Optical chaos synchronization in a cascaded injection experiment.

We experimentally study the synchronization of chaos generated by semiconductor lasers in a cascade injection configuration, i.e., a tunable master laser is used to generate chaos by optical injection in a transmitter laser that injects light into a receiver laser. Chaos synchronization between the transmitter and the receiver lasers is achieved with a correlation coefficient of 90% for a measurement bandwidth up to 35 GHz. Two parameter regions of good synchronization are found, corresponding to the alignment of the oscillation frequencies of the receiver laser with either the transmitter laser or the master laser.

Zero-broadening slow light from photorefractive two-wave mixing.

The ability to delay short light pulses is a promising solution for all-optical telecommunications, but suffers from a large distortion of the delayed pulse as a consequence of the high material dispersion. In this Letter, we demonstrate the possibility to all-optically control the group delay in a photorefractive (PR) crystal by the use of the two-wave mixing (TWM) effect in the pulse regime at room temperature. Most importantly, we show that a proper choice of the pump pulse width in the TWM process enables us to slow down shorter or longer signal pulses without distortion. The technique is demonstrated both at visible (638 nm) and infrared (1064 nm) wavelengths and for slowed-down pulses with durations ranging from 10 ns up to 30 ms, hence confirming its broad applicability.

High-resolution dynamic consistency analysis of photonic time-delay reservoir computer.

We numerically investigate a time-delayed reservoir computer architecture based on a single-mode laser diode with optical injection and optical feedback. Through a high-resolution parametric analysis, we reveal unforeseen regions of high dynamic consistency. We demonstrate furthermore that the best computing performance is not achieved at the edge of consistency, as previously suggested in a coarser parametric analysis. This region of high consistency and optimal reservoir performances is highly sensitive to the data input modulation format.

Passively mode-locked high-frequency dual-VCSEL system.

Two VCSELs placed facing each other with one biased chip while the second chip is unbiased is shown as a promising alternative to the popularly used conventional SESAM mode-locked VECSEL to generate mode-locked pulses. We propose a theoretical model using time-delay differential rate equations and numerically show that the proposed dual-laser configuration functions as a typical gain-absorber system. Parameter space defined by laser facet reflectivities and current are used to show general trends in the exhibited nonlinear dynamics and pulsed solutions.

Wideband chaos induced by the optical injection of a frequency comb.

In this Letter, we experimentally demonstrate a method to improve the bandwidth and flatness of chaos from a laser diode using the optical injection of a frequency comb. Our results show that the injection of an optical frequency comb into a laser diode extends the area of chaotic dynamics to much broader injection parameters (injected power and detuning frequency). The increased number of injected lines and the injected comb spacing are used to control and significantly improve the chaos properties. We report a chaotic signal with a bandwidth of 32.8 GHz and a spectral flatness of 0.83.

Two dimensional Airy beam soliton.

We demonstrate the formation of a two dimensional Airy beam soliton in a photorefractive crystal. By simply varying the nonlinearity strength we identify several scenarios showing the coexistence between an Airy beam and the emerging soliton. The soliton output profile behaves according to the theoretical soliton existence curve and can be tailored by the nonlinearity strength even without modifying the input Airy beam shape. This last feature makes this Airy soliton distinct from the Gaussian beam generated photorefractive soliton.

Tailoring frequency combs through VCSEL polarization dynamics.

We investigate experimentally the nonlinear polarization dynamics of a VCSEL subject to optical injection of a frequency comb. By tuning the polarization of the injected comb to be orthogonal to that of the VCSEL, we demonstrate the generation of either a single polarization or a dual polarization frequency comb. The injection parameters (injected power and detuning frequency) are then used either to generate harmonics of the initial comb spacing or to increase the number of total output frequency lines up to 15 times the number of injected comb lines. Optimisation of the injection parameters yields a comb extending over 60 GHz for a comb spacing of 2 GHz with a carrier to noise ratio (CNR) of up to 60 dB. Our technique allows us to separately control the comb spacing, comb bandwidth, CNR and polarization. Our finding can be used for spectroscopy measurement and also for polarization division multiplexing in optical data communications.

Optimized properties of chaos from a laser diode.

We perform an experimental parametric study of the chaos generated by a laser diode subjected to phase-conjugate feedback. In addition to the typical figure of merit, i.e., chaos bandwidth, the corresponding spectral flatness and permutation entropy at delay is analyzed. Our experimental observations reveal that the chaos can be generated with a bandwidth of ≈29 GHz, a spectral flatness up to 0.75, and a permutation entropy at delay of up to 0.99. These optimized performances are maintained over a large range of parameters and have not been achieved in the conventional optical feedback configuration. Interestingly, reducing the pump current reduces the chaos bandwidth while keeping the spectral flatness and the permutation entropy at delay the same as observed for increased pump current. Our experimental findings are consistent with the presented numerical simulations produced using the Lang-Kobayashi model.

Nonlinear dynamics of a laser diode with an injection of an optical frequency comb.

We experimentally and theoretically demonstrate the variety of the nonlinear dynamics exhibited by a single frequency semiconductor laser subjected to optical injection from a frequency comb. The injection parameters (the detuning and the injection strength) and the comb properties (comb spacing and the amplitude of the injected comb lines) are varied to unveil several dynamics such as injection locking, wave-mixing, chaotic dynamics, and unlocked time-periodic dynamics corresponding to new comb solutions. The asymmetry of the injected comb is shown to modify the size of the injection locking region in the parameter space, as well as the common properties between the new comb solutions observed and the injected comb.

Slow light with photorefractive beam fanning.

The beam fanning naturally occurring in a photorefractive crystal is shown to slow down a single light pulse at room temperature. Slow light is demonstrated for both visible and infrared wavelength light pulses as short as the response time of the photorefractive crystal and with fractional delay- i.e ratio of delay to output pulse duration- up to 0.4.

Spatiotemporal complexity of chaos in a phase-conjugate feedback laser system.

An 852 nm semiconductor laser is experimentally subjected to phase-conjugate time-delayed feedback achieved through four-wave mixing in a photorefractive ($ {{\rm BaTiO}_{3}} $BaTiO3) crystal. Permutation entropy (PE) is used to uncover distinctive temporal signatures corresponding to the sub-harmonics of the round-trip time and the relaxation oscillations. Complex spatiotemporal outputs with high PE mostly upwards of $ \sim 0.85 $∼0.85 and chaos bandwidth (BW) up to $ \sim 31\;{\rm GHz} $∼31GHz are observed over feedback strengths up to 7%. The low-feedback region counterintuitively exhibits spatiotemporal reorganization, and the variation in the chaos BW is restricted within a small range of 1.66 GHz, marking the transition between the dynamics driven by the relaxation oscillations and the external cavity round-trip time. The immunity of the chaos BW and the complexity against such spatiotemporal reorganization show promise as an excellent candidate for secure communication applications.

Pattern generation and symbolic dynamics in a nanocontact vortex oscillator.

Harnessing chaos or intrinsic nonlinear behaviours of dynamical systems is a promising avenue toward unconventional information processing technologies. In this light, spintronic devices are promising because of the inherent nonlinearity of magnetization dynamics. Here, we demonstrate experimentally the potential for chaos-based schemes using nanocontact vortex oscillators by unveiling and characterizing their waveform patterns and symbolic dynamics using time-resolved electrical measurements. We dissociate nonlinear deterministic patterns from thermal fluctuations and show that the emergence of chaos results in the unpredictable alternation of well-defined patterns. With phase-space reconstruction techniques, we perform symbolic analyses of the time series and show that the oscillator exhibits maximal entropy and complexity at the centre of its incommensurate region. This suggests that such vortex-based systems are promising nanoscale sources of entropy that could be exploited for information processing.

Chaos in Magnetic Nanocontact Vortex Oscillators.

We present an experimental study of spin-torque driven vortex self-oscillations in magnetic nanocontacts. We find that, above a certain threshold in applied currents, the vortex gyration around the nanocontact is modulated by relaxation oscillations, which involve periodic reversals of the vortex core. This modulation leads to the appearance of commensurate but also, more interestingly here, incommensurate states, which are characterized by devil's staircases in the modulation frequency. We use frequency- and time-domain measurements together with advanced time-series analyses to provide experimental evidence of chaos in incommensurate states of vortex oscillations, in agreement with theoretical predictions.

Experimental reservoir computing using VCSEL polarization dynamics.

We realize an experimental setup of a time-delay reservoir using a VCSEL with optical feedback and optical injection. The VCSEL is operated in the injection-locking regime. This allows us to solve different information processing tasks, such as chaotic time-series prediction with a NMSE of 1.6×10-2 and nonlinear channel equalization with a SER of 1.5×10-2, improving state-of-the-art performance. We also demonstrate experimentally, through a careful statistical analysis, the impact of the VCSEL polarization dynamics on the performance of our architecture. More specifically, we confirm recent theoretical prediction stating that a polarization rotated feedback allows for the enhancement of the calculation performance compared to an isotropic feedback.

Counterpropagating interactions of self-focusing Airy beams.

We study the first experimental collisions of two incoherent self-focused counterpropagating Airy beams in a nonlinear crystal. Their interactions demonstrate that the self-focusing dynamics of the Airy beams can be spatially controlled by the counterpropagating Airy beam. By tuning the misalignment and the size of the beams, we can control the output position of the self-focused Airy beam and switch to multiple outputs. Also the nonlinearity strength enables to engineer the temporal stability of the resulting waveguide structure.

Improved slow light performances using photorefractive two-wave mixing.

We experimentally observe an ultralow effective group velocity of 0.9 cm/s of light pulses using the two-wave mixing process in an Sn2P2S6 (SPS):Te crystal at a visible wavelength. The time delay can be controlled through the nonlinear photorefractive gain and the input pulse duration. By optimizing the nonlinearity strength, we achieve a maximum fractional delay of 0.79 for a pulse duration of 100 ms. Our photorefractive slow light system allows combining low group velocity with large delay-bandwidth product for pulse durations spanning three orders of magnitude.

Wideband chaos from a laser diode with phase-conjugate feedback.

We analyze experimentally and theoretically the chaotic dynamics generated by a laser diode subjected to phase-conjugate feedback. Phase conjugation is obtained from four-wave mixing in a BaTiO3 photorefractive crystal. We demonstrate that the chaos bandwidth first increases linearly with feedback ratio but then saturates to relatively high values. With a single optical feedback, a chaos bandwidth up to about 18 GHz is achieved, which is about five times as large as the free-running laser diode relaxation oscillation frequency. Numerical simulations confirm our experimental observations and unveil that the finite depth penetration into the crystal is responsible for the observed saturation.

Enhanced performance of a reservoir computer using polarization dynamics in VCSELs.

We analyze the performance of a reservoir computer based on time-delay feedback and optical injection, which is drawing benefits from the high-speed polarization dynamics of a vertical cavity surface emitting laser. We show that such a system has high computation performance and yields deeper memory than an existing single-mode laser-based reservoir computer. Performance is demonstrated on several benchmarking tasks. In particular, the error rate is an order of magnitude smaller when performing channel equalization.

Stability analysis of a quantum cascade laser subject to phase-conjugate feedback.

We investigate the stability boundaries of a quantum cascade laser subject to phase-conjugate optical feedback. From a three-level model, we reduce our set of equations to the usual modified Lang-Kobayashi equations describing a semiconductor laser subject to phase-conjugate feedback. We then determine the Hopf bifurcation conditions, which we explore by using asymptotic methods. In the limit of large delays, we find approximations of the first Hopf bifurcation that is responsible for the destabilization of the system. We obtain an expression that depends only on three parameters: the feedback strength, the line-width enhancement factor, and the pump current. From this expression, we study the stability boundaries of our system. We compare our results with the initial three-level model using a continuation method. We find qualitative and quantitative agreements of the stability boundaries with the two methods. Finally, we compare our findings with the ones obtained for a quantum cascade laser subject to conventional optical feedback.

Sustained oscillations accompanying polarization switching in laser dynamics.

We report experimentally and theoretically the emergence of sustained oscillations over a slow and periodic polarization switching in a laser subjected to polarization rotated optical feedback. This phenomenon originates from a clear bifurcation point that marks the transition between sustained and damped oscillations on the plateaus. Analytical study reveals also that the frequency of this new oscillatory dynamics is independent of the time delay.