High-availability displacement sensing with multi-channel self mixing interferometry.

Laser self-mixing is in principle a simple and robust general purpose interferometric method, with the additional expressivity which results from nonlinearity. However, it is rather sensitive to unwanted changes in target reflectivity, which often hinders applications with non-cooperative targets. Here we analyze experimentally a multi-channel sensor based on three independent self-mixing signals processed by a small neural network. We show that it provides high-availability motion sensing, robust not only to measurement noise but also to complete loss of signal in some channels. As a form of hybrid sensing based on nonlinear photonics and neural networks, it also opens perspectives for fully multimodal complex photonics sensing.

Reconfigurable design of a thermo-optically addressed liquid-crystal phase modulator by a neural network.

We present a machine learning approach to program the light phase modulation function of an innovative thermo-optically addressed, liquid-crystal based, spatial light modulator (TOA-SLM). The designed neural network is trained with a little amount of experimental data and is enabled to efficiently generate prescribed low-order spatial phase distortions. These results demonstrate the potential of neural network-driven TOA-SLM technology for ultrabroadband and large aperture phase modulation, from adaptive optics to ultrafast pulse shaping.

Convolutional neural network for self-mixing interferometric displacement sensing.

Self-mixing interferometry is a well established interferometric measurement technique. In spite of the robustness and simplicity of the concept, interpreting the self-mixing signal is often complicated in practice, which is detrimental to measurement availability. Here we discuss the use of a convolutional neural network to reconstruct the displacement of a target from the self-mixing signal in a semiconductor laser. The network, once trained on periodic displacement patterns, can reconstruct arbitrarily complex displacement in different alignment conditions and setups. The approach validated here is amenable to generalization to modulated schemes or even to totally different self-mixing sensing tasks.

Success rate analysis of the response of an excitable laser to periodic perturbations.

We use statistical tools to characterize the response of an excitable system to periodic perturbations. The system is an optically injected semiconductor laser under pulsed perturbations of the phase of the injected field. We characterize the laser response by counting the number of pulses emitted by the laser, within a time interval, ΔT, that starts when a perturbation is applied. The success rate, SR(ΔT), is then defined as the number of pulses emitted in the interval ΔT, relative to the number of perturbations. The analysis of the variation of SR with ΔT allows separating a constant lag of technical origin and a frequency-dependent lag of physical and dynamical origin. Once the lag is accounted for, the success rate clearly captures locked and unlocked regimes and the transitions between them. We anticipate that the success rate will be a practical tool for analyzing the output of periodically forced systems, particularly when very regular oscillations need to be generated via small periodic perturbations.

Abnormal chiral events in a semiconductor laser with coherent injection.

We study experimentally and theoretically the dynamics of a spatially extended (along the propagation direction) oscillatory medium with coherent forcing. We observe abnormally high events, responsible for a different statistics of intensity and pulse height, in a regime where solitons and roll patterns are unstable. We focus on the formation of these high-peak events and their connection to the phase dynamics. Each abnormal event can be associated with a change in the slope of the phase time trace. Furthermore, the coexistence of ±2π phase rotations inside the cavity can be associated to the observation of abnormal events, similarly to recent predictions in bidimensional vortex turbulence.

Extreme events induced by collisions in a forced semiconductor laser.

We report on the experimental study of an optically driven multimode semiconductor laser with a 1 m cavity length. We observed a spatiotemporal regime where real-time measurements reveal very high-intensity peaks in the laser field. Such a regime, which coexists with the locked state and with stable phase solitons, is characterized by the emergence of extreme events that produce heavy tail statistics in the probability density function. We interpret the extreme events as collisions of spatiotemporal structures with opposite chirality. Numerical simulations of the semiconductor laser model, showing very similar dynamical behavior, substantiate our evidences and corroborate the description of interactions such as collisions between phase solitons and transient structures with different phase rotations.

Front pinning and localized states analogues in long-delayed bistable systems.

Localized structures have been observed in many spatially extended systems of either biological, chemical, or physical nature. Here, we study experimentally front pinning and dissipative localized structures in a delayed optical system based on a bistable semiconductor laser with optoelectronic feedback. We observe that many of the concepts known to apply to spatially localized structures also apply in this context, with specificities related to the lack of reversibility symmetry. Numerical simulations based on purely prototypical modeling reproduce very well the experimental findings, which indicates that the results do not depend on the specific physical system under consideration, but are, on the contrary, very generic features of time delayed systems.

Nonvolatile polarization control of a bistable VCSEL.

We report experimental evidence of nonvolatile all-optical memory operation using the two linear polarization states emitted from a GaAs oxide-confined VCSEL. The two polarization states coexist in a large range of pumping currents and substrate temperatures, and they can be controlled all-optically by exposing the device to polarization selective feedback, to crossed polarization reinjection orby injecting external light pulses. The active polarization state is recovered after powering off and on the VCSEL, while memory is lost if the substrate temperature is varied.

Deterministic optical rogue waves.

Experimental observations of rare giant pulses or rogue waves were done in the output intensity of an optically injected semiconductor laser. The long-tailed probability distribution function of the pulse amplitude displays clear non-Gaussian features that confirm the rogue wave character of the intensity pulsations. Simulations of a simple rate equation model show good qualitative agreement with the experiments and provide a framework for understanding the observed extreme amplitude events as the result of a deterministic nonlinear process.

Characterizing the response of chaotic systems.

We characterize the response of a chaotic system by investigating ensembles of, rather than single, trajectories. Time-periodic stimulations are experimentally and numerically investigated. This approach allows detecting and characterizing a broad class of coherent phenomena that go beyond generalized and phase synchronization. In particular, we find that a large average response is not necessarily related to the presence of standard forms of synchronization. Moreover, we study the stability of the response, by introducing an effective method to determine the largest nonzero eigenvalue -γ1 of the corresponding Liouville-type operator, without the need of directly simulating it. The exponent γ1 is a dynamical invariant, which complements the standard characterization provided by the Lyapunov exponents.

Coherent master equation for laser modelocking.

Modelocked lasers constitute the fundamental source of optically-coherent ultrashort-pulsed radiation, with huge impact in science and technology. Their modeling largely rests on the master equation (ME) approach introduced in 1975 by Hermann A. Haus. However, that description fails when the medium dynamics is fast and, ultimately, when light-matter quantum coherence is relevant. Here we set a rigorous and general ME framework, the coherent ME (CME), that overcomes both limitations. The CME predicts strong deviations from Haus ME, which we substantiate through an amplitude-modulated semiconductor laser experiment. Accounting for coherent effects, like the Risken-Nummedal-Graham-Haken multimode instability, we envisage the usefulness of the CME for describing self-modelocking and spontaneous frequency comb formation in quantum-cascade and quantum-dot lasers. Furthermore, the CME paves the way for exploiting the rich phenomenology of coherent effects in laser design, which has been hampered so far by the lack of a coherent ME formalism.

Splitting in the pinning-depinning transition of fronts in long-delayed bistable systems.

We investigate the formation of localized domains through front pinning in a periodically forced, bistable semiconductor laser with long-delayed optoelectronic feedback. At difference with 1D spatially extended systems, the transition from the pinning to the propagation regime occurs via two separated bifurcations, each corresponding to the unpinning of one of the fronts surrounding the localized domain. The bifurcation splitting is systematically explored, unveiling the crucial role played by the forcing frequency. The experimental results are reproduced and interpreted by means of a prototypical model of our system.

Topological solitons as addressable phase bits in a driven laser.

Optical localized states are usually defined as self-localized bistable packets of light, which exist as independently controllable optical intensity pulses either in the longitudinal or transverse dimension of nonlinear optical systems. Here we demonstrate experimentally and analytically the existence of longitudinal localized states that exist fundamentally in the phase of laser light. These robust and versatile phase bits can be individually nucleated and canceled in an injection-locked semiconductor laser operated in a neuron-like excitable regime and submitted to delayed feedback. The demonstration of their control opens the way to their use as phase information units in next-generation coherent communication systems. We analyse our observations in terms of a generic model, which confirms the topological nature of the phase bits and discloses their formal but profound analogy with Sine-Gordon solitons.

Experimental evidence of van der Pol-Fitzhugh-Nagumo dynamics in semiconductor optical amplifiers.

Thermo-optical pulsing in semiconductor amplifiers is experimentally shown to correspond to a very common excitable scenario (the van der Pol-Fitzhugh-Nagumo system). Self-sustained oscillations appear in the sequence predicted by this simple dynamical model as we change either the injection level or the bias current. Periodic modulation of these parameters leads to the characteristic phase-locking structure. Furthermore, coherence resonance is observed when external noise is added to the system.

Coupled optical excitable cells.

In this work we investigate experimentally the dynamics of two coupled optical excitable cells, namely, two semiconductor lasers with optical feedback. We analyze the dynamics observed in terms of the statistical properties of the time series and in terms of the phase space reconstruction from the data. We build a model based on a simple set of deterministic equations (on a two torus) plus noise in order to capture the essential features of the dynamics observed. We discuss the validity of our theoretical results in terms of families of excitable systems and coupling terms.

Efficient illumination for microsecond tracking microscopy.

The possibility to observe microsecond dynamics at the sub-micron scale, opened by recent technological advances in fast camera sensors, will affect many biophysical studies based on particle tracking in optical microscopy. A main limiting factor for further development of fast video microscopy remains the illumination of the sample, which must deliver sufficient light to the camera to allow microsecond exposure times. Here we systematically compare the main illumination systems employed in holographic tracking microscopy, and we show that a superluminescent diode and a modulated laser diode perform the best in terms of image quality and acquisition speed, respectively. In particular, we show that the simple and inexpensive laser illumination enables less than 1 µs camera exposure time at high magnification on a large field of view without coherence image artifacts, together with a good hologram quality that allows nm-tracking of microscopic beads to be performed. This comparison of sources can guide in choosing the most efficient illumination system with respect to the specific application.

Experimental evidence of stochastic resonance in an excitable optical system.

Experimental evidence of stochastic resonance in an excitable optical system is reported. We apply a sinusoidal forcing to the system and, for a finite external noise level, we find a frequency for which the excitable pulsing occurs periodically at the frequency imposed by the modulation. This resonant frequency matches the inverse of the average escape time of the stochastically driven system (i.e., without forcing). The same resonance is found by varying the noise level for fixed forcing frequencies. We discuss different indicators in order to describe quantitatively the degree of resonance.

Cavity solitons as pixels in semiconductor microcavities.

Cavity solitons are localized intensity peaks that can form in a homogeneous background of radiation. They are generated by shining laser pulses into optical cavities that contain a nonlinear medium driven by a coherent field (holding beam). The ability to switch cavity solitons on and off and to control their location and motion by applying laser pulses makes them interesting as potential 'pixels' for reconfigurable arrays or all-optical processing units. Theoretical work on cavity solitons has stimulated a variety of experiments in macroscopic cavities and in systems with optical feedback. But for practical devices, it is desirable to generate cavity solitons in semiconductor structures, which would allow fast response and miniaturization. The existence of cavity solitons in semiconductor microcavities has been predicted theoretically, and precursors of cavity solitons have been observed, but clear experimental realization has been hindered by boundary-dependence of the resulting optical patterns-cavity solitons should be self-confined. Here we demonstrate the generation of cavity solitons in vertical cavity semiconductor microresonators that are electrically pumped above transparency but slightly below lasing threshold. We show that the generated optical spots can be written, erased and manipulated as objects independent of each other and of the boundary. Numerical simulations allow for a clearer interpretation of experimental results.