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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Non-local correlations via chaotic itinerancy in VCSEL with optical feedback.

Similar to edge-emitting lasers, vertical cavity surface emitting lasers (VCSELs) subjected to optical feedback are known for exhibiting erratic fluctuations of their optical power at slow and fast time scales; these are called low-frequency fluctuations (LFF). Here, we demonstrate both experimentally and numerically that the chaotic itinerancy in phase space associated with LFF has a deep connection with the creation of non-local correlations at multiple time scales between the two linear polarization modes. Our result provides a novel framework to interpret the unknown origin of spectral signatures in the optical power of chaotic lasers with optical feedback, which were observed in the past two decades.

Vectorial extreme events in VCSEL polarization dynamics.

We report on the occurrence of extreme events (EEs) in the polarization dynamics of vertical cavity surface emitting lasers with optical feedback. We have identified two types of EEs based on numerical simulations: vectorial and scalar events corresponding, respectively, to the emission of a high-power pulse in both linear polarizations simultaneously and in single linear polarization. We show that these two types of events follow the typical statistics of rogue waves. Finally, we observe that an emission in both polarizations leads to a larger generation rate of EEs with a saturation over a wide range of feedback strength by comparison to a single-polarization mode emission.

High-order external cavity modes and restabilization of a laser diode subject to a phase-conjugate feedback.

We experimentally report the sequence of bifurcations destabilizing and restabilizing a laser diode with phase-conjugate feedback when the feedback rate is increased. Specifically, we successively observe the initial steady state, undamped relaxation oscillations, quasi-periodicity, chaos, and oscillating solutions at harmonics up to 13 times the external cavity frequency but also the restabilization to a steady state. The experimental results are qualitatively well reproduced by a model that accounts for the time the light takes to penetrate the phase-conjugate mirror. The theory points out that the system restabilizes through a Hopf bifurcation whose frequency is a harmonic of the external cavity frequency.

Polarization dynamics induced by parallel optical injection in a single-mode VCSEL.

We report an experimental study of the polarization nonlinear dynamics in a 1550 nm single-mode vertical-cavity surface-emitting laser (VCSEL) subject to parallel optical injection. Experimentally measured stability maps identifying regions of different nonlinear dynamics for various values of bias current are reported. We show that VCSELs with more than a 35 dB polarization mode suppression ratio can have rich nonlinear dynamics in both linear polarizations, including periodic and chaotic behaviors appearing simultaneously in both polarization modes.

Bistability Controlled by Convection in a Pattern-Forming System.

We analyze the transition from convective to absolute dynamical instabilities in a nonlinear optical system forming patterns, i.e., a photorefractive crystal in a single feedback configuration. We demonstrate that the convective regime is directly related to the bistability area in which the homogeneous steady state coexists with a pattern solution. Outside this domain, the system exhibits either a homogeneous steady state or an absolute dynamical regime. We evidence that the bistability area can be greatly increased by adjusting the mirror tilt angle and/or by applying an external background illumination on the photorefractive crystal.