Period-doubling cascades and chaos in a semiconductor laser with optical injection

Chaotic microlasers caused by internal mode interaction for random number generation

Chaotic semiconductor lasers have been widely investigated for generating unpredictable random numbers, especially for lasers with external optical feedback. Nevertheless, chaotic lasers under external feedback are hindered by external feedback loop time, which causes correlation peaks for chaotic output. Here, we demonstrate the first self-chaotic microlaser based on internal mode interaction for a dual-mode microcavity laser, and realize random number generation using the self-chaotic laser output. By adjusting mode frequency interval close to the intrinsic relaxation oscillation frequency, nonlinear dynamics including self-chaos and period-oscillations are predicted and realized numerically and experimentally due to internal mode interaction. The internal mode interaction and corresponding carrier spatial oscillations pave the way of mode engineering for nonlinear dynamics in a solitary laser. Our findings provide a novel and easy method to create controllable and robust optical chaos for high-speed random number generation.

Tunable, low-phase-noise microwave signals from an optically injected semiconductor laser with opto-electronic feedback

We experimentally demonstrate the generation of microwave signals with linewidths below 3 Hz and a tuning range over 35 GHz from a semiconductor laser subject to optical injection and opto-electronic feedback. The feedback loop uses neither a microwave spectral filter nor an amplifier to achieve a reduction in the microwave linewidth of six orders of magnitude. Two microwave frequencies, 25.4 and 45.9 GHz, are chosen to highlight single-sideband phase measurements of -105 and -95  dBc/Hz at a 10-kHz offset, respectively. Finally, we demonstrate that longer-term stability can be further improved via asymmetric mutual injection.

Polarization dynamics induced by parallel optical injection in a single-mode VCSEL

We report an experimental study of the polarization nonlinear dynamics in a 1550 nm single-mode vertical-cavity surface-emitting laser (VCSEL) subject to parallel optical injection. Experimentally measured stability maps identifying regions of different nonlinear dynamics for various values of bias current are reported. We show that VCSELs with more than a 35 dB polarization mode suppression ratio can have rich nonlinear dynamics in both linear polarizations, including periodic and chaotic behaviors appearing simultaneously in both polarization modes.

Turbulent chimeras in large semiconductor laser arrays

Semiconductor laser arrays have been investigated experimentally and theoretically from the viewpoint of temporal and spatial coherence for the past forty years. In this work, we are focusing on a rather novel complex collective behavior, namely chimera states, where synchronized clusters of emitters coexist with unsynchronized ones. For the first time, we find such states exist in large diode arrays based on quantum well gain media with nearest-neighbor interactions. The crucial parameters are the evanescent coupling strength and the relative optical frequency detuning between the emitters of the array. By employing a recently proposed figure of merit for classifying chimera states, we provide quantitative and qualitative evidence for the observed dynamics. The corresponding chimeras are identified as turbulent according to the irregular temporal behavior of the classification measure.

Randomness evaluation for an optically injected chaotic semiconductor laser by attractor reconstruction

State-space reconstruction is investigated for evaluating the randomness generated by an optically injected semiconductor laser in chaos. The reconstruction of the attractor requires only the emission intensity time series, allowing both experimental and numerical evaluations with good qualitative agreement. The randomness generation is evaluated by the divergence of neighboring states, which is quantified by the time-dependent exponents (TDEs) as well as the associated entropies. Averaged over the entire attractor, the mean TDE is observed to be positive as it increases with the evolution time through chaotic mixing. At a constant laser noise strength, the mean TDE for chaos is observed to be greater than that for periodic dynamics, as attributed to the effect of noise amplification by chaos. After discretization, the Shannon entropies continually generated by the laser for the output bits are estimated in providing a fundamental basis for random bit generation, where a combined output bit rate reaching 200 Gb/s is illustrated using practical tests. Overall, based on the reconstructed states, the TDEs and entropies offer a direct experimental verification of the randomness generated in the chaotic laser.

Polarization switching and injection locking in vertical-cavity surface-emitting lasers subject to parallel optical injection

Polarization switching in a long-wavelength vertical-cavity surface-emitting laser (VCSEL) under parallel optical injection is analyzed in a theoretical and experimental way. For the first time, to our knowledge, we report experimentally a state in which injection locking of the parallel polarization and excitation of the free-running orthogonal polarization of the VCSEL are simultaneously obtained. We obtain very simple analytical expressions that describe both linear polarizations. We show that the power of both linear polarizations depend linearly on the injected power in such a way that the total power emitted by the VCSEL is constant. We perform a linear stability analysis of this solution to characterize the region of parameters in which it can be observed. Our measurements qualitatively confirm the previous theoretical predictions.

Time-delay signature of chaos in 1550 nm VCSELs with variable-polarization FBG feedback

Based on the framework of spin-flip model (SFM), the output characteristics of a 1550 nm vertical-cavity surface-emitting laser (VCSEL) subject to variable-polarization fiber Bragg grating (FBG) feedback (VPFBGF) have been investigated. With the aid of the self-correlation function (SF) and the permutation entropy (PE) function, the time-delay signature (TDS) of chaos in the VPFBGF-VCSEL is evaluated, and then the influences of the operation parameters on the TDS of chaos are analyzed. The results show that the TDS of chaos can be suppressed efficiently through selecting suitable coupling coefficient and feedback rate of the FBG, and is weaker than that of chaos generated by traditional variable-polarization mirror feedback VCSELs (VPMF-VCSELs) or polarization-preserved FBG feedback VCSELs (PPFBGF-VCSELs).

All-optical switching with a dual-state, single-section quantum dot laser via optical injection

An all-optical switching mechanism via optical injection of an InAs/GaAs quantum dot laser is presented. Relative state suppression in excess of 40 dB is achieved, and experimental switching times of the order of a few hundred picoseconds are demonstrated.

Tunable microwave generation of a monolithic dual-wavelength distributed feedback laser

The dynamic behavior of a monolithic dual-wavelength distributed feedback laser was fully investigated and mapped. The combination of different driving currents for master and slave lasers can generate a wide range of different operational modes, from single mode, period 1 to chaos. Both the optical and microwave spectrum were recorded and analyzed. The detected single mode signal can continuously cover from 15GHz to 50GHz, limited by photodetector bandwidth. The measured optical four-wave-mixing pattern indicates that a 70GHz signal can be generated by this device. By applying rate equation analysis, the important laser parameters can be extracted from the spectrum. The extracted relaxation resonant frequency is found to be 8.96GHz. With the full operational map at hand, the suitable current combination can be applied to the device for proper applications.

Direct generation of broadband chaos by a monolithic integrated semiconductor laser chip

A solitary monolithic integrated semiconductor laser (MISL) chip with a size of 780 micrometer is designed and fabricated for broadband chaos generation. Such a MISL chip consists of a DFB section, a phase section and an amplification section. Test results indicate that under suitable operation conditions, this laser chip can be driven into broadband chaos. The generated chaos covers an RF frequency range, limited by our measurement device, of 26.5GHz, and possesses significant dimension and complexity. Moreover, the routes into and out of chaos are also characterized through extracting variety dynamical states of temporal waveforms, phase portraits, RF spectra and statistical indicators.

Failure of the α factor in describing dynamical instabilities and chaos in quantum-dot lasers

We show that the long-established concept of a linewidth-enhancement factor α to describe carrier-induced refractive index changes in semiconductor lasers breaks down in quantum-dot (QD) lasers when describing complex dynamic scenarios, found, for example, under high-excitation or optical injection. By comparing laser simulations using a constant α factor with results from a more complex nonequilibrium model that separately treats gain and refractive index dynamics, we examine the conditions under which an approximation of the amplitude-phase coupling by an α factor becomes invalid. The investigations show that while a quasiequilibrium approach for conventional quantum well lasers is valid over a reasonable parameter range, allowing one to introduce an α factor as a constant parameter, the concept is in general not applicable to predict QD laser dynamics due to the different time scales of the involved scattering processes.

Two-frequency injection on a multimode vertical-cavity surface-emitting laser

We have studied experimentally effects of two-frequency optical injection on a multimode vertical-cavity surface-emitting laser (VCSEL). The injected signal comes from another VCSEL. Polarization switching (PS) with and without frequency locking occurs for relatively small frequency detuning. Outside the regime of polarization switching, the VCSEL demonstrates two types of instabilities. The instability regions and boundaries of PS of each transverse mode are mapped in the parameter plane of frequency detuning versus injected power.

Nonlinear semiconductor lasers and amplifiers for all-optical information processing

The nonlinear properties of semiconductor lasers and laser amplifiers when subject to optical injection are reviewed and new results are presented for multisection lasers, vertical cavity semiconductor optical amplifiers, and surface-emitting lasers. The main underlying material parameters are outlined and the key design approaches are discussed for both edge-emitting and vertical cavity devices. An overview of theoretical modeling approaches is discussed and a summary of key experimental results is presented. The practical use of optically injected edge-emitting and vertical cavity semiconductor lasers and laser amplifiers is illustrated with examples of applications including, among others, optical logic and chaotic communication.

Dynamic behavior of an injection-locked quantum-dash Fabry-Perot laser at zero-detuning

This work investigates the behavior of a zero-detuned optically-injected quantum-dash Fabry-Perot laser as the injected field ratio is increased from near-zero to levels resulting in stable locking. Using a normalized model describing optically-injected semiconductor lasers, variations in the slave laser's free-running characteristics are shown to have a strong impact on the coupled system's behavior. The theoretical model is verified experimentally using a high resolution spectrometer. It is found that the quantum-dash laser has the technological advantage of a low linewidth enhancement factor at low bias currents that suppresses undesirable Period-2 and chaotic behavior. Such observations suggest that optically-injected quantum-dash lasers can be used as an enabling component for tunable photonic oscillators.

Using chaos for remote sensing of laser radiation

An idea is proposed for detecting a weak laser signal from a remote source in the presence of strong background noise. The scheme exploits dynamical nonlinearities arising from heterodyning signal and reference fields inside an active reference laser cavity. This paper shows that for certain reference laser configurations, the resulting bifurcations in the reference laser may be used as warning of irradiation by a laser source.

Excitable phase slips in an injection-locked single-mode quantum-dot laser

An experimental study of the dynamics of a single-mode quantum-dot semiconductor laser undergoing optical injection is described for the first time, to our knowledge. In particular, the first observation of excitable pulses near the locking boundaries for both positive and negative detuning is reported, indicating locking via a saddle-node bifurcation for both signs of the detuning. The phase evolution of the slave electric-field during pulsing was measured and confirmed that the pulses result from 2pi phase slips. The interpulse-time statistics were analyzed, and a Kramers-like distribution was obtained.

Nonlinear dynamics in laser polarization conversion by stimulated scattering in nematic liquid crystal films

We present a study of the nonlinear dynamics of a coherent polarization conversion process in nematic liquid crystal films. This effect is mediated by two-beam coupling between the incident polarized laser and its orthogonally polarized (lower-frequency) noise component scattered by the director axis fluctuations. A complete model for the director dynamics derived from the basic equations is presented. The existence of complex, time-, and intensity-dependent dynamics of the director motion such as oscillations and various bifurcations including period doubling is revealed.

Noise-induced chaos in an optically injected semiconductor laser model

The chaos induced by an intrinsic spontaneous-emission noise in an optically injected semiconductor laser is investigated through a single-mode injection model. A method is developed to quantitatively study the scale-dependent noise effect in general, and the noise-induced chaotic feature in particular. We find that noise at an experimentally measured level can induce chaos in the system. This suggests that noise-induced chaos may indeed exist in real systems. Certain required characteristics for noise to induce chaos are identified: the periodic state itself, when subject to weak noise, should undergo a process that is much more diffusive than the Brownian motion, and the adjacent chaotic states should still behave chaotically on certain finite scales when subject to noise. We believe they are generic features for noise to induce chaos. The correlation dimension of the clean and noisy attractors is also calculated to study noise-induced changes in the geometrical structure of the attractors.