade ótica em frequência nesses sistemas com realimentação filtrada, determinando as condições espectrais do filtro de realimentação necessárias para o aparecimento de histerese que leva a biestabilidade. Palavras-chave Laser semicondutor, realimentação ótica, sistema dinâmico, biestabilidade em frequência, histerese.
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Papers by Hugo L D S Cavalcante