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Optical chaos has a wide range of applications in communications, such as secure communication, high-resolution lidar ranging, optical time domain reflectometer, and high-rate physical random bit generator. In recent years, external-cavity feedback semiconductor lasers (ECLs) are the most common chaotic laser generation systems due to their characteristics of wide bandwidth, large amplitude, and simple structure, and the dynamic characteristics of chaotic signals have attracted much attention. However, limited by the relaxation oscillation of the laser, the energy of the chaotic signal directly generated by ECL is mainly concentrated at high relaxation oscillation frequency. Thus, the low-frequency component encounters the problem of energy loss. In practical applications, the signal detection/acquisition device usually responds to a 3-dB low-pass filtering characteristic. Therefore, the available effective bandwidth of the chaotic signal should actually be 3-dB bandwidth. The lack of low-frequency components will limit the energy utilization rate of chaotic signals and restrict the relevant performances of chaotic applications (such as reliability and transmission of chaotic secure communication, randomness and generation rate of physical random bits, measurement accuracy and range of lidar ranging or optical time-domain reflectometer). In the paper, we propose a broadband chaos generation scheme with simple structure and losing no low-frequency components. Specifically, we experimentally analyze the radio frequency (RF) spectra of the single-mode and the multi-mode output from an optical feedback Fabry-Perot (FP) semiconductor laser after and before filtering. The experimental results show that comparing with the multi-mode chaotic signal, the low-frequency energy of the single-mode chaotic spectrum is enhanced by 25 dB, and the 3-dB bandwidth of the single-mode chaotic signal can reach 6 GHz. Further theoretical analysis demonstrates that the enhancement of low-frequency component in the single-mode chaotic signal is caused by the mode-competing in multi-mode laser. It is concluded that this method can well solve the problem of low-frequency energy loss in conventional optical feedback chaotic systems, and is beneficial to improving the energy utilization rate of chaotic signals, which is of great significance for improving the performance of chaotic secure communication, random bit generation, lidar ranging, optical time domain reflectometer, and other relevant applications. -
Keywords:
- chaotic laser /
- multi-mode laser /
- mode-competing
[1] Argyris A, Syvridis D, Larger L, Annovazzi-Lodi V, Colet P, Fischer I, García-Ojalvo J, Mirasso C R, Pesquera L, Shore K A 2005 Nature 438 343
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[4] Wang Y C, Wang B J, Wang A B 2008 IEEE Photon. Technol. Lett. 20 1636
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[8] 唐曦, 吴加贵, 夏光琼, 吴正茂 2011 60 110509
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[10] Li N Q, Kim B, Chizhevsky V N, Loequet A, Bloch M, Citrin D S, Pan W 2014 Opt. Express 22 6634
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[11] Quay C H L, Maxwell I Z, Hudgings J A 2001 J. Appl. Phys. 90 5856
Google Scholar
[12] Rontani D, Locquet A, Sciamanna M, Citrin D S 2007 Opt. Lett. 32 2960
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[17] Wang A B, Yang Y B, Wang B J, Zhang B B, Li L, Wang Y C 2013 Opt. Express 21 8701
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图 1 基于光反馈FP激光器混沌频谱特性分析实验装置(FP-LD, 法布里-珀罗激光二极管; PC, 偏振控制器; VOA, 可调光衰减器; FM, 光纤反射镜; EDFA, 掺铒光纤放大器; BPF, 可调光滤波器; PD, 光电探测器; ESA, 频谱仪; OSA, 光谱仪)
Figure 1. Experimental setup for the RF spectrum analysis of optical feedback FP laser (FP-LD, Fabry-Perot laser diode; PC, polarization controller; VOA, variable optical attenuator; FM, fiber mirror; EDFA, erbium-doped fiber amplifier; BPF, optical bandpass filter; PD, photodetector; ESA, electrical spectrum analyzer; OSA, optical spectrum analyzer).
图 2 多模混沌激光特性实验结果 (a)光谱; (b)频谱
Figure 2. Characteristics of the multi-mode chaos: (a) Optical spectrum; (b) RF spectrum.
图 3 m = –1, 0, +1模式下的单模混沌信号特性实验结果 (a1)—(a3)光谱; (b1)—(b3)频谱
Figure 3. Characteristics of single-mode chaotic signals (m = –1, 0, +1): (a1)−(a3) Optical spectra; (b1)−(b3) RF spectra.
图 4 多纵模光反馈FP激光器数值仿真结果 (a) 光谱(M = 15); (b) 频谱
Figure 4. Numerical results of multi-mode FP-LD with optical feedback: (a) Optical spectrum (M = 15); (b) power spectrum.
图 5 光反馈多模激光器在3个模式(m = –1, 0, +1)下单模混沌信号的模拟结果 (a1)—(a3) 频谱; (b1)—(b3) 时序; (c1)—(c3) 互相关函数
Figure 5. Simulation results of single-mode chaotic signals (m = –1, 0, +1): (a1)−(a3) Power spectra; (b1)−(b3) time series; (c1)−(c3) cross-correlations.
表 1 光反馈FP激光器仿真参数
Table 1. Simulation parameters of FP-LD with optical feedback.
参数 符号 参考值 模式总数目 M 15 线宽增强因子 α 3.5 内腔损耗系数 γ 0.283 ps–1 载流子损耗系数 γe 6.21 × 10-4 ps–1 归一化电流系数 C 1.5 内腔环行时间 τ 7.3 ps 增益峰值频率 ωc $2{\text{π}} \times 193.7$ THz 增益宽度 Δωg $2{\text{π}} \times 10$ THz 增益饱和系数 s 1 × 10–7 微分增益系数 gc 3.2 × 10–9 透明载流子数 N0 1.25 × 108 反馈系数 kt 0.020 ps–1 反馈延时 τt 2 ns 自发辐射率 β 5 ps–1 
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[1] Argyris A, Syvridis D, Larger L, Annovazzi-Lodi V, Colet P, Fischer I, García-Ojalvo J, Mirasso C R, Pesquera L, Shore K A 2005 Nature 438 343
Google Scholar
[2] Lin F L, Liu J M 2004 IEEE J. Sel. Top. Quantum Electron. 10 991
Google Scholar
[3] Al-Suhail, G A, Tahir, F R, Abd, M H, Pham, V T, Fortuna L 2018 Commun. Nonlinear Sci. Numer. Simul. 57 80
Google Scholar
[4] Wang Y C, Wang B J, Wang A B 2008 IEEE Photon. Technol. Lett. 20 1636
Google Scholar
[5] Uchida A, Amano K, Inoue M, Hirano K, Naito S, Someya H, Oowada I, Kurashige T, Shiki M, Yoshimori S, Yoshimura K, Davis P 2008 Nat. Photon. 2 728
Google Scholar
[6] Kanter I, Aviad Y, Reidler I, Cohen E, Rosenbluh M 2010 Nat. Photon. 4 58
Google Scholar
[7] Li P, Wang Y C, Zhang J Z 2010 Opt. Express 18 20360
Google Scholar
[8] 唐曦, 吴加贵, 夏光琼, 吴正茂 2011 60 110509
Google Scholar
Tang X, Wu J G, Xia G Q, Wu Z M 2011 Acta Phys. Sin. 60 110509
Google Scholar
[9] Wang A B, Li P, Zhang J G, Zhang J Z, Li L, Wang Y C 2013 Opt. Express 21 20452
Google Scholar
[10] Li N Q, Kim B, Chizhevsky V N, Loequet A, Bloch M, Citrin D S, Pan W 2014 Opt. Express 22 6634
Google Scholar
[11] Quay C H L, Maxwell I Z, Hudgings J A 2001 J. Appl. Phys. 90 5856
Google Scholar
[12] Rontani D, Locquet A, Sciamanna M, Citrin D S 2007 Opt. Lett. 32 2960
Google Scholar
[13] Wu J G, Xia G Q, Tang X, Lin X D, Deng T, Fan Li, Wu Z M 2010 Opt. Express 18 6661
Google Scholar
[14] Li N Q, Pan W, Locquet A, Chizhevsky V N, Citrin, D S 2015 IEEE J. Sel. Top. Quantum Electron. 21 1
Google Scholar
[15] Al-Bayati B M, Ahmad A K, Al-Naimee K A M 2018 J. Opt. Soc. Am. B 35 918
Google Scholar
[16] Huang H M, Lin L C, Chen C Y, Arsenijevic D, Bimberg D, Lin F Y, Grillot F 2018 Opt. Express 26 1743
Google Scholar
[17] Wang A B, Yang Y B, Wang B J, Zhang B B, Li L, Wang Y C 2013 Opt. Express 21 8701
Google Scholar
[18] Wang A B, Wang B J, Li L, Wang Y C, Shore K A 2015 IEEE J. Sel. Top. Quantum Electron. 21 531
Google Scholar
[19] Wang A B, Wang Y C, Yang Y B, Zhang M J, Xu H, Wang B J 2013 Appl. Phys. Lett. 102 031112
Google Scholar
[20] Buldu J M, Garcia-Ojalvo J, Torrent M C 2005 IEEE J. Quantum Electron. 41 164
Google Scholar
[21] Yang Q, Wu Z M, Wu G J, Xia G Q 2008 Opt. Commun. 281 5025
Google Scholar
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