Observation of additional delayed-time in chaos synchronization of uni-directionally coupled VCSELs.

We report an experimental and numerical investigation on the existence of additional delayed-time in chaos synchronization of two uni-directionally coupled vertical-cavity surface-emitting lasers (VCSELs) for the first time. Under a generalized synchronization scenario, we demonstrate that there exists an additional delayed-time in addition to the time-of-flight between the two coupled VCSELs. The cross-correlation function analysis has been used as a method to determine the coupling delay and synchronization quality between two uni-directionally coupled chaotic VCSELs. We show that the injection strength significantly influences the additional delayed-time, and the injection strength analysis eventually substantiates the existence of additional delayed-time between the coupled lasers in experiments. The experimental results are in accordance with the numerical results. Additionally, we numerically study the effect of laser's internal parameter mismatches on additional delayed-time and synchronization quality between the lasers.

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.

Generation of polarization-resolved wideband unpredictability-enhanced chaotic signals based on vertical-cavity surface-emitting lasers subject to chaotic optical injection.

A system framework is proposed and analyzed for generating polarization-resolved wideband unpredictability-enhanced chaotic signals based on a slave vertical-cavity surface-emitting laser (S-VCSEL) driven by an injected optical chaos signal from a master VCSEL (M-VCSEL) under optical feedback. After calculating the time series outputs from the M-VCSEL under optical feedback and the S-VCSEL under chaotic optical injection by using the spin-flip model (SFM), the unpredictability degree (UD) is evaluated by permutation entropy (PE), and the bandwidth of the polarization-resolved outputs from the M-VCSEL and S-VCSEL are numerically investigated. The results show that, under suitable parameters, both the bandwidth and UD of two polarization components (PCs) outputs from the S-VCSEL can be enhanced significantly compared with that of the driving chaotic signals output from the M-VCSEL. By simulating the influences of the feedback and injection parameters on the bandwidth and UD of the polarization-resolved outputs from S-VCSEL, related operating parameters can be optimized.

Tbits/s physical random bit generation based on mutually coupled semiconductor laser chaotic entropy source.

Using two mutually coupled semiconductor lasers (MC-SLs) outputs as chaotic entropy sources, a scheme for generating Tbits/s ultra-fast physical random bit (PRB) is demonstrated and analyzed experimentally. Firstly, two entropy sources originating from two chaotic outputs of MC-SLs are obtained in parallel. Secondly, by adopting multiple optimized post-processing methods, two PRB streams with the generation rate of 0.56 Tbits/s are extracted from the two entropy sources and their randomness are verified by using NIST Special Publication 800-22 statistical tests. Through merging the two sets of 0.56 Tbits/s PRB streams by an interleaving operation, a third set of 1.12 Tbits/s PRB stream, which meets all the quality criteria of NIST statistical tests, can be further acquired. Finally, after additionally taking into account the restriction of the min-entropy, the generation rate of two sets of PRB stream from the two entropy sources can still attain 0.48 Tbits/s, and then a third set of merging PRB stream is 0.96 Tbits/s. Moreover, for the sequence length of the order of 10 Gbits, the statistical bias and serial correlation coefficient of three sets of PRB streams are also analyzed.

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).

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.

Impact of optical feedback on current-induced polarization behavior of 1550 nm vertical-cavity surface-emitting lasers.

Polarization switching (PS) between two orthogonal linearly polarized fundamental modes is experimentally observed in commercial free-running 1550 nm vertical-cavity surface-emitting lasers (VCSELs) (Raycan). The characteristics of this PS are strongly modified after introducing a polarization-preserved (PP) or polarization-orthogonal (PO) optical feedback. Under the case that the external cavity is approximately 30 cm, the PP optical feedback results in the PS point shifting toward a lower injection current, and the region within which the two polarization modes coexist is enlarged with the increase of the PP feedback strength. Under too-strong PP feedback levels, the PS disappears. The impact of PO optical feedback on VCSEL polarization behavior is quite similar to that of PP optical feedback, but larger feedback strength is needed to obtain similar results.

Evolution of time delay signature of chaos generated in a mutually delay-coupled semiconductor lasers system.

In this paper, evolution of time delay (TD) signature of chaos generated in a mutual delay-coupled semiconductor lasers (MDC-SLs) system is investigated experimentally and theoretically. Two statistical methods, including self-correlation function (SF) and permutation entropy (PE), are used to estimate the TD signature of chaotic time series. Through extracting the characteristic peak from the SF curve, a series of TD signature evolution maps are firstly obtained in the parameter space of coupled strength and frequency detuning. Meantime, the influences of injection current on the evolution maps of TD signature have been discussed, and the optimum scope of TD signature suppression is also specified. An overall qualitative agreement between our theoretical and experimental results is obtained.

Chaos synchronization in mutually coupled semiconductor lasers with asymmetrical bias currents.

We experimentally and numerically investigated the chaos synchronization characteristics of mutually coupled semiconductor lasers (MCSLs) with asymmetrical bias currents. Experimental results show that, asymmetrical bias current level of two MCSLs has obvious influence on chaos synchronization between them, and stable leader-laggard chaos synchronization can be realized under relatively large asymmetrical bias current levels. Moreover, the influences of frequency detuning and mutually coupling strength between the two lasers on chaos synchronization performance have also been discussed. Theoretical simulations basically conform to our experimental observations.

Bidirectional chaos communication between two outer semiconductor lasers coupled mutually with a central semiconductor laser.

Based on a linear chain composed of a central semiconductor laser and two outer semiconductor lasers, chaos synchronization and bidirectional communication between two outer lasers have been investigated under the case that the central laser and the two outer lasers are coupled mutually, whereas there exists no coupling between the two outer lasers. The simulation results show that high-quality and stable isochronal synchronization between the two outer lasers can be achieved, while the cross-correlation coefficients between the two outer lasers and the central laser are very low under proper operation condition. Based on the high performance chaos synchronization between the two outer lasers, message bidirectional transmissions of bit rates up to 20 Gbit/s can be realized through adopting a novel decoding scheme which is different from that based on chaos pass filtering effect. Furthermore, the security of bidirectional communication is also analyzed.

Time delay signature concealment of optical feedback induced chaos in an external cavity semiconductor laser.

The time delay (TD) signature concealment of optical feedback induced chaos in an external cavity semiconductor laser is experimentally demonstrated. Both the evolution curve and the distribution map of TD signature are obtained in the parameter space of external feedback strength and injection current. The optimum parameter scope of the TD signature concealment is also specified. Furthermore, the approximately periodic evolution relation between TD signature and external cavity length is observed and indicates that the intrinsic relaxation oscillation of semiconductor laser may play an important role during the process of TD signature suppression.

Dual-channel chaos synchronization and communication based on unidirectionally coupled VCSELs with polarization-rotated optical feedback and polarization-rotated optical injection.

A novel dual-channel chaotic synchronization configuration is proposed. This system is constructed on the basis of two unidirectionally coupled vertical-cavity surface-emitting lasers (VCSELs), where a VCSEL subjected to polarization-rotated optical feedback is used as a transmitter and the other VCSEL subjected to polarization-rotated optical injection is used as a receiver. The synchronization and communication performances of such a system are numerically investigated. The results show that, similar to polarization-preserved coupled system with polarization-preserved optical feedback at the T-VCSEL port and polarization-preserved optical injection at the R-VCSEL port, such polarization-rotated coupled system can also realize complete synchronization between each pair of linear polarization (LP) modes and the total output of T-VCSEL and R-VCSEL. Compared with the polarization-preserved coupled system, this proposed system has higher tolerance to mismatched parameters. Furthermore, the average intensities of two orthogonal LP modes are almost the same so that this framework may be used to realize dual-channel chaos communication. Under the additive chaos modulation (ACM) encryption scheme, the encoded messages can be successfully extracted for both of orthogonal LP modes.

Suppression of time delay signatures of chaotic output in a semiconductor laser with double optical feedback.

We experimentally and numerically demonstrate the time delay (TD) signature suppression of chaotic output in a double optical feedback semiconductor laser (DOF-SL) system. Two types of TD signature suppression are demonstrated by adjusting the lengths and the feedback power ratios of the two external cavities. One can significantly eliminate all TD signatures of the DOF-SL system and the corresponding power spectrum distribution becomes quite smooth and flat, the other suppresses one of two TD signatures and remains another one.

Multistability in a semiconductor laser with optoelectronic feedback.

The multistability in a single-mode distributed feedback semiconductor laser with delayed optoelectronic feedback is observed experimentally. For a given delay time, the observed dynamical state of the laser output is critically dependent on the process of varying the delay time and is limited by the range of variation. Various routes of delay time variation results in multistabilities characterized by states of different time series and power spectra.

Analysis of bistable steady characteristics and dynamic stability of linearly tapered nonlinear Bragg gratings.

Based on the nonlinearly coupled mode equations (NLCME), the bistable steady characteristics and dynamic stability of linearly tapered nonlinear Bragg grating (LT-NLBG) have been investigated in detail. The results show that, when the device is tuned near an edge of "photonic band gap" (PBG), in contrast with the free-tapered grating, the negative-tapered grating enhances the switching-on threshold, but increases the on-off switching ratio, enlarges the stable regime, and strengthens the stability significantly. On the other hand, the positive-tapered grating decreases the switching-on threshold, but lower the on-off switching ratio, and worsen the stability remarkably.

Optical generation of a precise microwave frequency comb by harmonic frequency locking.

A semiconductor laser under negative optoelectronic feedback is applied to the generation of a microwave frequency comb through the nonlinear dynamics. The laser system is operated in a harmonic frequency-locked pulsing state, where its power spectrum is a microwave frequency comb that consists of multiples of a locking frequency. Every frequency component of the comb can be simultaneously stabilized by simply injecting an external microwave modulation at any component of the comb. This phenomenon can be viewed as a kind of microwave injection locking of the laser dynamics.