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.

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.

Fully controllable multichannel waveguides induced by counterpropagating Bessel beams.

We theoretically analyze the waveguiding structures photo-induced by two incoherent counter-propagating Bessel beams (BBs) in a biased photorefractive crystal. We demonstrate that the cross-coupling of two BBs enables adressable channels and tunability of the forming guiding structures. The truncation parameter of the BBs, their Bessel orders and the misalignment between the two beams are all key parameters for tailoring the characteristics of the photo-induced waveguides such as the number of outputs, the output intensity levels and the distance between each output channel. Accordingly, we optimized the different parameters for designing not only a fully tunable Y-coupler but also optical splitters with up to five outputs and even more complex star couplers for all-optical interconnect applications. Finally, we report on the stability behavior of the photo-induced platform. The stability threshold depends on the nonlinearity parameter beyond which the beams display time-periodic, quasi-periodic and turbulent dynamics where spatially localized instabilities can be observed. All these results suggest more opportunities for fully controllable complex waveguiding structures and new all-optical solutions for active components in optical telecommunication and innovative ways of performing optical computing based on spatiotemporal chaos.

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.

Multiple input/output waveguides light-induced by a single Bessel beam for all-optical interconnects.

We numerically study photo-induced waveguides using a single Bessel beam in a photorefractive (PR) medium. Under self-focusing nonlinearity, we demonstrate the possibility for creating complex waveguiding structures with multiple input/output channels. The truncation of the incoming Bessel beam, the nonlinearity of the PR medium, the light intensity, and the order and the size of the Bessel beam are the key parameters for achieving different configurations with high guiding efficiencies. As such, not only classical X or Y couplers but also more complex structures can be generated with up to 7 identified inputs/outputs. These results provide large opportunities for all-optical interconnects.

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.

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.

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.

Mapping of external cavity modes for a laser diode subject to phase-conjugate feedback.

We numerically investigate the dynamics of a semiconductor laser subject to phase-conjugate optical feedback. We explore the effects of the laser model and feedback parameters for the generation of time-periodic oscillations of the output power at harmonics of the external cavity frequency, i.e., dynamical solutions that have been named external cavity modes. We point out that both the experimentally tunable and other parameters have an influence on the frequency of such dynamics. Since the delay has to exist, it is not the relevant parameter as we show that the feedback rate fixes the frequency of the periodic self-pulsations. The interaction length of the crystal and the ratio between carrier and photon lifetimes tend to filter out high frequencies as they increase. Finally, the linewidth enhancement factor unlocks high frequencies as it increases. We conclude by providing a situation which leads to periodic solutions with higher frequencies using a set of realistic values of parameters.

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.

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.

Airy beam self-focusing in a photorefractive medium.

The unique bending and shape-preserving properties of optical Airy beams offer a large range of applications in for example beam routing, optical waveguiding, particle manipulation and plasmonics. In these applications and others, the Airy beam may experience nonlinear light-matter interactions which in turn modify the Airy beam properties and propagation. A well-known example is light self-focusing that leads to the formation of spatial soliton. Here, we unveil experimentally the self-focusing properties of a 1D-Airy beam in a photorefractive crystal under focusing conditions. The transient evolution involves both self-bending and acceleration of the initially launched Airy beam due to the onset of an off-shooting soliton and the resulting nonlocal refractive index perturbation. Both the transient and stationary self-focusing properties can be tuned by varying the bias electric field, the injected Airy beam power and the background illumination.

High-frequency chaotic dynamics enabled by optical phase-conjugation.

Wideband chaos is of interest for applications such as random number generation or encrypted communications, which typically use optical feedback in a semiconductor laser. Here, we show that replacing conventional optical feedback with phase-conjugate feedback improves the chaos bandwidth. In the range of achievable phase-conjugate mirror reflectivities, the bandwidth increase reaches 27% when compared with feedback from a conventional mirror. Experimental measurements of the time-resolved frequency dynamics on nanosecond time-scales show that the bandwidth enhancement is related to the onset of self-pulsing solutions at harmonics of the external-cavity frequency. In the observed regime, the system follows a chaotic itinerancy among these destabilized high-frequency external-cavity modes. The recorded features are unique to phase-conjugate feedback and distinguish it from the long-standing problem of time-delayed feedback dynamics.

Laser diode nonlinear dynamics from a filtered phase-conjugate optical feedback.

The rate equations for a laser diode subject to a filtered phase-conjugate optical feedback are studied both analytically and numerically. We determine the Hopf bifurcation conditions, which we explore by using asymptotic methods. Numerical simulations of the laser rate equations indicate that different pulsating intensity regimes observed for a wide filter progressively disappear as the filter width increases. We explain this phenomenon by studying the coalescence of Hopf bifurcation points as the filter width increases. Specifically, we observe a restabilization of the steady-state solution for moderate width of the filter. Above a critical width, an isolated bubble of time-periodic intensity solutions bounded by two successive Hopf bifurcation points appears in the bifurcation diagram. In the limit of a narrow filter, we then demonstrate that only two Hopf bifurcations from a stable steady state are possible. These two Hopf bifurcations are the Hopf bifurcations of a laser subject to an injected signal and for zero detuning.