Reservoir computing has recently been introduced as a new paradigm in the eld of machine learning. It is
based on the dynamical properties of a network of randomly connected nodes or neurons and shows to be very
promising to solve complex classication problems in a computationally ecient way. The key idea is that an
input generates nonlinearly transient behavior rendering transient reservoir states suitable for linear classication.
Our goal is to study up to which extent systems with delay, and especially photonic systems, can be used as
reservoirs.
Recently an new architecture has been proposed1 , based on a single nonlinear node with delayed feedback.
An electronic1 and an opto-electronic implementation2, 3 have been demonstrated and both have proven to be
very successful in terms of performance. This simple conguration, which replaces an entire network of randomly
connected nonlinear nodes with one single hardware node and a delay line, is signicantly easier to implement
experimentally. It is no longer necessary to construct an entire network of hundreds or even thousands of circuits,
each one representing a node. With this approach one node and a delay line suce to construct a computational
unit.
In this manuscript, we present a further investigation of the properties of delayed feedback congurations
used as a reservoir. Instead of quantifying the performance as an error obtained for a certain benchmark, we
now investigate a task-independent property, the linear memory of the system.
The time evolution of the output of a semiconductor laser subject to optical feedback can exhibit high-dimensional
chaotic fluctuations. In this contribution, our aim is to quantify the complexity of the chaotic time-trace generated
by a semiconductor laser subject to delayed optical feedback. To that end, we discuss the properties of two
recently introduced complexity measures based on information theory, namely the permutation entropy (PE)
and the statistical complexity measure (SCM). The PE and SCM are defined as a functional of a symbolic
probability distribution, evaluated using the Bandt-Pompe recipe to assign a probability distribution function to
the time series generated by the chaotic system. In order to evaluate the performance of these novel complexity
quantifiers, we compare them to a more standard chaos quantifier, namely the Kolmogorov-Sinai entropy. Here,
we present numerical results showing that the statistical complexity and the permutation entropy, evaluated at
the different time-scales involved in the chaotic regime of the laser subject to optical feedback, give valuable
information about the complexity of the laser dynamics.
We review three two-mode models for different semiconductor laser structures: Vertical-Cavity Surface-Emitting Lasers (VCSELs), Twin-Stripe Semiconductor-Lasers (TSSL), and Semiconductor Ring Lasers (SRL). The VCSELs model and TSSL model display rich dynamic behavior when a saturable absorber is embedded in the cavity. VCSELs with saturable absorber showed polarization chaos, which found applications in encoded communications; TSSLs with saturable absorber show coherent locked states as well as chaotic behavior; and SRLs show a complex two-mode dynamics giving rise to bidirectional operation, alternate oscillations and spontaneous symmetry breaking toward quasi-unidirectional bistable solutions, with potential applications to all-optical switching.
We have theoretically investigated the bifurcation scenario that leads to the emergence of a bistable regime in a two-mode model for a Semiconductor Ring Laser. The bistability takes place between two quasi-unidirectional solutions for the electric field, which are selected as stable solutions via gain-crossaturation, for well-above threshold operating conditions. Furthermore, we analyzed the switching properties of a single Semiconductor Ring Laser (SRL) operating in the bistable regime, under coherent optical pulse injection, in view of the possible implementation of a single SRL
an optically adressable memory element. The result is that the response time and the minimum switching energy respectively attain values the order of a few tenth of ps, and 1 fJ. Those values are espected to scale down with the device radius, due to the consequent decreasing of the cavity flight time. We have observed that the fast switching dynamic is due to an energy redistribution process between the two counterpropagating modes, that does not involve the (slow) carrier density through field-medium energy exchange processes. This allows to attain time scales much faster than the typical limit represented by the inverse of relaxation oscillation frequency.
We theoretically investigate the polarization-resolved dynamics of two vertical-cavity surface-emitting semiconductor lasers that are mutually coupled through coherent optical injection. We find a sequence of bistable polarization switchings that can be induced by either changing the coupling strength or the optical propagation phase. The successive polarization switchings are correlated to the creation of new compound-cavity modes when these parameters are continuously varied. The switching dynamics and the role of asymetries are also discussed.
We present recent results obtained for an optical chaos communications system using optoelectronic devices. These devices are used to improve privacy and security in information transmission. Two kind of chaos based emitters and receivers are described: a semiconductor laser subject to all-optical feedback and operating in a non-linear regime and a semiconductor laser subject to non-linear electro-optical feedback and operating in a linear regime. We show that both configuration give very good synchronization properties and are suitable for message enconding/decoding at bit rates as high as Gbit/s.
We investigate the synchronization properties of two mutually-coupled semiconductor lasers (SL) in a face to face configuration, when a non-negligible injection delay time is taken into account. Under the appropriate conditions, we derive a thermodynamic potential analog to the one studied by Mork et al. and by Lenstra for a semiconductor laser subject to an optical feedback. In this context, the role that noise and detuning play in the dynamics of the system is clearly identified. When operating in the Low Frequency Fluctuations (LFF) regime, the effect of the detuning on the leader-laggard operation is also analyzed. Finally, we focus on the short intercavity regime and we study the influence of the detuning and the propagation phase on the dynamics of each laser.
We study the dynamics of two Vertical Cavity Surface Emitting Lasers (VCSELs), when they are bidirectionally coupled through the mutual injection of their coherent optical fields. In the long distance limit between the lasers, we focus on the Low Frequency Fluctuations (LFF) regime and we investigate the polarization-resolved dynamics of each laser under the effect of detuning. In the short distance limit, the influence of the propagation phase parameter is also evaluated. For large spin-flip rates, it is found that a change in the propagation phase may induce a sudden switch in the polarization mode that becomes dominant. Extensive simulations scanning the Coupling-Detuning space are performed for both long and short injection delay times.
Mutually-coupled semiconductor lasers are of great current interest because of the important insight they provide into coupled physical, chemical, and biological systems. Two semiconductor lasers either with or without optoelectronic feedback are mutually coupled together through optoelectronic paths. It is found that mutual coupling can significantly affect the dynamics of the semiconductor lasers, depending on the coupling delay time and the coupling strength. Interesting phenomena such as generation of chaos, quasiperiodic and period-doubling bifurcation to chaos, and death by delay are observed. Synchronization of the chaotic outputs from mutually coupled semiconductor lasers is also observed.
In the present work we review recent results concerning stochastic phenomena in semiconductor lasers with optical feedback which operate in the low-frequency fluctuation (LFF) regime. Under these conditions the output intensity of the laser shows an irregular pulsated behavior in the form of sudden intensity dropouts. In the first two sections we show numerically the existence of stochastic and coherence resonance in the dropout appearance. These resonances are caused by the help of external colored noise introduced through the pumping current of the laser. In the third section we describe a recently reported new type of stochastic resonance, where a nonlinear system shows a resonance at a frequency not present neither at its internal time scales nor at any external perturbation. This phenomenon, known as ghost resonance, is reported both numerically and experimentally.
We present results on the state of the art in optoelectronic devices for chaos generation and message encryption/extraction. We concentrate on two kind of chaos based emitters and receivers: a semiconductor laser subject to all optical feedback and operating in a non linear regime and a semiconductor laser subject to nonlinear
electro optical feedback and operating in a linear regime. We show that both configuration give very good synchronization properties and are suitable for message enconding/decoding at bit rates as high as Gbit/s.
Optical chaos communications is becoming a hot topic since it is considered as a possible way to improve privacy and security in information transmission. To this end, a message can be encoded within a chaotic carrier generated by an emitter operating in a non-linear regime and decoded by an appropriate receiver. Consequently, the design and implementation of emitters and receivers that operate in a chaotic regime is a very important issue. To this end, two different architectures have been mainly followed: semiconductor lasers subject to all optical feedback and semiconductor lasers subject to electro-optical feedback. In the former, chaos is obtained from the light re-injected into the device that induces the laser to operate in a nonlinear regime. In the latter, the laser acts as a linear device that transforms a chaotic electrical input, generated in a combined electro-optical loop, into chaotic light. Encrypted information within the chaotic carrier can be recovered at a receiver that has to synchronize and match with the emitter. In this talk, both approaches to design the optoelectronic devices will be reviewed.
We have studied the dynamical behaviour of two semiconductor lasers subject to an optoelectronic bidirectional coupling and optionally to feedback, considering non-zero delay times in the propagation of the signals between both lasers and through each feedback loop in the case the latter exists. Starting from delayed rate equations
for the photon and carrier densities, we have investigated the stability of the fixed points and limit cycles of the system as function of the coupling and feedback strengths, as well as the delay times. From this analysis, quasiperiodic route to chaos and several interesting phenomena like the recently discovered "death by delay"
are predicted for this system.
We show both numerically and experimentally that a semiconductor laser prepared in an excitable state and driven by two weak periodic signals with different frequencies is able to resonate at a ghost frequency, i.e., a frequency that is not present in the forcing signal. The small signal modulation together with the complex internal dynamics of the system produces this resonance. This is an eminently nonlinear effect that agrees with the recent theoretical predictions by Chialvo et. al. [PHys. Rec. E. 65, 050902(R),2002].
We report the observation of synchrony in two unidirectionally coupled (master-slave) model neurons (implemented by electronic circuits) in a noisy environment. Both neurons are subjected to the same random stimulus, and there is a recurrent inhibitory delayed connection in the slave neuron. We observe that synchrony occurs shifted tin time, such that the slave neuron anticipates, i.e., forecasts, the response of the master neuron. By incorporating the effects of unidirectional coupling, delayed feedback and common noise into models of two spiking neurons, we are able to simulate successfully the experimental observations.
Semiconductor lasers with optical feedback are prone to exhibit unstable behavior. When working near threshold with moderate to low optical feedback, intensity dropouts are observed. These intensity drops, also called low-frequency fluctuations, occur both in single-mode and multimode semiconductor lasers. In this paper, the dynamics of the power distribution between the longitudinal modes of a multimode semiconductor laser is experimentally and numerically analyzed in the low-frequency fluctuation regime. It is observed that power dropouts of the total intensity, corresponding to drops in the dominant modes of the laser, are invariably accompanied by sudden activations of several longitudinal side modes. These activations are seen not to be simultaneous to the dropouts of the main modes, but to occur after them. The phenomenon is statistically analyzed in a systematic way, and the corresponding delay is estimated, leading to the conclusion that the side mode activation is a consequence of the dropouts of the dominant modes. A multimode extension of the Lang-Kobayashi equations is used to model the experimental setup. Numerical simulations also exhibit a time delay between the side-mode activation and the power dropout of the total intensity.
We numerically study the entrainment of two unidirectional coupled single-mode semiconductor lasers in a master-slave configuration. The emitter laser is an external-cavity laser subject to optical feedback that operates in a chaotic regime while the receiver has no optical feedback and consequently operates under CW when it is uncoupled (open loop scheme). We compare the performance of this scheme with the close loop one in which both emitter and receiver are subjected to optical feedback and operate in a chaotic state. We compute the degree of entrainment or synchronization of the two lasers as a function of the detuning, the emitter-receiver coupling constant and the feedback rate of the receiver. We find that the close loop scheme has, in general, a larger region of synchronization when compared with the open loop. We also study the possibility of message encoding and decoding in the both open and close loops and their robustness against parameters mismatch. Finally we compute the time it takes the system to recover the synchronization or entrainment state when the coupling between the two subsystems is lost. We find that this time is much larger in the close loop than in the open one.
We develop a model that describes the polarization dynamics of VCSELs with an absorbing region surrounding the active zone. We find that the dynamical behavior of the optical field is organized in four regions: stable linearly-polarized operation, intensity pulsations of a linearly-polarized component, pulsations of both total intensity and polarization, and polarization self-pulsations with constant total intensity. We characterize the four regions by computing the polarization resolved optical and power spectra. The predicted scenario agrees with recent experimental results.
In this contribution, we analyze the synchronization properties of two chaotic optical field generated by two VCSELs in presence of a saturable absorber. The vectorial nature of the chaotic field requires a continuous control scheme to achieve a high-quality synchronization between the two sources. We proposed a novel encoding scheme, exploiting a two contact VCSEL structure, which allows an easy and direct modulation of the transmitter. The added degree of freedom constituted by the chaos in polarization allows a reduction of the probability error (or enhancement of the transmission capacity) at the receiver.
In this paper we present numerical and experimental investigations on the synchronization of the instabilities originated by the mutual coupling of two semiconductor lasers in face to face configuration. We have restricted ourselves to the analysis of two lasers with identical parameters and operating at the same frequency. Numerical simulations are based on standard rate equations for each semiconductor laser whereas the mutual injection is modeled by including delayed optical fields. Experiments are performed using almost identical Fabry Perot lasers coupled through the TE component. As soon as the coupling strength is increased we observe fluctuations in the power dynamics that appears synchronized except for a small time lag. This asymmetric operation of the perfectly symmetric system allows to differentiate between leader and laggard lasers. Synchronization properties are studied making use of the synchronization plots and cross-correlation measurements. Extensive investigations of the dependence of the time traces and correlation degree on the coupling strength and current level demonstrate good agreement between numerical and experimental observations.
We develop a mesoscopic model of semiconductor dynamics for vertical-cavity surface-emitting lasers which allows us to describe polarization and transverse mode dynamics simultaneously. Within this model, we study the selection processes and the turn-on delay for the switch-on of different transverse modes in gain-guided VCSELs. We consider different active-region diameters, excitation conditions and current shapes. Following the application of the current pulse, transverse modes become excited in a quite definite sequence. After the turn-on, the VCSEL initially switches-on in the fundamental transverse mode, but higher-order transverse modes become excited later. In general, the results obtained are in qualitative agreement with experiments reported recently. Finally, we discuss the current shape dependence on the transverse mode selection at threshold.
We discuss mechanisms of polarization switching (PS) in Vertical Cavity Surface Emitting Lasers (VCSELs) within a mesoscopic approach based on an explicit form of a frequency- dependent complex susceptibility of the QW semi-conductor material. Cavity anisotropies, spin carrier dynamics and thermal shift of the gain curve are also taken into account in this framework. For large birefringence we find a PS due to thermal shift. For small birefringence we find a different PS, from the high-gain to the low-gain polarization state, that occurs at constant temperature. We characterize polarization partition noise in terms of power spectra. Transverse effects for PS in gain guided VCSELs are also considered.
An analysis is performed of the effects of strong optical feedback on the characteristics of single-transverse mode VCSELs. Consideration is given to the cases of short (1.5 cm) and long (15 cm) external cavities. When the laser is operated well above threshold in a short external cavity with high reflectivity, a strong dependence on the accumulated external cavity phase is observed. Stable operation is found for an optimum phase while for other values of the phase chaotic dynamics is observed. Such behavior is not seen near threshold where the laser output is stable for any accumulated phase. For the longer external cavity the influence of the phase term is found to be insignificant: chaotic behavior is seen in the output over a wide range of operating currents.
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