Abstract

We numerically demonstrate the generation of wide-band laser chaos with flat power spectrum in a 2D circular-side hexagonal resonator (CSHR) microlaser subject to long-cavity optical feedback. The bandwidth and flatness of the chaotic power spectrum are investigated under different bias currents and optical feedback rates. Under low bias current, the bandwidth under an optimized optical feedback rate increases obviously as raising bias current and the power spectrum flatten simultaneously. Under high bias current, the optimized bandwidth gradually tends toward stabilization, with corresponding flatness less than 5 dB. We compare the chaotic power spectra with small-signal modulation response (SSR) curves under different bias currents. It can be concluded that wide-band and flat SSR indicates wide-band and flat chaotic power spectrum. This work argues that we can enhance laser chaos by using a laser device with wide-band and flat SSR and simple optical feedback configuration, which is significantly beneficial to synchronization-based applications including chaos communication and key distribution

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Laser chaos has attracted many research interests, which can find important applications in secure communication [14], physical random bit generation [57], key distribution [8,9], lidar ranging [10], and optical time domain reflectometers [11,12]. Distributed feedback (DFB) semiconductor laser with an external-cavity optical feedback from a mirror is usually used as chaotic light source due to dynamical complexity and simple configuration capable of photonic integration [13]. However, in DFB semiconductor laser, chaos oscillation typically has a sharp power spectrum with a limited bandwidth of a few gigahertz. The non-uniform spectral density and limited bandwidth seriously restrict the encryption speed of chaos communication and key distribution speed.

Many methods have been proposed to enhance chaos bandwidth and meliorate power spectrum flatness of laser chaos. These methods can be classified into two types. The first type is introducing additional optical injection or complex feedback schemes, such as optical injection from a continuous-wave laser into a chaotic DFB laser or vice versa [14,15], optical mutual-injection between two lasers [16], a laser with phase conjugation feedback [17] or self-phase-modulated optical feedback [18]. The second type is utilizing the phase-to-intensity conversion of chaotic laser by external setup such as a fiber ring resonator with an inbuilt optical filter [19,20], optical heterodyning and or electrical heterodyning [21,22]. By above methods, chaos bandwidth from 10 GHz to 50 GHz can be achieved. However, the configuration complexity of chaotic light source is also greatly added, making chaos synchronization a tough challenge. Therefore, it is of greatly importance to generate wide-band and flat-spectrum laser chaos by simple optical feedback configuration for synchronization-based applications, such as chaos secure communication and chaos-based physical key distribution.

In DFB semiconductor laser with an external-cavity mirror feedback, the chaos oscillation with sharp power spectrum and limited bandwidth is due to the relaxation oscillation. Moreover, the relaxation oscillation also dominates the small-signal modulation response (SSR). It is noted that 2D microcavity lasers with whispering-gallery-mode resonator can obtain flat SSR [23], resulted from the weak laser response to relaxation oscillation. It can be inferred that the microcavity lasers can also generate flat-power-spectrum laser chaos because of the weak laser response to relaxation oscillation.

Recently, Xiao et al. reported a circular-side hexagonal resonator (CSHR) microlaser with 1.55 µm single mode emission and a flat SSR with the 3 dB bandwidth of 13 GHz [24]. In this paper, we numerically investigate the bandwidth and flatness of chaotic power spectrum from the CSHR microlaser subject to optical feedback to demonstrate the possibility and conditions of generating wide-band and flat laser chaos. The effect of bias current and optical feedback rate on laser chaos is analyzed in detail and the comparison with SSR is also given. Results support that the microlaser with wide-band and flat SSR can generate wide-band and flat-spectrum laser chaos, and the profile of power spectrum is almost identical to the SSR curve.

2. Theoretical model

Figure 1 shows the schematic diagram of the CSHR microlaser subject to mirror feedback, the feedback time delay τf = 5ns. Based on the Lang-Kobayashi equations, the rate equations of the mirror-feedback CSHR microlaser is given as below [23,2527]:

$$\frac{{\textrm{d}n}}{{\textrm{d}t}} = \frac{{\eta I}}{{q{V_\textrm{a}}}} - An - B{n^2} - C{n^3} - {v_\textrm{g}}gs,$$
$$\frac{{\textrm{d}s}}{{\textrm{d}t}} = [\Gamma {v_\textrm{g}}g - {\alpha _\textrm{i}}{v_\textrm{g}} - \frac{1}{{{\tau _{\textrm{pc}}}}}]s + \Gamma \beta B{n^2} + 2{\kappa _\textrm{f}}\sqrt {s(t - {\tau _\textrm{f}}) \cdot s} \cos {\mathrm{\theta} ,}$$
$$\frac{{\textrm{d}\phi }}{{\textrm{d}t}} = \frac{\alpha }{2}[\Gamma {v_\textrm{g}}g - {\alpha _\textrm{i}}{v_\textrm{g}} - \frac{1}{{{\tau _{\textrm{pc}}}}}] - {\kappa _\textrm{f}}\sqrt {s(t - {\tau _\textrm{f}})/s} \sin {\mathrm{\theta},}$$
where n is the carrier density, s is the photon density, and ϕ is the phase of optical field, I is the bias current, κf = κ/τL is the optical feedback rate, where κ and τL represent the amplitude feedback coefficient and the round-trip time [27]. vg= c/ng is the lasing mode group velocity, and τpc = Q/ω is the photon lifetime of the cold cavity mode. The gain coefficient g of the strained quantum well material is:
$$g = \frac{{{g_0}}}{{1 + \varepsilon s}}\textrm{ln(}\frac{{n + {N_\textrm{s}}}}{{{N_{\textrm{tr}}} + {N_\textrm{s}}}}),$$
The feedback optical phase θ is:
$$ {\mathrm{\theta}} = \omega {\tau _\textrm{f}} + \phi - \phi (t - {\tau _\textrm{f}}).$$

 figure: Fig. 1.

Fig. 1. Schematic diagram of the circular-side hexagonal resonator (CSHR) microlaser with optical feedback.

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Note that the Eqs. (1)–(3) are based on Lang-Kobayashi model, which only considers the time variation and ignores the spatial distribution in the cavity, so they are applicable to other semiconductor lasers, such as traditional DFB lasers and VCSELs. The special parameters for the CSHR microlasers are the small mode volume Va/Γ and the high Q factor which are simultaneously achieved due to whispering gallery modes. According to the following expression of relaxation frequency fR, the CSHR microlaser can achieve an enhanced fR at a large bias current due to small mode volume and low threshold resulted from high Q factor,

$${f_\textrm{R}} = \frac{1}{{2 {\mathrm{\pi}}}}{\left( {{v_\textrm{g}}{a_n}\frac{\eta }{{q{V_\textrm{a}}\textrm{/}\Gamma }}} \right)^{1/2}}{({I - {I_{\textrm{th}}}} )^{1/2}},$$
where an=∂g/∂n is differential gain at steady state. According to the small-signal response function [23,28]
$$H(f) = \frac{{{f_{\textrm{R}}}^{2}}}{{{f_{\textrm{R}}}^2 - {f^2} + j({{\raise0.7ex\hbox{$f$} \!\mathord{\left/ {\vphantom {f {2 {\mathrm{\pi}}}}} \right.}\!\lower0.7ex\hbox{${{2{\mathrm{\pi}} }}$}}} )\gamma }},$$
the laser response at fR, which usually is the peak height of |H(f)|2, is (2πfR/γ)2, where γ=KfR2+γ0 is the damping factor, K factor describes the damping of the response and γ0 denotes the damping factor offset. One can derive that the relaxation oscillation response decreases as the relaxation frequency increases, so that, a flat and wide-band SSR is obtained by the CSHR microlaser.

The descriptions of other symbols and the selected values for simulation are shown in Table 1, based on Ref. [2327]. The rate equations are numerically calculated by using the fourth-order Runge-Kutta method with a step length of 5 ps.

Tables Icon

Table 1. Parameter values for CSHR microlaser used in simulation

3. Numerical results

Figure 2(a) shows the SSR curves of the CSHR microlaser under different bias currents. As shown, a resonance peak resulted from relaxation oscillation can be observed. Under the bias currents of 5Ith, 8Ith and 12Ith, the resonance peak frequencies are 7.7 GHz, 9.1 GHz, and 9.7 GHz, and the peak heights are 4.8 dB, 2.9 dB, 1.35 dB, respectively. With the increase of bias current, the resonance peak frequency increases and the peak height is greatly suppressed. In theory, as the bias current increases, both the relaxation oscillation frequency and damping factor increase. Therefore, the resonance peak frequency is less than the relaxation oscillation frequency [28], as shown in Fig. 2(b). Under the bias currents of 5Ith, 8Ith and 12Ith, the relaxation oscillation frequencies are 8.8 GHz, 11.3 GHz and 13.7 GHz, and the damping factors are 27.8 GHz, 45.7 GHz and 66.7 GHz, respectively.

 figure: Fig. 2.

Fig. 2. (a) the CSHR microlaser small-signal response curves and (b) resonance peak frequency and height as well as relaxation oscillation frequency as functions of bias current.

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Here, we artificially set a critical value to distinguish whether the SSR curve is flat. When the height of the resonance peak is less than 3 dB, it is considered that the SSR curve is flat, and the corresponding bias current range is considered as high current. Otherwise it is considered as low current if the resonance peak height is greater than 3 dB. In the following, we also refer to this standard to distinguish high and low current.

Figure 3 shows simulated results of optical spectra, time series, power spectra and autocorrelation functions (ACF) obtained by the CSHR microlaser under the bias current of I = 5Ith, corresponding to the black curve in Fig. 2(a). The behaviors are similar to that of the laser chaos produced by traditional DFB laser with optical feedback, with the disadvantages of low frequency energy loss and insufficient effective bandwidth. When the feedback rate is 12.4 ns−1, relaxation oscillation mode can be seen in the optical spectrum of chaos, relaxation oscillation signature exists in the time series, and the power spectrum has a sharp peak at relaxation oscillation frequency. Accordingly, the relaxation oscillation signature can be clearly reflected in ACF curve, which is evaluated by the height of sidelobe located at τR. With the increase of the feedback rate, the energy of the relaxation oscillation mode in the optical spectrum decreases, the relaxation oscillation frequency peak of power spectrum weakens, the complexity of time series increases, and the height of the sidelobe peak of ACF curve reduction but is always greater than the background noise. Besides, the ACF curve has a correlation peak at τf as depicted in Figs. 3(a4)–3(c4), which can be eliminated by grating feedback [29].

 figure: Fig. 3.

Fig. 3. Simulated typical chaos states of the CSHR microlaser biased at I=5Ith: (a1-a4) κf = 12.4 ns−1, (b1-b4) κf = 27.5 ns−1, and (c1-c4) κf = 38.5 ns−1. From left to right: optical spectra, time series, power spectra and auto-correlation functions.

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In order to quantitatively analyze the features of the chaos produced by the CSHR microlaser, the definition of bandwidth and flatness are given as follows. The bandwidth is defined as the width of the band that close to the highest peak of power spectrum, where 80% energy is contained within [30]. Two performance indexes are used to judge the flatness of power spectrum: one is the relaxation oscillation signature in the ACF curve, the other one is the filtered flatness. Owing to the external cavity oscillation is obvious, which affects the observation of the general power spectrum flatness. We use the fluctuation range of the filtered power spectrum profile curve after 0.2 GHz filtering within 80% energy band to measure the flatness, as drawn in the red line in Figs. 3(a3)–3(c3). This method can refer to the grating feedback to eliminate the external cavity characteristics [29]. As shown in Fig. 3(a3) as an example, the bandwidth of the microlaser is 8.5 GHz, the filtered flatness is 7.8 dB.

Figure 4 shows simulated results of the CSHR microlaser under the bias current of 12Ith, corresponding to the red curve in Fig. 2(a). It should be pointed that the needed optical feedback rate for same dynamic state vary with the increase of bias current. Therefore, compared with Fig. 3, higher optical feedback rate is needed. The magnification of damping leads to the suppression of relaxation oscillation, and the laser output becomes more complex. As shown in Figs. 4(a1)–4(a4), the laser is in a weak feedback state, it presents an initial chaotic state which has not been fully developed. Therefore, relaxation oscillation signature can be seen clearly in the power spectrum, and the energy distribution is unbalanced, where most of the energy is limited in the neighborhood of relaxation oscillation frequency, and the relaxation oscillation signature cannot be hidden in background noise. When the feedback rate reaches 27.5 ns−1, the flat and wide-band laser chaos is observed in Figs. 4(b1)–4(b4), which has no relaxation oscillation signature. The energy of the low-frequency oscillation component is greatly increased, and the relaxation oscillation signature can be hidden in background noise. When the feedback rate increases to 38.5 ns−1, the low-frequency energy increases, but the high-frequency remains unchanged, resulting in a slight decrease in bandwidth and a slight deterioration in flatness, as demonstrated in Fig. 4(c3). The possible reason is that the damping factor is excessive under the strong feedback rate, and the resonance peak frequency is different from the relaxation oscillation frequency, referring to Fig. 2(b).

 figure: Fig. 4.

Fig. 4. Simulated typical chaos states of the CSHR microlaser biased at I = 12Ith: (a1-a4) κf = 22ns−1, (b1-b4) κf = 27.5 ns−1, and (c1-c4) κf = 38.5 ns−1. From left to right: optical spectra, time series, power spectra and auto-correlation functions.

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Then, the influence regulation of the optical feedback rate on the bandwidth, flatness and relaxation oscillation signature under the two bias currents is compared, as shown in Fig. 5. The crosses represent the single standard deviation of the ACF background noise. Obviously, the evolution of the three parameters are corresponding to each other. Under low bias current of 5Ith (squares), with the increase of optical feedback rate, the chaos bandwidth increases and the power spectrum flattens, but the relaxation oscillation signature is always larger than the background noise. Under high bias current of 12Ith (circles), with the increase of optical feedback rate, the bandwidth increases and then decreases slightly, the flatness firstly decreases from 7.5 dB to 3.8 dB and then increases, and the relaxation oscillation signature of ACF curve are suppressed. It can be concluded that there exist an optimized range of optical feedback rate for generation of wide-band laser chaos under a certain bias current.

 figure: Fig. 5.

Fig. 5. Effects of feedback rate on (a) chaos bandwidth, (b) power spectrum flatness, and (c) relaxation oscillation signature obtained at bias currents of 5Ith (squares) and 12Ith (circles).

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Figure 6 shows the influence of bias current on laser chaos. With the increase of bias current, the bandwidth widens, the power spectrum flattens, and the relaxation oscillation signature weakens and gradually hide in the background noise. But there are some special cases under higher current. At the feedback rate of 27.5 ns−1 (squares), the chaos is underdeveloped, resulting in the decrease of bandwidth, the deterioration of power spectrum and the enhancement of relaxation oscillation signature. At the feedback rate of 30 ns−1 (circles), because of the phenomenon of power spectrum roll off, the declination angle of frequency power spectrum enlargement under high current, which leads to the deterioration of power spectrum flatness.

 figure: Fig. 6.

Fig. 6. Effects of bias current on (a) chaos bandwidth, (b) power spectrum flatness, and (c) relaxation oscillation signature obtained at feedback rates of κf = 27.5 ns−1 (squares) and 30 ns−1 (circles).

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To further analyze the laser chaos produced from the CSHR mircolaser, maps of the bandwidth and flatness in the parameter space of I/Ith and κf are displayed in Figs. 7(a)–7(b). The maximum chaos bandwidth under different bias currents is shown as the dashed line in Fig. 7(a), and it is compared with the SSR 3 dB bandwidth of a solitary laser in Fig. 7(c). It can be observed that the maximum chaos bandwidth is close to the SSR 3 dB bandwidth. Under the high bias current of I ≥ 8Ith (the critical bias current), the maximum chaos bandwidth is more than 14 GHz, and the corresponding flatness is less than 5 dB. This indicates that the CSHR mircolaser under high bias current can produce the wide-band and flat-spectrum laser chaos. It is believed that there is relevance between the SSR curve and the chaotic power spectrum of the microlaser.

 figure: Fig. 7.

Fig. 7. (a) Chaos bandwidth, (b) power spectrum flatness in parameter space (I, κf), and (c) the maximum chaos bandwidth achievable at different currents (denoted by dashed line in Fig. 7(a)) and the corresponding power spectrum flatness as well as 3 dB modulation bandwidth of solitary laser as functions of bias current.

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The largest Lyapunov exponent is one of important parameter measures for the complexity of deterministic chaos. As shown in Fig. 8, with the increase of bias current, the value of largest Lyapunov exponents is about doubled, and the largest values is about 3.4 ns−1 at bias current of 15Ith and feedback rate of 30 ns−1. Referring to Fig. 6, it can be concluded that the increase of largest Lyapunov exponent is related to the widening of bandwidth, which is the result of the suppression of relaxation oscillation signature. Meantime, the largest Lyapunov exponent can be further improved by suppressing the time-delay signature.

 figure: Fig. 8.

Fig. 8. Largest Lyapunov exponent as a function of bias current.

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4. Conclusion

The chaos bandwidth and power spectrum flatness of the CSHR microlaser with optical feedback under different bias currents and optical feedback rates are studied. The results show that with the optimization of bias current and optical feedback rate, the low frequency energy of spectrum is compensated and the relaxation oscillation is restrained. At high bias current, the CSHR microlaser has a flat and wide-band SSR curve and the CSHR microlaser with simple optical feedback can generate wide-band and flat-spectrum laser chaos. Due to the model based on Lang-Kobayashi equations does not include spatial distribution of light in cavity, it is inferred that other semiconductor lasers having a flat and wide-band SSR can also generate a wideband and flat-spectrum chaos with optical feedback. This is of great significance in practical applications such as chaos communication, key distribution and random number generation. Huang et al. have carried out the experimental research on the generation of a microwave signal by microring laser with optical injection [31]. And next, we will conduct the experimental research on the generation of chaos from the CSHR microlaser with optical feedback.

Funding

National Natural Science Foundation of China (61731014, 61822509, 61927811, 61961136002); Shanxi Talent Program (201805D211027); Shanxi "1331 Project" Key Innovative Research Team; Program for the Top Young and Middle-aged Innovative Talents of Higher Learning Institutions of Shanxi; Program for Guangdong Introducing Innovative and Enterpreneurial Teams; International Cooperation of Key R&D Program of Shanxi Province (201903D421012).

Disclosures

The authors declare no conflicts of interest.

References

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References

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  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).
    [Crossref]
  2. R. Lavrov, M. Jacquot, and L. Larger, “Nonlocal nonlinear electro-optic phase dynamics demonstrating 10 Gb/s chaos communications,” IEEE J. Quantum Electron. 46(10), 1430–1435 (2010).
    [Crossref]
  3. M. Sciamanna and K. A. Shore, “Physics and applications of laser diode chaos,” Nat. Photonics 9(3), 151–162 (2015).
    [Crossref]
  4. N. Jiang, A. Zhao, C. Xue, J. Tang, and K. Qiu, “Physical secure optical communication based on private chaotic spectral phase encryption/decryption,” Opt. Lett. 44(7), 1536–1539 (2019).
    [Crossref]
  5. 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]
  6. I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
    [Crossref]
  7. X. Z. Li, S. S. Li, J. P. Zhuang, and S. C. Chan, “Random bit generation at tunable rates using a chaotic semiconductor laser under distributed feedback,” Opt. Lett. 40(17), 3970–3973 (2015).
    [Crossref]
  8. N. Jiang, C. Xue, D. Liu, Y. Lv, and K. Qiu, “Secure key distribution based on chaos synchronization of VCSELs subject to symmetric random-polarization optical injection,” Opt. Lett. 42(6), 1055–1058 (2017).
    [Crossref]
  9. C. P. Xue, N. Jiang, K. Qiu, and Y. X. Lv, “Key distribution based on synchronization in bandwidth-enhanced random bit generators with dynamic post-processing,” Opt. Express 23(11), 14510–14519 (2015).
    [Crossref]
  10. F. Y. Lin and J. M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. 10(5), 991–997 (2004).
    [Crossref]
  11. X. Y. Dong, A. B. Wang, J. G. Zhang, H. Han, T. Zhao, X. L. Liu, and Y. C. Wang, “Combined attenuation and high-resolution fault measurements using chaos-OTDR,” IEEE Photonics J. 7(6), 1–6 (2015).
    [Crossref]
  12. Y. C. Wang, B. J. Wang, and A. B. Wang, “Chaotic correlation optical time domain reflectometer utilizing laser diode,” IEEE Photonics Technol. Lett. 20(19), 1636–1638 (2008).
    [Crossref]
  13. A. Uchida, “Optical Communication with Chaotic Lasers: Applications of Nonlinear Dynamics and Synchronization,” Wiley, New York (2012).
  14. A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photonics Technol. Lett. 20(19), 1633–1635 (2008).
    [Crossref]
  15. A. Uchida, T. Heil, Y. Liu, P. Davis, and T. Aida, “High-frequency broad-band signal generation using a semiconductor laser with a chaotic optical injection,” IEEE J. Quantum Electron. 39(11), 1462–1467 (2003).
    [Crossref]
  16. L. J. Qiao, T. S. Lv, Y. Xu, M. J. Zhang, J. Z. Zhang, T. Wang, R. K. Zhou, Q. Wang, and H. C. Xu, “Generation of flat wideband chaos based on mutual injection of semiconductor lasers,” Opt. Lett. 44(22), 5394–5397 (2019).
    [Crossref]
  17. E. Mercier, D. Wolfersberger, and M. Sciamanna, “High-frequency chaotic dynamics enabled by optical phase-conjugation,” Sci. Rep. 6(1), 18988 (2016).
    [Crossref]
  18. A. K. Zhao, N. Jiang, S. Q. Liu, C. P. Xue, J. M. Tang, and K. Qiu, “Wideband complex-enhanced chaos generation using a semiconductor laser subject to delay-interfered self-phase-modulated feedback,” Opt. Express 27(9), 12336–12348 (2019).
    [Crossref]
  19. A. B. Wang, Y. C. Wang, Y. B. Yang, M. J. Zhang, H. Xu, and B. J. Wang, “Generation of flat-spectrum wideband chaos by fiber ring resonator,” Appl. Phys. Lett. 102(3), 031112 (2013).
    [Crossref]
  20. Y. H. Hong, X. F. Chen, P. S. Spencer, and K. A. Shore, “Enhanced flat broadband optical chaos using low-cost VCSEL and fiber ring resonator,” IEEE J. Quantum Electron. 51(3), 1–6 (2015).
    [Crossref]
  21. A. B. Wang, B. J. Wang, L. Li, Y. C. Wang, and K. A. Shore, “Optical heterodyne generation of high- dimensional and broadband white chaos,” IEEE J. Sel. Top. Quantum Electron. 21(6), 531–540 (2015).
    [Crossref]
  22. C. H. Cheng, Y. C. Chen, and F. Y. Lin, “Chaos time delay signature suppression and bandwidth enhancement by electrical heterodyning,” Opt. Express 23(3), 2308–2319 (2015).
    [Crossref]
  23. X. M. Lv, L. X. Zou, Y. Z. Huang, Y. D. Yang, J. L. Xiao, Q. F. Yao, and J. D. Lin, “Influence of Mode Q Factor and Absorption Loss on Dynamical Characteristics for Semiconductor Microcavity Lasers by Rate Equation Analysis,” IEEE J. Quantum Electron. 47(12), 1519–1525 (2011).
    [Crossref]
  24. Z. X. Xiao, Y. Z. Huang, Y. D. Yang, J. L. Xiao, and X. W. Ma, “Single-mode unidirectional-emission circular-side hexagonal resonator microlasers,” Opt. Lett. 42(7), 1309–1312 (2017).
    [Crossref]
  25. X. M. Lv, Y. Z. Huang, L. X. Zou, H. Long, and Y. Du, “Optimization of direct modulation rate for circular microlasers by adjusting mode Q factor,” Laser Photonics Rev. 7(5), 818–829 (2013).
    [Crossref]
  26. Y. Z. Huang, X. W. Ma, Y. D. Yang, and J. L. Xiao, “Review of the dynamic characteristics of AlGaInAs/InP microlasers subject to optical injection,” Semicond. Sci. Technol. 31(11), 113002 (2016).
    [Crossref]
  27. X. W. Ma, Y. Z. Huang, H. Long, Y. D. Yang, F. L. Wang, J. L. Xiao, and Y. Du, “Experimental and Theoretical Analysis of Dynamical Regimes for Optically Injected Microdisk Lasers,” J. Lightwave Technol. 34(22), 5263–5269 (2016).
    [Crossref]
  28. L. A. Coldren and S. W. Corzine, “Diode Lasers and Photonic Integrated Circuits,” Wiley, New York (1995).
  29. D. M. Wang, L. S. Wang, T. Zhao, H. Gao, Y. C. Wang, X. F. Chen, and A. B. 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]
  30. F. Y. Lin, Y. K. Chao, and T. C. Wu, “Effective Bandwidths of Broadband Chaotic Signals,” IEEE J. Quantum Electron. 48(8), 1010–1014 (2012).
    [Crossref]
  31. L. X. Zou, Y. Z. Huang, X. M. Lv, B. W. Liu, H. Long, Y. D. Yang, J. L. Xiao, and Y. Du, “Modulation characteristics and microwave generation for AlGaInAs/InP microring lasers under four-wave mixing,” Photonics Res. 2(6), 177–181 (2014).
    [Crossref]

2019 (3)

2017 (3)

2016 (3)

Y. Z. Huang, X. W. Ma, Y. D. Yang, and J. L. Xiao, “Review of the dynamic characteristics of AlGaInAs/InP microlasers subject to optical injection,” Semicond. Sci. Technol. 31(11), 113002 (2016).
[Crossref]

X. W. Ma, Y. Z. Huang, H. Long, Y. D. Yang, F. L. Wang, J. L. Xiao, and Y. Du, “Experimental and Theoretical Analysis of Dynamical Regimes for Optically Injected Microdisk Lasers,” J. Lightwave Technol. 34(22), 5263–5269 (2016).
[Crossref]

E. Mercier, D. Wolfersberger, and M. Sciamanna, “High-frequency chaotic dynamics enabled by optical phase-conjugation,” Sci. Rep. 6(1), 18988 (2016).
[Crossref]

2015 (7)

X. Y. Dong, A. B. Wang, J. G. Zhang, H. Han, T. Zhao, X. L. Liu, and Y. C. Wang, “Combined attenuation and high-resolution fault measurements using chaos-OTDR,” IEEE Photonics J. 7(6), 1–6 (2015).
[Crossref]

C. P. Xue, N. Jiang, K. Qiu, and Y. X. Lv, “Key distribution based on synchronization in bandwidth-enhanced random bit generators with dynamic post-processing,” Opt. Express 23(11), 14510–14519 (2015).
[Crossref]

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

Y. H. Hong, X. F. Chen, P. S. Spencer, and K. A. Shore, “Enhanced flat broadband optical chaos using low-cost VCSEL and fiber ring resonator,” IEEE J. Quantum Electron. 51(3), 1–6 (2015).
[Crossref]

A. B. Wang, B. J. Wang, L. Li, Y. C. Wang, and K. A. Shore, “Optical heterodyne generation of high- dimensional and broadband white chaos,” IEEE J. Sel. Top. Quantum Electron. 21(6), 531–540 (2015).
[Crossref]

C. H. Cheng, Y. C. Chen, and F. Y. Lin, “Chaos time delay signature suppression and bandwidth enhancement by electrical heterodyning,” Opt. Express 23(3), 2308–2319 (2015).
[Crossref]

X. Z. Li, S. S. Li, J. P. Zhuang, and S. C. Chan, “Random bit generation at tunable rates using a chaotic semiconductor laser under distributed feedback,” Opt. Lett. 40(17), 3970–3973 (2015).
[Crossref]

2014 (1)

L. X. Zou, Y. Z. Huang, X. M. Lv, B. W. Liu, H. Long, Y. D. Yang, J. L. Xiao, and Y. Du, “Modulation characteristics and microwave generation for AlGaInAs/InP microring lasers under four-wave mixing,” Photonics Res. 2(6), 177–181 (2014).
[Crossref]

2013 (2)

X. M. Lv, Y. Z. Huang, L. X. Zou, H. Long, and Y. Du, “Optimization of direct modulation rate for circular microlasers by adjusting mode Q factor,” Laser Photonics Rev. 7(5), 818–829 (2013).
[Crossref]

A. B. Wang, Y. C. Wang, Y. B. Yang, M. J. Zhang, H. Xu, and B. J. Wang, “Generation of flat-spectrum wideband chaos by fiber ring resonator,” Appl. Phys. Lett. 102(3), 031112 (2013).
[Crossref]

2012 (1)

F. Y. Lin, Y. K. Chao, and T. C. Wu, “Effective Bandwidths of Broadband Chaotic Signals,” IEEE J. Quantum Electron. 48(8), 1010–1014 (2012).
[Crossref]

2011 (1)

X. M. Lv, L. X. Zou, Y. Z. Huang, Y. D. Yang, J. L. Xiao, Q. F. Yao, and J. D. Lin, “Influence of Mode Q Factor and Absorption Loss on Dynamical Characteristics for Semiconductor Microcavity Lasers by Rate Equation Analysis,” IEEE J. Quantum Electron. 47(12), 1519–1525 (2011).
[Crossref]

2010 (2)

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[Crossref]

R. Lavrov, M. Jacquot, and L. Larger, “Nonlocal nonlinear electro-optic phase dynamics demonstrating 10 Gb/s chaos communications,” IEEE J. Quantum Electron. 46(10), 1430–1435 (2010).
[Crossref]

2008 (3)

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]

Y. C. Wang, B. J. Wang, and A. B. Wang, “Chaotic correlation optical time domain reflectometer utilizing laser diode,” IEEE Photonics Technol. Lett. 20(19), 1636–1638 (2008).
[Crossref]

A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photonics Technol. Lett. 20(19), 1633–1635 (2008).
[Crossref]

2005 (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).
[Crossref]

2004 (1)

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

2003 (1)

A. Uchida, T. Heil, Y. Liu, P. Davis, and T. Aida, “High-frequency broad-band signal generation using a semiconductor laser with a chaotic optical injection,” IEEE J. Quantum Electron. 39(11), 1462–1467 (2003).
[Crossref]

Aida, T.

A. Uchida, T. Heil, Y. Liu, P. Davis, and T. Aida, “High-frequency broad-band signal generation using a semiconductor laser with a chaotic optical injection,” IEEE J. Quantum Electron. 39(11), 1462–1467 (2003).
[Crossref]

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.

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]

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]

Aviad, Y.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[Crossref]

Chan, S. C.

Chao, Y. K.

F. Y. Lin, Y. K. Chao, and T. C. Wu, “Effective Bandwidths of Broadband Chaotic Signals,” IEEE J. Quantum Electron. 48(8), 1010–1014 (2012).
[Crossref]

Chen, X. F.

D. M. Wang, L. S. Wang, T. Zhao, H. Gao, Y. C. Wang, X. F. Chen, and A. B. 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]

Y. H. Hong, X. F. Chen, P. S. Spencer, and K. A. Shore, “Enhanced flat broadband optical chaos using low-cost VCSEL and fiber ring resonator,” IEEE J. Quantum Electron. 51(3), 1–6 (2015).
[Crossref]

Chen, Y. C.

Cheng, C. H.

Cohen, E.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[Crossref]

Coldren, L. A.

L. A. Coldren and S. W. Corzine, “Diode Lasers and Photonic Integrated Circuits,” Wiley, New York (1995).

Colet, P.

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]

Corzine, S. W.

L. A. Coldren and S. W. Corzine, “Diode Lasers and Photonic Integrated Circuits,” Wiley, New York (1995).

Davis, P.

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]

A. Uchida, T. Heil, Y. Liu, P. Davis, and T. Aida, “High-frequency broad-band signal generation using a semiconductor laser with a chaotic optical injection,” IEEE J. Quantum Electron. 39(11), 1462–1467 (2003).
[Crossref]

Dong, X. Y.

X. Y. Dong, A. B. Wang, J. G. Zhang, H. Han, T. Zhao, X. L. Liu, and Y. C. Wang, “Combined attenuation and high-resolution fault measurements using chaos-OTDR,” IEEE Photonics J. 7(6), 1–6 (2015).
[Crossref]

Du, Y.

X. W. Ma, Y. Z. Huang, H. Long, Y. D. Yang, F. L. Wang, J. L. Xiao, and Y. Du, “Experimental and Theoretical Analysis of Dynamical Regimes for Optically Injected Microdisk Lasers,” J. Lightwave Technol. 34(22), 5263–5269 (2016).
[Crossref]

L. X. Zou, Y. Z. Huang, X. M. Lv, B. W. Liu, H. Long, Y. D. Yang, J. L. Xiao, and Y. Du, “Modulation characteristics and microwave generation for AlGaInAs/InP microring lasers under four-wave mixing,” Photonics Res. 2(6), 177–181 (2014).
[Crossref]

X. M. Lv, Y. Z. Huang, L. X. Zou, H. Long, and Y. Du, “Optimization of direct modulation rate for circular microlasers by adjusting mode Q factor,” Laser Photonics Rev. 7(5), 818–829 (2013).
[Crossref]

Fischer, I.

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]

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]

Han, H.

X. Y. Dong, A. B. Wang, J. G. Zhang, H. Han, T. Zhao, X. L. Liu, and Y. C. Wang, “Combined attenuation and high-resolution fault measurements using chaos-OTDR,” IEEE Photonics J. 7(6), 1–6 (2015).
[Crossref]

He, H. C.

A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photonics Technol. Lett. 20(19), 1633–1635 (2008).
[Crossref]

Heil, T.

A. Uchida, T. Heil, Y. Liu, P. Davis, and T. Aida, “High-frequency broad-band signal generation using a semiconductor laser with a chaotic optical injection,” IEEE J. Quantum Electron. 39(11), 1462–1467 (2003).
[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. H.

Y. H. Hong, X. F. Chen, P. S. Spencer, and K. A. Shore, “Enhanced flat broadband optical chaos using low-cost VCSEL and fiber ring resonator,” IEEE J. Quantum Electron. 51(3), 1–6 (2015).
[Crossref]

Huang, Y. Z.

Z. X. Xiao, Y. Z. Huang, Y. D. Yang, J. L. Xiao, and X. W. Ma, “Single-mode unidirectional-emission circular-side hexagonal resonator microlasers,” Opt. Lett. 42(7), 1309–1312 (2017).
[Crossref]

Y. Z. Huang, X. W. Ma, Y. D. Yang, and J. L. Xiao, “Review of the dynamic characteristics of AlGaInAs/InP microlasers subject to optical injection,” Semicond. Sci. Technol. 31(11), 113002 (2016).
[Crossref]

X. W. Ma, Y. Z. Huang, H. Long, Y. D. Yang, F. L. Wang, J. L. Xiao, and Y. Du, “Experimental and Theoretical Analysis of Dynamical Regimes for Optically Injected Microdisk Lasers,” J. Lightwave Technol. 34(22), 5263–5269 (2016).
[Crossref]

L. X. Zou, Y. Z. Huang, X. M. Lv, B. W. Liu, H. Long, Y. D. Yang, J. L. Xiao, and Y. Du, “Modulation characteristics and microwave generation for AlGaInAs/InP microring lasers under four-wave mixing,” Photonics Res. 2(6), 177–181 (2014).
[Crossref]

X. M. Lv, Y. Z. Huang, L. X. Zou, H. Long, and Y. Du, “Optimization of direct modulation rate for circular microlasers by adjusting mode Q factor,” Laser Photonics Rev. 7(5), 818–829 (2013).
[Crossref]

X. M. Lv, L. X. Zou, Y. Z. Huang, Y. D. Yang, J. L. Xiao, Q. F. Yao, and J. D. Lin, “Influence of Mode Q Factor and Absorption Loss on Dynamical Characteristics for Semiconductor Microcavity Lasers by Rate Equation Analysis,” IEEE J. Quantum Electron. 47(12), 1519–1525 (2011).
[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]

Jacquot, M.

R. Lavrov, M. Jacquot, and L. Larger, “Nonlocal nonlinear electro-optic phase dynamics demonstrating 10 Gb/s chaos communications,” IEEE J. Quantum Electron. 46(10), 1430–1435 (2010).
[Crossref]

Jiang, N.

Kanter, I.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[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]

Larger, L.

R. Lavrov, M. Jacquot, and L. Larger, “Nonlocal nonlinear electro-optic phase dynamics demonstrating 10 Gb/s chaos communications,” IEEE J. Quantum Electron. 46(10), 1430–1435 (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]

Lavrov, R.

R. Lavrov, M. Jacquot, and L. Larger, “Nonlocal nonlinear electro-optic phase dynamics demonstrating 10 Gb/s chaos communications,” IEEE J. Quantum Electron. 46(10), 1430–1435 (2010).
[Crossref]

Li, L.

A. B. Wang, B. J. Wang, L. Li, Y. C. Wang, and K. A. Shore, “Optical heterodyne generation of high- dimensional and broadband white chaos,” IEEE J. Sel. Top. Quantum Electron. 21(6), 531–540 (2015).
[Crossref]

Li, S. S.

Li, X. Z.

Lin, F. Y.

C. H. Cheng, Y. C. Chen, and F. Y. Lin, “Chaos time delay signature suppression and bandwidth enhancement by electrical heterodyning,” Opt. Express 23(3), 2308–2319 (2015).
[Crossref]

F. Y. Lin, Y. K. Chao, and T. C. Wu, “Effective Bandwidths of Broadband Chaotic Signals,” IEEE J. Quantum Electron. 48(8), 1010–1014 (2012).
[Crossref]

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

Lin, J. D.

X. M. Lv, L. X. Zou, Y. Z. Huang, Y. D. Yang, J. L. Xiao, Q. F. Yao, and J. D. Lin, “Influence of Mode Q Factor and Absorption Loss on Dynamical Characteristics for Semiconductor Microcavity Lasers by Rate Equation Analysis,” IEEE J. Quantum Electron. 47(12), 1519–1525 (2011).
[Crossref]

Liu, B. W.

L. X. Zou, Y. Z. Huang, X. M. Lv, B. W. Liu, H. Long, Y. D. Yang, J. L. Xiao, and Y. Du, “Modulation characteristics and microwave generation for AlGaInAs/InP microring lasers under four-wave mixing,” Photonics Res. 2(6), 177–181 (2014).
[Crossref]

Liu, D.

Liu, J. M.

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

Liu, S. Q.

Liu, X. L.

X. Y. Dong, A. B. Wang, J. G. Zhang, H. Han, T. Zhao, X. L. Liu, and Y. C. Wang, “Combined attenuation and high-resolution fault measurements using chaos-OTDR,” IEEE Photonics J. 7(6), 1–6 (2015).
[Crossref]

Liu, Y.

A. Uchida, T. Heil, Y. Liu, P. Davis, and T. Aida, “High-frequency broad-band signal generation using a semiconductor laser with a chaotic optical injection,” IEEE J. Quantum Electron. 39(11), 1462–1467 (2003).
[Crossref]

Long, H.

X. W. Ma, Y. Z. Huang, H. Long, Y. D. Yang, F. L. Wang, J. L. Xiao, and Y. Du, “Experimental and Theoretical Analysis of Dynamical Regimes for Optically Injected Microdisk Lasers,” J. Lightwave Technol. 34(22), 5263–5269 (2016).
[Crossref]

L. X. Zou, Y. Z. Huang, X. M. Lv, B. W. Liu, H. Long, Y. D. Yang, J. L. Xiao, and Y. Du, “Modulation characteristics and microwave generation for AlGaInAs/InP microring lasers under four-wave mixing,” Photonics Res. 2(6), 177–181 (2014).
[Crossref]

X. M. Lv, Y. Z. Huang, L. X. Zou, H. Long, and Y. Du, “Optimization of direct modulation rate for circular microlasers by adjusting mode Q factor,” Laser Photonics Rev. 7(5), 818–829 (2013).
[Crossref]

Lv, T. S.

Lv, X. M.

L. X. Zou, Y. Z. Huang, X. M. Lv, B. W. Liu, H. Long, Y. D. Yang, J. L. Xiao, and Y. Du, “Modulation characteristics and microwave generation for AlGaInAs/InP microring lasers under four-wave mixing,” Photonics Res. 2(6), 177–181 (2014).
[Crossref]

X. M. Lv, Y. Z. Huang, L. X. Zou, H. Long, and Y. Du, “Optimization of direct modulation rate for circular microlasers by adjusting mode Q factor,” Laser Photonics Rev. 7(5), 818–829 (2013).
[Crossref]

X. M. Lv, L. X. Zou, Y. Z. Huang, Y. D. Yang, J. L. Xiao, Q. F. Yao, and J. D. Lin, “Influence of Mode Q Factor and Absorption Loss on Dynamical Characteristics for Semiconductor Microcavity Lasers by Rate Equation Analysis,” IEEE J. Quantum Electron. 47(12), 1519–1525 (2011).
[Crossref]

Lv, Y.

Lv, Y. X.

Ma, X. W.

Mercier, E.

E. Mercier, D. Wolfersberger, and M. Sciamanna, “High-frequency chaotic dynamics enabled by optical phase-conjugation,” Sci. Rep. 6(1), 18988 (2016).
[Crossref]

Mirasso, C. R.

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]

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).
[Crossref]

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).
[Crossref]

Pesquera, L.

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]

Qiao, L. J.

Qiu, K.

Reidler, I.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[Crossref]

Rosenbluh, M.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[Crossref]

Sciamanna, M.

E. Mercier, D. Wolfersberger, and M. Sciamanna, “High-frequency chaotic dynamics enabled by optical phase-conjugation,” Sci. Rep. 6(1), 18988 (2016).
[Crossref]

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

Shore, K. A.

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

A. B. Wang, B. J. Wang, L. Li, Y. C. Wang, and K. A. Shore, “Optical heterodyne generation of high- dimensional and broadband white chaos,” IEEE J. Sel. Top. Quantum Electron. 21(6), 531–540 (2015).
[Crossref]

Y. H. Hong, X. F. Chen, P. S. Spencer, and K. A. Shore, “Enhanced flat broadband optical chaos using low-cost VCSEL and fiber ring resonator,” IEEE J. Quantum Electron. 51(3), 1–6 (2015).
[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]

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]

Spencer, P. S.

Y. H. Hong, X. F. Chen, P. S. Spencer, and K. A. Shore, “Enhanced flat broadband optical chaos using low-cost VCSEL and fiber ring resonator,” IEEE J. Quantum Electron. 51(3), 1–6 (2015).
[Crossref]

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).
[Crossref]

Tang, J.

Tang, J. M.

Uchida, A.

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]

A. Uchida, T. Heil, Y. Liu, P. Davis, and T. Aida, “High-frequency broad-band signal generation using a semiconductor laser with a chaotic optical injection,” IEEE J. Quantum Electron. 39(11), 1462–1467 (2003).
[Crossref]

A. Uchida, “Optical Communication with Chaotic Lasers: Applications of Nonlinear Dynamics and Synchronization,” Wiley, New York (2012).

Wang, A. B.

D. M. Wang, L. S. Wang, T. Zhao, H. Gao, Y. C. Wang, X. F. Chen, and A. B. 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]

X. Y. Dong, A. B. Wang, J. G. Zhang, H. Han, T. Zhao, X. L. Liu, and Y. C. Wang, “Combined attenuation and high-resolution fault measurements using chaos-OTDR,” IEEE Photonics J. 7(6), 1–6 (2015).
[Crossref]

A. B. Wang, B. J. Wang, L. Li, Y. C. Wang, and K. A. Shore, “Optical heterodyne generation of high- dimensional and broadband white chaos,” IEEE J. Sel. Top. Quantum Electron. 21(6), 531–540 (2015).
[Crossref]

A. B. Wang, Y. C. Wang, Y. B. Yang, M. J. Zhang, H. Xu, and B. J. Wang, “Generation of flat-spectrum wideband chaos by fiber ring resonator,” Appl. Phys. Lett. 102(3), 031112 (2013).
[Crossref]

A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photonics Technol. Lett. 20(19), 1633–1635 (2008).
[Crossref]

Y. C. Wang, B. J. Wang, and A. B. Wang, “Chaotic correlation optical time domain reflectometer utilizing laser diode,” IEEE Photonics Technol. Lett. 20(19), 1636–1638 (2008).
[Crossref]

Wang, B. J.

A. B. Wang, B. J. Wang, L. Li, Y. C. Wang, and K. A. Shore, “Optical heterodyne generation of high- dimensional and broadband white chaos,” IEEE J. Sel. Top. Quantum Electron. 21(6), 531–540 (2015).
[Crossref]

A. B. Wang, Y. C. Wang, Y. B. Yang, M. J. Zhang, H. Xu, and B. J. Wang, “Generation of flat-spectrum wideband chaos by fiber ring resonator,” Appl. Phys. Lett. 102(3), 031112 (2013).
[Crossref]

Y. C. Wang, B. J. Wang, and A. B. Wang, “Chaotic correlation optical time domain reflectometer utilizing laser diode,” IEEE Photonics Technol. Lett. 20(19), 1636–1638 (2008).
[Crossref]

Wang, D. M.

Wang, F. L.

Wang, L. S.

Wang, Q.

Wang, T.

Wang, Y. C.

D. M. Wang, L. S. Wang, T. Zhao, H. Gao, Y. C. Wang, X. F. Chen, and A. B. 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]

A. B. Wang, B. J. Wang, L. Li, Y. C. Wang, and K. A. Shore, “Optical heterodyne generation of high- dimensional and broadband white chaos,” IEEE J. Sel. Top. Quantum Electron. 21(6), 531–540 (2015).
[Crossref]

X. Y. Dong, A. B. Wang, J. G. Zhang, H. Han, T. Zhao, X. L. Liu, and Y. C. Wang, “Combined attenuation and high-resolution fault measurements using chaos-OTDR,” IEEE Photonics J. 7(6), 1–6 (2015).
[Crossref]

A. B. Wang, Y. C. Wang, Y. B. Yang, M. J. Zhang, H. Xu, and B. J. Wang, “Generation of flat-spectrum wideband chaos by fiber ring resonator,” Appl. Phys. Lett. 102(3), 031112 (2013).
[Crossref]

Y. C. Wang, B. J. Wang, and A. B. Wang, “Chaotic correlation optical time domain reflectometer utilizing laser diode,” IEEE Photonics Technol. Lett. 20(19), 1636–1638 (2008).
[Crossref]

A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photonics Technol. Lett. 20(19), 1633–1635 (2008).
[Crossref]

Wolfersberger, D.

E. Mercier, D. Wolfersberger, and M. Sciamanna, “High-frequency chaotic dynamics enabled by optical phase-conjugation,” Sci. Rep. 6(1), 18988 (2016).
[Crossref]

Wu, T. C.

F. Y. Lin, Y. K. Chao, and T. C. Wu, “Effective Bandwidths of Broadband Chaotic Signals,” IEEE J. Quantum Electron. 48(8), 1010–1014 (2012).
[Crossref]

Xiao, J. L.

Z. X. Xiao, Y. Z. Huang, Y. D. Yang, J. L. Xiao, and X. W. Ma, “Single-mode unidirectional-emission circular-side hexagonal resonator microlasers,” Opt. Lett. 42(7), 1309–1312 (2017).
[Crossref]

X. W. Ma, Y. Z. Huang, H. Long, Y. D. Yang, F. L. Wang, J. L. Xiao, and Y. Du, “Experimental and Theoretical Analysis of Dynamical Regimes for Optically Injected Microdisk Lasers,” J. Lightwave Technol. 34(22), 5263–5269 (2016).
[Crossref]

Y. Z. Huang, X. W. Ma, Y. D. Yang, and J. L. Xiao, “Review of the dynamic characteristics of AlGaInAs/InP microlasers subject to optical injection,” Semicond. Sci. Technol. 31(11), 113002 (2016).
[Crossref]

L. X. Zou, Y. Z. Huang, X. M. Lv, B. W. Liu, H. Long, Y. D. Yang, J. L. Xiao, and Y. Du, “Modulation characteristics and microwave generation for AlGaInAs/InP microring lasers under four-wave mixing,” Photonics Res. 2(6), 177–181 (2014).
[Crossref]

X. M. Lv, L. X. Zou, Y. Z. Huang, Y. D. Yang, J. L. Xiao, Q. F. Yao, and J. D. Lin, “Influence of Mode Q Factor and Absorption Loss on Dynamical Characteristics for Semiconductor Microcavity Lasers by Rate Equation Analysis,” IEEE J. Quantum Electron. 47(12), 1519–1525 (2011).
[Crossref]

Xiao, Z. X.

Xu, H.

A. B. Wang, Y. C. Wang, Y. B. Yang, M. J. Zhang, H. Xu, and B. J. Wang, “Generation of flat-spectrum wideband chaos by fiber ring resonator,” Appl. Phys. Lett. 102(3), 031112 (2013).
[Crossref]

Xu, H. C.

Xu, Y.

Xue, C.

Xue, C. P.

Yang, Y. B.

A. B. Wang, Y. C. Wang, Y. B. Yang, M. J. Zhang, H. Xu, and B. J. Wang, “Generation of flat-spectrum wideband chaos by fiber ring resonator,” Appl. Phys. Lett. 102(3), 031112 (2013).
[Crossref]

Yang, Y. D.

Z. X. Xiao, Y. Z. Huang, Y. D. Yang, J. L. Xiao, and X. W. Ma, “Single-mode unidirectional-emission circular-side hexagonal resonator microlasers,” Opt. Lett. 42(7), 1309–1312 (2017).
[Crossref]

Y. Z. Huang, X. W. Ma, Y. D. Yang, and J. L. Xiao, “Review of the dynamic characteristics of AlGaInAs/InP microlasers subject to optical injection,” Semicond. Sci. Technol. 31(11), 113002 (2016).
[Crossref]

X. W. Ma, Y. Z. Huang, H. Long, Y. D. Yang, F. L. Wang, J. L. Xiao, and Y. Du, “Experimental and Theoretical Analysis of Dynamical Regimes for Optically Injected Microdisk Lasers,” J. Lightwave Technol. 34(22), 5263–5269 (2016).
[Crossref]

L. X. Zou, Y. Z. Huang, X. M. Lv, B. W. Liu, H. Long, Y. D. Yang, J. L. Xiao, and Y. Du, “Modulation characteristics and microwave generation for AlGaInAs/InP microring lasers under four-wave mixing,” Photonics Res. 2(6), 177–181 (2014).
[Crossref]

X. M. Lv, L. X. Zou, Y. Z. Huang, Y. D. Yang, J. L. Xiao, Q. F. Yao, and J. D. Lin, “Influence of Mode Q Factor and Absorption Loss on Dynamical Characteristics for Semiconductor Microcavity Lasers by Rate Equation Analysis,” IEEE J. Quantum Electron. 47(12), 1519–1525 (2011).
[Crossref]

Yao, Q. F.

X. M. Lv, L. X. Zou, Y. Z. Huang, Y. D. Yang, J. L. Xiao, Q. F. Yao, and J. D. Lin, “Influence of Mode Q Factor and Absorption Loss on Dynamical Characteristics for Semiconductor Microcavity Lasers by Rate Equation Analysis,” IEEE J. Quantum Electron. 47(12), 1519–1525 (2011).
[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.

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]

Zhang, J. G.

X. Y. Dong, A. B. Wang, J. G. Zhang, H. Han, T. Zhao, X. L. Liu, and Y. C. Wang, “Combined attenuation and high-resolution fault measurements using chaos-OTDR,” IEEE Photonics J. 7(6), 1–6 (2015).
[Crossref]

Zhang, J. Z.

Zhang, M. J.

L. J. Qiao, T. S. Lv, Y. Xu, M. J. Zhang, J. Z. Zhang, T. Wang, R. K. Zhou, Q. Wang, and H. C. Xu, “Generation of flat wideband chaos based on mutual injection of semiconductor lasers,” Opt. Lett. 44(22), 5394–5397 (2019).
[Crossref]

A. B. Wang, Y. C. Wang, Y. B. Yang, M. J. Zhang, H. Xu, and B. J. Wang, “Generation of flat-spectrum wideband chaos by fiber ring resonator,” Appl. Phys. Lett. 102(3), 031112 (2013).
[Crossref]

Zhao, A.

Zhao, A. K.

Zhao, T.

D. M. Wang, L. S. Wang, T. Zhao, H. Gao, Y. C. Wang, X. F. Chen, and A. B. 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]

X. Y. Dong, A. B. Wang, J. G. Zhang, H. Han, T. Zhao, X. L. Liu, and Y. C. Wang, “Combined attenuation and high-resolution fault measurements using chaos-OTDR,” IEEE Photonics J. 7(6), 1–6 (2015).
[Crossref]

Zhou, R. K.

Zhuang, J. P.

Zou, L. X.

L. X. Zou, Y. Z. Huang, X. M. Lv, B. W. Liu, H. Long, Y. D. Yang, J. L. Xiao, and Y. Du, “Modulation characteristics and microwave generation for AlGaInAs/InP microring lasers under four-wave mixing,” Photonics Res. 2(6), 177–181 (2014).
[Crossref]

X. M. Lv, Y. Z. Huang, L. X. Zou, H. Long, and Y. Du, “Optimization of direct modulation rate for circular microlasers by adjusting mode Q factor,” Laser Photonics Rev. 7(5), 818–829 (2013).
[Crossref]

X. M. Lv, L. X. Zou, Y. Z. Huang, Y. D. Yang, J. L. Xiao, Q. F. Yao, and J. D. Lin, “Influence of Mode Q Factor and Absorption Loss on Dynamical Characteristics for Semiconductor Microcavity Lasers by Rate Equation Analysis,” IEEE J. Quantum Electron. 47(12), 1519–1525 (2011).
[Crossref]

Appl. Phys. Lett. (1)

A. B. Wang, Y. C. Wang, Y. B. Yang, M. J. Zhang, H. Xu, and B. J. Wang, “Generation of flat-spectrum wideband chaos by fiber ring resonator,” Appl. Phys. Lett. 102(3), 031112 (2013).
[Crossref]

IEEE J. Quantum Electron. (5)

Y. H. Hong, X. F. Chen, P. S. Spencer, and K. A. Shore, “Enhanced flat broadband optical chaos using low-cost VCSEL and fiber ring resonator,” IEEE J. Quantum Electron. 51(3), 1–6 (2015).
[Crossref]

X. M. Lv, L. X. Zou, Y. Z. Huang, Y. D. Yang, J. L. Xiao, Q. F. Yao, and J. D. Lin, “Influence of Mode Q Factor and Absorption Loss on Dynamical Characteristics for Semiconductor Microcavity Lasers by Rate Equation Analysis,” IEEE J. Quantum Electron. 47(12), 1519–1525 (2011).
[Crossref]

F. Y. Lin, Y. K. Chao, and T. C. Wu, “Effective Bandwidths of Broadband Chaotic Signals,” IEEE J. Quantum Electron. 48(8), 1010–1014 (2012).
[Crossref]

R. Lavrov, M. Jacquot, and L. Larger, “Nonlocal nonlinear electro-optic phase dynamics demonstrating 10 Gb/s chaos communications,” IEEE J. Quantum Electron. 46(10), 1430–1435 (2010).
[Crossref]

A. Uchida, T. Heil, Y. Liu, P. Davis, and T. Aida, “High-frequency broad-band signal generation using a semiconductor laser with a chaotic optical injection,” IEEE J. Quantum Electron. 39(11), 1462–1467 (2003).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

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

A. B. Wang, B. J. Wang, L. Li, Y. C. Wang, and K. A. Shore, “Optical heterodyne generation of high- dimensional and broadband white chaos,” IEEE J. Sel. Top. Quantum Electron. 21(6), 531–540 (2015).
[Crossref]

IEEE Photonics J. (1)

X. Y. Dong, A. B. Wang, J. G. Zhang, H. Han, T. Zhao, X. L. Liu, and Y. C. Wang, “Combined attenuation and high-resolution fault measurements using chaos-OTDR,” IEEE Photonics J. 7(6), 1–6 (2015).
[Crossref]

IEEE Photonics Technol. Lett. (2)

Y. C. Wang, B. J. Wang, and A. B. Wang, “Chaotic correlation optical time domain reflectometer utilizing laser diode,” IEEE Photonics Technol. Lett. 20(19), 1636–1638 (2008).
[Crossref]

A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photonics Technol. Lett. 20(19), 1633–1635 (2008).
[Crossref]

J. Lightwave Technol. (1)

Laser Photonics Rev. (1)

X. M. Lv, Y. Z. Huang, L. X. Zou, H. Long, and Y. Du, “Optimization of direct modulation rate for circular microlasers by adjusting mode Q factor,” Laser Photonics Rev. 7(5), 818–829 (2013).
[Crossref]

Nat. Photonics (3)

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

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[Crossref]

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).
[Crossref]

Opt. Express (4)

Opt. Lett. (5)

Photonics Res. (1)

L. X. Zou, Y. Z. Huang, X. M. Lv, B. W. Liu, H. Long, Y. D. Yang, J. L. Xiao, and Y. Du, “Modulation characteristics and microwave generation for AlGaInAs/InP microring lasers under four-wave mixing,” Photonics Res. 2(6), 177–181 (2014).
[Crossref]

Sci. Rep. (1)

E. Mercier, D. Wolfersberger, and M. Sciamanna, “High-frequency chaotic dynamics enabled by optical phase-conjugation,” Sci. Rep. 6(1), 18988 (2016).
[Crossref]

Semicond. Sci. Technol. (1)

Y. Z. Huang, X. W. Ma, Y. D. Yang, and J. L. Xiao, “Review of the dynamic characteristics of AlGaInAs/InP microlasers subject to optical injection,” Semicond. Sci. Technol. 31(11), 113002 (2016).
[Crossref]

Other (2)

L. A. Coldren and S. W. Corzine, “Diode Lasers and Photonic Integrated Circuits,” Wiley, New York (1995).

A. Uchida, “Optical Communication with Chaotic Lasers: Applications of Nonlinear Dynamics and Synchronization,” Wiley, New York (2012).

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Figures (8)

Fig. 1.
Fig. 1. Schematic diagram of the circular-side hexagonal resonator (CSHR) microlaser with optical feedback.
Fig. 2.
Fig. 2. (a) the CSHR microlaser small-signal response curves and (b) resonance peak frequency and height as well as relaxation oscillation frequency as functions of bias current.
Fig. 3.
Fig. 3. Simulated typical chaos states of the CSHR microlaser biased at I=5Ith: (a1-a4) κf = 12.4 ns−1, (b1-b4) κf = 27.5 ns−1, and (c1-c4) κf = 38.5 ns−1. From left to right: optical spectra, time series, power spectra and auto-correlation functions.
Fig. 4.
Fig. 4. Simulated typical chaos states of the CSHR microlaser biased at I = 12Ith: (a1-a4) κf = 22ns−1, (b1-b4) κf = 27.5 ns−1, and (c1-c4) κf = 38.5 ns−1. From left to right: optical spectra, time series, power spectra and auto-correlation functions.
Fig. 5.
Fig. 5. Effects of feedback rate on (a) chaos bandwidth, (b) power spectrum flatness, and (c) relaxation oscillation signature obtained at bias currents of 5Ith (squares) and 12Ith (circles).
Fig. 6.
Fig. 6. Effects of bias current on (a) chaos bandwidth, (b) power spectrum flatness, and (c) relaxation oscillation signature obtained at feedback rates of κf = 27.5 ns−1 (squares) and 30 ns−1 (circles).
Fig. 7.
Fig. 7. (a) Chaos bandwidth, (b) power spectrum flatness in parameter space (I, κf), and (c) the maximum chaos bandwidth achievable at different currents (denoted by dashed line in Fig. 7(a)) and the corresponding power spectrum flatness as well as 3 dB modulation bandwidth of solitary laser as functions of bias current.
Fig. 8.
Fig. 8. Largest Lyapunov exponent as a function of bias current.

Tables (1)

Tables Icon

Table 1. Parameter values for CSHR microlaser used in simulation

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

d n d t = η I q V a A n B n 2 C n 3 v g g s ,
d s d t = [ Γ v g g α i v g 1 τ pc ] s + Γ β B n 2 + 2 κ f s ( t τ f ) s cos θ ,
d ϕ d t = α 2 [ Γ v g g α i v g 1 τ pc ] κ f s ( t τ f ) / s sin θ ,
g = g 0 1 + ε s ln( n + N s N tr + N s ) ,
θ = ω τ f + ϕ ϕ ( t τ f ) .
f R = 1 2 π ( v g a n η q V a / Γ ) 1 / 2 ( I I th ) 1 / 2 ,
H ( f ) = f R 2 f R 2 f 2 + j ( f / f 2 π 2 π ) γ ,

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