Optoelectronic Feedback Research Articles

Resonant properties of the memory capacity of a laser-based reservoir computer with filtered optoelectronic feedback.

We provide a comprehensive analysis of the resonant properties of the memory capacity of a reservoir computer based on a semiconductor laser subjected to time-delayed filtered optoelectronic feedback. Our analysis reveals first how the memory capacity decreases sharply when the input-data clock cycle is slightly time-shifted from the time delay or its multiples. We attribute this effect to the inertial properties of the laser. We also report on the damping of the memory-capacity drop at resonance with a decrease of the virtual-node density and its broadening with the filtering properties of the optoelectronic feedback. These results are interpretated using the eigenspectrum of the reservoir obtained from a linear stability analysis. Then, we unveil an invariance in the minimum value of the memory capacity at resonance with respect to a variation of the number of nodes if the number is big enough and quantify how the filtering properties impact the system memory in and out of resonance.

Stochastic dynamics of a semiconductor laser with delayed optoelectronic feedback and noise

Semiconductor lasers(SLs), versatile tools in communication, medicine, and scientific research, demand close examination of their dynamic behavior. With their unique geometric forms and diminutive sizes, these lasers possess a heightened sensitivity to noise. In this paper, we delve into time-delay semiconductor laser systems, noise included, honing in on time-delays’ effects on noisy laser equations. Carrier density (N) and laser intensity (I) constitute the core parameters that define the performance of these lasers, and we scrutinize their dynamic trajectories. A cutting-edge method fusing stochastic center manifold theory with the stochastic averaging method enables us to probe the stochastic dynamical attributes of semiconductor laser equations. We uncover that the time-delay parameter (τ 1) produces varied consequences on the laser system’s stability under both positive and negative optical feedback conditions. The negative feedback typically bolsters laser performance, fostering increased stability, whereas the positive counterpart could incite instability. By deftly managing the time-delay parameter, one can fine-tune the dynamic performance of semiconductor lasers, mitigating output power fluctuations and tightening linewidths, thereby augmenting stability and spectral purity. Moreover, in the realm of positive optical feedback scenarios, adroitly modifying the time-delay parameter can quell instability to a degree, paving the way for a novel regulatory approach to optimize laser performance. This lays the groundwork for further enhancement of semiconductor laser performance, as well as curbing the detrimental effects of noise on their operation.

Low-frequency regular pulse and intermittent oscillation in a mid-infrared interband cascade laser with optoelectronic feedback.

In this work, we experimentally investigate the nonlinear dynamics of a mid-infrared interband cascade laser (ICL) subject to optoelectronic feedback (OEF) through inspecting the time series and power spectrum of the laser output. The results show that, within the range of feedback strength limited by the experiment condition, the ICL sequentially presents stable state, continuously periodical oscillation (CPO), low-frequency regular pulse (LF-RP) and intermittent oscillation state with the increase of feedback strength. For the LF-RP state, the peak-to-peak value and the oscillation period increase with the increase of feedback strength. For the intermittent oscillation state, the time series is composed of the laminar region and burst region appeared alternately, and the average value and standard deviation for the duration of burst region gradually decrease with the increase of feedback strength.

Nonlinear quantum dot light emitting diode dynamics and synchronization with optoelectronic feedback

We studies a three-variable dimensionless model for a quantum dot light emitting diode (QD-LED) subject to optoelectronic feedback (OEFB). In dependence of the feedback strength and delay-time we analyze complex bifurcation scenarios for the intensity of the emitted light as well as time series, fast Fourier translate (FFT) and phase plane of all dynamic variables in order to elucidate the dynamics of the light emitting diode. The chaotic dynamic is completely determined by both the variation of the OEFB strength and delay-time of the QD-LED, as evidenced by bifurcation diagram. Our results show that small delay time lead to repeat periodicity of the light emitting towards OEFB. Furthermore, we study chaos synchronization of two QD-LED which are coupled via a unidirectional and bidirectional coupling system. When periodic systems are non-identical, both unidirectional and bidirectional systems depending on the coupling strength parameter the system exhibits completely synchronization. Residual chaos, the mean coherence and entropy are discussed as well.

Sub-Hz Closed-Loop Electro-Optomechanical Oscillator with Gallium Phosphide Photonic Crystal Integrated on SoI Circuitry.

We report on a new approach of a low phase noise electro-optomechanical oscillator directly working in the GHz frequency range. The developed nanoscale oscillator is a one-dimensional photonic crystal made of gallium phosphide (GaP), heterogeneously integrated on silicon-on-insulator circuitry. Based on the strong interaction between the optical mode at the telecommunication wavelength and the mechanical mode in GHz, ultra-pure mechanical oscillations are enabled and directly imprinted on an optical carrier. Further stabilization is achieved with a delayed optoelectronic feedback loop using integrated electro-mechanical self-injection. We achieve a short-term stability of 0.7 Hz linewidth and a long-term stability with an Allan deviation below 10-7 Hz/Hz at 10 s averaging time, which represents an important step toward fully integrated optomechanical oscillators. Integrability and the low phase noise of this oscillator address some of the most important needs of optoelectronic oscillators and pave the way toward on-chip integrated microwave oscillators for microwave applications such as RADARs.

A novel secure communication system using optoelectronic feedback in semiconductor laser

A novel secure communication system using optoelectronic feedback in semiconductor laser

Key Space Enhancement of Chaos Communication Using Semiconductor Lasers with Spectrum-Programmable Optoelectronic Feedback

We propose a scheme for key-space-enhanced chaos secure communication using semiconductor lasers with spectrum-programmable optoelectronic feedback. This feedback consists of multiple parallel optoelectronic feedback loops composed of bandpass filters and radio-frequency amplifiers. The centre frequencies of the filters and gain coefficients of the amplifiers increase the key space. We use 12 parallel filtered feedback loops to analyse the effects of parameter mismatch on the synchronization quality. The simulation result indicates that the key space reaches approximately 2100 at a data rate of 10 Gbit/s, and it can be further enhanced by increasing the number of feedback loops. These results suggest an alternative approach for security-enhanced optical chaos communication.

Enhanced optoelectronic reservoir computation using semiconductor laser with double delay feedbacks.

We numerically explored the enhanced performance and physical mechanism of semiconductor laser (SL) based reservoir computation (RC) with double optoelectronic feedback (DOEF). One-step and multistep Santa Fe time series predictions were used as standard test benchmarks in this work. We found that in the optimized parameter region the normalized mean square error (NMSE) of an SL-based RC under DOEF is smaller than an SL-based RC with single optoelectronic feedback (SOEF). In addition, the performance improvement is more obvious for multistep prediction, which is particularly suitable for more complex tasks that requires a higher memory capability (MC). The enriched node states (optical intensity of the virtual nodes for each sample) and the enhanced MC of the proposed DOEF were verified by a comparison to SOEF under the optimized feedback strength. The influence of the feedback strength and the delay difference on the NMSE and the MC was also investigated. Our study should be helpful in the design of a high-performance optoelectronic RC based on an SL.

Impact of filtering on photonic time-delay reservoir computing.

We analyze the modification of the computational properties of a time-delay photonic reservoir computer with a change in its feedback bandwidth. For a reservoir computing configuration based on a semiconductor laser subject to filtered optoelectronic feedback, we demonstrate that bandwidth selection can lead to a flat-topped eigenvalue spectrum for which a large number of system frequencies are weakly damped as a result of the attenuation of modulational instability by feedback filtering. This spectral configuration allows for the optimization of the reservoir in terms of its memory capacity, while its computational ability appears to be only weakly affected by the characteristics of the filter.

Doublet structure in the optical spectrum of a semiconductor laser with optoelectronic feedback in a square-wave regime

We observe an optical spectrum consisting of a doublet in the output of a semiconductor laser diode with optoelectronic feedback in a dynamical regime in which a self-sustained square-wave modulation is observed, depending on injection current and feedback strength. The doublet frequency splitting is strongly correlated with the duty cycle of the square wave; both parameters as well as the relative magnitude of the peaks are observed to vary with the feedback level. A rate equation model reproduces the spectral doublets. The appearance of the doublet is attributed to active medium gain saturation and refractive index dependence on the carrier density.

Simultaneous modulation format identification and OSNR monitoring based on optoelectronic reservoir computing.

An approach for simultaneous modulation format identification (MFI) and optical signal-to-noise ratio (OSNR) monitoring in digital coherent optical communications is proposed based on optoelectronic reservoir computing (RC) and the signal's amplitude histograms (AHs) obtained after the adaptive post-equalization. The optoelectronic RC is implemented using a Mach-Zehnder modulator and optoelectronic delay feedback loop. We investigate the performance of the proposed model with the number of symbols, bins of AHs and the hyperparameters of optoelectronic RC. The results show that 100% MFI accuracy can be achieved simultaneously with accurate OSNR estimation for different modulation formats under study. The lowest achievable OSNR estimation mean absolute errors for the dual-polarization (DP)-quadrature phase-shift keying signal, the DP-16-ary quadrature amplitude modulation (16QAM) signal, and the DP-64QAM signal are 0.2 dB, 0.32 dB and 0.53 dB, respectively. The robustness of the proposed scheme is also evaluated when the optoelectronic RC is in presence of additive white Gaussian noises. Then, a proof of concept experiment is demonstrated to further verify our proposed method. The proposed approach offers a potential solution for next-generation intelligent optical performance monitoring in the physical layer.

INFLUENCES OF THE GAIN COEFFICIENT ON THE NONLINEAR OSCILLATOR’S DYNAMICAL REGIMES OF MACH-ZEHNDER MODULATOR MZM WITH OPTOELECTRONIC FEEDBACK

In this research we have modeled the Mach-Zehnder Modulator MZM with optoelectronic feedback OEF as optoelectronic oscillator OEO. The model is based on the Integro-Differential equation, which includes nonlinear effects from MZM device with time delay feedback arise from optoelectronic feedback OEF. Numerical simulation of our OEO model demonstrated wide regimes of complex oscillations, ranged from period one, period doubling, mixed mode, quasi-period and chaotic oscillations, that is with increasing the value of the linear gain coefficient. This effect was verified by the bifurcation diagram of maxima values of RF-voltages versus control parameter which in this case is the linear gain coefficient value, which depicted the route to chaos of OEO system. Keywords: Optoelectronic Feedback, Optoelectronic Oscillator, Chaos Control

Characteristic Study on Parallel Reservoir Computation Based on VCSEL Dynamics With Optoelectronic Feedback

We proposed a new reservoir computation (RC) structure using polarization dynamics of vertical cavity surface emitting lasers (VCSELs) with optoelectronic feedback. Santa-Fe time-series prediction and nonlinear channel equalization were used to evaluate its parallel processing capability. We numerically discussed the effects of feedback strength, injection strength, frequency detuning, injection current and scaling factors on the RC performance of the system. The results show that, the operation range of negative feedback is larger than that of positive feedback; under appropriate feedback and lager injection strengths, good RC performance can be achieved for a wider injection current; with continuous variation of feedback strength from negative to positive values, the optimized location for frequency detuning moves from positive to negative values. We also evaluated the processing rate of proposed RC structure. The related study is helpful for the design and optimization of VCSEL-based RC under optoelectronic feedback.

WDM-VLLC and White-Lighting Ring Networks With Optical Add-Drop Multiplexing Scheme

A wavelength-division-multiplexing (WDM)-visible laser light communication (VLLC) and white-lighting ring network with a 150-Gbit/s accumulative transmission rate at central station (CS), a 50-Gbit/s transmission rate at optical node, and a 604-lux white-lighting at CS is successfully demonstrated. Red, green, and blue laser diodes employing two-stage injection locking and optoelectronic feedback techniques are utilized to afford the dual functions of high-speed VLLC links and white-light illumination at reading/writing-level. By deploying optical add-drop multiplexing scheme, this newly-built WDM-VLLC and white-lighting ring network is promising since it allows a point-to-multipoint link and a two-way operation in free-space transmission. Impressively low bit error rate of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−9</sup> , clear PAM4 eye diagrams, and qualified white-lighting for reading and writing are achieved through 7.5 m/9 m/10.5 m/12 m VLLC link with 5 m plastic optical fiber transmission. Such constructed WDM-VLLC and white-lighting ring network shows a potential one for the evolution of high-speed VLLC with white-lighting for reading/writing.

Chaotic optical communications at 56 Gbit/s over 100-km fiber transmission based on a chaos generation model driven by long short-term memory networks.

Chaotic optical communication technology is considered as an effective secure communication technology, which can protect information from a physical layer and is compatible with the existing optical networks. At present, to realize long-distance chaos synchronization is still a very difficult problem, mainly because well-matched hardware cannot always be guaranteed between the transmitter and receiver. In this Letter, we introduce long short-term memory (LSTM) networks to learn a nonlinear dynamics model of an opto-electronic feedback loop, and then apply the trained deep learning model to generate a chaotic waveform for encryption and decryption at the transmitter and receiver. Furthermore, to improve the security, we establish a deep learning model pool which consists of different gain trained models and different delay trained models, and use a digital signal to drive chaos synchronization between the receiver and transmitter. The proposed scheme is experimentally verified in chaotic-encrypted 56-Gbit/s PAM-4 systems, and a decrypted performance below 7%FEC threshold (BER = 3.8×10-3) can be achieved over a 100-km fiber transmission.

Widely tunable frequency-doubling optoelectronic oscillator using a polarization modulator and a phase-shifted fiber Bragg grating

A frequency-doubling optoelectronic oscillator with wideband frequency tunability implemented using a polarization modulator (PolM) and a phase-shifted fiber Bragg grating (PS-FBG) is proposed and experimentally demonstrated. In the proposed structure, the output from the PolM is divided into two branches by an optical coupler. In the lower branch, an optoelectronic feedback loop is formed in which a tunable microwave photonic filter (MPF) is constructed by the joint operation of the PolM, the PS-FBG, a tunable laser source (TLS), a polarization controller (PC), and a polarizer, the MPF serves as an oscillation mode selector that its central frequency is a function of the frequency difference between the TLS and the notch of the PS-FBG. In the upper branch, an equivalent Mach–Zehnder modulator (MZM) is performed by the joint use of the PolM, a second PC, and a second polarizer, the second PC is adjusted to let the bias point of the MZM located at the minimum transmission point (MITP), which generates an optical signal with two sidebands at the ±first orders. By beating the two sidebands at a second photodetector (PD), a frequency-doubled microwave signal is generated. By simply adjusting the wavelength of the TLS, the central frequency of the MPF is shifted, and the fundamental oscillation and its frequency-doubled signals can be tuned. The detailed theoretical study is achieved, and a verified experiment is established. A fundamental oscillation signal with a frequency tuning range from 9.39 to 15.4 GHz is generated in the OEO loop, which is multiplied to generate a tunable frequency-doubled signal. Their overall performances are also investigated.

Variable Repetition Rate Picosecond Master Oscillator for Photoelectron Gun

In this work, aiming at the master oscillator of the photoelectron gun with a variable repetition rate of electron bunches, a picosecond solid-state laser subject to delayed optoelectronic feedback and RF loss modulation is studied. Loss modulation is performed using an electro-optical modulator with zero bias at the second accelerator frequency subharmonic. Optoelectronic negative feedback uses an intracavity electro-optical modulator and a fast high-voltage photodiode mounted as close as possible to the modulator crystal. An analytical formula is obtained for the pulse duration, and estimates are given for Nd and Yb based media and L, S, C and X-band used in modern linear accelerators. Numerical simulation proves that the control is suitable for pulse-repetitive operation. The proposed approach solves the problem of laser pulse shortening and locking the master oscillator, and therefore, electron bunches in photoelectron guns, to the high-stable RF generator controlling accelerator functioning.

High-performance linear frequency-modulated signal generation based on optically injected semiconductor laser with dual-loop optoelectronic feedback

&lt;sec&gt;Linear frequency-modulated (LFM) waveforms have numerous applications in high-resolution radar detection, high-speed wireless communication, and high precision measurement. The generation of LFM microwave signals based on conventional electronic technologies is limited in their center frequency and bandwidth, which are usually less than a few gigahertz. Fortunately, the inherently large bandwidth offered by photonic technology is very hopeful of breaking through the electronic bottleneck. A variety of photonics-based approaches to generating the LFM waveforms have been reported, including the frequency-to-time mapping method and the external modulation method. However, these solutions suffer poor tunability or expensive RF sources. In recent years, the LFM waveform generation based on optically injected semiconductor lasers (OISLs) has attracted increasing attention. By introducing a low-speed electrical signal to control the period-one (P1) dynamics of an OISL, the LFM waveforms with a large bandwidth are generated. Nonetheless, the generated microwave signal has poor spectral purity, which restricts its many practical applications.&lt;/sec&gt;&lt;sec&gt;In this work, a high-performance microwave LFM waveform generation scheme based on an OISL with dual-loop optoelectronic feedback is proposed and demonstrated experimentally. In this scheme, the optical injection strength of an OISL is controlled first by a triangular-like voltage signal to generate LFM waveforms with a large bandwidth. Then, the quality of the generated LFM signal is comprehensively improved by introducing a delay-matched dual-loop optoelectronic feedback structure. Based on the Fourier domain mode locking principle (FDML) and the self-injection locking technique, both a short-delay optoelectronic feedback loop and a long-delay optoelectronic feedback loop are introduced to simultaneously improve the spectral purity and phase stability of the generated LFM signals. In the proof-of-concept experiment, by analyzing the spectral quality and phase deviation of the generated LFM signal, a comb contrast of 40 dB, a comb linewidth of 1 kHz, and a phase deviation ∆&lt;i&gt;φ&lt;/i&gt; of less than π/3 are simultaneously obtained. In addition, the parameters such as bandwidth and center frequency of the generated LFM signal generated can be flexibly tuned, and an LFM signal with a large bandwidth up to 8 GHz (18–26 GHz) is generated in the experiment. The proposed scheme features a simple and compact structure, high spectral quality and flexible tuning, thus may find applications in broadband radar and high-speed communication systems.&lt;/sec&gt;

Optical square-wave generation in a semiconductor laser with optoelectronic feedback.

We report self-sustained optical square-wave (SW) generation in a semiconductor laser diode subjected to delayed optoelectronic feedback on its injection current (J). This optoelectronic oscillator relies on nonlinear effects present in both the laser diode and in the optoelectronic feedback loop through amplifier saturation. The repetition rate of the SW is an integer multiple of the inverse of the loop delay, while the duty cycle can be tuned with J.

Self-sustaining MoS2 nanomechanical oscillators and feedback cooling

We report on the experimental demonstration of self-sustaining feedback oscillators referenced to ultrathin molybdenum disulfide (MoS2) nanomechanical resonators vibrating in the ∼10 to 20 MHz range. Based on comprehensive open-loop characterization of MoS2 resonators with dynamic ranges up to 85 dB, self-sustaining oscillators are constructed by incorporating the MoS2 resonators into an optoelectronic feedback circuitry. The prototyped MoS2 self-sustaining oscillators generate stable radio frequency waveforms with frequency stability (measured in Allan deviation) down to ∼2 × 10−5 and phase noise mainly limited by electronic thermal noise. Beyond self-sustaining oscillations, we demonstrate feedback cooling of thermomechanical motion of a bilayer (2L) MoS2 resonator from 300 K to 255 K by tuning the phase in the feedback, suppressing or “squashing” the noise level of the system.