Broadband chaos generation in a distributed-feedback laser by selecting residual side modes.

Chaotic dynamics with spectral broadening is experimentally obtained by selective excitation of residual side modes in a distributed-feedback (DFB) laser. For the single-mode laser that emits only at the main mode when free-running, feedback to a residual side mode is introduced via a fiber Bragg grating (FBG). The FBG feedback suppresses the main mode, selectively excites the residual side mode, and generates broadband chaotic dynamics. Such a chaos of the residual side mode has a broad electrical bandwidth reaching at least 26 GHz, which corresponds to a significant broadening by over 50% when compared with the main mode. The dynamics are attributed entirely to the one selected mode without invoking multimode interactions. The wavelength is tunable beyond 10 nm by using different FBGs. Through avoiding multimode interactions, this approach of broadband chaos generation is potentially simple to model and thus promising for applications.

Perturbing period-one laser dynamics for frequency-modulated microwave generation with external locking.

Period-one (P1) dynamics of two lasers under a common injection are perturbed for externally locked frequency-modulated continuous-wave (FMCW) generation. The first laser is injected into P1 dynamics at frequency f 0, where the dynamics is perturbed by a slow modulation to induce adiabatic sweeping for FMCW generation and a fast modulation to seed the whole comb for external locking. The second laser is injected into a faster P1 dynamics at 3f 0 that is perturbed for harmonic locking. The central frequency is boosted to 4f 0 by coherently combining the lasers. FMCW generation with external locking is demonstrated with a sweep range of 6 GHz, comb contrast enhanced to 42 dB, and 4f 0 reaching 80 GHz. Inherent competition between external locking and frequency modulation is revealed, although an optimal strength is identified for locking the whole comb. Wide tuning of the central frequency is also supported.

Chaotic dimension enhancement by optical injection into a semiconductor laser under feedback.

Optical injection into a chaotic laser under feedback is investigated for dimension enhancement. Although injecting a solitary laser is known to be low-dimensional, injecting the laser under feedback is found to enhance the correlation dimension D2 in experiments. Using an exceptionally large data size with a very large reconstruction embedding dimension, efficient computation is enabled by averaging over many short segments to carefully estimate D2. The dimension enhancement can be achieved together with time-delay signature suppression. The enhancement of D2 as a fundamental geometric quantifier of attractors is useful in applications of chaos.

Cascaded injection of semiconductor lasers in period-one oscillations for millimeter-wave generation.

Period-one (P1) oscillations in semiconductor lasers are applicable in photonic millimeter-wave (mm-wave) generation. P1 oscillation can be invoked by optically injecting a laser, where the phase noise can be suppressed by modulation. To increase the frequency range of mm-wave generation, cascaded injection is investigated for enhancing the P1 oscillation harmonics. Relative to the optical frequency of the injection from a master laser, P1 oscillation at frequency f0 is induced in a primary slave laser which, in turn, injects a secondary slave laser for enhancing the harmonic at 2f0. Experimentally, photonic mm-wave generation at 2f0=72 GHz is demonstrated using P1 oscillations at f0=36 GHz. Subharmonic locking by modulation at f0/4=9 GHz can suppress the output phase noise to -87 dBc/Hz at 10 kHz offset. The mm-wave power can be strengthened by the coherent addition from the master laser. The mm-wave frequency can be tuned by varying the operating conditions of the lasers. Extension to higher frequencies is possible using the approach of cascaded injection.

Chaotic time-delay signature suppression with bandwidth broadening by fiber propagation.

Chaotic emission of a semiconductor laser is investigated through propagation over a fiber for achieving broadening of the bandwidth and suppression of the time-delay signature (TDS). Subject to delayed optical feedback, the laser first generates chaos with a limited bandwidth and an undesirable TDS. The laser emission is then delivered over a standard single-mode fiber for experiencing self-phase modulation, together with anomalous group-velocity dispersion, which leads to the broadening of the optical bandwidth and suppression of the TDS in the intensity signal. The effects are enhanced as the input power launched to the fiber increases. By experimentally launching up to 340 mW into a 20 km fiber, the TDS is suppressed by 10 times to below 0.04, while the bandwidth is broadened by six times to above 100 GHz. The improvement of the chaotic signal is potentially useful in random bit generation and range detection applications.

Experimental investigation on feedback insensitivity in semiconductor ring lasers.

The insensitivity to optical feedback is experimentally measured for a semiconductor ring laser (SRL) and compared to that of a Fabry-Perot laser (FPL) fabricated with the same technology and on the same material. An analysis of the optical spectra reveals that the SRL remains nearly unaffected for values of optical feedback as strong as -23 dB. Furthermore, through both optical linewidth and self-mixing measurements, we show that the tolerance to feedback in SRLs is 25-30 dB stronger than in FPLs. This property makes SRLs very interesting candidates for the development of feedback-insensitive optical sources.

Mapping the contribution and strategic distribution patterns of neuroimaging features of small vessel disease in poststroke cognitive impairment.

OBJECTIVES: Individual neuroimaging features of small vessel disease (SVD) have been reported to influence poststroke cognition. This study aimed to investigate the joint contribution and strategic distribution patterns of multiple types of SVD imaging features in poststroke cognitive impairment. METHODS: We studied 145 first-ever ischaemic stroke patients with MRI and Montreal Cognitive Assessment (MoCA) examined at baseline. The local burdens of acute ischaemic lesion (AIL), white matter hyperintensity, lacune, enlarged perivascular space and cross-sectional atrophy were quantified and entered into support vector regression (SVR) models to associate with the global and domain scores of MoCA. The SVR models were optimised with feature selection through 10-fold cross-validations. The contribution of SVD features to MoCA scores was measured by the prediction accuracy in the corresponding SVR model after optimisation. RESULTS: The combination of the neuroimaging features of SVD contributed much more to the MoCA deficits on top of AILs compared with individual SVD features, and the cognitive impact of different individual SVD features was generally similar. As identified by the optimal SVR models, the important SVD-affected regions were mainly located in the basal ganglia and white matter around it, although the specific regions varied for MoCA and its domains. CONCLUSIONS: Multiple types of SVD neuroimaging features jointly had a significant impact on global and domain cognitive functionings after stroke on top of AILs. The map of strategic cognitive-relevant regions of SVD features may help clinicians to understand their complementary impact on poststroke cognition.

Tunable switching between stable and periodic states in a semiconductor laser with feedback.

Feedback-induced switching between two nonlinear dynamical states is observed in a semiconductor laser. The single-mode laser is subject to optical feedback in the long-cavity regime. In every round-trip time τ, the feedback is found to switch the laser from a stable state to a periodic state. The stable state corresponds to a continuous-wave emission at a single optical frequency. The periodic state corresponds to emission at another optical frequency with sidebands generated from a sustained relaxation oscillation. Such regular switching between the stable and periodic states is first unveiled numerically. Experimentally, the resultant intensity time series is confirmed as comprising of a square-wave envelope repeating in τ, which is modulated on a microwave carrier near the relaxation resonance frequency. Additionally, the duty cycle for the periodic state is found as continuously tunable by adjusting the feedback strength. The tunable state switching is applicable to square-wave modulated photonic microwave generation.

Contribution of off-resonant states to the phase noise of quantum dot lasers.

The phase noise of quantum dot lasers is investigated theoretically by coupling the Langevin noise sources into the rate equations. The off-resonant populations in the excited state and in the carrier reservoir contribute to the phase noise of ground-state emission lasers through the phase-amplitude coupling effect. This effect arises from the optical-noise induced carrier fluctuations in the off-resonant states. In addition, the phase noise has low sensitivity to the carrier scattering rates.

Optically injected InAs/GaAs quantum dot laser for tunable photonic microwave generation.

We present an experimental investigation on the period-one dynamics of an optically injected InAs/GaAs quantum dot laser as a photonic microwave source. It is shown that the microwave frequency of the quantum dot laser's period-one oscillation is continuously tunable through the adjustment of the frequency detuning. The microwave power is enhanced by increasing the injection strength providing that the operation is away from the Hopf bifurcation, whereas the second-harmonic distortion of the electrical signal is well reduced by increasing the detuning frequency. Both strong optical injection and high detuning frequency are favorable for obtaining a single sideband optical signal. In addition, particular period-one oscillation points of low sensitivity to the frequency detuning are found close to the Hopf bifurcation line.

Frequency-modulated microwave generation with feedback stabilization using an optically injected semiconductor laser.

Generation of frequency-modulated continuous-wave (FMCW) microwave signals is investigated using the period-one (P1) dynamics of a semiconductor laser. A modulated optical injection drives the laser into P1 oscillation with a modulated microwave frequency, while adding feedback to the injection reduces the microwave phase noise. Using simply a single-mode laser, the tunability of P1 dynamics allows for wide tuning of the central frequency of the FMCW signal. A sweep range reaching 7.7 GHz is demonstrated with a sweep rate of 0.42 GHz/ns. When the external modulation frequency matches the reciprocal of the feedback delay time, feedback stabilization is manifested as an increase of the frequency comb contrast by 30 dB for the FMCW microwave signal.

Square-wave oscillations in a semiconductor ring laser subject to counter-directional delayed mutual feedback.

Square-wave (SW) switching of the lasing direction in a semiconductor ring laser (SRL) is investigated using counter-directional mutual feedback. The SRL is electrically biased to a regime that supports lasing in either counter-clockwise (CCW) or clockwise (CW) direction. The CCW and CW modes are then counter-directionally coupled by optical feedback, where the CCW-to-CW and CW-to-CCW feedback are delayed by τ1 and τ2, respectively. The mutual feedback invokes SW oscillations of the CCW and CW emission intensities with a period of T≈τ1+τ2. When τ1=τ2, symmetric SWs with a duty cycle of 50% are obtained, where the switching time and electrical linewidth of the SWs can be reduced to, respectively, 1.4 ns and 1.1 kHz by strengthening the feedback. When τ1≠τ2, asymmetric SWs are obtained with a tunable duty cycle of τ1/(τ1+τ2). High-order symmetric SWs with a period of T=(τ1+τ2)/n can also be observed for some integer n. Symmetric SWs of order n=13 with a period of T=10.3 ns are observed experimentally.

Phase noise characteristics of microwave signals generated by semiconductor laser dynamics.

Phase noise of the period-one (P1) nonlinear dynamical oscillation in an optically injected semiconductor laser is numerically investigated. The P1 dynamics causes the laser output intensity to oscillate at a widely tunable frequency for photonic microwave generation, although the intrinsic spontaneous emission in the laser inevitably degrades the microwave signal and manifests as the oscillation phase noise. To characterize the phase noise, the P1 microwave linewidth is first numerically examined through the rate equations with a Langevin term. The P1 microwave linewidth is found to vary with the injection parameters. It is nearly minimized when the microwave power maximizes. Owing to the laser nonlinearities, the P1 microwave linewidth can even be smaller than the free-running optical linewidth. By adding an optical feedback to the laser, the P1 microwave linewidth is found to reduce as the feedback strength and feedback delay increase, in which an inverse-square dependency is followed asymptotically. By modification to a dual-loop feedback, noisy side peaks around the central P1 frequency are effectively suppressed through the Vernier effect. The dual-loop feedback maintains a low phase noise variance over a wide tuning range of the P1 frequency, while allowing long delay times for significant P1 microwave linewidth narrowing.

Polarization-resolved time-delay signatures of chaos induced by FBG-feedback in VCSEL.

Polarization-resolved chaotic emission intensities from a vertical-cavity surface-emitting laser (VCSEL) subject to feedback from a fiber Bragg grating (FBG) are numerically investigated. Time-delay (TD) signatures of the feedback are examined through various means including self-correlations of intensity time-series of individual polarizations, cross-correlation of intensities time-series between both polarizations, and permutation entropies calculated for the individual polarizations. The results show that the TD signatures can be clearly suppressed by selecting suitable operation parameters such as the feedback strength, FBG bandwidth, and Bragg frequency. Also, in the operational parameter space, numerical maps of TD signatures and effective bandwidths are obtained, which show regions of chaotic signals with both wide bandwidths and weak TD signatures. Finally, by comparing with a VCSEL subject to feedback from a mirror, the VCSEL subject to feedback from the FBG generally shows better concealment of the TD signatures with similar, or even wider, bandwidths.

Modulation instability in a highly nonlinear fiber for discrete-time pulsed random bit generation.

A simple yet high-speed scheme by utilizing modulation instability (MI) on the discrete-time generation of random bits is proposed and demonstrated experimentally. We develop MI pulses by pumping a highly nonlinear fiber in the anomalous dispersion regime using a mode-locked laser. MI pulses contain fluctuating pulse-to-pulse variations of peak intensities for extraction into random bits. At a repetition rate of 10 GHz, 5 bits are extracted from each pulse in generating random bits at 50 Gbps, as verified by the National Institute of Standards and Technology test suite.

Experimental investigation of anti-colliding pulse mode-locked semiconductor lasers.

We experimentally demonstrate anti-colliding pulse mode-locking (ACPML) in an integrated semiconductor laser. The device geometry consists of a gain section and a saturable absorber (SA) section located immediately next to one of the cavity facets. After depositing a low-reflection coating on the SA facet and a high-reflection coating on the gain section facet, the threshold is unchanged, while the modulation of the SA is increased. The data presented here confirm that the ACPML configuration improves the peak output power of the pulses, reduces the amplitude fluctuation and timing jitter, and expands the biasing parameter range over which the stable mode-locking operation occurs.

Random bit generation at tunable rates using a chaotic semiconductor laser under distributed feedback.

A semiconductor laser with distributed feedback from a fiber Bragg grating (FBG) is investigated for random bit generation (RBG). The feedback perturbs the laser to emit chaotically with the intensity being sampled periodically. The samples are then converted into random bits by a simple postprocessing of self-differencing and selecting bits. Unlike a conventional mirror that provides localized feedback, the FBG provides distributed feedback which effectively suppresses the information of the round-trip feedback delay time. Randomness is ensured even when the sampling period is commensurate with the feedback delay between the laser and the grating. Consequently, in RBG, the FBG feedback enables continuous tuning of the output bit rate, reduces the minimum sampling period, and increases the number of bits selected per sample. RBG is experimentally investigated at a sampling period continuously tunable from over 16 ns down to 50 ps, while the feedback delay is fixed at 7.7 ns. By selecting 5 least-significant bits per sample, output bit rates from 0.3 to 100 Gbps are achieved with randomness examined by the National Institute of Standards and Technology test suite.

Tunable photonic microwave generation using optically injected semiconductor laser dynamics with optical feedback stabilization.

The period-one (P1) nonlinear dynamics of a semiconductor laser subject to both optical injection and optical feedback are investigated for photonic microwave generation. The optical injection first drives the laser into P1 dynamics so that its intensity oscillates at a microwave frequency. A dual-loop optical feedback then stabilizes the fluctuations of the oscillation frequency. Photonic generation at 45.424 GHz is demonstrated with a linewidth below 50 kHz using a laser with a relaxation resonance frequency of only 7 GHz. The dual-loop feedback effectively narrows the linewidth by over an order of magnitude, reduces the phase noise variance by more than 500 times, and suppresses side peaks in the power spectrum.

Random bit generation using an optically injected semiconductor laser in chaos with oversampling.

Random bit generation is experimentally demonstrated using a semiconductor laser driven into chaos by optical injection. The laser is not subject to any feedback so that the chaotic waveform possesses very little autocorrelation. Random bit generation is achieved at a sampling rate of 10 GHz even when only a fractional bandwidth of 1.5 GHz within a much broader chaotic bandwidth is digitized. By retaining only 3 least significant bits per sample, an output bit rate of 30 Gbps is attained. The approach requires no complicated postprocessing and has no stringent requirement on the electronics bandwidth.