Time-delay signature concealment of polarizationresolved chaos outputs in vertical-cavity surface-emitting lasers with variable-polarization filtered optical feedback

Through employing permutation entropy and the self-correlation function, the time-delay signature(TDS) of a vertical-cavity surface-emitting laser(VCSEL) with variable-polarization filtered optical feedback(VPFOF) is evaluated theoretically. The work shows that the feedback rate η, polarizer angle θp, and filter bandwidth Λ have an obvious influence on the TDS. The evolution maps of the TDS in parameter spaceeη; ΛT and eη; θpT are simulated for searching the chaos with weak TDS. Furthermore, compared with a VCSEL with polarization-preserved filtered optical feedback and a VCSEL with variable-polarization mirror optical feedback, this VPFOF–VCSEL shows superiority in TDS suppression.     

Conceal time-delay signature of chaotic vertical-cavity surface-emitting lasers by variable-polarization optical feedback

Time-delay (TD) signatures of chaotic outputs generated by vertical-cavity surface-emitting lasers (VCSELs) are investigated quantitatively by using two proposed estimators, the peak signal to mean ratio (PSMR) calculated based on the auto-correlation function, and the valley signal to mean ratio (VSMR) calculated based on an information-theory-based estimator, the permutation entropy (PE) function. The VCSELs subject to variable-polarization optical feedback (VPOF) are considered, and the effects of polarizer angle, feedback strength, feedback delay and injection current are discussed. When the feedback strength is small, the TD signatures for the fully developed chaotic outputs of VCSELs can be well concealed for all polarizer angles. While for large feedback strength, the TD signatures cannot be concealed for any polarizer angle. However, for moderate feedback strength, the TD signatures of VCSELs with VPOF at intermediate polarizer angles can be better concealed than those of VCSELs with conventional polarization-selected optical feedback. Thus, the VCSELs with VPOF are extremely interesting for the security-enhanced chaotic optical communication systems.     

Influence of polarization mode competition on chaotic unpredictability of vertical-cavity surface-emitting lasers with polarization-rotated optical feedback

The chaotic unpredictability of vertical-cavity surface-emitting lasers (VCSELs) with polarization-rotated optical feedback is evaluated quantitatively via the normalized permutation entropy H. The effect of polarization mode competition (PMC) is explored. For weak PMC, the H for X-polarization mode, Y-polarization mode, and total output are close to each other, while for strong PMC, the H for the total output is the highest one, which indicates that the permutation entropy is an effective tool for quantifying chaotic unpredictability of VCSELs and provides valuable information for choosing the proper chaotic carrier.     

Polarization message encoding through vectorial chaos synchronization in vertical-cavity surface-emitting lasers

We show that self-pulsating vertical-cavity surface-emitting lasers can exhibit vectorial chaos, i.e., chaos in both intensity and polarization. The achievable synchronization degree of two such lasers is high when using a continuous control scheme and unidirectional coupling. We propose a novel encryption scheme, where the phase of the vectorial field is modulated. Therefore, the total intensity of these lasers remains synchronized while the intensities in the polarization modes (de)synchronize following the phase modulation at a ps time scale. This technique allows for transmission of secure data at high bit rates that are not limited by the relaxation oscillation frequency.     

基于光反馈的单向耦合注入垂直腔表面发射激光器的矢量混沌同步特性研究

基于自旋反向模型(SFM)，数值研究了基于光反馈的单向耦合注入垂直腔表面发射激光器的矢量混沌同步特性，研究结果表明：当外部光反馈时间等于光从发射系统到接收系统传输时间时， x偏振模和y偏振模都能接收最好的完全混沌同步质量.若外部光反馈时间不等于传输时间且注入电流接近阈值电流时，占主导的y偏振模能暂时实现较好的完全混沌同步质量.相比较而言，占主导地位的x偏振模至始至终获得很差的同步质量，另外，当系统输出为混合偏振模时，混合偏振模中的每一个线性偏振模获得很差完全同步质量.然而，当注入电流远大于阈值电流时，系统输出仅为y偏振模，这时y偏振模能稳定地实现最好的完全混沌同步质量.最后，当接收激光器受到线性偏振模的强注入时，每一个注入线性偏振模能与接收激光器输出的对应的线性偏振模实现很好的注入锁定同步.然而，每一个占主导的线性偏振模比另一被抑制的线性偏振模获得更差注入锁定同步质量、如果有相等的能量的两个线性偏振模同时存在，这两个线性偏振模获得差不多一致的注入锁定混同步质量， 换句话说，能量较少的线性偏振能获得较高的注入锁定同步质量. 关键词： 线性偏振态 垂直腔表面发射激光器 完全矢量混沌同步 强注入锁定矢量混沌同步     

Enhanced chaos synchronization in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers with polarization-preserved injection

We experimentally study chaos synchronization in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers (VCSELs) with polarization-preserved and polarization-selected optical injection. The measurements show, in agreement with theoretical predictions, that the maximum cross coefficient of 0.884 obtained with polarization-preserved optical injection is significantly higher than the maximum cross coefficient of 0.724 obtained with polarization-selected optical injection.     

Chaos dynamics in vertical-cavity surface-emitting semiconductor lasers with polarization-selected optical feedback

We study experimentally and numerically the dynamic states of chaotic oscillations in vertical-cavity surface-emitting semiconductor lasers (VCSELs) with polarization-selected optical feedback. We identify the regimes of fully-developed chaotic states, low-frequency fluctuations (LFFs), and coexistent states of LFFs and stable oscillation for the variations of the bias injection current and the optical feedback ratio. In particular, coexistent states of LFFs and stable oscillations are observed at higher optical feedback ratio and lower bias injection current. We draw maps of dynamic states in the space of the bias injection current and the optical feedback ratio. The qualitative agreement between the theory and the experiment is found.     

Wave chaos in real-world vertical-cavity surface-emitting lasers

We report the onset of wave chaos in a real-world vertical-cavity surface-emitting laser. In a joint experimental and modeling approach we demonstrate that a small deformation in one layer of the complicated laser structure changes the emission properties qualitatively. Based on the analysis of the spatial emission profiles and spectral eigenvalue spacing distributions, we attribute these changes to the transition from regular behavior to wave chaos, and justify the full analogy to two-dimensional billiards by model calculations. Hence, these lasers represent fascinating devices for wave chaos studies.     

Complete chaotic synchronization characteristics of the linear-polarization mode of vertical-cavity surface-emitting semiconductor lasers with isotropic optical feedback

Based on the SFM model [M. San Miguel, Q. Feng, J.V. Moloney, Phys. Rev. A. 52 (1995) 1728.], complete chaotic synchronization characteristics of linear-polarization (LP) Mode of the vertical-cavity surface-emitting semiconductor lasers (VCSELs) with isotropic optical feedback are numerically investigated. When the propagation time τ_c of light from the transmitter to the receiver equals to the external cavity round-trip time τ, and the central frequency of the T_VCSEL matches that of the R_VCSEL, in large scale region of the feedback coefficient and the injection current where the x-polarization mode as well as the y-polarization mode obtains high synchronization quality at the same time. However, in the central frequency mismatch regions where the x- and y-polarization mode can obtain inferior synchronization quality at same time. But for τ_c ≠ τ, each LP mode of the mixed polarization modes achieved inferior synchronization quality at the same time. Besides, with big enough injection current, the output of the system with the same central frequency in two lasers is entirely governed by the y-polarization mode when the feedback coefficient and Δτ(=τ_c − τ) fixed at a certain value. So the system can realize steadily good synchronization of the completely dominant y-polarization mode. But the synchronization quality of the completely dominated y-polarization mode can be deteriorated by increasing absolute frequency detuning value. Besides, in positive frequency mismatch regions where the influence of the same frequency detuning value on the synchronization quality of the entirely governed y-polarization mode becomes smaller than in negative frequency detuning regions. At last, when τ is given and the central frequency of the T_VCSEL matches that of the R_VCSEL, the influence of the τ_c is not a simple time-shift in the time-evolution of the receiver VCSEL, which has serious influence on the complete synchronization quality of each LP mode.     

Observation of the synchronization of chaos in mutually injected vertical-cavity surface-emitting semiconductor lasers

Synchronization of chaotic oscillations was observed in mutually injected vertical-cavity surface-emitting lasers (VCSELs) in a low-frequency fluctuation regime. In the experiments, only one of the two polarization modes (x mode) showed synchronized oscillations, and the other polarization components (y mode) were synchronized as a result of the effect of anticorrelated oscillations that is a characteristic feature of VCSELs.     

Using polarization properties to enhance performance of chaos synchronization communication between vertical-cavity surface-emitting lasers

Enhanced chaos synchronization communication between vertical-cavity surface-emitting lasers (VCSELs) is investigated numerically, by adopting a polarization communication protocol where one polarization mode is used as the chaotic carrier and the orthogonal polarization mode is used as the disturbed signal. The chaos synchronization quality for the receiver laser (RL) and attacker laser (AL) are analyzed in terms of the cross-correlation coefficient. There are two distinct regions of good synchronization quality in the injection parameters space. In the first region, good synchronization quality can be ensured for both the RL and AL. In the second region, only the RL can realize chaos synchronization. We further discuss the security enhancement by comparing the communication performance between RL and AL for injection parameters within the second region. The results show that successful and robust decoding is only achievable for the RL.     

Numerical characterization of time delay signature in chaotic vertical-cavity surface-emitting lasers with optical feedback

We have discussed numerically the characterization of time delay (TD) signature in a chaotic vertical-cavity surface-emitting laser (VCSEL) subject to optical feedback, where the results for polarization-preserved optical feedback (PPOF) and polarization-rotated optical feedback (PROF) are presented comparatively. It is found that, when the feedback strength is moderate, TD signature can be retrieved successfully by analyzing the total intensity, intensities of x-linearly polarized (x-LP) mode, and y-LP mode in a VCSEL with PPOF; while for PROF case, the intensity amplitude peaks in autocorrelation function (ACF)/delayed mutual information (DMI) of the two orthogonal LP modes are located at multiple values of TD. Furthermore, the influence of the feedback strength and time delay has been investigated. The results show that, a further increase of the feedback strength (roughly>40 ns^?1) leads to the successful identification of the TD signature in the two LP mode intensities of VCSELs with PROF. It is also observed that the estimation of TD depends significantly on the value of the spin–flip relaxation rate (γ_s). For low relaxation rates the TD signature could be much easier to be revealed by the two LP modes than that for large values of relaxation rate in VCSELs with PROF. Finally the influence of injection current and the device linear anisotropies is investigated, and the results of TD estimation are confirmed by calculating permutation entropy (PE).     

Suppressing nonlinear dynamics induced by external optical feedback in vertical-cavity surface-emitting lasers

A numerical study of using external optical injection to suppress the nonlinear dynamics introduced by external optical feedback in vertical-cavity surface-emitting lasers (VCSELs) has been undertaken. The model under consideration is a master–slave configuration where the master VCSEL provides the continuous wave to control the nonlinear behaviors arising in the slave VCSEL. Simulation results indicate that the feedback-induced nonlinear dynamics (e.g. chaotic, single-periodic, and multi-periodic oscillations), relative intensity noise (RIN) as well as the coherence collapse can be suppressed effectively as long as the injection is strong enough to overcome the nonlinear effects of the feedback.     

Suppression of polarization switching in vertical-cavity surface-emitting lasers by use of optical feedback

The polarization properties of vertical-cavity surface-emitting lasers (VCSELs) subject to optical feedback are studied experimentally. It is thereby demonstrated that polarization-selective optical feedback can be utilized to entirely eliminate VCSEL polarization switching over the entire device operating range.     

Polarization dynamics and low-frequency fluctuations in vertical-cavity surface-emitting lasers subjected to optical feedback

The dynamics of vertical-cavity surface-emitting lasers with isotropic optical feedback from a distant reflector is studied experimentally and numerically. Low-frequency fluctuations with sudden drop-outs of power are found to be qualitatively independent of the amount of excitation of the second polarization component. The latter is shown to be controlled to a great extent by the intrinsic dichroism of the solitary laser. The experimental findings are in very good qualitative agreement with simulations. The characteristic features of a doublet in the radio-frequency spectra around the external-cavity round-trip frequency are discussed. PACS 42.55.Px; 42.60.Mi; 42.65.Sf     

Bandwidth-enhanced chaos synchronization in strongly injection-locked semiconductor lasers with optical feedback

Bandwidth-enhanced chaos synchronization in strongly injection-locked semiconductor lasers with optical feedback is numerically studied based on laser rate equations. The bandwidth of the chaotic carrier frequency in a semiconductor laser with optical feedback is expanded roughly three times by strong optical injection compared with the bandwidth when there is no optical injection. Using a bandwidth-enhanced semiconductor laser as a chaotic transmitter and receiver, we synchronized transmitter and the receiver lasers in a complete chaos synchronization scheme.     

Synchronization of chaos in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers

Synchronization of chaos is achieved experimentally in unidirectionally coupled external-cavity vertical-cavity surface-emitting semiconductor lasers operating in an open-loop regime. Synchronization is observed when the polarization of the transmitter is perpendicular to the polarization (x polarization) of the free-running receiver. The ratio of transmitter output to y-polarized receiver output power shows normal (positive-slope) synchronization. However, inverse (negative-slope) synchronization is found to arise between the transmitter output and the x-polarized receiver output power.     

光反馈诱发长波长垂直腔面发射激光器低功耗偏振开关

基于扩展的自旋反转模型,对光反馈诱发下长波长垂直腔面发射激光器中的低功耗偏振开关进行了理论研究.研究表明:长波长垂直腔面发射激光器在自由运行下未能获得的偏振开关现象,可以通过引入中等强度的偏振旋转光反馈来实现.对比强弱两种不同的线性色散效应,发现了一些有趣的现象:弱线性色散条件下更易于在低注入电流下获得偏振开关,并且产生偏振开关所需的反馈强度具有更大的调控范围;强色散效应中未能始终获得偏振开关,会出现两模共存区,并且偏振开关出现的注入电流值较高.同时,观察到的偏振模跳变和多偏振开关现象类似于短波长垂直腔面发射激光器,因而证实这两类激光器在偏振开关的本质规律上是相似的.此外,还对长波长垂直腔面发射激光器不易在低注入电流下获得偏振开关的原因进行了分析,并给出了合理的解释.     

Tailoring wave chaos in vertical-cavity surface-emitting lasers via polarization control

We demonstrate that polarization control in combination with the geometrical shape affects wave chaos phenomena in vertical-cavity surface-emitting lasers (VCSELs). In a grating-polarization-stabilized VCSEL, we demonstrate wave chaos in one polarization mode and a transition from wave chaos to regular behavior in the other orthogonal polarization mode. We quantify the amount of chaoticity via the Brody nearest-neighbor distribution. Comparing with a reference VCSEL without a surface-grating, we explain these results and their injection current dependence by the surface-grating-induced mode selection and a change in the effective resonator shape.     

Stable anticipation synchronization in mutually coupled vertical-cavity surface-emitting lasers system

Two vertical-cavity surface-emitting lasers(VCSELs) are mutually coupled through a partially transparent mirror (PTM) placed in the pathway. The PTM plays the role of external mirror,which controls the feedback strength and coupling strength.We numerically simulate this system by establishing a visible SIMULINK model.The results demonstrate that the anticipation synchronization is achieved and it can tolerate some extent frequency detuning.Moreover,the system shows similar chaos-pass filtering effect on unidirectionally coupled system even both VCSELs are modulated.This system allows simultaneously bidirectional secure message transmission on public channels.