Time-delay Signature Of Chaos Research Articles

Evolution of the time delay signature of chaos generated in three types of optical injection systems.

The time delay signature (TDS) of chaos generated in three schemes of optical injection has been investigated, and the mechanism of TDS suppression (TDSS) is revealed. The first scheme is a continuous-wave (CW) laser unidirectionally injecting into a chaotic laser, and the TDS of the chaotic laser is suppressed below 0.08 in this structure. The second scheme is a chaotic laser unidirectionally injecting into a CW laser, where the parameter range of TDSS lower than 0.06 of this structure is the largest among the three schemes. The third scheme is two CW lasers coupling to each other, and two chaotic lasers with TDS (T D S<0.1) suppression can be obtained simultaneously. For the further analysis of the mechanism of TDSS, the quasi-linear relationship between the synchronization coefficient and TDS is revealed. This study will provide insight into the generation of chaotic lasers by optical injection and promote the application of chaotic lasers.

Effect of resolution bandwidth and video bandwidth on the characterization of chaos in a radio-frequency spectrum analyzer.

The effect of resolution bandwidth (RBW) and video bandwidth (VBW) of a radio-frequency spectrum analyzer on the characteristics of a power spectrum for chaos generated by a semiconductor laser with external optical feedback is investigated experimentally and numerically. We describe the spectral characteristics with effective bandwidth and time-delay signature (TDS) quantificationally. The experimental results demonstrate that the ratio of VBW to RBW has a significant impact on the smoothness of the power spectrum and effective bandwidth of chaos. Meanwhile, the RBW affects the resolution of periodical peaks of the power spectrum and the TDS of chaos, which is obtained by the power spectrum. The incorrect characterization of chaos can be avoided by setting the RBW to no more than 0.1 times as much as the resonance frequency of the external cavity of chaos and setting the VBW/RBW to no more than 0.01. The simulation results qualitatively agree with the analysis of the experiment.

Simultaneous bandwidth-enhanced and time delay signature-suppressed chaos generation in semiconductor laser subject to feedback from parallel coupling ring resonators.

We propose and demonstrate an external-feedback semiconductor laser-based chaos generation scheme supporting simultaneous bandwidth enhancement and excellent time-delay-signature (TDS) suppression, by using parallel-coupling ring resonators (PCRR) as reflector. The characteristics of effective bandwidth and TDS of chaotic signals generated in three indicative PCRR configurations are thoroughly investigated. The numerical results demonstrate that with the nonlinear feedback of PCRR, the TDS of chaos can be efficiently suppressed toward an indistinguishable level, and the bandwidth of chaos in the proposed scheme can also be enhanced, with respect to the conventional optical feedback configuration. The proposed scheme shows a flexible way to generate wideband complex chaos.

Wideband Polarization-Resolved Chaos With Time-Delay Signature Suppression in VCSELs Subject to Dual Chaotic Optical Injections

Both the polarization-resolved chaotic bandwidth enhancement and time-delay signature suppression have been numerically investigated based on a slave vertical-cavity surface-emitting laser (S-VCSEL) driven by dual chaotic optical injections (DCOIs) from two master VCSELs (M-VCSELs) under optical feedbacks. The bandwidth and time-delay signature of polarization-resolved chaos generated in VCSELs are evaluated quantitatively via the effective bandwidth and autocorrelation function, respectively. The results show that, in contrast to the polarization-resolved chaos generated from S-VCSEL subject to single chaotic optical injection, for the equivalent injection conditions, the chaos generated by the DCOI configuration can simultaneously realize the bandwidth enhancement and time-delay signature suppression in the distinctly wider injection parameter spaces of injection strength and frequency detuning. By further exploring the influences of different injection parameters from two injection M-VCSELs on the bandwidth and time-delay signature of chaos, it is found that for the DCOI, the moderate injection strengths and relatively larger frequency detuning of two different injection paths are preferred to obtain the desired wideband polarization-resolved chaos with successful time-delay signature suppression.

Effect of Bias Current on Complexity and Time Delay Signature of Chaos in Semiconductor Laser With Time-Delayed Optical Feedback

The effect of bias current on the complexity and time-delay signature of chaotic signals in semiconductor lasers with polarization preserved optical feedback has been studied experimentally and theoretically. The peak value of the autocorrelation coefficient and the normalized permutation entropy at the feedback round trip time are used to quantify the time delay signature and complexity, respectively. The results show that the time-delay signature is approximately in an inverse relationship with the complexity of chaos when the semiconductor laser is subject to low or strong optical feedback. However, the inverse relationship disappears when the laser operates at higher bias currents with intermediate feedback strength. The simulation results are qualitatively agreed with the experimental results.

Effect of Gain Nonlinearity on Time Delay Signature of Chaos in External-Cavity Semiconductor Lasers

The effects of gain nonlinearity on the time delay signature (TDS) of both intensity and phase chaos in semiconductor lasers (SLs) with optical feedback are investigated numerically. The SLs subject to single-path feedback are mainly considered, and SLs with dual-path feedback are also discussed for the sake of generality. The TDS is evaluated via both auto-correlation function (ACF) and permutation entropy function. It is found that the TDS is more sensitive to nonlinear gain factor (NGF) for large injection current and low feedback strength. For given feedback strength, the peak heights of ACF for both intensity and phase chaos around TDS can be decreased by using SL with low NGF, especially when the injection current is relative high. Furthermore, with low NGF, successful TDS concealment can be achieved in wider region in the parameter planes of feedback strength and injection current. Hence, careful selection of an internal parameter is an effective candidate for TDS concealment in wider parameter region, which is complementary to the existing techniques by controlling the external parameters, and thus is highly desirable for expanding the key space for chaos-based secure communication.

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).

Conceal Time Delay Signature of Chaos in Semiconductor Lasers With Dual-Path Injection

The time delay (TD) signatures of chaotic signals in semiconductor lasers (SLs) with dual-path injection (DPI) are investigated numerically and experimentally based on the autocorrelation function and the permutation entropy function, and are compared with those for chaotic signals in SLs with single-path injection (SPI). Both the intensity and phase chaos are considered. The regions of injection strength and frequency detuning contributing to TD concealment are identified. The optimal selection of injection delays for the DPI case is also suggested. It is found that, for both intensity and phase chaos, the TD signature for the DPI case can be better concealed in wider parameter regions than that for the SPI case, which is highly desirable for security-enhanced chaotic communication systems as well as high-speed random number generators based on chaotic SLs.

Analysis of delay time signature in broadband chaos generated by an optoelectronic oscillator

Chaotic laser characteristics of an optoelectronic oscillator are investigated theoretically and numerically, and the influences of the offset phase and the feedback strength on the time-delay signature of chaos which is generated by an optoelectronic oscillator are studied, based on the method of autocorrelation function. Numerical analyses show that the increase of the feedback strength can further suppress or even conceal the time-delay signature. The closer to the extreme point of the transmission curve the operating point corresponding to the DC offset phase, the weaker the time-delay signature is. The time-delay signature can be suppressed obviously as the offset phase is set to be 0. We also find that the sign of the correlation coefficient corresponding to the time-delay signature is changed when the offset phase and the phase shift caused by the delay feedback produce a phase-shift value of π/2.

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.