Abstract

We report on the dynamics of free-running and optically injected VCSELs. In particular, the powerful measures including the 0-1 test for chaos and permutation entropy are used for locating the chaotic dynamics in a free-running VCSEL, which illustrates the effects of some key parameters on the chaotic region. In order to enhance chaotic dynamics, the output of the free-running VCSEL (master) is injected to another free-running VCSEL (slave). Our results show that the chaotic dynamics of the slave VCSEL can be greatly enhanced, i.e., both the bandwidth and complexity, while this occurs only outside of the injection locking region where the correlation between the mater and slave lasers is low. To take advantage of these enhanced chaotic dynamics exhibiting extremely high complexity and broadband bandwidth, a three-laser synchronization scheme is proposed and demonstrated. These findings pave the way to the generation of high-quality chaos (no time-delay signature, high bandwidth and complexity) and notably chaos-based applications based on free-running and optically injected VCSELs.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Optical chaos has attracted widespread attention for its potential applications in secure optical communication [1,2], high-speed random bit generation [3–6], chaotic radar [7], compressive sensing [8] and reservoir computing [9]. The important chaotic sources can be readily generated by various types of semiconductor lasers (SLs), such as edge-emitting laser [10–13], vertical-cavity surface-emitting lasers (VCSELs) [14–17], semiconductor ring lasers [18], quantum well (QW) [19, 20] and dot (QD) lasers [21], quantum cascade lasers [22], and nano-lasers [23]. But, it is known that SLs belong to Class B type lasers [24] and output chaos because of the inclusion of more degrees of freedom, that is, under external forcing or modulation, including optical feedback [25, 26], current modulation [27], optoelectronic feedback [28, 29], mutual coupling [30], etc. Among them, external cavity semiconductor lasers (ECSLs) have attracted much attention due to their simplicity and the promising rich nonlinear dynamics [25]. However, the additional degree of freedom may impose restrictions in return. For example, an external cavity introduces the additional time-delay due to the finite propagation of light into the chaotic signals, which is known as ‘time-delay signature’ (TDS) in the literature [25] and may degrade the security of chaos-based communication, or prevent the generated random bit sequence from passing the standard randomness tests. Regarding this signature, various important schemes have been proposed and demonstrated theoretically and/or experimentally to suppress or even eliminate it [31–36]. For example, Wu et al have demonstrated experimentally and numerically that the TDS could be suppressed from the intensity chaos by adopting double optical feedback to SL [31]. Hong et al. have introduced a new concept to quantify the TDS in a three-cascade VCSELs system, and found that the TDS can be totally concealed over a wide frequency detuning region, while the resulting chaos has a higher bandwidth [32]. Xiang et al. have successfully removed the TDS from the chaotic output in ECSLs by using a complex dual chaos injection scheme [34]. Li et al. have proven that the TDS can be substantially suppressed both in phase and amplitude by means of chaos injection in conjunction with large values of the linewidth enhancement factor [35]. Jiang et al. have investigated that the TDS of chaotic signal can be suppressed by injecting the output of a chaotic general ECSL into an optical time lens module, where the bandwidth can be greatly enhanced [36]. Most of these schemes indeed provide promising solutions to the TDS concealment but at the expense of increasing the system complexity, which can be seen as a drawback for photonic integrated circuits (PICs) of chaos emitters. Thus, it is of prime importance to find alternative ways to generate optical chaos where the system structure is simple (i.e., no feedback or mutual coupling loop) and promising for future PICs. Fortunately, Virte et al. have found that deterministic polarization chaos can be generated in a free-running QD VCSEL (grown and described by Hopfer et al. [37]), which remains the first counter-example of a free-running laser generating chaos [38]. It is accepted that the nonlinear coupling between two elliptically polarized modes accounts for the chaos generation in a free-running VCSEL, which has also been reproduced and explained by using the well-known spin-flip model [39, 40]. Later on, they have proven the feasibility of the applications in random number generation and chaos synchronization [41, 42]. More recently, they have demonstrated experimentally similar polarization chaos can be obtained in off-the-shelf VCSELs, i.e., a commercially available quantum-well (QW) VCSEL in conjunction with the mechanically applied in-plane anisotropic strain [43]. Inspired by those important findings, we believe a comprehensive study on the characterization of chaotic dynamics in those simple VCSELs is called for, which can provide a better understanding of the influence of some key parameters on the chaos generation and pave the way to the wide spread use of solitary VCSELs for chaos-based applications as mentioned above.

In addition to TDS mentioned above, other properties of optical chaos have also been widely studied in the past few years, such as bandwidth [36], complexity [44], or the combination of bandwidth and complexity [26]. These properties are of prime importance to enhance the performance of chaos-based applications. For example, three-cascaded lasers with enhanced bandwidth and complexity have been used to generate physical random numbers, where the maximum generation rate can reach 1.2Tb/s [45]. Such a high bit rate indeed benefits from the enhanced properties of optical chaos. It should be noted that, even though the feasibility of chaos generation in a free-running VCSEL has been demonstrated, the bandwidth and complexity are rather low and thus cannot meet the demand of high bandwidth and security of modern communications. Thus, it would be of interest to study whether the properties of optical chaos generated by a free-running VCSEL can be greatly improved by using the some simple but effective approaches, for example, an optical injection scheme, which will be applied to our system and testified.

In this paper, we first study nonlinear dynamics of a free-running VCSEL, where two widely used measures including the 0-1 test for chaos and permutation entropy (PE) are introduced to analyze and characterize the effects of the key parameters on the chaotic region. Further, we construct a master-slave VCSEL configuration and focus on the bandwidth and unpredictability of the salve VCSEL as well as their relation to chaos synchronization between master and slave VCSELs. Finally, a three VCSEL system is suggested, which allows for high-quality chaos synchronization between enhanced chaos with extremely wide bandwidth and high complexity.

2. Theory

Our simulations are based on the simulating the well-known spin-flip model. The rate equations for a free-running VCSEL, i.e., the master laser in a master-slave configuration are written as [39, 42]

dE±dt=κ(1+iα)(N±n1)E±(iγp+γa)E
dNdt=γ(Nμ+(N+n)|E+|2+(Nn)|E|2)
dndt=γsnγ((N+n)|E+|2(Nn)|E|2)
where E+and Estand for the slowly varying electrical fields for the right and left circular polarization (RCP and LCP). N is the total carrier inversion, and nis the difference between carrier inversions with opposite spins. Other parameters are the field decay rate κ, the linewidth enhancement factor α, the carrier decay rate γ, the injection current μ, the spin-flip relaxation rate γs, and the phase and amplitude anisotropies γp and γa. The following parameters are kept constant κ=600ns1, γ=1ns1, andγa=0.7ns1 [39, 42], while γp, γs, μ and α are varied according to the illustrative purpose.

Since we attempt to enhance the properties of chaotic dynamics generated by a free-running VCSEL through optical injection, a master-slave scheme will be used. Here the rate equations of the slave VCSEL extended from the basic spin-flip model read [42]

dF±dt=κ(1+iα)(Ns±ns1)F±(iγp+γa)FiΔF±+kinE±.
dNsdt=γ(Nsμ+(Ns+ns)|F+|2+(Nsns)|F|2).
dnsdt=γsnsγ((Ns+ns)|F+|2(Nsns)|F|2).
where F+ and Fare the RCP and LCP fields of the slave VCSEL. Likewise, Ns is the total carrier inversion, andnsis the difference between carrier inversions with opposite spins. Regarding the effect of unidirectional optical injection, we assume that Δis the angular frequency detuning and kin is the injection strength.

Polarization dynamics of VCSEL in different systems have been studied in many works [16, 17, 46–48], in this study, we analyze and characterize VCSEL dynamics by using the widely used 0-1 test for chaos, which has been detailed in [49], and the powerful PE, which is derived from the information theory, as a complexity measurement. The computation of PE has been given in several previous works; one can refer to [50] and references therein for more details. Here, we would like to emphasize that large PE indicates high unpredictability degree, which is a highly desired property to ensure security for chaos-based communication systems. One can have 0PE1, withPE=0corresponding to a regular, predictable dynamic, andPE=1 to a fully random, unpredictable one.

In our simulations, the embedding parametersDx=5(embedding dimension) andτe=1(embedding delay) are specified as in [50]. Each time series is obtained after sampling process, where the sampling period isΩs=10ps. To meet the statistical significance of the results, each time series is then divided into several disjointed sections withT=5000points, and a statistical average over different windows is performed to computeH.

In addition, we will consider the correlation between chaotic time series. By following [51], we can define the cross-correlation coefficient as

Cm,s=[Im(t)Im(t)][Is(t)Is(t)]|Im(t)Im(t)|2|Is(t)Is(t)|2.
where subscripts m and sdenote two laser systems, is the time average, and I(t)=|E(t)|2stands for the chaotic intensity time series. The value C=1 represents prefect synchronization and C=0 stands for no correlation.

3. Results

In this section, we present the numerical simulation results by integrating the rate Eqs. (1)-(6) with the forth-order Runge-Kutta algorithm. The results are mainly represented by using high-resolution two-dimensional maps of 0-1 test for chaos and PEcomputed from intensity time series. The effects of important parameters including the pump rate μ, the linear birefringence rate γp, the spin-flip relaxation rate γs, and the linewidth enhancement factor α on chaotic dynamics will be explored in some details. It should be noted that since the results for RCP and LCP are almost identical, only those for RCP are presented, unless otherwise stated.

3.1 Effects of the parameters on the chaos region of a free-running VCSEL

In [39], Virte et al. have shown the stability and instability of a free-running VCSEL by using combined methods of direct numerical simulations and a continuation method. Here we show more details about dynamics of free-running VCSELs. Figure 1 shows the time series and the corresponding RF spectra as the pump rate μincreases, where the parameters are α=3, γp=25ns1, and γs=20ns1. From the time-series plots it is clear that a solitary VCSEL can be destabilized through a Hopf bifurcation and other further complex bifurcations by increasing the pump rate. Under proper conditions, it can operate in various dynamical regimes, including steady state, periodicity, quasiperiodicity and complex dynamics including chaos. The corresponding spectra clearly verify these dynamics. Our results agree well with those in [39], which make us become more confident about our following studies.

 

Fig. 1 (a) Intensity time series and (b) the corresponding spectrum of a free-running VCSEL, whereα=3, γp=25ns1, andγs=20ns1.

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Figure 2 shows the typical one-parameter bifurcations of a free-running VCSEL as the pump current is increased, where the parameters are the same as those in Fig. 1. Both the results for RCP and LCP are shown to confirm that they are identical and thus one of them is needed for illustrative purposes. In the bifurcation diagram, the maximum and minimum of intensity time series are shown. As can be seen from this figure, a free-running VCSEL allows for a diversity of dynamics via a period-doubling route to chaos, which is similar to the one found in a solitary spin VCSEL [20]. This is expected since the physical mechanism of instability for both of them is the nonlinear coupling between two elliptically polarized modes.

 

Fig. 2 One-parameter bifurcation diagrams of a free-running VCSEL with increasing pump current: (a) RCP and (b) LCP. The parameters are the same as those in Fig. 1.

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To obtain a global view of the dynamics and the effects of key parameters mentioned above, we show high-resolution two-dimensional maps of the 0-1 test for chaos and PE side by side. Let us first consider the effects of γp (x-axis) and μ (y-axis). These two parameters can be seen as controllable parameters since one can easily change the pump current μ in the experiments while the birefringence γpcan be controlled through the applied in-plane anisotropic strain [43]. The results for the 0-1 test for chaos and PE in the (γp,μ) plane are shown in Fig. 3, where several values of are considered. In the case of the 0-1 test for chaos, chaos is highlighted by red, while in the case of PE, blue represents steady-state (PE=0) and yellow stands for high values of PE, viz., PE>0.9. Several phenomena can be discovered from this figure. First, given a properγp, increasing μis helpful to obtain chaos, which is consistent with the results in Figs. 1 and 2. Second, in all cases considered, the chaotic region resembles a well-defined ‘tongue ’-like shape and the tongue tip is located at the bottom left corner of the parameter space. As γsis decreased, the tongue becomes larger, which means that the chaotic region grows in size, and in the meantime, the tongue tip is moved towards smaller values of γpandμ. Actually, the fact that the smaller the spin-flip relaxation rate γs, the larger region of chaos can be obtained coincides with the finding in spin VCSELs [20]. Third, as γsreaches a critical value, roughlyγs=25ns-1, the chaotic region saturates. Finally, the results for the 0-1 test for chaos and PE agree well with each other. That is, chaotic region always corresponds to the region with values of PE close to 1. In addition, PE provides more information about dynamics; for example, the region for PE=0 means steady state, while other values between 0 and 1 represent periodicity and quasiperodicity other than chaos.

 

Fig. 3 (a)The two-dimensional map of the 0-1 test for chaos and (b) PE of the free-running VCSEL in the (γp,μ) plane as γsis varied, whereα=3. (a1, b1)γs=100ns1, (a2, b2)γs=50ns1, (a3, b3)γs=25ns1, and (a4, b4)γs=5ns1 .

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Figure 4 shows the results of the 0-1 test for chaos and PE in the (γs,μ) plane for several values of γp. For a large value of γp, chaos is generated for a VCSEL pumped extremely above the threshold [see Figs. 4(a1) and 4(b1)]. As γpdecreases, the chaotic region expands; see Figs. 4(a2, a3) and 4(b2, b3). However, as γpis further decreased, chaos is found in a very small area [see Figs. 4(a4) and 4(b4)]. All of the information can be obtained either from the 0-1 test for chaos or from the PE.

 

Fig. 4 (a) The two-dimensional map of the 0-1 test for chaos and (b)PEof the free-running VCSEL in the (γs,μ) plane as γpis varied, whereα=3, (a1, b1)γp=100ns1, (a2, b2)γp=50ns1, (a3, b3)γp=25ns1, and (a4, b4)γp=5ns1

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We now are interested to uncover changes in the dynamics of a free-running VCSEL in the (γs,γp) plane as the pump current is varied. As an example, Fig. 5 shows the results for the 0-1 test for chaos and PE, where α=3and μis increased from 2 to 10. It can be clearly seen that chaotic dynamics is extremely sensitive to the variation ofμ. For a small value ofμ, chaos is mainly obtained for smaller values of γsandγp. As μincreases, chaos can be seen in a larger range of γpand the whole range of γs, indicating chaotic region expands in size. However, asμ is larger than a critical value, the portion and location of chaotic region remain almost unchanged as μ is further increased. This also indicates that one can reduce the independence of chaos on γsandγpby always pumping VCSEL at large values of the injection current, which is very useful for experimental investigations. Again, the results for both measures, i.e., the 0-1 test for chaos and PE are in good agreement with each other.

 

Fig. 5 (a)The two-dimensional map of the 0-1 test for chaos and (b) PE of the free-running VCSEL with varying γs(x-axis) and γp(y-axis), whereα=3, (a1, b1): μ=2, (a2, b3)μ=5, (a3,b3)μ=8,(a4,b4) μ=10

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It is well known that in conventional lasers, the linewidth enhancement factor α, which quantify the coupling between amplitude and phase of the electric field, plays an important role in the dynamics [35]. It is of interest to study if this parameter plays a similar role in the free-running VCSEL dynamics. In Fig. 6, we present the results for the 0-1 test for chaos and PEin the (γs,γp) plane for a fixed value of pump current but several different values of α. Comparison among these subfigures clearly indicates that increasing αis beneficial to the enhancement of chaos region. In other words, it is always easier to obtain chaos in a free-running VCSEL with larger values ofα, which provides necessary instructions for laser design and fabrications for chaos-based applications.

 

Fig. 6 (a1-c1, a2-c2) The two-dimensional map of the 0-1 test for chaos and (a3-c3, a4-b4) PEof the free-running VCSEL with varying γs(x-axis) and γp(y-axis). Left: μ=5; right: μ=8. First row: α=1, second: α=2, third: α=6.

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3.2 Enhanced chaotic dynamics in an optically injected VCSEL and their synchronization issue

As has been discussed above, although a free-running VCSEL allows for chaos generation in a wide range of parameters, some drawbacks still exist, such as low bandwidth and complexity. In this section, we first construct a master-slave configuration based on two free-running VCSELs and discuss bandwidth and complexity of the slave VCSEL, as well as synchronization between two VCSELs. Then, a high-quality chaos synchronization scheme for synchronizing enhanced dynamics generated by optically injected VCSELs is proposed and demonstrated numerically.

First, the bandwidth of the slave VCSEL is studied. The parameters for the master VCSEL modeled by Eqs. (1)-(3) are chosen such that the laser operates in a chaotic regime. The corresponding parameters are μ=2,α=3,γp=25ns1and γs=20ns1, and kept constant in what follows. For simplicity, we consider identical parameter values for the master and slave lasers, but the frequency detuning between them will also be introduced for the purpose of enhancing the output dynamics of the slave laser. It is expected that under proper conditions, chaos injection will gives rise to chaos operation in the slave VCSEL, which is modeled by Eqs. (4)-(6), in the wide parameter space (In fact, the slave laser also operates in a chaotic regime in the absence of injection for the considered parameters.). For this reason, the 0-1 test will not be applied to the slave VCSEL. Two examples of chaos bandwidth of the VCSEL are shown in Fig. 7, where only the results for RCP are shown since RCP and LCP exhibit identical dynamical behavior. Here the bandwidth is defined as the range between DC and the frequency that contains 80% of the spectral power [52]. In Fig. 7 (a) we fix the injection ratio kin but vary the frequency detuning Δf in a wide range, i.e., kin=60ns-1. It is interesting to observe that one can increase the bandwidth by considering large values of frequency detuning, especially for a large positive detuning. This produces a concave shape, with its bottom corresponding to low bandwidth range equal to that of the master free running VCSEL. This is attributed to the injection-locking effect as observed in other conventional optically injected lasers [53]. The asymmetry of the curve shape is caused by the relatively large value of linewidth enhancement factor, i.e., α=3, which accounts for the coupling between amplitude and phase of the electric field. Figure 7 (b) shows the variation of chaos bandwidth of the slave VCSEL as a function of the injection ratio kinfor a fixed frequency detuning Δf=30GHz. It is clearly seen that for the considered positive detuning, as the injection ratio increases, the bandwidth is improved gradually and almost saturates at very large values of kin.

 

Fig. 7 The bandwidth of the slave VCSEL as a function of (a) frequency detuning Δfand (b) injection strength kin, where (a) kin=60ns-1, and (b) Δf=30GHz. Other parameters areμ=2,α=3,γp=25ns1andγs=20ns1.

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Figure 8 shows a two-dimensional map of the bandwidth of the slave VCSEL computed from the RCP. The horizontal axis corresponds to frequency detuningΔf, while the vertical axis to the injection ratio kin. The V-shape blue area indicates the injection –locking region, where the master and slave VCSELs exhibit identical bandwidth. Outside this region, chaos bandwidth enhancement is observed and its asymmetric property is seen, where positive detuning is preferred for the enhancement of chaos bandwidth, in accordance with the observation in other optical injection systems [52]. This means that the injection scheme used in this study is highly effective for enhancing the limited bandwidth of a free-running VCSEL. In addition, these results further confirm those in Fig. 7.

 

Fig. 8 Two-dimensional map of the bandwidth of the slave VCSEL shown in the plane of (Δf,kin). Other parameters are μ=2,α=3,γp=25ns1andγs=20ns1.

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Next, we will study the unpredictability property of optical chaos generated by the slave VCSEL. To this end, we adopt PE, whose parameter setting is given in Section 2, to quantify chaos complexity. Figure 9 shows the PE variation against either frequency detuning Δf or injection strength kin. The parameter setting is the same as that in Fig. 7. A comparison between Fig. 7 and Fig. 9 shows that one can expect the simultaneous enhancement of bandwidth and complexity under proper circumstances. We further present the two-dimensional PE map in Fig. 10. As expected, higher PEvalues are obtained outside the injection-locking region, especially for positive detuning values. This trend coincides well with bandwidth variation shown in Fig. 8. This indicates that it is possible to obtain enhanced chaotic dynamics with broadband bandwidth >30 GHz and high complexity (PE~1) in wide regions of the parameter space of interest.

 

Fig. 9 PE of the slave VCSEL as a function of (a) frequency detuning Δfand (b) injection strength kin, where (a) kin=60ns1 and (b) Δf=30GHz. Other parameters are μ=2,α=3,γp=25ns1andγs=20ns1.

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Fig. 10 Two-dimensional PEmap computed from the slave VCSEL shown in the plane of (Δf,kin). Other parameters are μ=2,α=3,γp=25ns1andγs=20ns1.

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We further consider the correlation between the master and slave VCSELs. The reason is that we want to obtain high-quality chaos synchronization between optimized chaotic signals, i.e., exhibiting higher bandwidth and complexity. The cross-correlation coefficient given in Eq. (8) is used to quantify the correlation. The result is shown in Fig. 11. It is clear that high-quality chaos synchronization is seen only in the injection—locking region, where the correlation is extremely high (C>0.95). However, in this region, the bandwidth and complexity of the slave output are low due to the injection-locking effect. Outside this region, the slave output can be enhanced due to the interaction between the injection light and the electric field of the slave VCSEL. For these reasons, the master-slave configuration is not the desirable system for chaos-based communications which require chaos possessing high complexity and broadband bandwidth.

 

Fig. 11 The calculated cross-correlation coefficient shown in the plane of (Δf,kin). Other parameters are μ=2,α=3,γp=25ns1andγs=20ns1.

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Finally, we propose a novel chaotic system that allows for perfectly synchronizing enhanced chaotic signals generated by optically injected VCSELs. Specifically, it consists of three VCSELs, i.e., one free-running master VCSEL and two free-running slave VCSELs; both slaves are subject to unidirectional injection from the same master, while there is no direct link between the two slaves. In fact, such a synchronization and communication scheme has been applied to other lasers [54–56]. Figure 12 shows a typical example of high-quality chaos synchronization between the two slave lasers. The results for intensity time series, RF spectrum, and time-shift cross-correlation coefficient clearly indicate that the slave laser output is enhanced as expected and can be highly correlated under proper conditions, while their correlation to the master laser is rather low. The next step is to construct chaos-based communication based on the current synchronization scheme, which offers enhanced security and high-speed message exchange (either unidirectional or bidirectional) [56]. However, the corresponding study is beyond the scope of the current article and will be carried out elsewhere.

 

Fig. 12 (a) Intensity time traces and (b) RF spectrum of three VCSELs, (c) the correlation between any two lasers of the prosed system, where Δf=30GHz and kin=60ns1. Other parameters are μ=2,α=3,γp=25ns1and γs=20ns1.

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4. Conclusion

In summary, we have studied the dynamics of free-running and optically injected VCSELs, with the help of the 0-1 test for chaos and PE. The effects of several key parameters on chaotic dynamics of VCSELs are clarified based on high-resolution two-dimensional color maps of these two measures. We have also considered the master-slave configuration, where the chaotic output of the slave VCSEL can be greatly enhanced under proper conditions. Finally, we have proposed a three-laser scheme to synchronize the bandwidth- enhanced and complexity-improved chaos generated by the slave VCSELs. Additionally, no time-delay signature is expected since neither feedback nor mutual coupling is introduced. Therefore, these findings are of interest for chaos-based applications, such as secure communications and random number generation.

Funding

National Natural Science Foundation of China (61775185); Sichuan Science and Technology Program (2018HH0002).

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23. H. Han and K. A. Shore, “Dynamical characteristics of nano-lasers subject to optical injection and phase conjugate feedback,” IET Optoelectron. 12(1), 25–29 (2018). [CrossRef]  

24. J. Ohtsubo, Semiconductor Lasers: Stability, Instability and Chaos (Springer, 2007).

25. D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: A dynamical point of view,” IEEE J. Quantum Electron. 45(7), 879–891 (2009). [CrossRef]  

26. D. Rontani, E. Mercier, D. Wolfersberger, and M. Sciamanna, “Enhanced complexity of optical chaos in a laser diode with phase-conjugate feedback,” Opt. Lett. 41(20), 4637–4640 (2016). [CrossRef]   [PubMed]  

27. M. Sciamanna, F. Rogister, O. Deparis, P. Mégret, M. Blondel, and T. Erneux, “Bifurcation to polarization self-modulation in vertical-cavity surface-emitting lasers,” Opt. Lett. 27(4), 261–263 (2002). [CrossRef]   [PubMed]  

28. G. Q. Xia, S.-C. Chan, and J. M. Liu, “Multistability in a semiconductor laser with optoelectronic feedback,” Opt. Express 15(2), 572–576 (2007). [CrossRef]   [PubMed]  

29. M. Cheng, L. Deng, H. Li, and D. Liu, “Enhanced secure strategy for electro-optic chaotic systems with delayed dynamics by using fractional Fourier transformation,” Opt. Express 22(5), 5241–5251 (2014). [CrossRef]   [PubMed]  

30. N. Jiang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, L. Yang, and D. Zheng, “Multiaccess optical chaos communication using mutually coupled semiconductor lasers subjected to identical external injections,” IEEE Photonics Technol. Lett. 22(10), 676–678 (2010). [CrossRef]  

31. J. G. Wu, G. Q. Xia, and Z. M. Wu, “Suppression of time delay signatures of chaotic output in a semiconductor laser with double optical feedback,” Opt. Express 17(22), 20124–20133 (2009). [CrossRef]   [PubMed]  

32. Y. Hong, A. Quirce, B. Wang, S. Ji, K. Panajotov, and P. S. Spencer, “Concealment of chaos time-delay signature in three-cascaded vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 52(8), 1–8 (2016).

33. D. Wang, L. Wang, T. Zhao, H. Gao, Y. Wang, X. Chen, and A. Wang, “Time delay signature elimination of chaos in a semiconductor laser by dispersive feedback from a chirped FBG,” Opt. Express 25(10), 10911–10924 (2017). [CrossRef]   [PubMed]  

34. S. Y. Xiang, W. Pan, A. J. Wen, N. Q. Li, L. Y. Zhang, L. Shang, and H. X. Zhang, “Conceal time delay signature of chaos in semiconductor lasers with dual-path injection,” IEEE Photonics Technol. Lett. 25(14), 1398–1401 (2013). [CrossRef]  

35. N. Li, W. Pan, A. Locquet, and D. S. Citrin, “Time-delay concealment and complexity enhancement of an external-cavity laser through optical injection,” Opt. Lett. 40(19), 4416–4419 (2015). [CrossRef]   [PubMed]  

36. N. Jiang, C. Wang, C. Xue, G. Li, S. Lin, and K. Qiu, “Generation of flat wideband chaos with suppressed time delay signature by using optical time lens,” Opt. Express 25(13), 14359–14367 (2017). [CrossRef]   [PubMed]  

37. F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89(14), 141106 (2006). [CrossRef]  

38. M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2012). [CrossRef]  

39. M. Virte, K. Panajotov, and M. Sciamanna, “Bifurcation to nonlinear polarization dynamics and chaos in vertical-cavity surface-emitting lasers,” Phys. Rev. A 87(1), 013834 (2013). [CrossRef]  

40. Q. Feng, J. V. Moloney, and J. V. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728–1739 (1995). [CrossRef]   [PubMed]  

41. M. Virte, E. Mercier, H. Thienpont, K. Panajotov, and M. Sciamanna, “Physical random bit generation from chaotic solitary laser diode,” Opt. Express 22(14), 17271–17280 (2014). [CrossRef]   [PubMed]  

42. M. Virte, M. Sciamanna, and K. Panajotov, “Synchronization of polarization chaos from a free-running VCSEL,” Opt. Lett. 41(19), 4492–4495 (2016). [CrossRef]   [PubMed]  

43. T. R. Raddo, K. Panajotov, B. V. Borges, and M. Virte, “Strain induced polarization chaos in a solitary VCSEL,” Sci. Rep. 7(1), 14032 (2017). [CrossRef]   [PubMed]  

44. S. Xiang, W. Pan, L. Yan, B. Luo, X. Zou, N. Jiang, and K. Wen, “Influence of polarization mode competition on chaotic unpredictability of vertical-cavity surface-emitting lasers with polarization-rotated optical feedback,” Opt. Lett. 36(3), 310–312 (2011). [CrossRef]   [PubMed]  

45. R. Sakuraba, K. Iwakawa, K. Kanno, and A. Uchida, “Tb/s physical random bit generation with bandwidth-enhanced chaos in three-cascaded semiconductor lasers,” Opt. Express 23(2), 1470–1490 (2015). [CrossRef]   [PubMed]  

46. B. S. Ryvkin, K. Panajotov, E. A. Avrutin, I. Veretennicoff, and H. Thienpont, “Optical-injection-induced polarization switching in polarization-bistable vertical-cavity surface-emitting lasers,” J. Appl. Phys. 96(11), 6002–6007 (2004). [CrossRef]  

47. I. Gatare, J. Buesa, H. Thienpont, K. Panajotov, and M. Sciamanna, “Polarization switching bistability and dynamics in vertical-cavity surface-emitting laser under orthogonal optical injection,” Opt. Quantum Electron. 38(4–6), 429–443 (2006). [CrossRef]  

48. I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76(3), 031803 (2007). [CrossRef]  

49. G. A. Gottwald and I. Melbourne, “On the Implementation of the 0-1 Test for Chaos,” SIAM J. Appl. Dyn. Syst. 8(1), 129–145 (2009). [CrossRef]  

50. N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, X. H. Zou, and L. Y. Zhang, “Bandwidth and unpredictability properties of semiconductor ring lasers with chaotic optical injection,” Opt. Laser Technol. 53(1), 45–50 (2013). [CrossRef]  

51. M. Sciamanna, I. Gatare, A. Locquet, and K. Panajotov, “Polarization synchronization in unidirectionally coupled vertical-cavity surface-emitting lasers with orthogonal optical injection,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5), 056213 (2007). [CrossRef]   [PubMed]  

52. N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, and X. H. Zou, “Loss of time delay signature in broadband cascade-coupled semiconductor lasers,” IEEE Photonics Technol. Lett. 24(23), 2187–2190 (2012). [CrossRef]  

53. N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, X. H. Zou, L. Y. Zhang, and P. H. Mu, “Photonic generation of wideband time-delay-signature-eliminated chaotic signals utilizing an optically injected semiconductor laser,” IEEE J. Quantum Electron. 48(10), 1339–1345 (2012). [CrossRef]  

54. V. Annovazzi-Lodi, G. Aromataris, M. Benedetti, and S. Merlo, “Private message transmission by common driving of two chaotic lasers,” IEEE J. Quantum Electron. 46(2), 258–264 (2010). [CrossRef]  

55. K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012). [CrossRef]   [PubMed]  

56. N. Q. Li, W. Pan, L. S. Yan, B. Luo, X. H. Zou, and S. Y. Xiang, “Enhanced two-channel optical chaotic communication using isochronous synchronization,” IEEE J. Sel. Top. Quantum Electron. 19(4), 0600109 (2013). [CrossRef]  

References

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  18. R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Loss of time-delay signature in chaotic semiconductor ring lasers,” Opt. Lett. 37(13), 2541–2543 (2012).
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  19. M. J. Wishon, A. Locquet, C. Y. Chang, D. Choi, and D. S. Citrin, “Crisis route to chaos in semiconductor lasers subjected to external optical feedback,” Phys. Rev. A 97(3), 033849 (2018).
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  20. N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Stability and bifurcation analysis of spin-polarized vertical-cavity surface-emitting lasers,” Phys. Rev. A 96(1), 013840 (2017).
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  21. N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Mapping bifurcation structure and parameter dependence in quantum dot spin-VCSELs,” Opt. Express 26(11), 14636 (2018).
    [Crossref]
  22. L. Jumpertz, K. Schires, M. Carras, M. Sciamanna, and F. Grillot, “Chaotic light at mid-infrared wavelength,” Light Sci. Appl. 5(6), e16088 (2016).
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  23. H. Han and K. A. Shore, “Dynamical characteristics of nano-lasers subject to optical injection and phase conjugate feedback,” IET Optoelectron. 12(1), 25–29 (2018).
    [Crossref]
  24. J. Ohtsubo, Semiconductor Lasers: Stability, Instability and Chaos (Springer, 2007).
  25. D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: A dynamical point of view,” IEEE J. Quantum Electron. 45(7), 879–891 (2009).
    [Crossref]
  26. D. Rontani, E. Mercier, D. Wolfersberger, and M. Sciamanna, “Enhanced complexity of optical chaos in a laser diode with phase-conjugate feedback,” Opt. Lett. 41(20), 4637–4640 (2016).
    [Crossref] [PubMed]
  27. M. Sciamanna, F. Rogister, O. Deparis, P. Mégret, M. Blondel, and T. Erneux, “Bifurcation to polarization self-modulation in vertical-cavity surface-emitting lasers,” Opt. Lett. 27(4), 261–263 (2002).
    [Crossref] [PubMed]
  28. G. Q. Xia, S.-C. Chan, and J. M. Liu, “Multistability in a semiconductor laser with optoelectronic feedback,” Opt. Express 15(2), 572–576 (2007).
    [Crossref] [PubMed]
  29. M. Cheng, L. Deng, H. Li, and D. Liu, “Enhanced secure strategy for electro-optic chaotic systems with delayed dynamics by using fractional Fourier transformation,” Opt. Express 22(5), 5241–5251 (2014).
    [Crossref] [PubMed]
  30. N. Jiang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, L. Yang, and D. Zheng, “Multiaccess optical chaos communication using mutually coupled semiconductor lasers subjected to identical external injections,” IEEE Photonics Technol. Lett. 22(10), 676–678 (2010).
    [Crossref]
  31. J. G. Wu, G. Q. Xia, and Z. M. Wu, “Suppression of time delay signatures of chaotic output in a semiconductor laser with double optical feedback,” Opt. Express 17(22), 20124–20133 (2009).
    [Crossref] [PubMed]
  32. Y. Hong, A. Quirce, B. Wang, S. Ji, K. Panajotov, and P. S. Spencer, “Concealment of chaos time-delay signature in three-cascaded vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 52(8), 1–8 (2016).
  33. D. Wang, L. Wang, T. Zhao, H. Gao, Y. Wang, X. Chen, and A. Wang, “Time delay signature elimination of chaos in a semiconductor laser by dispersive feedback from a chirped FBG,” Opt. Express 25(10), 10911–10924 (2017).
    [Crossref] [PubMed]
  34. S. Y. Xiang, W. Pan, A. J. Wen, N. Q. Li, L. Y. Zhang, L. Shang, and H. X. Zhang, “Conceal time delay signature of chaos in semiconductor lasers with dual-path injection,” IEEE Photonics Technol. Lett. 25(14), 1398–1401 (2013).
    [Crossref]
  35. N. Li, W. Pan, A. Locquet, and D. S. Citrin, “Time-delay concealment and complexity enhancement of an external-cavity laser through optical injection,” Opt. Lett. 40(19), 4416–4419 (2015).
    [Crossref] [PubMed]
  36. N. Jiang, C. Wang, C. Xue, G. Li, S. Lin, and K. Qiu, “Generation of flat wideband chaos with suppressed time delay signature by using optical time lens,” Opt. Express 25(13), 14359–14367 (2017).
    [Crossref] [PubMed]
  37. F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89(14), 141106 (2006).
    [Crossref]
  38. M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2012).
    [Crossref]
  39. M. Virte, K. Panajotov, and M. Sciamanna, “Bifurcation to nonlinear polarization dynamics and chaos in vertical-cavity surface-emitting lasers,” Phys. Rev. A 87(1), 013834 (2013).
    [Crossref]
  40. Q. Feng, J. V. Moloney, and J. V. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728–1739 (1995).
    [Crossref] [PubMed]
  41. M. Virte, E. Mercier, H. Thienpont, K. Panajotov, and M. Sciamanna, “Physical random bit generation from chaotic solitary laser diode,” Opt. Express 22(14), 17271–17280 (2014).
    [Crossref] [PubMed]
  42. M. Virte, M. Sciamanna, and K. Panajotov, “Synchronization of polarization chaos from a free-running VCSEL,” Opt. Lett. 41(19), 4492–4495 (2016).
    [Crossref] [PubMed]
  43. T. R. Raddo, K. Panajotov, B. V. Borges, and M. Virte, “Strain induced polarization chaos in a solitary VCSEL,” Sci. Rep. 7(1), 14032 (2017).
    [Crossref] [PubMed]
  44. S. Xiang, W. Pan, L. Yan, B. Luo, X. Zou, N. Jiang, and K. Wen, “Influence of polarization mode competition on chaotic unpredictability of vertical-cavity surface-emitting lasers with polarization-rotated optical feedback,” Opt. Lett. 36(3), 310–312 (2011).
    [Crossref] [PubMed]
  45. R. Sakuraba, K. Iwakawa, K. Kanno, and A. Uchida, “Tb/s physical random bit generation with bandwidth-enhanced chaos in three-cascaded semiconductor lasers,” Opt. Express 23(2), 1470–1490 (2015).
    [Crossref] [PubMed]
  46. B. S. Ryvkin, K. Panajotov, E. A. Avrutin, I. Veretennicoff, and H. Thienpont, “Optical-injection-induced polarization switching in polarization-bistable vertical-cavity surface-emitting lasers,” J. Appl. Phys. 96(11), 6002–6007 (2004).
    [Crossref]
  47. I. Gatare, J. Buesa, H. Thienpont, K. Panajotov, and M. Sciamanna, “Polarization switching bistability and dynamics in vertical-cavity surface-emitting laser under orthogonal optical injection,” Opt. Quantum Electron. 38(4–6), 429–443 (2006).
    [Crossref]
  48. I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76(3), 031803 (2007).
    [Crossref]
  49. G. A. Gottwald and I. Melbourne, “On the Implementation of the 0-1 Test for Chaos,” SIAM J. Appl. Dyn. Syst. 8(1), 129–145 (2009).
    [Crossref]
  50. N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, X. H. Zou, and L. Y. Zhang, “Bandwidth and unpredictability properties of semiconductor ring lasers with chaotic optical injection,” Opt. Laser Technol. 53(1), 45–50 (2013).
    [Crossref]
  51. M. Sciamanna, I. Gatare, A. Locquet, and K. Panajotov, “Polarization synchronization in unidirectionally coupled vertical-cavity surface-emitting lasers with orthogonal optical injection,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5), 056213 (2007).
    [Crossref] [PubMed]
  52. N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, and X. H. Zou, “Loss of time delay signature in broadband cascade-coupled semiconductor lasers,” IEEE Photonics Technol. Lett. 24(23), 2187–2190 (2012).
    [Crossref]
  53. N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, X. H. Zou, L. Y. Zhang, and P. H. Mu, “Photonic generation of wideband time-delay-signature-eliminated chaotic signals utilizing an optically injected semiconductor laser,” IEEE J. Quantum Electron. 48(10), 1339–1345 (2012).
    [Crossref]
  54. V. Annovazzi-Lodi, G. Aromataris, M. Benedetti, and S. Merlo, “Private message transmission by common driving of two chaotic lasers,” IEEE J. Quantum Electron. 46(2), 258–264 (2010).
    [Crossref]
  55. K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
    [Crossref] [PubMed]
  56. N. Q. Li, W. Pan, L. S. Yan, B. Luo, X. H. Zou, and S. Y. Xiang, “Enhanced two-channel optical chaotic communication using isochronous synchronization,” IEEE J. Sel. Top. Quantum Electron. 19(4), 0600109 (2013).
    [Crossref]

2018 (3)

M. J. Wishon, A. Locquet, C. Y. Chang, D. Choi, and D. S. Citrin, “Crisis route to chaos in semiconductor lasers subjected to external optical feedback,” Phys. Rev. A 97(3), 033849 (2018).
[Crossref]

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Mapping bifurcation structure and parameter dependence in quantum dot spin-VCSELs,” Opt. Express 26(11), 14636 (2018).
[Crossref]

H. Han and K. A. Shore, “Dynamical characteristics of nano-lasers subject to optical injection and phase conjugate feedback,” IET Optoelectron. 12(1), 25–29 (2018).
[Crossref]

2017 (6)

2016 (5)

M. Virte, M. Sciamanna, and K. Panajotov, “Synchronization of polarization chaos from a free-running VCSEL,” Opt. Lett. 41(19), 4492–4495 (2016).
[Crossref] [PubMed]

D. Rontani, D. Choi, C. Y. Chang, A. Locquet, and D. S. Citrin, “Compressive sensing with optical chaos,” Sci. Rep. 6(1), 35206 (2016).
[Crossref] [PubMed]

Y. Hong, A. Quirce, B. Wang, S. Ji, K. Panajotov, and P. S. Spencer, “Concealment of chaos time-delay signature in three-cascaded vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 52(8), 1–8 (2016).

L. Jumpertz, K. Schires, M. Carras, M. Sciamanna, and F. Grillot, “Chaotic light at mid-infrared wavelength,” Light Sci. Appl. 5(6), e16088 (2016).
[Crossref]

D. Rontani, E. Mercier, D. Wolfersberger, and M. Sciamanna, “Enhanced complexity of optical chaos in a laser diode with phase-conjugate feedback,” Opt. Lett. 41(20), 4637–4640 (2016).
[Crossref] [PubMed]

2015 (4)

2014 (3)

2013 (4)

S. Y. Xiang, W. Pan, A. J. Wen, N. Q. Li, L. Y. Zhang, L. Shang, and H. X. Zhang, “Conceal time delay signature of chaos in semiconductor lasers with dual-path injection,” IEEE Photonics Technol. Lett. 25(14), 1398–1401 (2013).
[Crossref]

M. Virte, K. Panajotov, and M. Sciamanna, “Bifurcation to nonlinear polarization dynamics and chaos in vertical-cavity surface-emitting lasers,” Phys. Rev. A 87(1), 013834 (2013).
[Crossref]

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, X. H. Zou, and L. Y. Zhang, “Bandwidth and unpredictability properties of semiconductor ring lasers with chaotic optical injection,” Opt. Laser Technol. 53(1), 45–50 (2013).
[Crossref]

N. Q. Li, W. Pan, L. S. Yan, B. Luo, X. H. Zou, and S. Y. Xiang, “Enhanced two-channel optical chaotic communication using isochronous synchronization,” IEEE J. Sel. Top. Quantum Electron. 19(4), 0600109 (2013).
[Crossref]

2012 (8)

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, and X. H. Zou, “Loss of time delay signature in broadband cascade-coupled semiconductor lasers,” IEEE Photonics Technol. Lett. 24(23), 2187–2190 (2012).
[Crossref]

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, X. H. Zou, L. Y. Zhang, and P. H. Mu, “Photonic generation of wideband time-delay-signature-eliminated chaotic signals utilizing an optically injected semiconductor laser,” IEEE J. Quantum Electron. 48(10), 1339–1345 (2012).
[Crossref]

M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2012).
[Crossref]

X.-Z. Li and S.-C. Chan, “Random bit generation using an optically injected semiconductor laser in chaos with oversampling,” Opt. Lett. 37(11), 2163–2165 (2012).
[Crossref] [PubMed]

L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutierrez, L. Pesquera, C. R. Mirasso, and I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20(3), 3241–3249 (2012).
[Crossref] [PubMed]

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Loss of time-delay signature in chaotic semiconductor ring lasers,” Opt. Lett. 37(13), 2541–2543 (2012).
[Crossref] [PubMed]

Y. H. Hong, P. S. Spencer, and K. A. Shore, “Enhancement of chaotic signal bandwidth in vertical-cavity surface-emitting lasers with optical injection,” J. Opt. Soc. Am. B 29(3), 415–419 (2012).
[Crossref]

2011 (2)

2010 (2)

V. Annovazzi-Lodi, G. Aromataris, M. Benedetti, and S. Merlo, “Private message transmission by common driving of two chaotic lasers,” IEEE J. Quantum Electron. 46(2), 258–264 (2010).
[Crossref]

N. Jiang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, L. Yang, and D. Zheng, “Multiaccess optical chaos communication using mutually coupled semiconductor lasers subjected to identical external injections,” IEEE Photonics Technol. Lett. 22(10), 676–678 (2010).
[Crossref]

2009 (4)

J. G. Wu, G. Q. Xia, and Z. M. Wu, “Suppression of time delay signatures of chaotic output in a semiconductor laser with double optical feedback,” Opt. Express 17(22), 20124–20133 (2009).
[Crossref] [PubMed]

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: A dynamical point of view,” IEEE J. Quantum Electron. 45(7), 879–891 (2009).
[Crossref]

K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Ploarization- and transverse-mode dynamics in optically injected and gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45(11), 1473–1481 (2009).
[Crossref]

G. A. Gottwald and I. Melbourne, “On the Implementation of the 0-1 Test for Chaos,” SIAM J. Appl. Dyn. Syst. 8(1), 129–145 (2009).
[Crossref]

2008 (2)

W. L. Zhang, W. Pan, B. Luo, M. Y. Wang, and X. H. Zou, “Polarization switching and hysteresis of VCSELs with time-varying optical injection,” IEEE J. Sel. Top. Quantum Electron. 14(3), 889–894 (2008).
[Crossref]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

2007 (3)

G. Q. Xia, S.-C. Chan, and J. M. Liu, “Multistability in a semiconductor laser with optoelectronic feedback,” Opt. Express 15(2), 572–576 (2007).
[Crossref] [PubMed]

M. Sciamanna, I. Gatare, A. Locquet, and K. Panajotov, “Polarization synchronization in unidirectionally coupled vertical-cavity surface-emitting lasers with orthogonal optical injection,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5), 056213 (2007).
[Crossref] [PubMed]

I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76(3), 031803 (2007).
[Crossref]

2006 (2)

I. Gatare, J. Buesa, H. Thienpont, K. Panajotov, and M. Sciamanna, “Polarization switching bistability and dynamics in vertical-cavity surface-emitting laser under orthogonal optical injection,” Opt. Quantum Electron. 38(4–6), 429–443 (2006).
[Crossref]

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89(14), 141106 (2006).
[Crossref]

2005 (2)

M. Sciamanna and K. Panajotov, “Two-mode injection locking in vertical-cavity surface-emitting lasers,” Opt. Lett. 30(21), 2903–2905 (2005).
[Crossref] [PubMed]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

2004 (2)

F.-Y. Lin and J.-M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. 10(5), 991–997 (2004).
[Crossref]

B. S. Ryvkin, K. Panajotov, E. A. Avrutin, I. Veretennicoff, and H. Thienpont, “Optical-injection-induced polarization switching in polarization-bistable vertical-cavity surface-emitting lasers,” J. Appl. Phys. 96(11), 6002–6007 (2004).
[Crossref]

2002 (1)

1995 (1)

Q. Feng, J. V. Moloney, and J. V. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728–1739 (1995).
[Crossref] [PubMed]

1980 (1)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[Crossref]

Adams, M. J.

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Mapping bifurcation structure and parameter dependence in quantum dot spin-VCSELs,” Opt. Express 26(11), 14636 (2018).
[Crossref]

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Stability and bifurcation analysis of spin-polarized vertical-cavity surface-emitting lasers,” Phys. Rev. A 96(1), 013840 (2017).
[Crossref]

Aida, H.

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

Alan Shore, K.

Amano, K.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Annovazzi-Lodi, V.

V. Annovazzi-Lodi, G. Aromataris, M. Benedetti, and S. Merlo, “Private message transmission by common driving of two chaotic lasers,” IEEE J. Quantum Electron. 46(2), 258–264 (2010).
[Crossref]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Appeltant, L.

Argyris, A.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Aromataris, G.

V. Annovazzi-Lodi, G. Aromataris, M. Benedetti, and S. Merlo, “Private message transmission by common driving of two chaotic lasers,” IEEE J. Quantum Electron. 46(2), 258–264 (2010).
[Crossref]

Avrutin, E. A.

B. S. Ryvkin, K. Panajotov, E. A. Avrutin, I. Veretennicoff, and H. Thienpont, “Optical-injection-induced polarization switching in polarization-bistable vertical-cavity surface-emitting lasers,” J. Appl. Phys. 96(11), 6002–6007 (2004).
[Crossref]

Benedetti, M.

V. Annovazzi-Lodi, G. Aromataris, M. Benedetti, and S. Merlo, “Private message transmission by common driving of two chaotic lasers,” IEEE J. Quantum Electron. 46(2), 258–264 (2010).
[Crossref]

Bimberg, D.

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89(14), 141106 (2006).
[Crossref]

Bloch, M.

Blondel, M.

Borges, B. V.

T. R. Raddo, K. Panajotov, B. V. Borges, and M. Virte, “Strain induced polarization chaos in a solitary VCSEL,” Sci. Rep. 7(1), 14032 (2017).
[Crossref] [PubMed]

Brunner, D.

Buesa, J.

I. Gatare, J. Buesa, H. Thienpont, K. Panajotov, and M. Sciamanna, “Polarization switching bistability and dynamics in vertical-cavity surface-emitting laser under orthogonal optical injection,” Opt. Quantum Electron. 38(4–6), 429–443 (2006).
[Crossref]

Carras, M.

L. Jumpertz, K. Schires, M. Carras, M. Sciamanna, and F. Grillot, “Chaotic light at mid-infrared wavelength,” Light Sci. Appl. 5(6), e16088 (2016).
[Crossref]

Cemlyn, B. R.

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Mapping bifurcation structure and parameter dependence in quantum dot spin-VCSELs,” Opt. Express 26(11), 14636 (2018).
[Crossref]

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Stability and bifurcation analysis of spin-polarized vertical-cavity surface-emitting lasers,” Phys. Rev. A 96(1), 013840 (2017).
[Crossref]

Chan, S.-C.

Chang, C. Y.

M. J. Wishon, A. Locquet, C. Y. Chang, D. Choi, and D. S. Citrin, “Crisis route to chaos in semiconductor lasers subjected to external optical feedback,” Phys. Rev. A 97(3), 033849 (2018).
[Crossref]

D. Rontani, D. Choi, C. Y. Chang, A. Locquet, and D. S. Citrin, “Compressive sensing with optical chaos,” Sci. Rep. 6(1), 35206 (2016).
[Crossref] [PubMed]

Chen, J. J.

Chen, X.

Cheng, M.

Chizhevsky, V. N.

Choi, D.

M. J. Wishon, A. Locquet, C. Y. Chang, D. Choi, and D. S. Citrin, “Crisis route to chaos in semiconductor lasers subjected to external optical feedback,” Phys. Rev. A 97(3), 033849 (2018).
[Crossref]

D. Rontani, D. Choi, C. Y. Chang, A. Locquet, and D. S. Citrin, “Compressive sensing with optical chaos,” Sci. Rep. 6(1), 35206 (2016).
[Crossref] [PubMed]

Citrin, D. S.

M. J. Wishon, A. Locquet, C. Y. Chang, D. Choi, and D. S. Citrin, “Crisis route to chaos in semiconductor lasers subjected to external optical feedback,” Phys. Rev. A 97(3), 033849 (2018).
[Crossref]

D. Rontani, D. Choi, C. Y. Chang, A. Locquet, and D. S. Citrin, “Compressive sensing with optical chaos,” Sci. Rep. 6(1), 35206 (2016).
[Crossref] [PubMed]

N. Li, W. Pan, A. Locquet, and D. S. Citrin, “Time-delay concealment and complexity enhancement of an external-cavity laser through optical injection,” Opt. Lett. 40(19), 4416–4419 (2015).
[Crossref] [PubMed]

N. Li, B. Kim, V. N. Chizhevsky, A. Locquet, M. Bloch, D. S. Citrin, and W. Pan, “Two approaches for ultrafast random bit generation based on the chaotic dynamics of a semiconductor laser,” Opt. Express 22(6), 6634–6646 (2014).
[Crossref] [PubMed]

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: A dynamical point of view,” IEEE J. Quantum Electron. 45(7), 879–891 (2009).
[Crossref]

Colet, P.

R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, “Digital key for chaos communication performing time delay concealment,” Phys. Rev. Lett. 107(3), 034103 (2011).
[Crossref] [PubMed]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Danckaert, J.

Davis, P.

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Deng, L.

Deng, T.

Deparis, O.

Erneux, T.

Fan, L.

Feng, Q.

Q. Feng, J. V. Moloney, and J. V. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728–1739 (1995).
[Crossref] [PubMed]

Fiol, G.

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89(14), 141106 (2006).
[Crossref]

Fischer, I.

L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutierrez, L. Pesquera, C. R. Mirasso, and I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20(3), 3241–3249 (2012).
[Crossref] [PubMed]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Gao, H.

García-Ojalvo, J.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Gatare, I.

K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Ploarization- and transverse-mode dynamics in optically injected and gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45(11), 1473–1481 (2009).
[Crossref]

I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76(3), 031803 (2007).
[Crossref]

M. Sciamanna, I. Gatare, A. Locquet, and K. Panajotov, “Polarization synchronization in unidirectionally coupled vertical-cavity surface-emitting lasers with orthogonal optical injection,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5), 056213 (2007).
[Crossref] [PubMed]

I. Gatare, J. Buesa, H. Thienpont, K. Panajotov, and M. Sciamanna, “Polarization switching bistability and dynamics in vertical-cavity surface-emitting laser under orthogonal optical injection,” Opt. Quantum Electron. 38(4–6), 429–443 (2006).
[Crossref]

Gottwald, G. A.

G. A. Gottwald and I. Melbourne, “On the Implementation of the 0-1 Test for Chaos,” SIAM J. Appl. Dyn. Syst. 8(1), 129–145 (2009).
[Crossref]

Grillot, F.

L. Jumpertz, K. Schires, M. Carras, M. Sciamanna, and F. Grillot, “Chaotic light at mid-infrared wavelength,” Light Sci. Appl. 5(6), e16088 (2016).
[Crossref]

Guo, X.

Guo, Y.

Gutierrez, J. M.

Han, H.

H. Han and K. A. Shore, “Dynamical characteristics of nano-lasers subject to optical injection and phase conjugate feedback,” IET Optoelectron. 12(1), 25–29 (2018).
[Crossref]

Harayama, T.

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

Henning, I. D.

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Mapping bifurcation structure and parameter dependence in quantum dot spin-VCSELs,” Opt. Express 26(11), 14636 (2018).
[Crossref]

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Stability and bifurcation analysis of spin-polarized vertical-cavity surface-emitting lasers,” Phys. Rev. A 96(1), 013840 (2017).
[Crossref]

Hirano, K.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Hong, Y.

Y. Hong, A. Quirce, B. Wang, S. Ji, K. Panajotov, and P. S. Spencer, “Concealment of chaos time-delay signature in three-cascaded vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 52(8), 1–8 (2016).

Hong, Y. H.

Hopfer, F.

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89(14), 141106 (2006).
[Crossref]

Inoue, M.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Iwakawa, K.

Ji, S.

Y. Hong, A. Quirce, B. Wang, S. Ji, K. Panajotov, and P. S. Spencer, “Concealment of chaos time-delay signature in three-cascaded vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 52(8), 1–8 (2016).

Jiang, N.

Jumpertz, L.

L. Jumpertz, K. Schires, M. Carras, M. Sciamanna, and F. Grillot, “Chaotic light at mid-infrared wavelength,” Light Sci. Appl. 5(6), e16088 (2016).
[Crossref]

Kanno, K.

Kim, B.

Kobayashi, K.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[Crossref]

Kovsh, A. R.

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89(14), 141106 (2006).
[Crossref]

Krestnikov, I. L.

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89(14), 141106 (2006).
[Crossref]

Kuntz, M.

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89(14), 141106 (2006).
[Crossref]

Kurashige, T.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Lang, R.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[Crossref]

Larger, L.

L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutierrez, L. Pesquera, C. R. Mirasso, and I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20(3), 3241–3249 (2012).
[Crossref] [PubMed]

R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, “Digital key for chaos communication performing time delay concealment,” Phys. Rev. Lett. 107(3), 034103 (2011).
[Crossref] [PubMed]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Ledentsov, N. N.

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89(14), 141106 (2006).
[Crossref]

Li, G.

Li, H.

Li, N.

Li, N. Q.

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Mapping bifurcation structure and parameter dependence in quantum dot spin-VCSELs,” Opt. Express 26(11), 14636 (2018).
[Crossref]

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Stability and bifurcation analysis of spin-polarized vertical-cavity surface-emitting lasers,” Phys. Rev. A 96(1), 013840 (2017).
[Crossref]

S. Y. Xiang, W. Pan, A. J. Wen, N. Q. Li, L. Y. Zhang, L. Shang, and H. X. Zhang, “Conceal time delay signature of chaos in semiconductor lasers with dual-path injection,” IEEE Photonics Technol. Lett. 25(14), 1398–1401 (2013).
[Crossref]

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, X. H. Zou, and L. Y. Zhang, “Bandwidth and unpredictability properties of semiconductor ring lasers with chaotic optical injection,” Opt. Laser Technol. 53(1), 45–50 (2013).
[Crossref]

N. Q. Li, W. Pan, L. S. Yan, B. Luo, X. H. Zou, and S. Y. Xiang, “Enhanced two-channel optical chaotic communication using isochronous synchronization,” IEEE J. Sel. Top. Quantum Electron. 19(4), 0600109 (2013).
[Crossref]

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, X. H. Zou, L. Y. Zhang, and P. H. Mu, “Photonic generation of wideband time-delay-signature-eliminated chaotic signals utilizing an optically injected semiconductor laser,” IEEE J. Quantum Electron. 48(10), 1339–1345 (2012).
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N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, and X. H. Zou, “Loss of time delay signature in broadband cascade-coupled semiconductor lasers,” IEEE Photonics Technol. Lett. 24(23), 2187–2190 (2012).
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F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89(14), 141106 (2006).
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M. J. Wishon, A. Locquet, C. Y. Chang, D. Choi, and D. S. Citrin, “Crisis route to chaos in semiconductor lasers subjected to external optical feedback,” Phys. Rev. A 97(3), 033849 (2018).
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D. Rontani, D. Choi, C. Y. Chang, A. Locquet, and D. S. Citrin, “Compressive sensing with optical chaos,” Sci. Rep. 6(1), 35206 (2016).
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N. Li, W. Pan, A. Locquet, and D. S. Citrin, “Time-delay concealment and complexity enhancement of an external-cavity laser through optical injection,” Opt. Lett. 40(19), 4416–4419 (2015).
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N. Li, B. Kim, V. N. Chizhevsky, A. Locquet, M. Bloch, D. S. Citrin, and W. Pan, “Two approaches for ultrafast random bit generation based on the chaotic dynamics of a semiconductor laser,” Opt. Express 22(6), 6634–6646 (2014).
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D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: A dynamical point of view,” IEEE J. Quantum Electron. 45(7), 879–891 (2009).
[Crossref]

M. Sciamanna, I. Gatare, A. Locquet, and K. Panajotov, “Polarization synchronization in unidirectionally coupled vertical-cavity surface-emitting lasers with orthogonal optical injection,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5), 056213 (2007).
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Luo, B.

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, X. H. Zou, and L. Y. Zhang, “Bandwidth and unpredictability properties of semiconductor ring lasers with chaotic optical injection,” Opt. Laser Technol. 53(1), 45–50 (2013).
[Crossref]

N. Q. Li, W. Pan, L. S. Yan, B. Luo, X. H. Zou, and S. Y. Xiang, “Enhanced two-channel optical chaotic communication using isochronous synchronization,” IEEE J. Sel. Top. Quantum Electron. 19(4), 0600109 (2013).
[Crossref]

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, and X. H. Zou, “Loss of time delay signature in broadband cascade-coupled semiconductor lasers,” IEEE Photonics Technol. Lett. 24(23), 2187–2190 (2012).
[Crossref]

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, X. H. Zou, L. Y. Zhang, and P. H. Mu, “Photonic generation of wideband time-delay-signature-eliminated chaotic signals utilizing an optically injected semiconductor laser,” IEEE J. Quantum Electron. 48(10), 1339–1345 (2012).
[Crossref]

S. Xiang, W. Pan, L. Yan, B. Luo, X. Zou, N. Jiang, and K. Wen, “Influence of polarization mode competition on chaotic unpredictability of vertical-cavity surface-emitting lasers with polarization-rotated optical feedback,” Opt. Lett. 36(3), 310–312 (2011).
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N. Jiang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, L. Yang, and D. Zheng, “Multiaccess optical chaos communication using mutually coupled semiconductor lasers subjected to identical external injections,” IEEE Photonics Technol. Lett. 22(10), 676–678 (2010).
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W. L. Zhang, W. Pan, B. Luo, M. Y. Wang, and X. H. Zou, “Polarization switching and hysteresis of VCSELs with time-varying optical injection,” IEEE J. Sel. Top. Quantum Electron. 14(3), 889–894 (2008).
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Melbourne, I.

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Merlo, S.

V. Annovazzi-Lodi, G. Aromataris, M. Benedetti, and S. Merlo, “Private message transmission by common driving of two chaotic lasers,” IEEE J. Quantum Electron. 46(2), 258–264 (2010).
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F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89(14), 141106 (2006).
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L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutierrez, L. Pesquera, C. R. Mirasso, and I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20(3), 3241–3249 (2012).
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Q. Feng, J. V. Moloney, and J. V. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728–1739 (1995).
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Q. Feng, J. V. Moloney, and J. V. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728–1739 (1995).
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K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
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Mu, P. H.

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, X. H. Zou, L. Y. Zhang, and P. H. Mu, “Photonic generation of wideband time-delay-signature-eliminated chaotic signals utilizing an optically injected semiconductor laser,” IEEE J. Quantum Electron. 48(10), 1339–1345 (2012).
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Muramatsu, J.

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
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Mutig, A.

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89(14), 141106 (2006).
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Naito, S.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
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R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Loss of time-delay signature in chaotic semiconductor ring lasers,” Opt. Lett. 37(13), 2541–2543 (2012).
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R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, “Digital key for chaos communication performing time delay concealment,” Phys. Rev. Lett. 107(3), 034103 (2011).
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Nizette, M.

I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76(3), 031803 (2007).
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Okumura, H.

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
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Oowada, I.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
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Ortin, S.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: A dynamical point of view,” IEEE J. Quantum Electron. 45(7), 879–891 (2009).
[Crossref]

Pan, W.

N. Li, W. Pan, A. Locquet, and D. S. Citrin, “Time-delay concealment and complexity enhancement of an external-cavity laser through optical injection,” Opt. Lett. 40(19), 4416–4419 (2015).
[Crossref] [PubMed]

N. Li, B. Kim, V. N. Chizhevsky, A. Locquet, M. Bloch, D. S. Citrin, and W. Pan, “Two approaches for ultrafast random bit generation based on the chaotic dynamics of a semiconductor laser,” Opt. Express 22(6), 6634–6646 (2014).
[Crossref] [PubMed]

S. Y. Xiang, W. Pan, A. J. Wen, N. Q. Li, L. Y. Zhang, L. Shang, and H. X. Zhang, “Conceal time delay signature of chaos in semiconductor lasers with dual-path injection,” IEEE Photonics Technol. Lett. 25(14), 1398–1401 (2013).
[Crossref]

N. Q. Li, W. Pan, L. S. Yan, B. Luo, X. H. Zou, and S. Y. Xiang, “Enhanced two-channel optical chaotic communication using isochronous synchronization,” IEEE J. Sel. Top. Quantum Electron. 19(4), 0600109 (2013).
[Crossref]

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, X. H. Zou, and L. Y. Zhang, “Bandwidth and unpredictability properties of semiconductor ring lasers with chaotic optical injection,” Opt. Laser Technol. 53(1), 45–50 (2013).
[Crossref]

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, and X. H. Zou, “Loss of time delay signature in broadband cascade-coupled semiconductor lasers,” IEEE Photonics Technol. Lett. 24(23), 2187–2190 (2012).
[Crossref]

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, X. H. Zou, L. Y. Zhang, and P. H. Mu, “Photonic generation of wideband time-delay-signature-eliminated chaotic signals utilizing an optically injected semiconductor laser,” IEEE J. Quantum Electron. 48(10), 1339–1345 (2012).
[Crossref]

S. Xiang, W. Pan, L. Yan, B. Luo, X. Zou, N. Jiang, and K. Wen, “Influence of polarization mode competition on chaotic unpredictability of vertical-cavity surface-emitting lasers with polarization-rotated optical feedback,” Opt. Lett. 36(3), 310–312 (2011).
[Crossref] [PubMed]

N. Jiang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, L. Yang, and D. Zheng, “Multiaccess optical chaos communication using mutually coupled semiconductor lasers subjected to identical external injections,” IEEE Photonics Technol. Lett. 22(10), 676–678 (2010).
[Crossref]

W. L. Zhang, W. Pan, B. Luo, M. Y. Wang, and X. H. Zou, “Polarization switching and hysteresis of VCSELs with time-varying optical injection,” IEEE J. Sel. Top. Quantum Electron. 14(3), 889–894 (2008).
[Crossref]

Panajotov, K.

T. R. Raddo, K. Panajotov, B. V. Borges, and M. Virte, “Strain induced polarization chaos in a solitary VCSEL,” Sci. Rep. 7(1), 14032 (2017).
[Crossref] [PubMed]

M. Virte, M. Sciamanna, and K. Panajotov, “Synchronization of polarization chaos from a free-running VCSEL,” Opt. Lett. 41(19), 4492–4495 (2016).
[Crossref] [PubMed]

Y. Hong, A. Quirce, B. Wang, S. Ji, K. Panajotov, and P. S. Spencer, “Concealment of chaos time-delay signature in three-cascaded vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 52(8), 1–8 (2016).

M. Virte, E. Mercier, H. Thienpont, K. Panajotov, and M. Sciamanna, “Physical random bit generation from chaotic solitary laser diode,” Opt. Express 22(14), 17271–17280 (2014).
[Crossref] [PubMed]

M. Virte, K. Panajotov, and M. Sciamanna, “Bifurcation to nonlinear polarization dynamics and chaos in vertical-cavity surface-emitting lasers,” Phys. Rev. A 87(1), 013834 (2013).
[Crossref]

M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2012).
[Crossref]

K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Ploarization- and transverse-mode dynamics in optically injected and gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45(11), 1473–1481 (2009).
[Crossref]

M. Sciamanna, I. Gatare, A. Locquet, and K. Panajotov, “Polarization synchronization in unidirectionally coupled vertical-cavity surface-emitting lasers with orthogonal optical injection,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5), 056213 (2007).
[Crossref] [PubMed]

I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76(3), 031803 (2007).
[Crossref]

I. Gatare, J. Buesa, H. Thienpont, K. Panajotov, and M. Sciamanna, “Polarization switching bistability and dynamics in vertical-cavity surface-emitting laser under orthogonal optical injection,” Opt. Quantum Electron. 38(4–6), 429–443 (2006).
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M. Sciamanna and K. Panajotov, “Two-mode injection locking in vertical-cavity surface-emitting lasers,” Opt. Lett. 30(21), 2903–2905 (2005).
[Crossref] [PubMed]

B. S. Ryvkin, K. Panajotov, E. A. Avrutin, I. Veretennicoff, and H. Thienpont, “Optical-injection-induced polarization switching in polarization-bistable vertical-cavity surface-emitting lasers,” J. Appl. Phys. 96(11), 6002–6007 (2004).
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Pesquera, L.

L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutierrez, L. Pesquera, C. R. Mirasso, and I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20(3), 3241–3249 (2012).
[Crossref] [PubMed]

R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, “Digital key for chaos communication performing time delay concealment,” Phys. Rev. Lett. 107(3), 034103 (2011).
[Crossref] [PubMed]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Qiu, K.

Quirce, A.

Y. Hong, A. Quirce, B. Wang, S. Ji, K. Panajotov, and P. S. Spencer, “Concealment of chaos time-delay signature in three-cascaded vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 52(8), 1–8 (2016).

Raddo, T. R.

T. R. Raddo, K. Panajotov, B. V. Borges, and M. Virte, “Strain induced polarization chaos in a solitary VCSEL,” Sci. Rep. 7(1), 14032 (2017).
[Crossref] [PubMed]

Rogister, F.

Rontani, D.

D. Rontani, E. Mercier, D. Wolfersberger, and M. Sciamanna, “Enhanced complexity of optical chaos in a laser diode with phase-conjugate feedback,” Opt. Lett. 41(20), 4637–4640 (2016).
[Crossref] [PubMed]

D. Rontani, D. Choi, C. Y. Chang, A. Locquet, and D. S. Citrin, “Compressive sensing with optical chaos,” Sci. Rep. 6(1), 35206 (2016).
[Crossref] [PubMed]

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: A dynamical point of view,” IEEE J. Quantum Electron. 45(7), 879–891 (2009).
[Crossref]

Ryvkin, B. S.

B. S. Ryvkin, K. Panajotov, E. A. Avrutin, I. Veretennicoff, and H. Thienpont, “Optical-injection-induced polarization switching in polarization-bistable vertical-cavity surface-emitting lasers,” J. Appl. Phys. 96(11), 6002–6007 (2004).
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Sakuraba, R.

Sang, L.

Schires, K.

L. Jumpertz, K. Schires, M. Carras, M. Sciamanna, and F. Grillot, “Chaotic light at mid-infrared wavelength,” Light Sci. Appl. 5(6), e16088 (2016).
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Sciamanna, M.

L. Jumpertz, K. Schires, M. Carras, M. Sciamanna, and F. Grillot, “Chaotic light at mid-infrared wavelength,” Light Sci. Appl. 5(6), e16088 (2016).
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D. Rontani, E. Mercier, D. Wolfersberger, and M. Sciamanna, “Enhanced complexity of optical chaos in a laser diode with phase-conjugate feedback,” Opt. Lett. 41(20), 4637–4640 (2016).
[Crossref] [PubMed]

M. Virte, M. Sciamanna, and K. Panajotov, “Synchronization of polarization chaos from a free-running VCSEL,” Opt. Lett. 41(19), 4492–4495 (2016).
[Crossref] [PubMed]

M. Sciamanna and K. A. Shore, “Physics and applications of laser diode chaos,” Nat. Photonics 9(3), 151–162 (2015).
[Crossref]

M. Virte, E. Mercier, H. Thienpont, K. Panajotov, and M. Sciamanna, “Physical random bit generation from chaotic solitary laser diode,” Opt. Express 22(14), 17271–17280 (2014).
[Crossref] [PubMed]

M. Virte, K. Panajotov, and M. Sciamanna, “Bifurcation to nonlinear polarization dynamics and chaos in vertical-cavity surface-emitting lasers,” Phys. Rev. A 87(1), 013834 (2013).
[Crossref]

M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2012).
[Crossref]

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: A dynamical point of view,” IEEE J. Quantum Electron. 45(7), 879–891 (2009).
[Crossref]

K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Ploarization- and transverse-mode dynamics in optically injected and gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45(11), 1473–1481 (2009).
[Crossref]

I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76(3), 031803 (2007).
[Crossref]

M. Sciamanna, I. Gatare, A. Locquet, and K. Panajotov, “Polarization synchronization in unidirectionally coupled vertical-cavity surface-emitting lasers with orthogonal optical injection,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5), 056213 (2007).
[Crossref] [PubMed]

I. Gatare, J. Buesa, H. Thienpont, K. Panajotov, and M. Sciamanna, “Polarization switching bistability and dynamics in vertical-cavity surface-emitting laser under orthogonal optical injection,” Opt. Quantum Electron. 38(4–6), 429–443 (2006).
[Crossref]

M. Sciamanna and K. Panajotov, “Two-mode injection locking in vertical-cavity surface-emitting lasers,” Opt. Lett. 30(21), 2903–2905 (2005).
[Crossref] [PubMed]

M. Sciamanna, F. Rogister, O. Deparis, P. Mégret, M. Blondel, and T. Erneux, “Bifurcation to polarization self-modulation in vertical-cavity surface-emitting lasers,” Opt. Lett. 27(4), 261–263 (2002).
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Shang, L.

S. Y. Xiang, W. Pan, A. J. Wen, N. Q. Li, L. Y. Zhang, L. Shang, and H. X. Zhang, “Conceal time delay signature of chaos in semiconductor lasers with dual-path injection,” IEEE Photonics Technol. Lett. 25(14), 1398–1401 (2013).
[Crossref]

Shchukin, V. A.

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89(14), 141106 (2006).
[Crossref]

Shiki, M.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
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Shore, K. A.

H. Han and K. A. Shore, “Dynamical characteristics of nano-lasers subject to optical injection and phase conjugate feedback,” IET Optoelectron. 12(1), 25–29 (2018).
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M. Sciamanna and K. A. Shore, “Physics and applications of laser diode chaos,” Nat. Photonics 9(3), 151–162 (2015).
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Y. H. Hong, P. S. Spencer, and K. A. Shore, “Enhancement of chaotic signal bandwidth in vertical-cavity surface-emitting lasers with optical injection,” J. Opt. Soc. Am. B 29(3), 415–419 (2012).
[Crossref]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Someya, H.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Soriano, M. C.

Spencer, P. S.

Y. Hong, A. Quirce, B. Wang, S. Ji, K. Panajotov, and P. S. Spencer, “Concealment of chaos time-delay signature in three-cascaded vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 52(8), 1–8 (2016).

Y. H. Hong, P. S. Spencer, and K. A. Shore, “Enhancement of chaotic signal bandwidth in vertical-cavity surface-emitting lasers with optical injection,” J. Opt. Soc. Am. B 29(3), 415–419 (2012).
[Crossref]

Susanto, H.

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Mapping bifurcation structure and parameter dependence in quantum dot spin-VCSELs,” Opt. Express 26(11), 14636 (2018).
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N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Stability and bifurcation analysis of spin-polarized vertical-cavity surface-emitting lasers,” Phys. Rev. A 96(1), 013840 (2017).
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Syvridis, D.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
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Tang, X.

Thienpont, H.

M. Virte, E. Mercier, H. Thienpont, K. Panajotov, and M. Sciamanna, “Physical random bit generation from chaotic solitary laser diode,” Opt. Express 22(14), 17271–17280 (2014).
[Crossref] [PubMed]

M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2012).
[Crossref]

K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Ploarization- and transverse-mode dynamics in optically injected and gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45(11), 1473–1481 (2009).
[Crossref]

I. Gatare, J. Buesa, H. Thienpont, K. Panajotov, and M. Sciamanna, “Polarization switching bistability and dynamics in vertical-cavity surface-emitting laser under orthogonal optical injection,” Opt. Quantum Electron. 38(4–6), 429–443 (2006).
[Crossref]

B. S. Ryvkin, K. Panajotov, E. A. Avrutin, I. Veretennicoff, and H. Thienpont, “Optical-injection-induced polarization switching in polarization-bistable vertical-cavity surface-emitting lasers,” J. Appl. Phys. 96(11), 6002–6007 (2004).
[Crossref]

Uchida, A.

R. Sakuraba, K. Iwakawa, K. Kanno, and A. Uchida, “Tb/s physical random bit generation with bandwidth-enhanced chaos in three-cascaded semiconductor lasers,” Opt. Express 23(2), 1470–1490 (2015).
[Crossref] [PubMed]

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Valle, A.

K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Ploarization- and transverse-mode dynamics in optically injected and gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45(11), 1473–1481 (2009).
[Crossref]

Van der Sande, G.

Veretennicoff, I.

B. S. Ryvkin, K. Panajotov, E. A. Avrutin, I. Veretennicoff, and H. Thienpont, “Optical-injection-induced polarization switching in polarization-bistable vertical-cavity surface-emitting lasers,” J. Appl. Phys. 96(11), 6002–6007 (2004).
[Crossref]

Verschaffelt, G.

Virte, M.

T. R. Raddo, K. Panajotov, B. V. Borges, and M. Virte, “Strain induced polarization chaos in a solitary VCSEL,” Sci. Rep. 7(1), 14032 (2017).
[Crossref] [PubMed]

M. Virte, M. Sciamanna, and K. Panajotov, “Synchronization of polarization chaos from a free-running VCSEL,” Opt. Lett. 41(19), 4492–4495 (2016).
[Crossref] [PubMed]

M. Virte, E. Mercier, H. Thienpont, K. Panajotov, and M. Sciamanna, “Physical random bit generation from chaotic solitary laser diode,” Opt. Express 22(14), 17271–17280 (2014).
[Crossref] [PubMed]

M. Virte, K. Panajotov, and M. Sciamanna, “Bifurcation to nonlinear polarization dynamics and chaos in vertical-cavity surface-emitting lasers,” Phys. Rev. A 87(1), 013834 (2013).
[Crossref]

M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2012).
[Crossref]

Wang, A.

Wang, B.

Y. Hong, A. Quirce, B. Wang, S. Ji, K. Panajotov, and P. S. Spencer, “Concealment of chaos time-delay signature in three-cascaded vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 52(8), 1–8 (2016).

Wang, C.

Wang, D.

Wang, L.

Wang, M. Y.

W. L. Zhang, W. Pan, B. Luo, M. Y. Wang, and X. H. Zou, “Polarization switching and hysteresis of VCSELs with time-varying optical injection,” IEEE J. Sel. Top. Quantum Electron. 14(3), 889–894 (2008).
[Crossref]

Wang, Y.

Wen, A. J.

S. Y. Xiang, W. Pan, A. J. Wen, N. Q. Li, L. Y. Zhang, L. Shang, and H. X. Zhang, “Conceal time delay signature of chaos in semiconductor lasers with dual-path injection,” IEEE Photonics Technol. Lett. 25(14), 1398–1401 (2013).
[Crossref]

Wen, K.

Werner, P.

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89(14), 141106 (2006).
[Crossref]

Wishon, M. J.

M. J. Wishon, A. Locquet, C. Y. Chang, D. Choi, and D. S. Citrin, “Crisis route to chaos in semiconductor lasers subjected to external optical feedback,” Phys. Rev. A 97(3), 033849 (2018).
[Crossref]

Wolfersberger, D.

Wu, J. G.

Wu, Z. M.

Wu, Z.-M.

Xia, G. Q.

Xia, G.-Q.

Xiang, S.

Xiang, S. Y.

S. Y. Xiang, W. Pan, A. J. Wen, N. Q. Li, L. Y. Zhang, L. Shang, and H. X. Zhang, “Conceal time delay signature of chaos in semiconductor lasers with dual-path injection,” IEEE Photonics Technol. Lett. 25(14), 1398–1401 (2013).
[Crossref]

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, X. H. Zou, and L. Y. Zhang, “Bandwidth and unpredictability properties of semiconductor ring lasers with chaotic optical injection,” Opt. Laser Technol. 53(1), 45–50 (2013).
[Crossref]

N. Q. Li, W. Pan, L. S. Yan, B. Luo, X. H. Zou, and S. Y. Xiang, “Enhanced two-channel optical chaotic communication using isochronous synchronization,” IEEE J. Sel. Top. Quantum Electron. 19(4), 0600109 (2013).
[Crossref]

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, X. H. Zou, L. Y. Zhang, and P. H. Mu, “Photonic generation of wideband time-delay-signature-eliminated chaotic signals utilizing an optically injected semiconductor laser,” IEEE J. Quantum Electron. 48(10), 1339–1345 (2012).
[Crossref]

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, and X. H. Zou, “Loss of time delay signature in broadband cascade-coupled semiconductor lasers,” IEEE Photonics Technol. Lett. 24(23), 2187–2190 (2012).
[Crossref]

N. Jiang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, L. Yang, and D. Zheng, “Multiaccess optical chaos communication using mutually coupled semiconductor lasers subjected to identical external injections,” IEEE Photonics Technol. Lett. 22(10), 676–678 (2010).
[Crossref]

Xue, C.

Yan, L.

Yan, L. S.

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, X. H. Zou, and L. Y. Zhang, “Bandwidth and unpredictability properties of semiconductor ring lasers with chaotic optical injection,” Opt. Laser Technol. 53(1), 45–50 (2013).
[Crossref]

N. Q. Li, W. Pan, L. S. Yan, B. Luo, X. H. Zou, and S. Y. Xiang, “Enhanced two-channel optical chaotic communication using isochronous synchronization,” IEEE J. Sel. Top. Quantum Electron. 19(4), 0600109 (2013).
[Crossref]

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, X. H. Zou, L. Y. Zhang, and P. H. Mu, “Photonic generation of wideband time-delay-signature-eliminated chaotic signals utilizing an optically injected semiconductor laser,” IEEE J. Quantum Electron. 48(10), 1339–1345 (2012).
[Crossref]

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, and X. H. Zou, “Loss of time delay signature in broadband cascade-coupled semiconductor lasers,” IEEE Photonics Technol. Lett. 24(23), 2187–2190 (2012).
[Crossref]

N. Jiang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, L. Yang, and D. Zheng, “Multiaccess optical chaos communication using mutually coupled semiconductor lasers subjected to identical external injections,” IEEE Photonics Technol. Lett. 22(10), 676–678 (2010).
[Crossref]

Yang, L.

N. Jiang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, L. Yang, and D. Zheng, “Multiaccess optical chaos communication using mutually coupled semiconductor lasers subjected to identical external injections,” IEEE Photonics Technol. Lett. 22(10), 676–678 (2010).
[Crossref]

Yoshimori, S.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Yoshimura, K.

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Zakharov, N. D.

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89(14), 141106 (2006).
[Crossref]

Zhang, H. X.

S. Y. Xiang, W. Pan, A. J. Wen, N. Q. Li, L. Y. Zhang, L. Shang, and H. X. Zhang, “Conceal time delay signature of chaos in semiconductor lasers with dual-path injection,” IEEE Photonics Technol. Lett. 25(14), 1398–1401 (2013).
[Crossref]

Zhang, J.

Zhang, L. Y.

S. Y. Xiang, W. Pan, A. J. Wen, N. Q. Li, L. Y. Zhang, L. Shang, and H. X. Zhang, “Conceal time delay signature of chaos in semiconductor lasers with dual-path injection,” IEEE Photonics Technol. Lett. 25(14), 1398–1401 (2013).
[Crossref]

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, X. H. Zou, and L. Y. Zhang, “Bandwidth and unpredictability properties of semiconductor ring lasers with chaotic optical injection,” Opt. Laser Technol. 53(1), 45–50 (2013).
[Crossref]

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, X. H. Zou, L. Y. Zhang, and P. H. Mu, “Photonic generation of wideband time-delay-signature-eliminated chaotic signals utilizing an optically injected semiconductor laser,” IEEE J. Quantum Electron. 48(10), 1339–1345 (2012).
[Crossref]

Zhang, W. L.

W. L. Zhang, W. Pan, B. Luo, M. Y. Wang, and X. H. Zou, “Polarization switching and hysteresis of VCSELs with time-varying optical injection,” IEEE J. Sel. Top. Quantum Electron. 14(3), 889–894 (2008).
[Crossref]

Zhao, T.

Zheng, D.

N. Jiang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, L. Yang, and D. Zheng, “Multiaccess optical chaos communication using mutually coupled semiconductor lasers subjected to identical external injections,” IEEE Photonics Technol. Lett. 22(10), 676–678 (2010).
[Crossref]

Zhong, Z. Q.

Zhong, Z.-Q.

Zou, X.

Zou, X. H.

N. Q. Li, W. Pan, L. S. Yan, B. Luo, X. H. Zou, and S. Y. Xiang, “Enhanced two-channel optical chaotic communication using isochronous synchronization,” IEEE J. Sel. Top. Quantum Electron. 19(4), 0600109 (2013).
[Crossref]

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, X. H. Zou, and L. Y. Zhang, “Bandwidth and unpredictability properties of semiconductor ring lasers with chaotic optical injection,” Opt. Laser Technol. 53(1), 45–50 (2013).
[Crossref]

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, X. H. Zou, L. Y. Zhang, and P. H. Mu, “Photonic generation of wideband time-delay-signature-eliminated chaotic signals utilizing an optically injected semiconductor laser,” IEEE J. Quantum Electron. 48(10), 1339–1345 (2012).
[Crossref]

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, and X. H. Zou, “Loss of time delay signature in broadband cascade-coupled semiconductor lasers,” IEEE Photonics Technol. Lett. 24(23), 2187–2190 (2012).
[Crossref]

N. Jiang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, L. Yang, and D. Zheng, “Multiaccess optical chaos communication using mutually coupled semiconductor lasers subjected to identical external injections,” IEEE Photonics Technol. Lett. 22(10), 676–678 (2010).
[Crossref]

W. L. Zhang, W. Pan, B. Luo, M. Y. Wang, and X. H. Zou, “Polarization switching and hysteresis of VCSELs with time-varying optical injection,” IEEE J. Sel. Top. Quantum Electron. 14(3), 889–894 (2008).
[Crossref]

Appl. Phys. Lett. (1)

F. Hopfer, A. Mutig, M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89(14), 141106 (2006).
[Crossref]

IEEE J. Quantum Electron. (6)

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, X. H. Zou, L. Y. Zhang, and P. H. Mu, “Photonic generation of wideband time-delay-signature-eliminated chaotic signals utilizing an optically injected semiconductor laser,” IEEE J. Quantum Electron. 48(10), 1339–1345 (2012).
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V. Annovazzi-Lodi, G. Aromataris, M. Benedetti, and S. Merlo, “Private message transmission by common driving of two chaotic lasers,” IEEE J. Quantum Electron. 46(2), 258–264 (2010).
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R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
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K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Ploarization- and transverse-mode dynamics in optically injected and gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45(11), 1473–1481 (2009).
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D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: A dynamical point of view,” IEEE J. Quantum Electron. 45(7), 879–891 (2009).
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Y. Hong, A. Quirce, B. Wang, S. Ji, K. Panajotov, and P. S. Spencer, “Concealment of chaos time-delay signature in three-cascaded vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 52(8), 1–8 (2016).

IEEE J. Sel. Top. Quantum Electron. (3)

W. L. Zhang, W. Pan, B. Luo, M. Y. Wang, and X. H. Zou, “Polarization switching and hysteresis of VCSELs with time-varying optical injection,” IEEE J. Sel. Top. Quantum Electron. 14(3), 889–894 (2008).
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F.-Y. Lin and J.-M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. 10(5), 991–997 (2004).
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N. Q. Li, W. Pan, L. S. Yan, B. Luo, X. H. Zou, and S. Y. Xiang, “Enhanced two-channel optical chaotic communication using isochronous synchronization,” IEEE J. Sel. Top. Quantum Electron. 19(4), 0600109 (2013).
[Crossref]

IEEE Photonics Technol. Lett. (3)

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, and X. H. Zou, “Loss of time delay signature in broadband cascade-coupled semiconductor lasers,” IEEE Photonics Technol. Lett. 24(23), 2187–2190 (2012).
[Crossref]

S. Y. Xiang, W. Pan, A. J. Wen, N. Q. Li, L. Y. Zhang, L. Shang, and H. X. Zhang, “Conceal time delay signature of chaos in semiconductor lasers with dual-path injection,” IEEE Photonics Technol. Lett. 25(14), 1398–1401 (2013).
[Crossref]

N. Jiang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, L. Yang, and D. Zheng, “Multiaccess optical chaos communication using mutually coupled semiconductor lasers subjected to identical external injections,” IEEE Photonics Technol. Lett. 22(10), 676–678 (2010).
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IET Optoelectron. (1)

H. Han and K. A. Shore, “Dynamical characteristics of nano-lasers subject to optical injection and phase conjugate feedback,” IET Optoelectron. 12(1), 25–29 (2018).
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J. Appl. Phys. (1)

B. S. Ryvkin, K. Panajotov, E. A. Avrutin, I. Veretennicoff, and H. Thienpont, “Optical-injection-induced polarization switching in polarization-bistable vertical-cavity surface-emitting lasers,” J. Appl. Phys. 96(11), 6002–6007 (2004).
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J. Opt. Soc. Am. B (1)

Light Sci. Appl. (1)

L. Jumpertz, K. Schires, M. Carras, M. Sciamanna, and F. Grillot, “Chaotic light at mid-infrared wavelength,” Light Sci. Appl. 5(6), e16088 (2016).
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Nat. Photonics (3)

M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2012).
[Crossref]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
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M. Sciamanna and K. A. Shore, “Physics and applications of laser diode chaos,” Nat. Photonics 9(3), 151–162 (2015).
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Nature (1)

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
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Opt. Express (11)

N. Li, B. Kim, V. N. Chizhevsky, A. Locquet, M. Bloch, D. S. Citrin, and W. Pan, “Two approaches for ultrafast random bit generation based on the chaotic dynamics of a semiconductor laser,” Opt. Express 22(6), 6634–6646 (2014).
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L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutierrez, L. Pesquera, C. R. Mirasso, and I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20(3), 3241–3249 (2012).
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J. J. Chen, Z. M. Wu, X. Tang, T. Deng, L. Fan, Z. Q. Zhong, and G. Q. Xia, “Generation of polarization-resolved wideband unpredictability-enhanced chaotic signals based on vertical-cavity surface-emitting lasers subject to chaotic optical injection,” Opt. Express 23(6), 7173–7183 (2015).
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N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Mapping bifurcation structure and parameter dependence in quantum dot spin-VCSELs,” Opt. Express 26(11), 14636 (2018).
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J. G. Wu, G. Q. Xia, and Z. M. Wu, “Suppression of time delay signatures of chaotic output in a semiconductor laser with double optical feedback,” Opt. Express 17(22), 20124–20133 (2009).
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G. Q. Xia, S.-C. Chan, and J. M. Liu, “Multistability in a semiconductor laser with optoelectronic feedback,” Opt. Express 15(2), 572–576 (2007).
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M. Cheng, L. Deng, H. Li, and D. Liu, “Enhanced secure strategy for electro-optic chaotic systems with delayed dynamics by using fractional Fourier transformation,” Opt. Express 22(5), 5241–5251 (2014).
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D. Wang, L. Wang, T. Zhao, H. Gao, Y. Wang, X. Chen, and A. Wang, “Time delay signature elimination of chaos in a semiconductor laser by dispersive feedback from a chirped FBG,” Opt. Express 25(10), 10911–10924 (2017).
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N. Jiang, C. Wang, C. Xue, G. Li, S. Lin, and K. Qiu, “Generation of flat wideband chaos with suppressed time delay signature by using optical time lens,” Opt. Express 25(13), 14359–14367 (2017).
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M. Virte, E. Mercier, H. Thienpont, K. Panajotov, and M. Sciamanna, “Physical random bit generation from chaotic solitary laser diode,” Opt. Express 22(14), 17271–17280 (2014).
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R. Sakuraba, K. Iwakawa, K. Kanno, and A. Uchida, “Tb/s physical random bit generation with bandwidth-enhanced chaos in three-cascaded semiconductor lasers,” Opt. Express 23(2), 1470–1490 (2015).
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Opt. Laser Technol. (1)

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, X. H. Zou, and L. Y. Zhang, “Bandwidth and unpredictability properties of semiconductor ring lasers with chaotic optical injection,” Opt. Laser Technol. 53(1), 45–50 (2013).
[Crossref]

Opt. Lett. (9)

S. Xiang, W. Pan, L. Yan, B. Luo, X. Zou, N. Jiang, and K. Wen, “Influence of polarization mode competition on chaotic unpredictability of vertical-cavity surface-emitting lasers with polarization-rotated optical feedback,” Opt. Lett. 36(3), 310–312 (2011).
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M. Virte, M. Sciamanna, and K. Panajotov, “Synchronization of polarization chaos from a free-running VCSEL,” Opt. Lett. 41(19), 4492–4495 (2016).
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N. Li, W. Pan, A. Locquet, and D. S. Citrin, “Time-delay concealment and complexity enhancement of an external-cavity laser through optical injection,” Opt. Lett. 40(19), 4416–4419 (2015).
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M. Sciamanna and K. Panajotov, “Two-mode injection locking in vertical-cavity surface-emitting lasers,” Opt. Lett. 30(21), 2903–2905 (2005).
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D. Rontani, E. Mercier, D. Wolfersberger, and M. Sciamanna, “Enhanced complexity of optical chaos in a laser diode with phase-conjugate feedback,” Opt. Lett. 41(20), 4637–4640 (2016).
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M. Sciamanna, F. Rogister, O. Deparis, P. Mégret, M. Blondel, and T. Erneux, “Bifurcation to polarization self-modulation in vertical-cavity surface-emitting lasers,” Opt. Lett. 27(4), 261–263 (2002).
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R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Loss of time-delay signature in chaotic semiconductor ring lasers,” Opt. Lett. 37(13), 2541–2543 (2012).
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X.-Z. Li and S.-C. Chan, “Random bit generation using an optically injected semiconductor laser in chaos with oversampling,” Opt. Lett. 37(11), 2163–2165 (2012).
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P. Li, J. Zhang, L. Sang, X. Liu, Y. Guo, X. Guo, A. Wang, K. Alan Shore, and Y. Wang, “Real-time online photonic random number generation,” Opt. Lett. 42(14), 2699–2702 (2017).
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Opt. Quantum Electron. (1)

I. Gatare, J. Buesa, H. Thienpont, K. Panajotov, and M. Sciamanna, “Polarization switching bistability and dynamics in vertical-cavity surface-emitting laser under orthogonal optical injection,” Opt. Quantum Electron. 38(4–6), 429–443 (2006).
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Photon. Res. (1)

Phys. Rev. A (5)

M. J. Wishon, A. Locquet, C. Y. Chang, D. Choi, and D. S. Citrin, “Crisis route to chaos in semiconductor lasers subjected to external optical feedback,” Phys. Rev. A 97(3), 033849 (2018).
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N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Stability and bifurcation analysis of spin-polarized vertical-cavity surface-emitting lasers,” Phys. Rev. A 96(1), 013840 (2017).
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I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76(3), 031803 (2007).
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M. Virte, K. Panajotov, and M. Sciamanna, “Bifurcation to nonlinear polarization dynamics and chaos in vertical-cavity surface-emitting lasers,” Phys. Rev. A 87(1), 013834 (2013).
[Crossref]

Q. Feng, J. V. Moloney, and J. V. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728–1739 (1995).
[Crossref] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

M. Sciamanna, I. Gatare, A. Locquet, and K. Panajotov, “Polarization synchronization in unidirectionally coupled vertical-cavity surface-emitting lasers with orthogonal optical injection,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5), 056213 (2007).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, “Digital key for chaos communication performing time delay concealment,” Phys. Rev. Lett. 107(3), 034103 (2011).
[Crossref] [PubMed]

Sci. Rep. (2)

D. Rontani, D. Choi, C. Y. Chang, A. Locquet, and D. S. Citrin, “Compressive sensing with optical chaos,” Sci. Rep. 6(1), 35206 (2016).
[Crossref] [PubMed]

T. R. Raddo, K. Panajotov, B. V. Borges, and M. Virte, “Strain induced polarization chaos in a solitary VCSEL,” Sci. Rep. 7(1), 14032 (2017).
[Crossref] [PubMed]

SIAM J. Appl. Dyn. Syst. (1)

G. A. Gottwald and I. Melbourne, “On the Implementation of the 0-1 Test for Chaos,” SIAM J. Appl. Dyn. Syst. 8(1), 129–145 (2009).
[Crossref]

Other (1)

J. Ohtsubo, Semiconductor Lasers: Stability, Instability and Chaos (Springer, 2007).

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Figures (12)

Fig. 1
Fig. 1 (a) Intensity time series and (b) the corresponding spectrum of a free-running VCSEL, where α=3, γ p = 25 ns 1 , and γ s = 20 ns 1 .
Fig. 2
Fig. 2 One-parameter bifurcation diagrams of a free-running VCSEL with increasing pump current: (a) RCP and (b) LCP. The parameters are the same as those in Fig. 1.
Fig. 3
Fig. 3 (a)The two-dimensional map of the 0-1 test for chaos and (b) PE of the free-running VCSEL in the ( γ p ,μ) plane as γ s is varied, where α=3. (a1, b1) γ s = 100 ns 1 , (a2, b2) γ s = 50 ns 1 , (a3, b3) γ s = 25 ns 1 , and (a4, b4) γ s = 5 ns 1 .
Fig. 4
Fig. 4 (a) The two-dimensional map of the 0-1 test for chaos and (b) PEof the free-running VCSEL in the ( γ s ,μ) plane as γ p is varied, where α=3, (a1, b1) γ p = 100 ns 1 , (a2, b2) γ p = 50 ns 1 , (a3, b3) γ p = 25 ns 1 , and (a4, b4) γ p = 5 ns 1
Fig. 5
Fig. 5 (a)The two-dimensional map of the 0-1 test for chaos and (b) PE of the free-running VCSEL with varying γ s (x-axis) and γ p (y-axis), where α=3, (a1, b1): μ=2, (a2, b3) μ=5, (a3,b3) μ=8,(a4,b4) μ=10
Fig. 6
Fig. 6 (a1-c1, a2-c2) The two-dimensional map of the 0-1 test for chaos and (a3-c3, a4-b4) PEof the free-running VCSEL with varying γ s (x-axis) and γ p (y-axis). Left: μ=5; right: μ=8. First row: α=1, second: α=2, third: α=6.
Fig. 7
Fig. 7 The bandwidth of the slave VCSEL as a function of (a) frequency detuning Δfand (b) injection strength k in , where (a) k in =60 ns -1 , and (b) Δf= 30 GHz. Other parameters are μ=2 , α=3 , γ p = 25 ns 1 and γ s = 20 ns 1 .
Fig. 8
Fig. 8 Two-dimensional map of the bandwidth of the slave VCSEL shown in the plane of ( Δf, k in ). Other parameters are μ=2 , α=3 , γ p = 25 ns 1 and γ s = 20 ns 1 .
Fig. 9
Fig. 9 PE of the slave VCSEL as a function of (a) frequency detuning Δfand (b) injection strength k in , where (a) k in = 60 ns 1 and (b) Δf= 30 GHz. Other parameters are μ=2 , α=3 , γ p = 25 ns 1 and γ s = 20 ns 1 .
Fig. 10
Fig. 10 Two-dimensional PEmap computed from the slave VCSEL shown in the plane of ( Δf, k in ). Other parameters are μ=2 , α=3 , γ p = 25 ns 1 and γ s = 20 ns 1 .
Fig. 11
Fig. 11 The calculated cross-correlation coefficient shown in the plane of ( Δf, k in ). Other parameters are μ=2 , α=3 , γ p = 25 ns 1 and γ s = 20 ns 1 .
Fig. 12
Fig. 12 (a) Intensity time traces and (b) RF spectrum of three VCSELs, (c) the correlation between any two lasers of the prosed system, where Δf= 30 GHz and k in = 60 ns 1 . Other parameters are μ=2 , α=3 , γ p = 25 ns 1 and γ s = 20 ns 1 .

Equations (7)

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d E ± dt =κ(1+iα)(N±n1) E ± (i γ p + γ a ) E
dN dt =γ(Nμ+(N+n) | E + | 2 +(Nn) | E | 2 )
dn dt = γ s nγ((N+n) | E + | 2 (Nn) | E | 2 )
d F ± dt = κ (1+i α )( N s ± n s 1) F ± (i γ p + γ a ) F iΔ F ± + k in E ± .
d N s dt = γ ( N s μ +( N s + n s ) | F + | 2 +( N s n s ) | F | 2 ).
d n s dt = γ s n s γ (( N s + n s ) | F + | 2 ( N s n s ) | F | 2 ).
C m,s = [ I m (t) I m (t) ][ I s (t) I s (t) ] | I m (t) I m (t) | 2 | I s (t) I s (t) | 2 .

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