Timing jitter reduction in semiconductor lasers induced by optical injection.

We present an experimental study of the effect of continuous-wave optical injection (OI) from a vertical-cavity surface-emitting laser (VCSEL) on the timing jitter of a gain-switched discrete-mode semiconductor laser (DML). Timing jitter was analyzed over a wide range of temperatures of the DML, which allowed tuning the detuning between the lasers emissions, and it was compared with the inter-pulse timing jitter. We have found that there is a range of detunings in which OI diminishes the jitter by 70% with respect to the jitter of the solitary DML. However, within this region, there are some detunings for which OI significantly increases the jitter.

Quantifying the synchronization of the spikes emitted by coupled lasers.

Synchronization phenomena is ubiquitous in nature, and in spite of having been studied for decades, it still attracts a lot of attention as is still challenging to detect and quantify, directly from the analysis of noisy signals. Semiconductor lasers are ideal for performing experiments because they are stochastic, nonlinear, and inexpensive and display different synchronization regimes that can be controlled by tuning the lasers' parameters. Here, we analyze experiments done with two mutually optically coupled lasers. Due to the delay in the coupling (due to the finite time the light takes to travel between the lasers), the lasers synchronize with a lag: the intensity time traces show well-defined spikes, and a spike in the intensity of one laser may occur shortly before (or shortly after) a spike in the intensity of the other laser. Measures that quantify the degree of synchronization of the lasers from the analysis of the intensity signals do not fully quantify the synchronicity of the spikes because they also take into account the synchronization of fast irregular fluctuations that occur between spikes. By analyzing only the coincidence of the spike times, we show that event synchronization measures quantify spike synchronization remarkably well. We show that these measures allow us to quantify the degree of synchronization and, also, to identify the leading laser and the lagging one.

Experimental study of spatial and temporal coherence in a laser diode with optical feedback.

Optical feedback can reduce the linewidth of a semiconductor laser by several orders of magnitude, but it can also cause line broadening. Although these effects on the temporal coherence of the laser are well known, a good understanding of the effects of feedback on the spatial coherence is still lacking. Here we present an experimental technique that allows discriminating the effects of feedback on temporal and spatial coherence of the laser beam. We analyze the output of a commercial edge-emitting laser diode, comparing the contrast of speckle images recorded using a multimode (MM) or single mode (SM) fiber and an optical diffuser, and also, comparing the optical spectra at the end of the MM or SM fiber. Optical spectra reveal feedback-induced line broadening, while speckle analyses reveal reduced spatial coherence due to feedback-excited spatial modes. These modes reduce the speckle contrast (SC) up to 50% when speckle images are recorded using the MM fiber, but do not affect the SC when the images are recorded using the SM fiber and diffuser, because the spatial modes that are excited by the feedback are filtered out by the SM fiber. This technique is generic and can be used to discriminate spatial and temporal coherence of other types of lasers and under other operating conditions that can induce a chaotic output.

Abrupt transition from low-coherence to high-coherence radiation in a semiconductor laser with optical feedback.

Semiconductor lasers are very sensitive to optical feedback. Although it is well known that coherent feedback lowers the threshold of the laser, the characteristics of the transition from low-coherence radiation-dominated by spontaneous emission-below threshold to high-coherence radiation-dominated by stimulated emission-above threshold have not yet been investigated. Here we show experimentally that, in contrast to the transition that occurs in the solitary laser, in the laser with feedback the transition to high-coherence emission can occur abruptly. We use the speckle technique to show that the transition varies from smooth to abrupt as the amount of light fed back to the laser increases.

Time crystal dynamics in a weakly modulated stochastic time delayed system.

Time crystal oscillations in interacting, periodically driven many-particle systems are highly regular oscillations that persist for long periods of time, are robust to perturbations, and whose frequency differs from the frequency of the driving signal. Making use of underlying similarities of spatially-extended systems and time-delayed systems (TDSs), we present an experimental demonstration of time-crystal-like behavior in a stochastic, weakly modulated TDS. We consider a semiconductor laser near threshold with delayed feedback, whose output intensity shows abrupt spikes at irregular times. When the laser current is driven with a small-amplitude periodic signal we show that the interaction of delayed feedback and modulation can generate long-range regularity in the timing of the spikes, which lock to the modulation and, despite the presence of noise, remain in phase over thousands of modulation cycles. With pulsed modulation we find harmonic and subharmonic locking, while with sinusoidal modulation, we find only subharmonic locking, which is a characteristic feature of time-crystal behavior.

Dynamics of a semiconductor laser with feedback and modulation: experiments and model comparison.

We study experimentally and numerically the dynamics of a semiconductor laser near threshold, subject to optical feedback and sinusoidal current modulation. The laser operates in the low frequency fluctuation (LFF) regime where, without modulation, the intensity shows sudden spikes at irregular times. Under particular modulation conditions the spikes lock to the modulation and their timing becomes highly regular. While the modulated LFF dynamics has received a lot of attention, an in-depth comparison with the predictions of the Lang-Kobayashi (LK) model has not yet been performed. Here we use the LK model to simulate the laser dynamics and use the Fano factor to quantify the regularity of the timing of the spikes. The Fano factor is calculated by counting the number of spikes in successive segments of the intensity time-series and keeps information about temporal order in the spike sequence that is lost when the analysis is based on the distribution of inter-spike intervals. Here we compare the spike timing regularity in experimental and in simulated spike sequences as a function of the modulation amplitude and frequency and find a good qualitative agreement. We find that in both experiments and simulation for appropriate conditions the spike timing can be highly regular, as revealed by very small values of the Fano factor.

Estimation of Wave Period from Pitch and Roll of a Lidar Buoy.

This work proposes a new wave-period estimation (L-dB) method based on the power-spectral-density (PSD) estimation of pitch and roll motional time series of a Doppler wind lidar buoy under the assumption of small angles (±22 deg) and slow yaw drifts (1 min), and the neglection of translational motion. We revisit the buoy's simplified two-degrees-of-freedom (2-DoF) motional model and formulate the PSD associated with the eigenaxis tilt of the lidar buoy, which was modelled as a complex-number random process. From this, we present the L-dB method, which estimates the wave period as the average wavelength associated to the cutoff frequency span at which the spectral components drop off L decibels from the peak level. In the framework of the IJmuiden campaign (North Sea, 29 March-17 June 2015), the L-dB method is compared in reference to most common oceanographic wave-period estimation methods by using a TriaxysTM buoy. Parametric analysis showed good agreement (correlation coefficient, ρ = 0.86, root-mean-square error (RMSE) = 0.46 s, and mean difference, MD = 0.02 s) between the proposed L-dB method and the oceanographic zero-crossing method when the threshold L was set at 8 dB.

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.

Remote recovery of audio signals from videos of optical speckle patterns: a comparative study of signal recovery algorithms.

Optical remote sensors are nowadays ubiquitously used, thanks to unprecedented advances in the last decade in photonics, machine learning and signal processing tools. In this work we study experimentally the remote recovery of audio signals from the silent videos of the movement of optical speckle patterns. This technique can be used even when in between the source and the receiver there is a medium that does not allow for the propagation of sound waves. We use a diode laser to generate a speckle pattern on the membrane of a loudspeaker and a low-cost CCD camera to record the video of the movement of the speckle pattern when the loudspeaker plays an audio signal. We perform a comparative analysis of six signal recovery algorithms. In spite of having different complexity and computational requirements, we find that the algorithms have (except for the simplest one) good performance in terms of the quality of the recovered signal. The best trade-off, in terms of computational costs and performance, is obtained with a new method that we propose, which recovers the signal from the weighted sum of the intensities of all the pixels, where the signs of the weights are determined by selecting a reference pixel and calculating the signs of the cross-correlations of the intensity of the reference pixel and the intensities of the other pixels.

Experimental characterization of the speckle pattern at the output of a multimode optical fiber.

Speckle patterns produced by coherent waves interfering with each other are undesirable in many imaging applications (for example, in laser projection systems) but on the other hand, they contain useful information that can be exploited (for example, for blood flow analysis or reconstruction of the object that generates the speckle). It is therefore important to understand how speckle can be enhanced or reduced by tailoring the coherence of laser light. Using a conventional semiconductor laser and a multimode optical fiber we study experimentally how the speckle pattern depends on the laser pump current and on the image acquisition settings. By varying the pump current from below to above the lasing threshold, and simultaneously tuning the image exposure time to compensate for the change in brightness, we find conditions that allow for recorded images with similar average intensity, but with speckle contrast (the standard deviation of the intensity over the average intensity) as low as 0.16, or as high as 0.99.

Quantifying the degree of locking in weakly forced stochastic systems.

Controlling an stochastic nonlinear system with a small amplitude signal is a fundamental problem with many practical applications. Quantifying locking is challenging, and current methods, such as spectral or correlation analysis, do not provide a precise measure of the degree of locking. Here we study locking in an experimental system, consisting of a semiconductor laser with optical feedback operated in the regime where it randomly emits abrupt spikes. To quantify the locking of the optical spikes to small electric perturbations, we use two measures, the success rate (SR) and the false positive rate (FPR). The SR counts the spikes that are emitted shortly after each perturbation, while the FPR counts the additional extra spikes. We show that the receiver operating characteristic (ROC) curve (SR versus FPR plot) uncovers parameter regions where the electric perturbations fully control the laser spikes, such that the laser emits, shortly after each perturbation, one and only one spike. To demonstrate the general applicability of the ROC analysis we also study a stochastic bistable system under square-wave forcing and show that the ROC curve allows identifying the parameters that produce best locking.

Language organization and temporal correlations in the spiking activity of an excitable laser: experiments and model comparison.

We introduce a method, based on symbolic analysis, to characterize the temporal correlations of the spiking activity exhibited by excitable systems. The technique is applied to the experimentally observed dynamics of a semiconductor laser with optical feedback operating in the low-frequency fluctuations regime, where the laser intensity displays irregular trains of sudden dropouts that can be interpreted as excitable pulses. Symbolic analysis transforms the series of interdropout time intervals into sequences of words, which represent the local ordering of a certain (small) number of those intervals. We then focus on the transition probabilities between pairs of words, showing that certain transitions are overrepresented (resulting in others being underrepresented) with respect to the surrogate series, provided the laser injection current is above a critical value. These experimental observations are in very good agreement with numerical simulations of the delay-differential Lang-Kobayashi model that is commonly used to describe this laser system, which supports the fact that the language organization reported here is generic and not a particular feature of the specific laser employed or the experimental time series analyzed. We also present results of simulations of the phenomenological nondelayed Eguia-Mindlin-Giudici(EMG) model and find that in this model the agreement between the experiments and the simulations is good at a qualitative, but not at a quantitative, level.

Quantifying stochasticity in the dynamics of delay-coupled semiconductor lasers via forbidden patterns.

We quantify the level of stochasticity in the dynamics of two mutually coupled semiconductor lasers. Specifically, we concentrate on a regime in which the lasers synchronize their dynamics with a non-zero lag time, and the leader and laggard roles alternate irregularly between the lasers. We analyse this switching dynamics in terms of the number of forbidden patterns of the alternate time series. The results reveal that the system operates in a stochastic regime, with the level of stochasticity decreasing as the lasers are pumped further away from their lasing threshold. This behaviour is similar to that exhibited by a single semiconductor laser subject to external optical feedback, as its dynamics shifts from the regime of low-frequency fluctuations to coherence collapse.