The nonlinear dynamics of transverse and polarization modes of a broad-area vertical-cavity surface-emitting laser (BA-VCSEL) exhibit, without any external perturbation, chaos with high correlation dimension, large bandwidth (BW), and good spectral flatness over a wide range of currents. We leverage this for high bit-rate entropy generation and random number generation (RNG), passing the NIST tests with rates up to 150 Gb/s, and observe a correlation between the correlation dimension and the number of passed NIST tests. The RNG shows consistent performance across a wide range of parameters. In contrast to other setups, our system does not require optical feedback or optical injection to generate chaos, making it simple, compact and robust.

Synchronization is the spontaneous alignment of the dynamics of weakly-coupled oscillators. In addition to temporal dynamics like periodic and chaotic oscillations, also the spatio-temporal dynamics of spatially-extended systems like wildlife populations can synchronize. We exploit here the intrinsic spatio-temporal complex dynamics of broad area lasers to demonstrate such synchronization at lab-scale. Broad-area vertical-cavity surface-emitting lasers (BA-VCSELs) exhibit chaos from the nonlinear coupling between laser modes with different spatial profiles and polarization. When coupling two BA-VCSELs, several synchronization and anti-synchronization regimes are observed, highlighting the complex interplay between oscillating modes with different frequencies and spatial patterns. The correlation coefficient varies between 0.2 and 0.9 depending on the dynamics and on the time scale under analysis. Besides its fundamental interest, our experiment with commercial devices marks the first step towards real-world spatial multiplexing in multiple user physical-layer secure communication based on chaos synchronization.

Reservoir computing (RC) is a machine learning (ML) model that has gained popularity in the recent decade due to its simplicity, versatility in solving temporal problems, and ease of implementation across various physical systems. This work explores the implementation of a photorefractive crystal as the reservoir in a reservoir computer. While previous studies have demonstrated the feasibility of using photorefractive materials for RC and other ML applications, a systematic investigation into the impact of the optical nonlinearity on the systems performance has yet to be conducted. To address this question, we develop a reservoir computer using a biased photorefractive crystal. By quantifying the system's optical nonlinearity and evaluating the performance of the reservoir computer, we reveal a correlation between these factors, providing new insights into optimizing photorefractive systems for machine learning tasks.

We theoretically analyze the nonlinear dynamics and routes to chaos in a multimode vertical cavity surface-emitting laser (MM-VCSEL) in free-running operation. Including higher order transverse modes (TMs) results in additional bifurcations at higher currents not found for single-mode VCSELs (SM-VCSELs). The resulting dynamics involve competition between modes with different transverse profiles and polarization and show good qualitative agreement with recent experiments.

Reservoir computing (RC) is a machine learning (ML) framework that has gained attention in recent years as the interest in alternative computing paradigms has grown. RC allows the utilization of physical systems to solve ML tasks. We demonstrate the use of the nonlinear photorefractive reservoir computer and perform tasks requiring both nonlinearity and memory, such as chaotic time series prediction. Changing the photorefractive response by adjusting the applied field and laser power controls the characteristics of the reservoir. Optimizing the characteristics of the reservoir for performing a 10-step Mackey–Glass (MG) time series prediction, we achieve a mean square error (MSE) of 5x10 −4 .

Broad-area edge-emitting semiconductor lasers exhibit multiple transverse modes whose nonlinear interaction via the gain medium results in spatio-temporal instabilities [1]. Hence, they are interesting testbeds for studying the dynamics of coupled oscillators. Our experiments demonstrate that groups of lasing modes of a commercial broad-area laser are spontaneously phase locked, while other modes are not locked [2]. The unexpected emergence of groups of synchronized modes coexisting with un synchronized ones is similar to chimera states in systems of coupled oscillators [3].

Neuromorphic computing using photonic systems has progressed significantly over recent years, in particular thanks to the development of innovative materials and systems that work as photonic neurons, photonic synapses and nonlinear optical transformations. We discuss here a proposal that makes use of a photorefractive crystal as a so-called reservoir computer (RC). Light is phase-encoded with optical input data and its transformation after passing the crystal is recorded and enables the training of the analog neural network weights. We systematically measure the nonlinearity of the resulting light-matter interaction and correlate that nonlinearity to the performance of the reservoir computer for different benchmark tasks. State-of-the-art performances are achieved for example for multi-step prediction of time-series generated by nonlinear systems.

This work presents a novel beam steering system combining a Risley prism and a variable magnification beam expander, enabling flexible, high-precision scanning across distances from a few meters to several kilometers, with consistent spatial resolution in the tens of centimeters and scan times in the hundreds of milliseconds. Unlike more complex solutions like fast steering mirrors or metasurfaces, the system uses just five lenses in a compact and cost-effective design. A key focus of this study is the positioning tolerance of the optical elements forming the beam expander. Detailed simulations and experiments were conducted to assess and optimize the sensitivity of each lens to displacement. These results are critical for ensuring precise alignment and managing production costs, making the system a strong candidate for industrial deployment in optical systems requiring versatile beam steering.

We experimentally report on the detection of chaos from a free-running commercial broad-area vertical-cavity surface-emitting laser (VCSEL) without the need for external perturbation such as optical feedback, injection, or current modulation. The evolution of nonlinear dynamics leading to chaotic behavior is studied, and the system’s complexity is characterized using chaos titration and correlation dimension. We link the occurrence of chaos with the complex interplay between the spatial laser mode competition and polarization dynamics.

This erratum corrects an error in [Opt. Express31, 8296 (2023)10.1364/OE.480388].

Broad-area semiconductor lasers are used in many high-power applications; however, their spatio-temporal dynamics are complex and intrinsically unstable due to the interaction between transverse lasing modes. Here a dynamical and ultrahigh-resolution spatio-spectral analysis of commercial broad-area lasers reveals multiplets of phase-locked first- and second-order transverse modes that are spontaneously created by the nonlinear dynamics of the laser. Phase locking between modes of different transverse order is confirmed by comparing the linewidths of the lasing modes with that of their beat note and by a direct measurement of their phase fluctuation correlations. The spontaneous phase locking is unexpected since the overall dynamics are unstable and the system lacks any intentional feature to induce locking. This partially synchronized dynamical state with groups of coexisting synchronized and unsynchronized laser modes is similar to chimera states found in networks of coupled oscillators, indicating that such states may exist in a wider range of systems than previously assumed. Nonlinearity-induced spontaneous phase locking of transverse modes is observed in a broad-area semiconductor laser.

Broad-area vertical-cavity surface-emitting lasers (BA-VCSELs) are multimode devices whose wide transverse section fosters the emergence of numerous transverse modes. Interactions between these modes generate complex dynamics, making these lasers particularly valuable for studying nonlinear behaviors in semiconductor lasers, with significant potential for applications in optical communication systems, signal processing, and advanced photonics [1].

In this work, we experimentally demonstrate the capacity of the photorefractive (PR) crystal to control the group velocity of light pulses, specifically at the telecommunication wavelength, by using the so-called beam fanning at room temperature. Significantly, we show for the first time that this method can effectively decelerate a modulated signal propagating through this material at 1310 nm. Furthermore, we illustrate that the performance of this slow light system can be adjusted by changing the intensity, duration, and angle of polarization of the input pulse. The results obtained through this technique can potentially improve the performance of specific components in telecommunication networks.

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.

The dynamics of a single-mode semiconductor laser induced by the optical injection of a frequency comb are analyzed through the lens of complexity. In particular, the focus is dynamics outside the injection-locking region. Permutation entropy (P.E.) and chaos bandwidth (C.BW.)are used to quantify complexity. Various numerically simulated system outputs across the frequency detuning range and for different injection strengths are considered. Numerically simulated outputs from a single-mode injection system in the absence of comb injection are compared to comment on the origin of the reported complexity. Furthermore, experimental outputs are used to confirm the findings. Despite the presence of periodic dynamics originating from the frequency comb, the presented system generates remarkably high complex outputs with P.E. up to 0.99 maintained over an extended period of observation and long timescales with C.BW. up to 25 GHz.

We experimentally explore a beam steering system implementing Risley prism and variable magnification beam expander. It adapts to scanning windows dimensions and distances, with a given spatial resolution, enabling scan in several hundreds milliseconds.

We analyse theoretically the nonlinear dynamics of a single-mode laser diode subjected to both optical injection and optical feedback. Detailed mappings of the laser dynamics reveal that, due to optical feedback (OF), the locking boundaries resulting from optical injection (OI) shift towards larger negative detunings and higher injection rates and display a periodic pattern of the injection locking boundaries. We demonstrate how feedback induces a cascade of quasiperiodic bifurcations associated with abrupt dynamic changes, hence altering the route to locking. A close inspection of the laser optical spectra for increasing feedback rate reveals the complex interplay between undamped relaxation oscillations and external cavity frequencies.