Purcell Cavity-enhanced Spontaneous Emission Factor Research Articles

Characterizing the chaotic dynamics of a semiconductor nanolaser subjected to FBG feedback.

Nonlinear dynamics of semiconductor nanolasers subjected to distributed feedbacks from fiber Bragg grating (FBG) are investigated through modified rate equations, which include the unique Purcell cavity-enhanced spontaneous emission factor F and spontaneous emission coupling factor β. In the analysis, the effects of F, β, frequency detuning, feedback strength, feedback delay, FBG bandwidth and length on chaotic performance are evaluated. It is observed that the approach of FBG feedback outperforms mirror feedback in terms of concealing time-delay signature and increasing effective bandwidth by choosing intermediate feedback strength and frequency detuning. Additionally, chaotic regions and the corresponding chaotic characteristics are revealed by dynamical mappings of nanolasers subjected to FBG feedback. The results show that decreased F, β and increased FBG bandwidth can extend the parameter range of chaos. However, the variation of feedback delay and FBG length has no obvious effect on TDS suppression and effective bandwidth enhancement. Most importantly, high quality optical chaos with low TDS and high effective bandwidth induced by increased dispersion is obtained within broad parameter regions considered, which is beneficial to achieving chaos-based applications.

Time delay concealment and unpredictability enhancement of nanolasers under external cavity regulation

As an important optical element of the optical integration in the future, nanolasers has been a research hotspot in recent years, and the corresponding structural engineering and output characteristics have been widely investigated. However, the nonlinear dynamical performances of nanolasers are rarely reported. Only some preliminary analyses of the dynamic behavior under the optical feedback, optical injection and mutual injection can be found. Some researches pointed out the future prospect of nanolasers, however, some chaos-based applications have not been explored. Therefore, we numerically investigate chaos dynamics in a nanolaser subjected to optical feedback and in another nanolaser subjected to chaotic injection from the former structure by using single mode rate equation, which includes the Purcell cavity-enhanced spontaneous emission factor <i>F</i> and spontaneous emission coupling factor <i>β</i>. The <i>F</i> denotes the ratio of the spontaneous emission rate into the cavity mode to the total spontaneous emission rate in the bulk medium in the absence of a cavity and <i>β</i> represents the fraction of spontaneous emitted photons which are coupled into cavity mode. Specifically, chaos time delay signature (TDS) and unpredictability are evaluated by the peak size of autocorrelation function (ACF) and permutation entropy (PE) respectively. Such kinds of calculations have the advantage of fast operation speed and anti-noise robustness. The results show that the increasing of bias current and the decreasing of gain saturation factor <i>ε</i>, <i>F</i> and <i>β</i> are beneficial to improving the unpredictability and suppressing TDS because the weak damping of the relaxation oscillation leads to strong oscillation. Large linewidth enhancement factor <i>α</i> will increase the number of laser oscillating modes, sideband modes, the spectral components, and enhance the dispersion effect, which will also weaken the information about outer cavity and improve the complexity of chaos. In addition, the above-mentioned chaos properties can be enhanced by injecting the chaos output from a nanolaser subjected to optical feedback into another (slave) nanolaser, which is due to the nonlinear interaction between the driving chaotic signal and the internal electric field of the slave nanolaser. Finally, two-dimensional maps depicting high unpredictability and TDS concealment in the parameter space of the frequency detuning and the injection strength are obtained. It can be found that unpredictability degree can be enhanced by choosing high detuning frequency and intermediate injection strength in the non-injection locking area. The numerical results pave the way for generating the high-quality chaotic sources on a chip or the photonic integrated circuits based on novel semiconductor nanolaser and its related applications.

Enhanced Prediction Performance of a Neuromorphic Reservoir Computing System Using a Semiconductor Nanolaser With Double Phase Conjugate Feedbacks

A neuromorphic reservoir computing (RC) system using a semiconductor nanolaser (SNL) with double phase conjugate feedbacks (PCF) is proposed for the first time and demonstrated numerically. The prediction performance of such RC system is investigated via Santa Fe chaotic time series prediction task. The Purcell cavity-enhanced spontaneous emission factor F and the spontaneous emission coupling factor β are included in the rate equations, and the influences of F and β on the prediction performance of such RC system are analyzed extensively. For the purpose of comparison, the prediction performance of SNL-based RC system with single PCF is also considered. The simulation results indicate that, compared with the SNL-based RC system with single PCF, enhanced prediction performance can be obtained for the SNL-based RC system with double PCF. Moreover, the influences of bias current, the modulation depth of input signal, feedback strength, as well as feedback delay, are also taken into account. The proposed SNL-based RC system subject to double PCF in this paper has the potential to develop the RC-based neuromorphic photonic integrated circuit.

High-Speed Neuromorphic Reservoir Computing Based on a Semiconductor Nanolaser With Optical Feedback Under Electrical Modulation

A high-speed neuromorphic reservoir computing system based on a semiconductor nanolaser with optical feedback (SNL-based RC) under electrical modulation is proposed for the first time and demonstrated numerically. A Santa-Fe chaotic time series prediction task is employed to quantify the prediction performance of the SNL-based RC system. The effects of the Purcell cavity-enhanced spontaneous emission factor F and the spontaneous emission coupling factor β on the proposed RC system are analyzed extensively. It is found that, in general, increased F and β extend the range of good prediction performance of the SNL-based RC system. Moreover, the influences of bias current and feedback phase are also considered. Due to the ultra-short photon lifetime in SNL, the information processing rate of the SNL-based RC system reaches 10Gpbs. The proposed high-speed SNL-based RC system in this paper provides theoretical guidelines for the design of RC-based integrated neuromorphic photonic systems.

Concealment of Time Delay Signature of Chaotic Semiconductor Nanolasers With Double Chaotic Optical Injections

The time delay signature (TDS) concealment properties of a novel semiconductor nanolaser subject to double chaotic optical injections are investigated numerically. The TDS concealment is evaluated by the peak size of the autocorrelation function (ACF). The effects of feedback rate, injection rate, frequency detuning, Purcell cavity-enhanced spontaneous emission factor, and spontaneous emission coupling factor on the TDS concealment are carefully examined. It is found that, with the double chaotic optical injections, the TDS can be concealed in wide ranges of feedback rate, injection rate, and frequency detuning. Moreover, better TDS concealment can be achieved for a smaller frequency detuning and a larger injection rate. The 2-D maps of peak size of ACF further show that the range of parameter space contributing to better TDS concealment is wider for a moderate Purcell cavity-enhanced spontaneous emission factor and a smaller spontaneous emission coupling factor. These results may be interesting for the enhanced chaotic sources on-a-chip based on novel semiconductor nanolasers.

Numerical Investigation on Feedback Insensitivity in Semiconductor Nanolasers

This paper presents numerical investigations into the effect of feedback phase on the stability of semiconductor nanolasers (SNLs) in the presence of the external optical feedback. For this purpose, numerical solutions are obtained from rate equations where the effects of Purcell cavity-enhanced spontaneous emission factor F and an enhanced spontaneous emission coupling factor β are included. In this way, a phase-insensitive stable SNL is identified when the feedback coupling fraction is below a critical threshold η c. Furthermore, the relationship between η c and two other important system parameters, namely the injection current ( I dc) and the initial external cavity length ( L 0), is studied. The results show that η c has a bi-exponential relationship with either I dc or L 0. Moreover, the influence of F on the η c is evaluated, and it is found that η c increases with the increase of F . The results presented in this paper provide practical guidelines for the design of phase-insensitive stable SNLs, which are useful for densely integrated photonic circuits based applications, such as optical communications and sensing.

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 β. 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, β. 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.

Dynamical characteristics of nano‐lasers subject to optical injection and phase conjugate feedback

The dynamics of nano-lasers has been analysed using rate equations which include the Purcell cavity-enhanced spontaneous emission factor F and the spontaneous emission coupling factor β. It is shown that when subject to optical injection and phase conjugate feedback, nano-lasers may exhibit remarkably stable small-amplitude oscillations with frequencies of order 300 GHz. Critically, it is established that such oscillations persist when the effects of noise are taken into account. 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, β. The effects of the feedback distance and bias currents are also considered. As the optical injection strength increases for fixed phase conjugate feedback and relatively short feedback distances, the nano-laser displays periodic dynamics and then enters stable locking. As the feedback distance increases, the quasi-periodic dynamics dominates. Increased bias current can also induce quasi-periodic behaviour albeit this may be ameliorated by reducing the strength of the phase conjugate feedback.

Zero Crosstalk Regime Direct Modulation of Mutually Coupled Nanolasers

The modulation properties of dually modulated mutually coupled nanolasers have been analysed using rate equations which include the Purcell cavity-enhanced spontaneous emission factor F and the spontaneous emission coupling factor β . Specific attention is given to zero crosstalk operating regimes where the responses of the nanolasers are independent. Such regimes may provide either bidirectional isolation where both nanolasers operate independently or unidirectional-isolation where one nanolaser is immune to the other nanolaser but not vice versa. Access to the bidirectional isolation zero-crosstalk regime is, in general, enabled by strong driving or large modulation depth of the nanolasers. Conversely, strong injection coupling and low modulation depth lead to the unidirectional isolation regime. The modulation responses of the nanolasers in both bidirectional and unidirectional isolated zero crosstalk regimes are presented. The availability of bidirectional-isolated zero crosstalk regimes is seen to offer opportunities for exploitation in photonic integrated circuits.

Zero Cross-Talk Regimes in Dually Modulated Mutually-Coupled Nano-lasers

The modulation properties of dually modulated mutually-coupled nano-lasers have been analyzed using rate equations which include the Purcell cavity-enhanced spontaneous emission factor F and the spontaneous emission coupling factor β. Analysis of the dynamical response of modulated mutually-coupled nano-lasers reveals the existence of regimes of zero cross-talk wherein the response of one nano-laser is not impacted by the dynamics of the other nano-laser. The availability of zero-cross talk regimes is seen to offer opportunities for exploitation in photonic integrated circuits.

Modulated Mutually Coupled Nano-Lasers

The dynamics of mutually coupled nano-lasers subject to direct current modulation has been analyzed using rate equations, which include the Purcell cavity-enhanced spontaneous emission factor $F$ and the spontaneous emission coupling factor $\beta $ . Subject to two different modulation frequencies, the mutually coupled nano-lasers display two general types of response. The laser with the lower modulation frequency simply exhibits a response at that modulation frequency. Thus, we term a zero cross-talk response. On the other hand, at higher modulation frequencies the system displays a variety of dynamical responses which, in addition to zero cross-talk, includes a range of behaviors, which are classified from low cross-talk through to a complicated non-linear response. The precise behavior being dependent on the depth of modulation and the laser bias currents. The operational significance of the zero cross-talk regime is that it permits access to a simple periodic response at the modulation frequency. With a view to utilization, it is established that the region of zero cross-talk response enlarges with increasing modulation depth and increasing bias current. In this way, conditions are established, in which the lasers may act independently. The propensity for zero cross-talk response under stronger driving is consistent with previous analysis wherein modulated nano-lasers may have superior characteristics in the large-signal regime.

Dynamics and Stability of Mutually Coupled Nano-Lasers

The dynamics of mutually coupled nano-lasers has been explored theoretically. Calculations have been performed using rate equations which include the Purcell cavity-enhanced spontaneous emission factor F and the spontaneous emission coupling factor β. In the analysis, the influence of F and β has been evaluated for varying optical injection strength and distance between the two lasers. It is observed that, in general, for increased bias current, the system can maintain stable output for a larger mutual coupling strength. It is also found that for short inter-laser distances and larger F, the stability of mutually coupled nano-lasers is enhanced.

Phase Conjugate Feedback Effects in Nano-Lasers

The response of the nanolasers subject to the phase conjugate feedback (PCF) has been analyzed. Calculations have been performed using rate equations, which include the Purcell cavity-enhanced spontaneous emission factor F and the spontaneous emission coupling factor β. In the analysis, the influence of F and β is evaluated for varying the feedback rate. It is observed that, in general, the onset of chaos occurs at a higher feedback rate for PCF than for conventional mirror feedback (CMF), where PCF has lower intensity noise in comparison with the CMF.

Optical Injection Effects in Nanolasers

The response of nanolasers subject to optical injection has been analyzed. Calculations have been performed using rate equations, which include the Purcell cavity-enhanced spontaneous emission factor F and the spontaneous emission coupling factor I². In the analysis, the influence of F and I² is evaluated for varying the injection strength and frequency detuning between the master and slave laser. It is observed that, in general, increased F and I² increases the stable locking region and have only a few regions of dynamic instability as compared with conventional semiconductor lasers over a large frequency detuning. It is also found that for larger F, the modulation bandwidths of 90 GHz can be achieved.

External Optical Feedback Effects in Semiconductor Nanolasers

The response of nanolasers subject to external optical feedback has been analyzed. Calculations have been performed using rate equations, which include the Purcell cavity-enhanced spontaneous emission factor F and the spontaneous emission coupling factor β. In the analysis, the influence of F and β is evaluated for varying distance from external mirror, current, and feedback rate. It is observed that, in general, increased F and β at low bias currents increases the critical feedback for which chaos occurs as compared to conventional lasers, whereas at higher bias currents, chaos occurs at lower feedback rates. It is also found that for larger F , when increasing the distance from external mirror, the feedback rate at which chaos occurs increases.

Analysis of the Direct Modulation Response of Nanowire Lasers

The response of nanolasers to direct current modulation has been analyzed in both the small-signal and large-signal regimes. Calculations have been performed using rate equations which include the Purcell cavity-enhanced spontaneous emission factor F and the spontaneous emission coupling factor β. It is observed that in general increased F and β reduce the 3-dB direct current modulation bandwidth. Conditions are identified where the peak modulation response at resonant frequencies 35 and 30 GHz can be achieved. For both small- and large-signal regimes, modulation bandwidth of approximately 55 GHz can be achieved.