Optical injection effects in electrically pumped semiconductor nano-laser arrays.

A theoretical analysis is performed on the response of electrically pumped nano-laser arrays to external optical injection. The response to both continuous wave and modulated optical injection is explored. Continuous wave injection is shown to excite several varieties of dynamical behaviour in the array elements including regular dynamics and quasi-periodic behaviour. The strength of the optical injection, the frequency detuning between the injected light and the target laser, and the magnitude of the Purcell spontaneous emission enhancement factor are shown to markedly affect the dynamics. When subject to modulated optical injection, the effects of frequency detuning and optical injection strength are the focus of attention. It is shown that the elements of the array subject to modulated optical injection exhibit oscillatory behaviour over broad regimes determined by the optical injection strength and the frequency detuning.

Scalable parallel ultrafast optical random bit generation based on a single chaotic microcomb.

Random bit generators are critical for information security, cryptography, stochastic modeling, and simulations. Speed and scalability are key challenges faced by current physical random bit generation. Herein, we propose a massively parallel scheme for ultrafast random bit generation towards rates of order 100 terabit per second based on a single micro-ring resonator. A modulation-instability-driven chaotic comb in a micro-ring resonator enables the simultaneous generation of hundreds of independent and unbiased random bit streams. A proof-of-concept experiment demonstrates that using our method, random bit streams beyond 2 terabit per second can be successfully generated with only 7 comb lines. This bit rate can be easily enhanced by further increasing the number of comb lines used. Our approach provides a chip-scale solution to random bit generation for secure communication and high-performance computation, and offers superhigh speed and large scalability.

Forecasting the chaotic dynamics of external cavity semiconductor lasers.

Chaotic time series prediction has been paid intense attention in recent years due to its important applications. Herein, we present a single-node photonic reservoir computing approach to forecasting the chaotic behavior of external cavity semiconductor lasers using only observed data. In the reservoir, we employ a semiconductor laser with delay as the sole nonlinear physical node. By investigating the effect of the reservoir meta-parameters on the prediction performance, we numerically demonstrate that there exists an optimal meta-parameter space for forecasting optical-feedback-induced chaos. Simulation results demonstrate that using our method, the upcoming chaotic time series can be continuously predicted for a time period in excess of 2 ns with a normalized mean squared error lower than 0.1. This proposed method only utilizes simple nonlinear semiconductor lasers and thus offers a hardware-friendly approach for complex chaos prediction. In addition, this work may provide a roadmap for the meta-parameter selection of a delay-based photonic reservoir to obtain optimal prediction performance.

Leader-laggard synchronization of polarization chaos in mutually coupled free-running VCSELs.

We systematically study the leader-laggard synchronization of polarization chaos in mutually coupled free-running vertical cavity surface emitting semiconductor lasers in two cases of parallel and orthogonal injection. Specifically, we quantitatively investigate the effect of critical external parameter mismatch such as the coupling intensity and frequency detuning on the leader-laggard relationship utilizing the cross-correlation function. When the difference between two main cross-correlation peak values exceeds 0.1, the leader-laggard relationship can be viewed to be stable. Our results demonstrate that compared with the coupling strength, the frequency detuning is the dominant factor in determining the stability of the leader-laggard relationship. The exchange of the leader-laggard role occurs within a frequency detuning region from -5 GHz to 5 GHz for both parallel and orthogonal injection. Once the leader-laggard relationship is stable, the difference between the two cross-correlation values can reach 0.242 for negative frequency detuning, but the corresponding value is only 0.146 under positive frequency detuning.

Time-delay signature suppression in delayed-feedback semiconductor lasers as a paradigm for feedback control in complex physiological networks.

Physiological networks, as observed in the human organism, involve multi-component systems with feedback loops that contribute to self-regulation. Physiological phenomena accompanied by time-delay effects may lead to oscillatory and even chaotic dynamics in their behaviors. Analogous dynamics are found in semiconductor lasers subjected to delayed optical feedback, where the dynamics typically include a time-delay signature. In many applications of semiconductor lasers, the suppression of the time-delay signature is essential, and hence several approaches have been adopted for that purpose. In this paper, experimental results are presented wherein photonic filters utilized in order to suppress time-delay signatures in semiconductor lasers subjected to delayed optical feedback effects. Two types of semiconductor lasers are used: discrete-mode semiconductor lasers and vertical-cavity surface-emitting lasers (VCSELs). It is shown that with the use of photonic filters, a complete suppression of the time-delay signature may be affected in discrete-mode semiconductor lasers, but a remnant of the signature persists in VCSELs. These results contribute to the broader understanding of time-delay effects in complex systems. The exploration of photonic filters as a means to suppress time-delay signatures opens avenues for potential applications in diverse fields, extending the interdisciplinary nature of this study.

Image recognition based on optical reservoir computing.

We propose an image recognition approach using a single physical node based optical reservoir computing. Specifically, an optically injected semiconductor laser with self-delayed feedback is used as the reservoir. We perform a handwritten-digit recognition task by greatly increasing the number of virtual nodes in delayed feedback using outputs from multiple delay times. Final simulation results confirm that the recognition accuracy can reach 99% after systematically optimizing the reservoir hyperparameters. Due to its simple architecture, this scheme may provide a resource-efficient alternative approach to image recognition.

Synchronization of polarization chaos in mutually coupled free-running VCSELs.

We numerically demonstrate and analyze polarization chaos synchronization between two free-running vertical cavity surface emitting semiconductor lasers (VCSELs) in the mutual coupling configuration under two scenarios: parallel injection and orthogonal injection. Specifically, we investigate the effect of external parameters (the bias current, frequency detuning and coupling coefficient) and internal parameters (the linewidth enhancement factor, spin-flip relaxation rate, field decay rate, carrier decay rate, birefringence and dichroism) on the synchronization quality. Finally simulation results confirm that in the parallel injection, chaotic synchronization can reach a cross-correlation coefficient of 0.99 within a range of parameter mismatch ±12%. On the other hand, the chaos synchronization for orthogonal injection only reaches a cross-correlation coefficient of 0.95 within a range of parameter mismatch ±3%.

Observation of flat chaos generation using an optical feedback multi-mode laser with a band-pass filter.

We demonstrate experimentally that flat and broadband chaotic signals can be easily generated by combining a multi-mode laser diode subject to optical feedback with a band-pass filter. Measurements are made of the RF spectra of multi-mode and single-mode outputs from an external cavity Fabry-Perot (FP) semiconductor laser before and after the filtering procedure. In this way it is found that in the chaos regime the low-frequency energy of the single-mode output is enhanced by about 25 dB comparing with that of the multi-mode output. Moreover, the associated 3-dB chaos bandwidth can reach around 6 GHz for the single mode case. Numerical demonstrations show mode competition is the physical origin of the low-frequency enhancement in the single-mode chaotic outputs.

Parallel optical random bit generator.

We present an optical approach for high-speed parallel random bit generation based on stochastic pulse-to-pulse fluctuation in the supercontinuum (SC). Through spectrally demultiplexing the SC pulse sequence into different wavelength channels, we simultaneously extract multiple independent fast random bit streams from each SC pulse subsequence via associated comparators in parallel. Proof-of-concept experiments demonstrate that using our method, four 10 Gb/s random bit streams are obtained from a SC pulse source with verified randomness. Moreover, this method also provides a promising strategy to fabricate ultrafast random bit generators with Tb/s throughput capacity just by increasing additional wavelength channels.

Analysis of high-frequency oscillations in mutually-coupled nano-lasers.

The dynamics of mutually coupled nano-lasers has been analyzed using rate equations which include the Purcell cavity-enhanced spontaneous emission factor F and the spontaneous emission coupling factor ß. It is shown that in the mutually-coupled system, small-amplitude oscillations with frequencies of order 100 GHz are generated and are maintained with remarkable stability. The appearance of such high-frequency oscillations is associated with the effective reduction of the carrier lifetime for larger values of the Purcell factor, F, and spontaneous coupling factor, ß. In mutually-coupled nano-lasers the oscillation frequency changes linearly with the frequency detuning between the lasers. For non-identical bias currents, the oscillation frequency of mutually-coupled nano-lasers also increases with bias current. The stability of the oscillations which appear in mutually coupled nano-lasers offers opportunities for their practical applications and notably in photonic integrated circuits.

Real-time online photonic random number generation.

We present a real-time scheme for ultrafast random number (RN) extraction from a broadband photonic entropy source. Ultralow jitter mode-locked pulses are used to sample the stochastic intensity fluctuations of the entropy source in the optical domain. A discrete self-delay comparison technology is exploited to quantize the sampled pulses into continuous RN streams directly. This scheme is bias free, eliminates the electronic jitter bottleneck confronted by currently available physical RN generators, and has no need for threshold tuning and post-processing. To demonstrate its feasibility, we perform a proof-of-principle experiment using an optically injected chaotic laser diode. RN streams at up to 7 Gb/s with verified randomness were thereby successfully extracted in real time. With the provision of a photonic entropy source with sufficient bandwidth, the present approach is expected to provide RN generation rates of several tens of gigabits per second.

Accessing cancer services in North West England: the Chinese population.

Relatively few Chinese patients access tertiary cancer services in North West England. We investigated the reasons behind this using a culturally sensitive questionnaire. The questionnaire, completed by 214 Chinese people in English, Cantonese or Mandarin, evaluated the Chinese population's access and satisfaction with primary care, understanding of cancer and awareness of local cancer services. Ninety-five per cent of respondents were registered with a general practitioner (GP) and 75% had accessed primary care in the last year. Satisfaction with GP consultations was high but a third of respondents reported a lack of confidence in local National Health Service (NHS) services. Only 57% of eligible women had attended cervical screening programmes. The overall understanding of the causes and treatment of cancer and cancer services in the North West was poor. Despite registration with primary healthcare, the Chinese population under-utilise cancer prevention programmes and tertiary cancer services because of a lack of awareness and understanding of cancer services in the North West. A significant proportion of the population is dissatisfied with the perceived slow service and lack confidence in services, with 41% considering using healthcare abroad. These data highlight the critical need to engage with, educate and support the Chinese population if they are to access NHS cancer services.

Thermal effects and dynamical hysteresis in the turn-on and turn-off of vertical-cavity surface-emitting lasers.

Thermal effects and dynamical hysteresis in VCSELs under dc modulation have been experimentally studied. The results show that the VCSEL turn-on and turn-off currents can display both positive hysteresis and negative hysteresis, depending on the current modulation frequency and on the substrate temperature. Numerical simulations of semiconductor laser rate equations, extended to take into account thermal effects, show a good agreement with the observations.

Nonlinear dynamics of semiconductor lasers with feedback and modulation.

The nonlinear dynamics of two semiconductor laser systems: (i) with optical feedback, and (ii) with optical feedback and direct current modulation are evaluated from multi-GHz-bandwidth output power time-series. Animations of compilations of the RF spectrum (from the FFT of the time-series) as a function of optical feedback level, injection current and modulation signal strength is demonstrated as a new tool to give insight into the dynamics. The results are contrasted with prior art and new observations include fine structure in the RF spectrum at low levels of optical feedback and non-stationary switching between periodic and chaotic dynamics for some sets of laser system parameters. Correlation dimension analysis successfully identifies periodic dynamics but most of the dynamical states are too complex to be extracted using standard algorithms.

Chaos synchronization regimes in multiple-time-delay semiconductor lasers.

This paper provides a report of chaos synchronization regimes which may be accessed in both unidirectionally and bidirectionally coupled multiple-time-delay semiconductor lasers. We demonstrate that in bidirectionally coupled multiple-time-delay lasers additional feedback can considerably enhance synchronization quality.

Enhanced chaos synchronization in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers with polarization-preserved injection.

We experimentally study chaos synchronization in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers (VCSELs) with polarization-preserved and polarization-selected optical injection. The measurements show, in agreement with theoretical predictions, that the maximum cross coefficient of 0.884 obtained with polarization-preserved optical injection is significantly higher than the maximum cross coefficient of 0.724 obtained with polarization-selected optical injection.

Experimental study of polarization switching of vertical-cavity surface-emitting lasers as a dynamical bifurcation.

We study the role of the bias current sweep rate in measurements of polarization switching (PS) of vertical-cavity surface-emitting lasers (VCSELs). We show that the polarization-resolved L-I (light-intensity) curve depends on the current sweep rate. As the current sweep rate increases, the PS occurs at higher bias currents for upward scans and at lower bias currents for downward scans. We also show that the delay of the dynamical bifurcation follows a power law relationship with the frequency of the ramp, in good agreement with recent theoretical predictions.

Correlation dimension signature of wideband chaos synchronization of semiconductor lasers.

Chaos data analysis has been performed on the chaotic output power time series data from a synchronized transmitter-receiver pair of semiconductor lasers. The system uses an asymmetric, bidirectional coupling configuration between the master (transmitter), which is a laser diode with optical feedback, and a stand-alone slave semiconductor laser. The correlation dimension of the chaotic time series has a minimum value of 4, which was obtained from high-bandwidth measurements. The correlation dimensions for both the master and the synchronized slave are identical when the cross-correlation coefficient of the synchronized chaos is above 0.9. These results establish correlation dimension analysis as an effective tool for the determination of the quality of wideband chaos synchronization.

Chaos-based communications at high bit rates using commercial fibre-optic links.

Chaotic signals have been proposed as broadband information carriers with the potential of providing a high level of robustness and privacy in data transmission. Laboratory demonstrations of chaos-based optical communications have already shown the potential of this technology, but a field experiment using commercial optical networks has not been undertaken so far. Here we demonstrate high-speed long-distance communication based on chaos synchronization over a commercial fibre-optic channel. An optical carrier wave generated by a chaotic laser is used to encode a message for transmission over 120 km of optical fibre in the metropolitan area network of Athens, Greece. The message is decoded using an appropriate second laser which, by synchronizing with the chaotic carrier, allows for the separation of the carrier and the message. Transmission rates in the gigabit per second range are achieved, with corresponding bit-error rates below 10(-7). The system uses matched pairs of semiconductor lasers as chaotic emitters and receivers, and off-the-shelf fibre-optic telecommunication components. Our results show that information can be transmitted at high bit rates using deterministic chaos in a manner that is robust to perturbations and channel disturbances unavoidable under real-world conditions.

Generalized synchronization in time-delayed systems.

We investigate the generalized synchronization between two unidirectionally linearly and nonlinearly coupled chaotic nonidentical Ikeda models and find existence conditions of the generalized synchronization. Also we study the chaos synchronization between nonidentical Ikeda models with variable feedback-delay times and find the existence and sufficient stability conditions for the retarded synchronization manifold with the coupling-delay lag time. Generalization of the approach to the wide class of nonlinear chaotic systems is also presented.