Coupled Semiconductor Lasers Research Articles

Spectral signatures of coexisting isolas and four-wave mixing under the effect of noise in photonic oscillators

The optical power spectrum is the prime observable to dissect, understand, and design the long- time behavior of small and large arrays of optically coupled semiconductor lasers. A long-standing issue has been identified within the literature of injection locking in photonic oscillators: first how the thickness of linewidth and the lineshape spectral envelope correlates with the deterministic evolution of the monochromatic injected laser oscillator and second how the presence of noise and the typically dense proximity in phase space of coexisting limit cycles of the coupled system are shaping and influencing the overall spectral behavior. In addition, we are critically interested in the regions where the basin of attraction has a fractal-like structure, still, the long-time orbits are P1 (period 1) and/or P3 (period 3) limit cycles. Numerically computed evidence shows that, when the coupled system lives in the regions of coexisting isolas and four-wave mixing (FWM) limit cycles, the overall optical power spectrum is deeply imprinted by a strong influence from the underlying noise sources. A particularly intriguing observation in this region of parameter space that we examine is that the isolas draw most of the trajectories on its phase space path.

Regulation of cluster synchronization in multilayer networks of delay coupled semiconductor lasers with the use of disjoint layer symmetry.

In real-world complex systems, heterogeneous components often interact in complex connection patterns and could be schematized by a formalism of multilayer network. In this work, the synchronization characteristics of multilayer network composed of semiconductor lasers (SLs) are investigated systematically. It is demonstrated that the interplay between different layers plays an important role on the synchronization patterns. We elucidate that the performance of cluster synchronization could be facilitated effectively with the introduction of disjoint layer symmetry into network topology. Intertwined stability of clusters from different layers could be decoupled into independent, and the parameter spaces for stable synchronization are extended significantly. The robustness of our proposed regulation scheme on operation parameters is numerically evaluated. Furthermore, the generality of presented theoretical results is validated in networks with more complex topology and multiple layers.

Tracking exceptional points above the lasing threshold

Recent studies on exceptional points (EPs) in non-Hermitian optical systems have revealed unique traits, including unidirectional invisibility, chiral mode switching and laser self-termination. In systems featuring gain/loss components, EPs are commonly accessed below the lasing threshold, i.e., in the linear regime. In this work, we experimentally demonstrate that EP singularities in coupled semiconductor nanolasers can be accessed above the lasing threshold, where they become branch points of a nonlinear dynamical system. Contrary to the common belief that unavoidable cavity detuning impedes the formation of EPs, here we demonstrate that such detuning is necessary for compensating the carrier-induced frequency shift, hence restoring the EP. Furthermore, we find that the pump imbalance at lasing EPs varies with the total pump power, enabling their continuous tracking. This work uncovers the unstable nature of EPs above laser threshold in coupled semiconductor lasers, offering promising opportunities for the realization of self-pulsing nanolaser devices and frequency combs.

Recognition of Noisy Digital Images Using the Asymmetric Coupling Semiconductor Chaotic Lasers Network

In this work, we construct a model of an asymmetrically coupled network of semiconductor chaotic lasers in order to recognize noisy digital images of digits 0–9, derived from different samples in the digital image sets 0–9 found within the MNIST dataset. Here, the lasers network consists of eight asymmetrically coupled semiconductor lasers. The chaotic lasers network is driven by the external inputs, which encode one noise digital image to be recognized. The outputs of the chaotic lasers network driven by a total of 40 samples from the digital image sets 0–9 are utilized as ten sets of reference signals. The output of the chaotic lasers network induced by one noisy digital image is used as a test signal. By judging the maximum of the correlations of the test signal with the ten sets of reference signals, all noisy digital images 0–9 can be recognized well under different noises. Moreover, we further explore the recognition rate for each noisy digital image under different noises and a fixed injection strength. It is found that all noisy digital images can be recognized well under a certain low injection strength. The recognition-rates of all noisy digital images can further decrease to a certain extent under higher noise and a fixed the injection strength. The injection strength has little influence on the recognition rate of one noise digital image target with lower noise. The recognition rate under higher noise maintains a higher value (more than 0.9) when the injection strength is smaller than a certain value, but for the larger injection strength, the recognition rate exhibits further decrease. The modeled chaotic lasers network can play the role of photonic accelerators for the recognition of the noisy digital images.

Theoretical and experimental characterization of non-Markovian anti-parity-time systems

Open systems with anti-parity-time ({{{{{{{mathcal{APT}}}}}}}}) or {{{{{{{mathcal{PT}}}}}}}} symmetry exhibit a rich phenomenology absent in their Hermitian counterparts. To date all model systems and their diverse realizations across classical and quantum platforms have been local in time, i.e., Markovian. Here we propose a non-Markovian system with anti-{{{{{{{mathcal{PT}}}}}}}}-symmetry where a single time-delay encodes the retention of memory, and experimentally demonstrate its consequences with two time-delay coupled semiconductor lasers. A transcendental characteristic equation with infinitely many eigenvalue pairs sets our model apart. We show that a sequence of amplifying-to-decaying dominant mode transitions is induced by the time delay in our minimal model. The signatures of these transitions quantitatively match results obtained from four, coupled, nonlinear rate equations for laser dynamics, and are experimentally observed as constant-width sideband oscillations in the laser intensity profiles. Our work introduces a paradigmatic non-Hermitian system with memory, paves the way for its realization in classical systems, and may apply to time-delayed feedback-control for quantum systems.

Method and system for simultaneously measuring six degrees of freedom motion errors of a rotary axis based on a semiconductor laser.

The rotary axis is the basis of rotational motion. The motion errors of a rotary axis have an extremely important impact on the accuracy of precision machining measuring equipment such as CNC machines, robot manipulators, and laser trackers. It is a difficult problem to realise the fast and precision simultaneous measurement of multi-degree-of-freedom motion errors of a rotary axis. Therefore, a novel method for the simultaneous measurement of six-degree-of-freedom motion errors of a rotary axis by a single-mode fiber coupled semiconductor laser is proposed in this paper. The corresponding system is developed, which has the advantages of high measurement efficiency, simple structure and low cost. A phase-solving method taking the advantages of both the eight-subdivision and the Cordic algorithm is proposed to solve the phase of interference signal, cannot only realize the high-resolution solving of the current signal phase but also quickly obtain high-precision interferometric results. A series of experiments were carried out on the developed system. An experimental system was built and a series of experiments were performed. The experimental results show that the standard deviation of stability for 1 hour of the six-degree-of-freedom measurement is 0.03 µm, 0.02 µm, 0.03 µm, 0.10 ' ' , 0.05 ' ' and 0.03 ' ' , respectively. The repeatability deviation of measuring a rotary axis is ±0.16 µm, ± 0.29 µm, ± 0.25 µm, ± 0.65 ' ' , ± 0.62 ' ' and ±13.42 ' ' , respectively. The maximum deviation of comparison with standard instruments is 0.46 µm, 1.00 µm, 0.49 µm, 1.06 ' ' , 1.53 ' ' and 0.74 ' ' , respectively. It provides a low-cost and high-precision measurement method for simultaneous measurement of six-degree-of-freedom motion errors of rotary axis of precision machining and measuring equipment.

High–Power 792 nm Fiber–Coupled Semiconductor Laser

The pumping of Tm-doped crystal or fiber by a 792 nm semiconductor laser is an important way to generate a mid-infrared laser, which is widely used in various fields. In this paper, a high–power 792 nm fiber–coupled semiconductor laser module was successfully fabricated with the output power of 232 W at a 10 A continuous current and the electro-optic conversion efficiency of 48.6%. The laser module is coupled with 24 chips into a fiber by spatial multiplexing and polarization combination technology. For a single emitting laser chip, the continuous wave (CW) output power and threshold current are 10.45 W at 10 A and 1.55 A, respectively. A polarization as high as 94% can also be realized, which is more suitable for laser spatial beam combining. The laser module was aged for more than 4000 h at 12 A and 25 °C without obvious power degradation.

Injection locking and coupling the emitters of large VCSEL arrays via diffraction in an external cavity.

Networks of semiconductor lasers are the foundation of numerous applications and fundamental investigations in nonlinear dynamics, material processing, lighting, and information processing. However, making the usually narrowband semiconductor lasers within the network interact requires both high spectral homogeneity and a fitting coupling concept. Here, we report how we use diffractive optics in an external cavity to experimentally couple vertical-cavity surface-emitting lasers (VCSELs) in a 5×5 array. Out of the 25 lasers, we succeed to spectrally align 22, all of which we lock simultaneously to an external drive laser. Furthermore, we show the considerable coupling interactions between the lasers of the array. This way, we present the largest network of optically coupled semiconductor lasers reported so far and the first detailed characterization of such a diffractively coupled system. Due to the high homogeneity of the lasers, the strong interaction between them, and the scalability of the coupling approach, our VCSEL network is a promising platform for experimental investigations of complex systems, and it has direct applications as a photonic neural network.

Hierarchical-dependent cluster synchronization in directed networks with semiconductor lasers.

Cluster synchronization in complex networks with mutually coupled semiconductor lasers (SLs) has recently been extensively studied. However, most of the previous works on cluster synchronization patterns have concentrated on undirected networks. Here, we numerically study the complete cluster synchronization patterns in directed networks composed of SLs, and demonstrate that the values of the SLs parameter and network parameter play a prominent role on the formation and stability of cluster synchronization patterns. Moreover, it is shown that there is a hierarchical dependency between the synchronization stability of different clusters in directed networks. The stability of one cluster can be affected by another cluster, but not vice versa. Without loss of generality, the results are validated in another SLs network with more complex topology.

Detections of the position-vectors of the multi targets located in a circular space based on an asymmetric coupling semiconductor lasers network.

We present a novel scheme for the detections of the position-vectors of the multi targets distributed in a circular space using multi channels of the probe chaotic waves emitted by the asymmetric coupling semiconductor lasers network (ACSLN), where these probe waves possess the attractive features of the time-space uncorrelation and wide bandwidth. Using these features, the accurate measurement for the position-vectors of the multi targets can be achieved by correlating the multi channels of the probe waves with their corresponding reference waves. The further research results show that the detections for the position-vectors of the multi targets possess very low relative errors that are no more than 0.22%. The ranging-resolutions for the multi targets located in a circular space can be achieved as high as 3 mm by optimizing some key parameters, such as injection current and injection strength. In addition, the ranging-resolutions exhibit excellent strong anti-noise performance even when the signal-to-noise ratio and relative noise intensity appear obvious enhancement. The detections for the position-vectors of the multi targets based on the ACSLN offers interesting perspectives for the potential applications in the driverless cars and the object tracking system with omnidirectional vision.

PT-symmetry in mutually coupled semiconductor lasers with a non-zero time delay

Existence of PT symmetric regime in a system of two semiconductor lasers coupled face to face is being reported. The coupling involves the field of one laser coupled to the field of the other with a time delay. We investigate the occurrence of PT symmetry and PT transition for non-zero, but small delay times. Eigen values are obtained theoretically for the field transformation matrix formulated using normalized Lang–Kobayashi rate equations. We show that for certain delay times, the system exhibits PT symmetry and a PT transition to broken PT symmetry as the detuning frequency and coupling strength are varied. A control on the coupling coefficient and frequency detuning between the lasers is shown to be an efficient mechanism towards fine control of the PT symmetry in coupled lasers.

Extreme events in two laterally-coupled semiconductor lasers.

Rogue waves (RWs) are extreme and rare waves that emerge unexpectedly in many natural systems and their formation mechanism and prediction have been extensively studied. Here, we numerically demonstrate the appearance of extreme events (EEs) for the first time, to the best of our knowledge, in the chaotic regimes of a two-element coupled semiconductor laser array. Based on coupled-mode theory, we characterize the occurrence of EEs by calculating the probability distribution, which confirms the RW-type feature of the intensity pulses, i.e., non-Gaussian distribution. Combining with the results of the 0-1 test for chaos, we confirm that EEs originate from deterministic nonlinearities in coupled semiconductor laser systems. We show that EEs can be predicted with a long anticipation time. Furthermore, simulation results manifest that the occurrence probability of EEs can be flexibly tuned by tailoring the coupling parameter space. With the help of two-dimension maps, the effects of key parameters, i.e., the waveguide structure and the pump level, on the formation of EEs are discussed systematically. This work provides a new platform for the research of EEs in a highly integrated structure and opens up a novel investigation field for coupled semiconductor laser arrays.

Generation of multiple low-correlation chaos signals using asymmetric coupling semiconductor lasers networks

We propose and numerically demonstrate a novel multiple delta-like autocorrelation chaos generation scheme in virtue of asymmetrically-coupled semiconductor lasers (ACSLs) networks. The properties of auto-correlation function (ACF), cross correlation, and effective bandwidth of the generated multiple chaos signals are systematically investigated in ACSLs networks with different topology and network sizes. The results show that not only delta-like ACF traces are obtained but also low cross correlations are observed in the chaotic signals outputted by ACSLs networks. Besides, the average effective bandwidth of generated multi-channel chaos can be greater than 20 GHz over a wide dynamic operation range. Moreover, the delta-like ACF, low correlation and wideband properties of multiple chaotic signals are robust to parameter mismatches between SLs. This work realizes wideband multi-channel chaos generation that simultaneously achieves delta-like ACF and low correlation, and is valuable for the applications in high-speed random bit generator, accurate multi-target, multi-angle radar detection, and ultrafast photonic decision making.

Optimizations of optical chaos in semiconductor lasers based on multiobjective genetic algorithms.

We investigated the frequency bandwidth, autocorrelation function, and complexity of chaotic temporal waveforms in unidirectionally coupled semiconductor lasers with time-delayed optical feedback. The effective bandwidth, peak value of autocorrelation function, and maximum Lyapunov exponent were simultaneously optimized by searching several control parameters of the laser systems based on multiobjective genetic algorithms. We found a conflicting relation between the effective bandwidth enhancement and the time-delay signature suppression, and a detailed relationship between the maximum Lyapunov exponent and the peak value of autocorrelation function.

Effects of High-${\rm{\beta }}$ on Phase-Locking Stability and Tunability in Laterally Coupled Lasers

Phase-locked laser arrays have been extensively investigated in terms of their stability and nonlinear dynamics. Specifically, enhancing the phase-locking stability allows laser arrays to generate high-power and steerable coherent optical beams for a plethora of applications, including remote sensing and optical communications. Compared to other coupling architectures, laterally coupled lasers are especially desirable since they allow for denser integration and simpler fabrication process. Here, we present the theoretical effects of varying the spontaneous emission factor <inline-formula><tex-math notation="LaTeX">$\beta $</tex-math></inline-formula>, an important parameter for micro- and nanoscale lasers, on the stability conditions of phase-locking for two laterally coupled semiconductor lasers. Through bifurcation analyses, we observe that increasing <inline-formula><tex-math notation="LaTeX">$\beta $</tex-math></inline-formula> contributes to the expanding of the in-phase stability region under all scenarios considered, including complex coupling coefficients, varying pump rates, and frequency detuning. Moreover, the effect is more pronounced for <inline-formula><tex-math notation="LaTeX">$\beta $</tex-math></inline-formula> approaching 1, thus underlining the significant advantages of implementing nanolasers with intrinsically high <inline-formula><tex-math notation="LaTeX">$\beta $</tex-math></inline-formula> in phase-locked laser arrays for high-power generation. We also show that the steady-state phase differences can be widely tuned &#x2013; up to <inline-formula><tex-math notation="LaTeX">$\pi $</tex-math></inline-formula> radians &#x2013; by asymmetrically pumping high-<inline-formula><tex-math notation="LaTeX">$\beta $</tex-math></inline-formula> coupled lasers. This demonstrates the potential of high-<inline-formula><tex-math notation="LaTeX">$\beta $</tex-math></inline-formula> nanolasers in building next-generation optical phased arrays requiring wide scanning angles with ultra-high resolution.

SIGNAL PROCESSING AND CYBERSECURITY IN SOME CHAOTIC OPTICAL COMMUNICTAION SYSTEMS

A chaos –geometric approach to investigation of complex chaotic dynamical systems is applied to an analysis, modeling and processing the time series of emission intensities of chaotic transmitter/receiver systems (two unidirectionally coupled semiconductor laser systems in the all-optical scheme) suited for encoding at rates of GBit/s. the problem of a signal processing is directly connected with the corresponding cybersecurity in some optical chaos communictaion systems. The estimated values for the dynamic and topologic invariants such as the correlation and Kaplan-York dimensions, Lyapunov indicators, Kolmogorov entropy etc for investigated chaotic signal time series of two unidirectionally coupled semiconductor laser systems in the all-optical scheme.

Multi-target ranging using an optical reservoir computing approach in the laterally coupled semiconductor lasers with self-feedback

We utilize three parallel reservoir computers using semiconductor lasers with optical feedback and light injection to model radar probe signals with delays. Three radar probe signals are generated by driving lasers constructed by a three-element laser array with self-feedback. The response lasers are implemented also by a three-element lase array with both delay-time feedback and optical injection, which are utilized as nonlinear nodes to realize the reservoirs. We show that each delayed radar probe signal can be predicted well and to synchronize with its corresponding trained reservoir, even when parameter mismatches exist between the response laser array and the driving laser array. Based on this, the three synchronous probe signals are utilized for ranging to three targets, respectively, using Hilbert transform. It is demonstrated that the relative errors for ranging can be very small and less than 0.6%. Our findings show that optical reservoir computing provides an effective way for applications of target ranging.

Chaos synchronization based on cluster fusion in asymmetric coupling semiconductor lasers networks.

A novel cluster fusion method is proposed, based on which chaos synchronization in asymmetric coupling semiconductor lasers (ACSLs) networks is systematically demonstrated. Take the cluster fusion of a mutually-coupled network composed of 7 semiconductor lasers (SLs) for instance, the characteristics of chaos synchronization as well as the influences of coupling strength, bias current, and mismatches of intrinsic parameters and injection strength on the quality of chaos synchronization in hybrid clusters composed of ACSLs are thoroughly investigated. The results show that by using cluster fusion, the ACSLs which originally belong to different clusters can form three types of new hybrid clusters, namely, trivial-hybrid cluster, trivial-nontrivial-hybrid cluster, and nontrivial-hybrid cluster. Compared with the low-correlation inter-cluster ACSLs of original SLs network, high-quality chaos synchronization is achieved in three types of newly generated hybrid clusters over a wide parameter range. Moreover, the cluster fusion and synchronization of side-SLs clusters of star-type SLs networks are also verified, which indicate the universality of the proposed method. This work provides a new way to realize the chaos synchronization among ACSLs of different clusters.

Predictive learning of multi-channel isochronal chaotic synchronization by utilizing parallel optical reservoir computers based on three laterally coupled semiconductor lasers with delay-time feedback.

In this work, we utilize three parallel optical reservoir computers to model three optical dynamic systems, respectively. Here, the three laser-elements in the response laser array with both delay-time feedback and optical injection are utilized as nonlinear nodes to realize three optical chaotic reservoir computers (RCs). The nonlinear dynamics of three laser-elements in the driving laser array are predictively learned by these three parallel RCs. We show that these three parallel reservoir computers can reproduce the nonlinear dynamics of the three laser-elements in the driving laser array with self-feedback. Very small training errors for their predictions can be realized by the optimization of two key parameters such as the delay-time and the interval of the virtual nodes. Moreover, these three parallel RCs to be trained will well synchronize with three chaotic laser-elements in the driving laser array, respectively, even when there are some parameter mismatches between the response laser array and the driving laser array. Our findings show that optical reservoir computing approach possibly provide a successful path for the realization of the high-quality chaotic synchronization between the driving laser and the response laser when their rate-equations imperfectly match each other.

Laser network decision making by lag synchronization of chaos in a ring configuration.

Photonic technologies are promising for solving complex tasks in artificial intelligence. In this paper, we numerically investigate decision making for solving the multi-armed bandit problem using lag synchronization of chaos in a ring laser-network configuration. We construct a laser network consisting of unidirectionally coupled semiconductor lasers, whereby spontaneous exchange of the leader-laggard relationship in the lag synchronization of chaos is observed. We succeed in solving the multi-armed bandit problems with three slot machines using lag synchronization of chaos by controlling the coupling strengths among the three lasers. Furthermore, we investigate the scalability of the proposed decision-making principle by increasing the number of slot machines and lasers. This study suggests a new direction in laser network-based decision making for future photonic intelligent functions.