Open Access
Add to BibSonomy
Abstract
A tri-mode micro-square laser under optical feedback is proposed and demonstrated to generate chaos with the broadband flat microwave spectrum. By adjusting lasing mode intensities, frequency intervals, and optical feedback strength, we can enhance the chaotic bandwidth significantly. The existence of two mode-beating peaks makes the flat bandwidth much larger than the relaxation oscillation frequency. Effective bandwidth of 35.3 GHz is experimentally achieved with the flatness of 8.3 dB from the chaotic output spectrum of the tri-mode mode laser under optical feedback.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Chaotic lasers have attracted a great attention for their important applications, such as random number generation [1–7], chaotic communication [8–11], optical logic [12,13], and chaotic sensing [14–16]. Above all these applications, random number generators play a key role in the fields of information security [17], quantum cryptography [18]. The speed of random bit generation is determined by the bandwidth and flatness of the chaotic signal [19–24]. However, the intensity of the microwave spectrum is concentrated near the relaxation oscillation frequency in the conventional semiconductor laser [5,25], which limits the bandwidth of the chaotic signal. To break through the constraint of the relaxation oscillation frequency, many methods have been proposed to enhance the bandwidth of the chaotic lasers. By injecting continuous-wave light to a laser diode, the chaotic signal bandwidth was enhanced from 6.2 GHz to 16.8 GHz [20]. The bandwidth and the flatness were improved to 32 GHz and 6.3 dB utilized the mutual injection between two DFB lasers [26], and 38.9 GHz and 4.2 dB by using a feedback loop with a high nonlinear optical fiber [27]. However, external optical injections or a high-power feedback system result in complex systems with additional components.
Recently, dual-mode microlasers with optical feedback were studied for improving chaotic output bandwidth. The dual-mode laser was studied to be easier to enter chaotic state than the single mode laser under a week feedback strength of -20 dB [28], and the effective bandwidth of the dual-mode laser was enhanced to 30.7 GHz by adjusting the suitable mode interval and mode-intensity ratio [29]. In this paper, we propose to generate broadband chaos utilizing a tri-mode micro-square laser (TMMSL) with optical feedback. Compared with the dual-mode feedback chaos [29], the extra mode-beating peak of TMMSL fills the notch of the microwave spectrum, which is beneficial to increase the bandwidth and flatten the microwave spectrum. The standard and effective bandwidth of 43.2 and 35.3 GHz are obtained under tri-mode optical feedback, compared with 31.3 and 30.7 GHz with dual-mode feedback.
2. Mode characteristics of a microcavity laser
The optical microscope image of the micro-square laser is shown in Fig. 1(a). The microlasers were fabricated using an AlGaInAs/InP laser wafer, with the active region consisted of eight compressively strained 6-nm-thick AlGaInAs quantum wells and nine 9-nm-thick AlGaInAs barrier layers. The side length of the square cavity is 30 µm and a 3-µm width waveguide is connected to one vertex of the cavity. The devices are laterally confined by a 220-nm SiNx layer and a benzocyclobutene (BCB) layer to form a planar structure. The patterned P-electrode of the TMMSL was designed to result in a non-uniform injection current, which forms the difference in refractive index between the covered and uncovered regions of the electrode to achieve controllable mode interval. The patterned contact window is opened on the center of the microcavity and the triangles at four vertexes, which is opposite to the dual-mode lasing square microlaser in [30]. The side length of the center square contact window is 18 µm, and the distance between the center square and the triangle contact windows is 6 µm. Figure 1(b) shows the curves of the output power and applied voltage versus bias current for a TMMSL. The laser threshold current is about 11 mA, and a resistance of 43 Ω is obtained including a microstrip resistance of 35 Ω by linearly fitting the V-I curve. The power coupled by a single mode fiber (SMF) reaches the maximum of 492 µW at 37 mA, and then drops rapidly due to the lasing mode transition as shown in the following laser spectra.
Fig. 1. (a) Microscopic image of a TMMSL. (b) Output power (solid circle) coupled by a single mode fiber and voltage (hollow square) for a TMMSL versus the injection current.
The simulated magnetic field (|Hz|) distributions of the three main TE modes in the square microcavity are shown in Fig. 2, which is simulated by the two-dimensional finite element method of the commercial software COMSOL Multiphysics. The side length and the waveguide width of the square laser are 30 µm and 3 µm, and the refractive indices of laser wafer, SiNx, and BCB are set as 3.2, 2.0, 1.54, respectively. The refractive index step Δn of the electrical injection regions and other regions is taken to be 0.001. We hope to reduce the mode interval with the increase of injection current instead of the case in [30]. The non-uniform injection scheme causes the cavity to form several regions with different refractive indices. Different transverse modes will experience different change of the refractive index caused by injection current, so mode intervals between different transverse modes can be adjusted by injection current. As Δn increases from -0.005 to 0.002, the wavelengths of the three main modes all increase, and the first mode increases faster than the other two modes, due to the influence of non-uniform injection current. In addition, the high-order modes also have high quality factors for realizing multi-transverse-mode lasing in a large square microcavity.
Fig. 2. Magnetic field (|Hz|) distributions of the fundamental, first-order, and second-order modes around 1555 nm in a non-uniform-injection square laser. The refractive index different Δn is set as 0.001.
The lasing spectra of the TMMSL at currents of 30, 37, 44 mA are shown in Fig. 3(a), which show the lasing of multiple longitudinal modes and transverse modes. In the longitudinal modes other that around 1542.5 nm, some transverses are suppressed due to the strong mode-competition between the transverse modes. The detailed transverse modes around 1542.5 nm are presented in Fig. 3(b), which are used for investigating chaotic behaviors of the microcavity laser under optical feedback. Three main lasing modes with intervals of 0.18 nm and 0.38 nm are observed at 37 mA, and the corresponding mode-beating frequencies (MBF) are 23.1 GHz and 48.1 GHz as shown in the microwave spectrum in Fig. 3 (c), which is measured using a high-speed photodetector. Figure 3(d) indicates the lasing mode frequency intervals as a function of bias current. The interval between the first- and second-order mode decrease with the increase of bias current caused by the patterned electrode. Since the mode fields of the higher-order transverse modes are more covered by the electrode, the second-order transverse mode is more susceptible to change in refractive index caused by the injection current than the other transverse modes. Thus, the red-shift speed of the second-order mode is faster due to a faster rising rate of refractive index with the bias current increase.
Fig. 3. (a) Lasing spectra of the TMMSL and (b) detailed lasing spectra of the modes around 1542 nm at 30, 37 and 44 mA. (c) Microwave spectrum of the TMMSL at 37 mA without feedback. (d) Frequency intervals as a function of bias current, hollow square for the interval of the fundamental and first-order mode, and solid circle for the interval of the first- and second-order mode.
3. Output characteristics under optical feedback
The experimental system consisting of a TMMSL and an optical feedback loop is shown in Fig. 4. The output of the microlaser is coupled into a SMF, and passes through an optical circulator (OC). Then the light from port 3 of the OC is amplified by an erbium-doped fiber amplifier (EDFA), which provides gain and controls the optical feedback strength in the loop. An optical band-pass filter (OBPF) after the EDFA is used to maintain only the three modes marked in Fig. 3(b) and eliminate the influence of the other modes. Finally, the light is split into two branches by an 80:20 fiber coupler (FC1). 80% of the light enters a polarization controller (PC), and returns into the microcavity laser at last, and 20% of the light enters a 1:99 FC2. The two outputs of the FC2 are respectively guided into an optical spectrum analyzer (OSA) and a photodetector (PD), which converts the optical signal into an electrical signal. A 50 GHz electric spectrum analyzer (ESA) and an oscilloscope are applied for monitoring the microwave spectrum and the waveform obtained from the high-speed PD.
Fig. 4. Experimental setup for the generation of wideband chaos based on a tri-mode microlaser with optical feedback. TMMSL, tri-mode micro-square laser. OC, optical circulator. EDFA, erbium-doped fiber amplifier. OBPF, optical band-pass filter. FC1, FC2, fiber coupler. PC, polarization controller. PD, photodetector. ESA, electric spectrum analyzer. OSC, oscilloscope. OSA, optical spectrum analyzer.
We first analyzed the relationship between the mode-intensity ratios (MIR) of the three modes and the bandwidth of the chaotic output intensity spectrum. Figures 5(a), 5(b), and 5(c) indicate the MIR, microwave spectrum, effective bandwidth, and flatness versus bias current, respectively. The effective and standard bandwidth are respectively defined as, starting from the strongest intensity and from the zero frequency, the bandwidth that occupies 80% of the total intensity within the microwave spectrum [31], and the flatness is defined as the intensity ratio of the maximum to the minimum in the range of 50 GHz. As demonstrated in [31], the effective bandwidth is closer to the actual bandwidth than the standard bandwidth. The flattest microwave spectrum curve can be observed at 37 mA as shown in Fig. 5(b). Figure 5(c) shows that a broad bandwidth (> 29.3 GHz) and the corresponding flatness (< 13.7 dB) are obtained at 37∼39 mA, which is corresponding to currents with the absolute value of MIRs less than 20 dB in Fig. 5(a). The bandwidth is affected by MIR, mode intervals, and feedback strength. As proposed in [29], a small MIR is conducive to generating a high-intensity beating peak and expanding bandwidth.
Fig. 5. (a) Mode-intensity ratios of the three modes as a function of bias current. The intensity ratios between the second-order and the first-order mode (black squares), the first-order and the fundamental mode (red circles), and the second-order and the fundamental mode (blue triangles). (b) Microwave spectra at bias currents of 15, 20, 37 and 44 mA under the same EDFA gain. There are 10 dB offsets between the curves of different bias currents. (c) Effective bandwidth (hollow circles) and flatness (solid squares) as functions of bias current.
We then investigated the influence of the feedback strength on the chaotic signal. The feedback strength is defined as the ratio of the feedback power into the port 1 to the lasing power measured at the port 2 of the OC in Fig. 4. Figures 6(a), 6(b), and 6(c) show the evolution of lasing spectrum, microwave spectrum, effective bandwidth, and flatness at different feedback strengths, respectively. As shown in Fig. 6(a), the lasing spectrum becomes wide as the feedback strength increases from -2.7 dB to 8.2 dB, with the main peaks marked as P0, P1, P2, and P3, respectively. Among them, P0 and P1 correspond to the 0th and 1st order modes, and P2 and P3 are generated by the split of the second-order-degenerate mode in Fig. 3(b). The lasing spectrum at a low feedback strength of -2.7 dB indicates that the chaotic state is generated by the feedback of the three main modes. At the feedback strength of 2 dB, the main lasing peaks are P1, P2, and P3, with the frequency intervals of 39.1 and 16.4 GHz, and MIRs of 6 dB and 4.2 dB. The nearly uniform lasing peaks with suitable intervals and small MIRs result in a wide mode-beating microwave spectrum with an effective bandwidth of 30 GHz. At the feedback strength of 5.2 dB, P3 becomes the main peak and P1 is 9.3 dB less than P3, which results in greatly reduction of beating microwave peak at high frequency between P1 and P2. So the microwave bandwidth is smaller at the feedback strength of 5.2 dB than that at 2 dB. At the feedback strength of 8.2 dB, the full-width at half-maximum of the lasing peaks is about 1 nm, which is larger than that of the dual-mode lasing microcavity laser [29]. Thus, a microwave spectrum with a wide bandwidth of 32.7 GHz was realized as shown in Fig. 6(b). Figure 6(c) indicates the effective bandwidth and the flatness as a function of the feedback strength. Due to the interaction between the relaxation oscillation frequency and the two MBFs, the microwave spectrum can maintain a flat microwave spectrum without notches. Therefore, the TMMSL can achieve and maintain a broad effective bandwidth over 27 GHz and a flatness less than 16.1 dB at the feedback strength from 8.2 to 2 dB. The microwave spectra obtained under the feedbacks of tri-mode (P0, P1 and P2), dual-mode (P1 and P2), and single-mode (P2), are compared in Fig. 6(d), obtained by adjusting the OBPF to feedback required modes into the microlaser. It intuitively demonstrates the advantages of TMMSL in terms of bandwidth and flatness optimization. The bias current and the feedback strength are set as 37 mA and 8.6 dB, respectively. In the case of tri-mode feedback, the effective bandwidth and the flatness are enhanced to 35.3 GHz and 8.3 dB. For the dual-mode feedback case, the lack of beating frequencies around 20 GHz results in the formation of a notch and the decrease of bandwidth. And for the single-mode feedback case, there is only one broad peak near 15 GHz due to the relaxation oscillation and the competition of the three modes, and a rapid decreasing in high frequency leads to the limited bandwidth. A stronger intensity in low frequency of dual-mode and single-mode feedback comes from a higher gain assigned to each mode while the total gain of EDFA is fixed. The results indicate that the tri-mode laser plays a better role on chaotic bandwidth optimization than dual-mode and single-mode laser.
Fig. 6. (a) Lasing spectra. P0, P1, P2, and P3 are used to mark the peaks. (b) Microwave spectra at feedback strengths of 8.2 dB, 5.2 dB, 2 dB, and -2.7 dB. (c) Effective bandwidth (hollow circle) and flatness (solid square) versus feedback strength. (d) Microwave spectra under optical feedbacks of tri-mode, dual-mode of the first- and second-order modes, and the second-order mode, respectively, for the feedback strength of 8.6 dB. (a) ∼ (d) are all under the injection current of 37 mA.
The advantages of TMMSL compared with dual-mode lasers [29] are further analyzed. For the dual-mode laser with optical feedback, due to the limited bandwidth of the MBF and the relaxation oscillation frequency, there is an upper limit on the bandwidth expansion regardless the MBF is small or large. Either the high frequency decreases rapidly or a notch is generated in the middle of the MBF and the relaxation oscillation frequency, which will result in a limited bandwidth. Therefore, increasing the number of MBF is a way to break the limit. In the case of the TMMSL, the smaller MBF around 23.2 GHz, which is generated by the mode beating of P0 and P1, can just fill the notch. Thus, a flatten microwave spectrum has the standard and effective bandwidth of 43.2 GHz and 35.3 GHz. Furthermore, the MBF of P0 and P2 of approximately 71 GHz may also contributes to the bandwidth enhancement in the range above 50 GHz. Although it cannot be directly observed due to the limitation of the ESA scanning range, the potential of bandwidth enhancement is indicated from the flatness with an intensity loss of less than 9 dB within 50 GHz.
4. Characteristics of the chaotic output
Finally, the time domain waveform of the chaotic signal is studied. A 50 ns time series of the chaotic signal sampled by the oscilloscope at Fig. 4 and the corresponding autocorrelation curve obtained from the time series of 400 ns length are shown in Figs. 7(a) and 7(b), respectively. The time series in Fig. 7(a) shows the noise-like waveform, which is consistent with the typical chaotic time-domain waveform. The autocorrelation function is near a Dirac delta function with a full-width at half-maximum of 0.23 ns at zero delay, as shown in the inset of Fig. 7(b). But a correlation peak at 212 ns is observed, which is related to the feedback loop time [32,33]. The corresponding loop length calculated to be about 42 m is consistent with the experimental loop length.
Fig. 7. (a) Time series of the chaotic state. (b) Autocorrelation function of the chaotic signal. The inset, detailed changes at 0 frequency. The correlation peak is at 212 ns.
The chaotic signal is sampled by the oscilloscope, and then converted to 8-bit digital signal sequences by a built-in analog-to-digital converter according to the ratio of the chaotic signal to the level range. To evaluate the statistical randomness of the digital bit sequences, we used the standard statistical test suite for random number generators provided by the National Institute of Standard Technology (NIST SP 800-22) [34]. The test items are executed using 1000 instances of 1 million bits with a significance level α = 0.01. The proportion of the tested random bit samples satisfying the condition for the p-value larger than α should be in the range of 0.99 ± 0.0094392 and the uniformity of the p-values (denoted as P-value) should be larger than 0.0001 [34]. For the tests which produce multiple P-value and proportions, the worst case is shown at Table 1. It indicates that the random bit sequences obtained from the TMMSL using 2 least significant bits (LSBs) at 5 GS/s sampling rate feedback chaos are sufficiently random to pass all the 15 NIST test items. The sampling rate is limited by the 2 GHz cut-off frequency of the oscilloscope, and the random-bit-generation rate can be further improved if an oscilloscope with a higher cut-off frequency is used.
Table 1. Results of statistical test suite NIST SP 800-22 for a set of 1000 sequences generated using 2 least significant bits. Each sequence is 1 Mbit.
5. Conclusion
In conclusion, we experimentally demonstrate a method for generating broadband chaotic signal by using a tri-mode whispering-gallery-mode laser with optical feedback. Compared with a dual-mode microlaser with optical feedback, the extra mode-beating frequency of the tri-mode laser fills the notch of the microwave spectrum, which greatly optimizes the bandwidth. By adjusting the feedback strength and the bias current to 8.6 dB and 37 mA, the effective bandwidth of 35.3 GHz and the flatness of 8.3 dB can be obtained. This broadband chaotic signal generated by a simple feedback system has great potential in the application of random number generators, chaotic sensing, and chaotic communications.
Funding
National Natural Science Foundation of China (61874113, 61935018); Strategic Priority Research Program of Chinese Academy of Sciences (XDB43000000).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. 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]
2. M. Sciamanna and K. A. Shore, “Physics and applications of laser diode chaos,” Nat. Photonics 9(3), 151–162 (2015). [CrossRef]
3. L. M. Zhang, B. W. Pan, G. C. Chen, L. Guo, D. Lu, L. J. Zhao, and W. Wang, “640-Gbit/s fast physical random number generation using a broadband chaotic semiconductor laser,” Sci. Rep. 7(1), 45900 (2017). [CrossRef]
4. I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-Speed Random Number Generation Based on a Chaotic Semiconductor Laser,” Phys. Rev. Lett. 103(2), 024102 (2009). [CrossRef]
5. K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010). [CrossRef]
6. N. Oliver, M. Cornelles Soriano, D. W. Sukow, and I. Fischer, “Fast Random Bit Generation Using a Chaotic Laser: Approaching the Information Theoretic Limit,” IEEE J. Quantum Electron. 49(11), 910–918 (2013). [CrossRef]
7. P. Li, Y. Guo, Y. Q. Guo, Y. L. Fan, X. M. Guo, X. L. Liu, K. A. Shore, E. Dubrova, B. J. Xu, Y. C. Wang, and A. B. Wang, “Self-balanced real-time photonic scheme for ultrafast random number generation,” APL Photonics 3(6), 061301 (2018). [CrossRef]
8. P. Colet and R. Roy, “Digital communication with synchronized chaotic lasers,” Opt. Lett. 19(24), 2056–2058 (1994). [CrossRef]
9. K. S. Halle, C. W. Wu, M. Itoh, and L. O. Chua, “Spread Spectrum Communication Through Modulation Of Chaos,” Int. J. Bifurcation Chaos Appl. Sci. Eng. 03(2), 469–477 (1993). [CrossRef]
10. C. R. Mirasso, P. Colet, and P. GarciaFernandez, “Synchronization of chaotic semiconductor lasers: Application to encoded communications,” IEEE Photonics Technol. Lett. 8(2), 299–301 (1996). [CrossRef]
11. G. D. VanWiggeren and R. Roy, “Communication with chaotic lasers,” Science 279(5354), 1198–1200 (1998). [CrossRef]
12. K. Murali, S. Sinha, and W. L. Ditto, “Implementation of NOR gate by a chaotic Chua's circuit,” Int. J. Bifurcation Chaos Appl. Sci. Eng. 13(9), 2669–2672 (2003). [CrossRef]
13. K. E. Chlouverakis and M. J. Adams, “Optoelectronic realisation of NOR logic gate using chaotic two-section lasers,” Electron. Lett. 41(6), 359–360 (2005). [CrossRef]
14. K. Myneni, T. A. Barr, B. R. Reed, S. D. Pethel, and N. J. Corron, “High-precision ranging using a chaotic laser pulse train,” Appl. Phys. Lett. 78(11), 1496–1498 (2001). [CrossRef]
15. F. Y. Lin and J. M. Liu, “Chaotic radar using nonlinear laser dynamics,” IEEE J. Quantum Electron. 40(6), 815–820 (2004). [CrossRef]
16. F. Y. Lin and J. M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. 10(5), 991–997 (2004). [CrossRef]
17. M. J. Bunner, A. Kittel, J. Parisi, I. Fischer, and W. Elsasser, “Estimation of delay times from a delayed optical feedback laser experiment,” Europhys. Lett. 42(4), 353–358 (1998). [CrossRef]
18. N. Gisin, G. G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002). [CrossRef]
19. F. Y. Lin and J. M. Liu, “Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. 221(1-3), 173–180 (2003). [CrossRef]
20. 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]
21. H. Someya, I. Oowada, H. Okumura, T. Kida, and A. Uchida, “Synchronization of bandwidth-enhanced chaos in semiconductor lasers with optical feedback and injection,” Opt. Express 17(22), 19536–19543 (2009). [CrossRef]
22. Y. Takiguchi, K. Ohyagi, and J. Ohtsubo, “Bandwidth-enhanced chaos synchronization in strongly injection-locked semiconductor lasers with optical feedback,” Opt. Lett. 28(5), 319–321 (2003). [CrossRef]
23. 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]
24. P. Li, Q. Cai, J. Zhang, B. Xu, Y. Liu, A. Bogris, K. A. Shore, and Y. Wang, “Observation of flat chaos generation using an optical feedback multi-mode laser with a band-pass filter,” Opt. Express 27(13), 17859–17867 (2019). [CrossRef]
25. Y. X. Wang, Z. W. Jia, Z. S. Gao, J. L. Xiao, L. S. Wang, Y. C. Wang, Y. Z. Huang, and A. B. Wang, “Generation of laser chaos with wide-band flat power spectrum in a circular-side hexagonal resonator microlaser with optical feedback,” Opt. Express 28(12), 18507–18515 (2020). [CrossRef]
26. 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]
27. Q. Yang, L. J. Qiao, M. J. Zhang, J. Z. Zhang, T. Wang, S. H. Gao, M. M. Chai, and P. Menjabin Mohiuddin, “Generation of a broadband chaotic laser by active optical feedback loop combined with a high nonlinear fiber,” Opt. Lett. 45(7), 1750–1753 (2020). [CrossRef]
28. Y. Z. Hao, C. G. Ma, Z. Z. Shen, J. C. Li, J. L. Xiao, Y. D. Yang, and Y. Z. Huang, “Comparison of single- and dual-mode lasing states of a hybrid-cavity laser under optical feedback,” Opt. Lett. 46(9), 2115–2118 (2021). [CrossRef]
29. C. G. Ma, J. L. Wu, J. L. Xiao, Y. T. Huang, Y. L. Li, Y. D. Yang, and Y. Z. Huang, “Wideband chaos generation based on a dual-mode microsquare laser with optical feedback,” Chin. Opt. Lett. 19(11), 111401 (2021). [CrossRef]
30. H. Long, Y. Z. Huang, X. W. Ma, Y. D. Yang, J. L. Xiao, L. X. Zou, and B. W. Liu, “Dual-transverse-mode microsquare lasers with tunable wavelength interval,” Opt. Lett. 40(15), 3548–3551 (2015). [CrossRef]
31. 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]
32. D. Rontani, A. Locquet, M. Sciamanna, and D. S. Citrin, “Loss of time-delay signature in the chaotic output of a semiconductor laser with optical feedback,” Opt. Lett. 32(20), 2960–2962 (2007). [CrossRef]
33. F. Albert, C. Hopfmann, S. Reitzenstein, C. Schneider, S. Hoefling, L. Worschech, M. Kamp, W. Kinzel, A. Forchel, and I. Kanter, “Observing chaos for quantum-dot microlasers with external feedback,” Nat. Commun. 2(1), 366 (2011). [CrossRef]
34. A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, and M. Levenson, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” National Institute of Standards and Technology, Special Publication 800–22, 2001 Revision 1, August 2008.
