Abstract

We investigate common-signal-induced synchronization in two multi-mode semiconductor lasers subject to a bandwidth-limited optical noise signal. Synchronization can be achieved when the number of longitudinal modes is matched between the two lasers. The peak wavelengths need to be matched between the two lasers to achieve synchronization. In contrast, small correlation is observed when the peak wavelengths are mismatched. The synchronization is degraded as the number of longitudinal modes in one of the lasers is decreased. However, large correlation is obtained if the overlapped modes are selected and compared. We discuss the possibility of an unauthorized user reproducing the synchronized waveforms. It is difficult to completely reproduce the synchronized waveforms using synchronization if the bandwidth of the noise drive signal is limited.

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

1. Introduction

Synchronization of chaos in coupled lasers has been investigated for several decades and used for engineering applications in optical secure communications [1–4] and secure key distribution [5–13]. Recently, coupled laser networks have been investigated intensively [14–20]. In these studies, lasers are coupled unidirectionally or mutually to achieve synchronization of chaos. In contrast, common-signal-induced synchronization has been reported to synchronize chaotic dynamical systems without coupling [21–30]. A common irregular signal (e.g., chaos or noise) is injected into uncoupled lasers, and synchronization of temporal irregular outputs can be observed among these lasers.

Common-signal-induced synchronization is a key technique for a scheme of information-theoretic secure key generation [31–35] and oblivious transfer for secure computation [36]. In this scheme, two legitimate users are assumed, each having a semiconductor laser with optical feedback. An optical noise signal is broadcasted and injected into the laser of each user [33,34]. Each user selects one of the two parameter values in the laser system (e.g., optical feedback phase of the external cavity) randomly and independently. Synchronization of the temporal waveforms of the laser outputs can be achieved when the two users select the same parameter values. Each user generates a bit from the synchronized temporal waveform and stores the parameter value and the corresponding bit in memory. The users exchange the parameter values over a public channel and generate secret keys from the bits whose corresponding parameter values are the same.

In this secure key distribution scheme, the fast phase fluctuation of the broadcasted optical noise signal must be undetectable and unrecordable by all users to avoid a sampling attack [31–37]. Using a sampling attack, an eavesdropper can test multiple observations of the eavesdropper’s laser output to estimate the synchronized temporal waveform by changing the variable parameter values if the eavesdropper can detect and store the broadcasted optical signal. Super-luminescent diodes (SLDs) are good candidates for generating fast and optical noise signals to avoid sampling attacks. Common-signal-induced synchronization has been reported in single-mode semiconductor lasers subject to an optical noise signal generated by an SLD [38–42]. However, the frequency bandwidth of the noise drive signal that is necessary to achieve synchronization is limited to within a few gigahertz in the case of single-mode semiconductor lasers [40,42]. This bandwidth required for synchronization is referred to as the principal frequency band [40]. To avoid the reproduction of the noise drive signal by an eavesdropper, it is important to increase the bandwidths of not only the broadcasted optical noise signal but also the laser systems used for synchronization.

The use of multi-mode semiconductor lasers can be a promising approach to increase the principal frequency band, instead of using single-mode lasers. There have been no reports on common-signal-induced synchronization in uncoupled multi-mode semiconductor lasers, although synchronization in coupled multi-mode semiconductor laser has been studied [43,44]. In addition, the principal frequency band of multi-mode lasers has not been experimentally investigated. A bandwidth-limited optical noise signal can be used to investigate the principal frequency band of multi-mode semiconductor lasers.

In this study, we investigate common-signal-induced synchronization in multi-mode semiconductor lasers subject to a bandwidth-limited optical noise signal. We use the output of an SLD as a common injection signal, and the bandwidth of the output of the SLD is controlled by using an optical wavelength filter. We investigate the synchronization characteristics between the two multi-mode semiconductor lasers when the bandwidth and the center wavelength of the wavelength filter are changed. We discuss the possibility of an eavesdropper reproducing the synchronized waveform when this multi-mode laser system is applied for secure key distribution.

2. Experimental setup for common-signal-induced synchronization

Figure 1 shows our experimental setup for common-signal-induced synchronization subject to a bandwidth-limited optical noise signal. An SLD (DenseLight Semiconductors, DL-CS5254A-FP) is used to generate a broadband noise drive signal. The center wavelength of the SLD is 1547.573 nm with a bandwidth of 40 nm (5 THz) (full width at half maximum) [42]. The injection current of the SLD is set as 250 mA. The noise drive signal generated from SLD is separated into two signals by a fiber coupler. Each noise drive signal is injected into a variable optical wavelength filter (Santec, OTF-970, 0.1 nm resolution) to generate a bandwidth-limited noise drive signal. The center wavelength of the noise drive signal can be selected from 1530 to 1610 nm, and the bandwidth of the wavelength can be set from 0.1 nm to 15.0 nm by using the wavelength filter. The bandwidth-limited output from the wavelength filter is sent to an erbium-doped fiber amplifier (EDFA, PriTel, FA-18-IO) to amplify the optical output, and a polarization controller is used to adjust the polarization direction of the noise drive signal.

 

Fig. 1 Experimental setup for common-signal-induced synchronization subject to a bandwidth-limited optical noise signal. Amp, electronic amplifier; ATT, optical attenuator; EDFA, erbium-doped fiber amplifier; FC, fiber coupler; Filter, variable wavelength filter; ISO, optical isolator; PC, polarization controller; PD, photodetector; SLD, super-luminescent diode.

Download Full Size | PPT Slide | PDF

Each bandwidth-limited noise drive signal is injected into a multi-longitudinal-mode Fabry–Perot semiconductor laser (Anritsu, GF5B5003DLL, wavelength of 1.5 μm). Two multi-mode semiconductor lasers are used in this experiment and referred to as the response 1 and 2 lasers, respectively. The two multi-mode semiconductor lasers were fabricated in the same process to match the cavity length and other laser parameter values. The longitudinal mode intervals of the multi-mode lasers are 0.288 nm. The injection currents of the response 1 and 2 lasers are set as 40.40 mA (2.0Ith,1) and 37.89 mA (1.9Ith,2), respectively, where Ith,1 = 20.2 mA and Ith,2 = 19.9 mA indicate the lasing thresholds of the response 1 and 2 lasers, respectively. The temperature of the response lasers is precisely controlled by a temperature controller to adjust the peak wavelengths between the two response lasers.

We observe the synchronization between the temporal waveforms of the outputs of the response 1 and 2 lasers. The outputs of the two lasers are converted into electric signals by photodetectors (New Focus, 1554-B, 12-GHz bandwidth). The converted signals are amplified by electric amplifiers (New Focus, 1422-LF, 20 GHz bandwidth), and the temporal waveforms of the amplified signals are measured using a digital oscilloscope (Tektronix, DPO71604B, 16-GHz bandwidth, 50 GigaSamples/s). Radio-frequency (RF) and optical spectra are measured using an RF spectrum analyzer (Agilent, N9010A-526, 26.5 GHz bandwidth) and an optical spectrum analyzer (Yokogawa, AQ6370B), respectively.

3. Experimental results

3.1 Synchronization with same number of longitudinal modes

First, we investigate the synchronization of the two multi-mode semiconductor lasers when the numbers of the longitudinal modes of the two lasers are changed simultaneously. Figure 2 shows the optical spectra of the noise drive signal and the two response laser outputs when the noise drive signal is filtered out with a bandwidth of 14.4 nm. In this case, the two response lasers oscillate with 50 longitudinal modes, as shown in Fig. 2(a), as a result of the injection of the bandwidth-limited noise drive signal into the response lasers. We carefully match the peak wavelengths of the longitudinal modes between the response 1 and 2 lasers by controlling the temperature of the lasers, as shown in Fig. 2(b). All the peak wavelengths can be matched between the two response lasers, because the interval of the longitudinal modes is exactly the same (0.288 nm). We also detune the peak wavelengths of the two response lasers, as shown in Figs. 2(c) and 2(d). Here, we set the peak wavelengths of the response 2 laser in the middle of the peak wavelengths of the response 1 laser, and the detuning of the peak wavelengths of the two lasers is 0.144 nm [Fig. 2(d)]. We compare the synchronization characteristics in these two cases of the matching and mismatching conditions of the peak wavelengths.

 

Fig. 2 Optical spectra of the noise drive signal and the two response laser outputs when the noise drive signal is filtered out with a bandwidth of 14.4 nm. By injecting the noise drive signal, 50 longitudinal modes are excited in the two response lasers. (a), (b) Matching condition of peak wavelengths. (c), (d) Mismatching condition of peak wavelengths. (b), (d) Enlarged views of (a) and (c).

Download Full Size | PPT Slide | PDF

Figure 3 shows the temporal waveforms of the two response laser outputs and their correlation plots when the peak wavelengths of the two response lasers are matched and mismatched. In the case of the wavelength matching condition [Figs. 3(a) and 3(b)], two temporal waveforms are synchronized to each other, and a linear correlation is observed. The cross-correlation value is 0.909 in Fig. 3(b). In contrast, synchronization is not achieved in the case of the wavelength-mismatching condition [Figs. 3(c) and 3(d)]. However, the correlation value is 0.243 in Fig. 3(d), and there is small correlation between the two response laser outputs. Some correlation can be obtained between the two response laser outputs even though the peak wavelengths are mismatched. This result is a unique characteristic of synchronization in multi-mode semiconductor lasers, because the correlation is almost zero in the case of single-mode semiconductor lasers without wavelength matching [42]. We speculate that some overlap exists between the peak and the bottom of the optical spectra in the two multi-mode lasers, as shown in Fig. 2(d), which may cause correlation between the temporal waveforms of the multi-mode lasers.

 

Fig. 3 (a), (c) Temporal waveforms of the two response laser outputs and (b), (d) their correlation plots when the peak wavelengths of the two response lasers are (a), (b) matched and (c), (d) mismatched.

Download Full Size | PPT Slide | PDF

Figure 4 shows the RF spectra of the temporal waveforms for the response 1 and 2 lasers, corresponding to Figs. 3(a) and 3(c). For the wavelength-matching condition, the RF spectra are very similar between the two response lasers, as shown in Fig. 4(a). For the wavelength-mismatching condition, the RF spectra are slightly different; however, they are almost identical, as shown in Fig. 4(b). The peak frequencies of the RF spectra at ~6 GHz in Figs. 4(a) and 4(b) correspond to the relaxation oscillation frequencies of the response lasers.

 

Fig. 4 RF spectra of response lasers 1 and 2 when the peak wavelengths of the two response lasers are (a) matched and (b) mismatched.

Download Full Size | PPT Slide | PDF

Figure 5 shows the temporal waveforms and the correlation plot between the drive-injection signal and the response 1 laser output for reference. The bandwidth of the drive-injection signal is limited by the photodetector up to 12 GHz. The temporal waveforms do not appear similar between the drive signal and response lasers in Fig. 5(a). In fact, the correlation plot of Fig. 5(b) shows that the correlation value is 0.401. Therefore, the response laser output has small correlation with the drive-injection signal.

 

Fig. 5 (a) Temporal waveforms of the drive-injection signal and the response 1 laser output and (b) its correlation plot.

Download Full Size | PPT Slide | PDF

Next, we simultaneously change both bandwidths of the noise drive signals injected into the two response lasers and investigate the synchronization property. The numbers of longitudinal modes of the two response lasers can be controlled by changing the bandwidths of the noise drive signals injected into the two response lasers. The optical injection power decreases as the bandwidths of the noise drive signals are reduced. Figure 6(a) shows the cross-correlation values of the two response laser outputs when the numbers of longitudinal modes of the response lasers are changed simultaneously by changing the bandwidths of the noise drive signals, for the matching and mismatching conditions of the peak wavelengths [i.e., corresponding to Figs. 2(b) and 2(d)]. For the wavelength-matching condition, the correlation value is almost constant at ~0.9 except for small numbers of modes less than 6. The correlation value decreases to ~0.8 for the single-mode case. For the mismatching condition, the correlation value decreases monotonically as the number of modes is reduced. The correlation is almost zero for small numbers of modes.

 

Fig. 6 Cross-correlation values between the two response laser outputs when the numbers of longitudinal modes of the two response lasers are changed simultaneously. (a) Optical injection power varies as the bandwidth of the noise drive signal is changed. (b) Optical injection power is fixed for different numbers of modes by adjusting the gain of the EDFAs as the bandwidths of the noise drive signals are changed simultaneously.

Download Full Size | PPT Slide | PDF

We propose two physical reasons why the correlation value decreases for small numbers of modes: (i) the injection power is reduced, and (ii) the numbers of modes are reduced. To clarify these reasons, we set a constant injection power (630 and 1060 μW for the response 1 and 2 lasers, respectively) of the noise drive signals to the response lasers for different numbers of longitudinal modes by adjusting the gain of the EDFAs. Figure 6(b) shows the correlation values as a function of the number of modes in the response lasers when the injection power is fixed for different numbers of modes. In the case of the wavelength matching condition in Fig. 6(b), the correlation values increase slightly from 0.90 to 0.95 as the number of modes deceases. Synchronization can be achieved for all numbers of longitudinal modes used in this experiment, and larger correlation values are obtained for smaller numbers of modes. Therefore, we understand that the reduction of the correlation value in Fig. 6(a) for small numbers of modes results from the lack of the injection power of the noise drive signals. In contrast, in the case of the wavelength-mismatching condition in Fig. 6(b), the correlation values are almost constant at ~0.2 and decrease for small numbers of modes less than 5. We attribute this reduction of the correlation value for the mismatching condition to the lack of the overlap of the optical spectra for small numbers of modes but not the lack of injection power.

Figure 7 shows the cross-correlation values between the two response lasers as the injection powers of the noise drive signals for the two response lasers are changed simultaneously under the wavelength-matching condition. We maintain the ratio of the injection power between the two response lasers. (Only the injection power for the response 1 laser is plotted on the horizontal axis in Fig. 7.) Synchronization can be achieved for both a single mode and 50 longitudinal modes for a large injection power. Therefore, a large injection power is needed to achieve synchronization. This is consistent with the result of Fig. 6(a), where the correlation value is reduced owing to the lack of optical injection power for the case of small numbers of modes. Injection locking (wavelength matching between the noise drive signal and the response laser) is not obtained by the injection of the noise drive signal, unlike the case of semiconductor lasers with coherent light injection [4], even though the wavelengths of the response lasers are red-shifted in the presence of the noise drive injection. Therefore, it is important to carefully control the wavelengths of the response lasers to be exactly matched by adjusting the temperature of the response lasers.

 

Fig. 7 Cross-correlation values between the two response lasers as the injection powers of the noise drive signals for the two response lasers are changed simultaneously under the wavelength-matching condition. The ratio of the injection power between the two response lasers is maintained. Only the injection power for the response 1 laser is plotted on the horizontal axis.

Download Full Size | PPT Slide | PDF

Next, we change the position of the peak wavelengths of the response 2 laser continuously to investigate the synchronization characteristics. Here, we set the bandwidth of the noise drive signal as 0.9 nm, so that three longitudinal modes are excited in both the response 1 and 2 lasers. We change the temperature of the response 2 laser to control the position of the peak wavelengths. Figure 8 shows the optical spectra of the two response lasers when the three peak wavelengths are matched and shifted. In Fig. 8(a), all the three peak wavelengths are matched between the two lasers, while two of the three peak wavelengths are matched in Fig. 8(b).

 

Fig. 8 Optical spectra of the response 1 and 2 lasers when the three peak wavelengths are matched and shifted. (a) All the three peak wavelengths are matched. (b) Two of the three peak wavelengths are matched.

Download Full Size | PPT Slide | PDF

Figure 9(a) shows the cross-correlation values when the peak wavelengths are changed continuously for the case of three longitudinal modes. We change the detuning of the peak wavelengths Δλ between the largest peak wavelengths of the two response lasers. The correlation value decreases when Δλ is changed and the peak wavelengths are mismatched. However, there is a local maximum of the correlation value of 0.46 at Δλ = ~0.3 nm. This correlation value corresponds to the case where two of the three peak wavelengths are matched, as shown in Fig. 8(b). The correlation value decreases again and another correlation peak of 0.16 appears at Δλ = ~0.6 nm, where one of the three peak wavelengths is matched. The correlation value at the local maxima decreases with a decrease in the number of overlapped longitudinal modes.

 

Fig. 9 Cross-correlation values when the peak wavelengths are changed continuously for the case of (a) three longitudinal modes and (b) 50, six, three, and one longitudinal mode. The curve for the three modes in (a) is replotted in (b) for comparison. The injection power is changed as the bandwidths of the noise drive signals (the numbers of modes in the response lasers) are changed.

Download Full Size | PPT Slide | PDF

Figure 9(b) shows the correlation values when Δλ is shifted for different numbers of longitudinal modes for the two response lasers. Here, we set the same number of longitudinal modes for the two response lasers by using the same bandwidths of the wavelength filters for the noise drive signals. For a large number of longitudinal modes [e.g., 50 modes, as indicated by the red line in Fig. 9(b)], the correlation values change periodically, and local maxima of the correlation values are observed with a mode interval of ~0.3 nm. These local maxima of the correlation values decrease as the number of modes is decreased for a large Δλ [e.g., six and three modes indicated by the blue and black lines, respectively, in Fig. 9(b)], because the fraction of the number of the modes that are overlapped between the two response lasers to the total number of the modes is decreased. No local maxima are observed for the single-mode (one-mode) lasers [indicated by the green line in Fig. 9(b)]. Therefore, larger correlation values can be obtained when the fraction of the number of modes that are overlapped between the two multi-mode lasers is large.

The tolerance of the parameter mismatch is important for achieving synchronization. The peak wavelength and the interval of the peak wavelengths must be precisely matched between the two response lasers, as shown in Fig. 9. In contrast, the injection power to the laser does not need to be precisely matched for synchronization. It would be difficult to fabricate the lasers with exactly the same internal cavity length and to match the interval of the peaks of the optical wavelengths. Rather, the peak of the optical wavelength can be easily adjusted by changing the temperature of the laser.

3.2 Synchronization with different numbers of longitudinal modes

Next, we mismatch the bandwidths of the noise drive signals for the two response lasers. The bandwidth of the noise drive signal injected into the response 1 laser is fixed at 14.4 nm, and the 50 longitudinal modes are obtained in the response 1 laser output. We reduce the bandwidth of the noise drive signal injected into the response 2 laser, whose number of modes is changed from 50 to 1.

Figure 10 shows the correlation values when the number of the longitudinal modes of only the response 2 laser is changed by varying the bandwidth of the noise drive signal, with that of the response 1 laser fixed at 50 modes. The correlation values decrease almost linearly with a decrease in the number of longitudinal modes of the response 2 laser. Therefore, for achieving synchronization, it is important to match the number of longitudinal modes between the two response lasers. We also plot the correlation value when the peak wavelengths are mismatched [e.g., Fig. 2(d)]. A similar tendency is observed in the case of the mismatching condition of the peak wavelengths, even though the correlation value is small (< 0.35).

 

Fig. 10 Cross-correlation values as the number of longitudinal modes for only the response 2 laser is changed, with that of the response 1 laser fixed at 50 modes. The correlation values for 50 modes differ from those in Figs. 3(b) and 3(d) owing to the different injection power.

Download Full Size | PPT Slide | PDF

To understand the synchronization property under the mismatch of the number of the selected modes, we use a fixed-wavelength filter (Alnair Labs, TFF-15-1-PM-L-025-FA, 1-nm bandwidth) to select longitudinal modes of the response 1 laser before the signal detection at the photodetector. We consider the situation where 50 and three longitudinal modes are excited in the response 1 and 2 lasers, respectively, by the noise signal injection. In this case, synchronization is not achieved, and the correlation value is very small. Under this condition, we investigate the synchronization quality when three of the 50 modes in the response 1 laser are selected in front of the photodetector for detection and compare it with that for three modes of the response 2 laser.

Figure 11 compares the optical spectra and the correlation plots between the response 1 and 2 lasers. First, we compare the output of the 50-mode response 1 laser with the output of the three-mode response 2 laser, as shown in Figs. 11(a) and 11(b). Synchronization is not achieved, and a small correlation value of 0.128 is obtained. Next, we compare the output of the three-mode response 1 laser selected from 50 modes obtained using the fixed-wavelength filter with the output of the three-mode response 2 laser, as shown in Figs. 11(c) and 11(d). In this case, the correlation value increases significantly to 0.583, indicating that the overlapped modes are somehow synchronized to each other. However, the dynamics of the total outputs differ between the response 1 and 2 lasers owing to the interaction among the longitudinal modes, and the synchronization is degraded even though some correlation is observed in the modal dynamics at the same peak wavelengths.

 

Fig. 11 (a), (c) Optical spectra and (b), (d) correlation plots between the response 1 and 2 lasers. (a), (b) Comparison between the outputs of the 50-mode response 1 laser and the three-mode response 2 laser. (c), (d) Comparison between the output of the three-mode response 1 laser selected from 50 modes obtained using the wavelength filter and the output of the three-mode response 2 laser.

Download Full Size | PPT Slide | PDF

According to these results in Sections 3.1 and 3.2, we summarize the conditions for achieving common-signal-induced synchronization in multi-mode semiconductor lasers with bandwidth-limited noise drive signals as follows. (i) The number of longitudinal modes must be matched, and (ii) the peak wavelengths must be matched. However, small correlation of ~0.2 is observed even though the peak wavelengths are mismatched. This is a unique characteristic of the common-signal-induced synchronization in multi-mode semiconductor lasers.

3.3 Reproduction of synchronized waveform by eavesdropper

In this section, we investigate the possibility of an eavesdropper reproducing synchronized waveforms when this multi-mode semiconductor laser system is applied for information-theoretic secure key distribution, as proposed in [33,34]. We assume that the eavesdropper has a similar laser to the response lasers for the legitimate users; however, the eavesdropper does not know the number of longitudinal modes required for synchronization. We consider the two following situations. The eavesdropper can generate correlated outputs from the reproduction of the response laser outputs (i) by using synchronization between the lasers of the eavesdropper and a legitimate user or (ii) by directly observing the noise drive signal. We assume that the legitimate users receive a broadband noise drive signal without using the wavelength filter. In contrast, the eavesdropper intends to receive and store a filtered drive signal in memory and uses it for many trials of the estimation of the laser parameter values for synchronization (i.e., the sampling attack in [33,34]).

Figure 12 shows the correlation values when the eavesdropper changes the bandwidth of the wavelength filter for the noise drive signal and changes the number of longitudinal modes in the laser of the eavesdropper to reproduce the response laser outputs by using synchronization. The correlation value between the eavesdropper and the legitimate users increases monotonically as the number of the longitudinal modes is increased [blue line in Fig. 12]. However, the correlation value between the eavesdropper and the legitimate users cannot reach the correlation values between the two legitimate users [red dotted line in Fig. 12]. We also measure the correlation values between the legitimate users and the noise drive signal [green line in Fig. 12], assuming that the eavesdropper can use the noise drive signal to reproduce the laser outputs of the legitimate users. Correlation values of ~0.4 are obtained, which are smaller than the correlation values between the eavesdropper and the legitimate users if the number of modes is larger than 10. Therefore, it is difficult for the eavesdropper to completely reproduce the laser outputs of the legitimate users by using either synchronization or direct detection of the noise drive signal. The difference in the correlation values between the red and blue lines decreases as the number of modes is increased in Fig. 12. However, the difference in the correlation values between the red and blue lines in Fig. 12 guarantees that secure key generation is possible [34].

 

Fig. 12 Cross-correlation values obtained when the eavesdropper changes the bandwidth of the wavelength filter for the noise drive signal and changes the number of longitudinal modes in the laser of the eavesdropper to reproduce the outputs of the lasers of the legitimate users by using synchronization (the blue line). The correlation values between the two legitimate users (the red dotted line) and between the noise drive signal and the legitimate users (the green line) are also shown. The correlation value between the two legitimate users is constant because the number of modes in the laser of the eavesdropper is changed.

Download Full Size | PPT Slide | PDF

The eavesdropper can be synchronized to the legitimate users with large correlation if the same drive-injection signal with the same number of modes is used. However, we consider the situation of the sampling attack [33,34] and assume that the broadband noise drive signal cannot be completely detected and recorded in memory by the eavesdropper. In this situation, there is a gap of the correlation between the two legitimate users and between the legitimate user and the eavesdropper, and the sampling attack can be avoided. This gap of the correlation guarantees information theoretic security in the present scheme.

4. Conclusions

We investigated common-signal-induced synchronization in multi-mode semiconductor lasers subject to a bandwidth-limited optical noise signal. We found that synchronization can be achieved when the number of longitudinal modes is matched between the two response lasers. The peak wavelengths must be matched to achieve synchronization. In contrast, small correlation is obtained even when the peak wavelengths are mismatched. This is a unique characteristic of common-signal-induced synchronization in multi-mode semiconductor lasers. Synchronization is degraded as the number of longitudinal modes of one of the lasers is decreased. However, large correlation can be obtained if the overlapped modes are selected and compared. We also discussed the possibility of an eavesdropper reproducing synchronized waveforms. It is difficult to completely reproduce the synchronized waveforms using synchronization if the bandwidth of the noise drive signal that can be recorded by the eavesdropper is limited.

The use of multi-mode semiconductor lasers could be promising for enhancing the difficulty of the attack in the scheme of information-theoretic secure key distribution.

Funding

Grants-in-Aid for Scientific Research from Japan Society for the Promotion of Science (JSPS KAKENHI Grant Number JP16H03878); JST CREST Grant Number JPMJCR17N2, Japan

References and links

1. G. D. VanWiggeren and R. Roy, “Communication with chaotic lasers,” Science 279(5354), 1198–1200 (1998). [CrossRef]   [PubMed]  

2. J.-P. Goedgebuer, L. Larger, and H. Porte, “Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode,” Phys. Rev. Lett. 80(10), 2249–2252 (1998). [CrossRef]  

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

4. A. Uchida, Optical Communication with Chaotic Lasers, Applications of Nonlinear Dynamics and Synchronization (Wiley-VCH, 2012).

5. A. Uchida, P. Davis, and S. Itaya, “Generation of information theoretic secure keys using a chaotic semiconductor laser,” Appl. Phys. Lett. 83(15), 3213–3215 (2003). [CrossRef]  

6. J. Scheuer and A. Yariv, “Giant fiber lasers: A new paradigm for secure key distribution,” Phys. Rev. Lett. 97(14), 140502 (2006). [CrossRef]   [PubMed]  

7. A. Zadok, J. Scheuer, J. Sendowski, and A. Yariv, “Secure key generation using an ultra-long fiber laser: transient analysis and experiment,” Opt. Express 16(21), 16680–16690 (2008). [CrossRef]   [PubMed]  

8. D. Bar-Lev and J. Scheuer, “Enhanced key-establishing rates and efficiencies in fiber laser key distribution systems,” Phys. Lett. A 373(46), 4287–4296 (2009). [CrossRef]  

9. E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E 74(4), 046201 (2006). [CrossRef]   [PubMed]  

10. I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18(17), 18292–18302 (2010). [CrossRef]   [PubMed]  

11. R. Vicente, C. R. Mirasso, and I. Fischer, “Simultaneous bidirectional message transmission in a chaos-based communication scheme,” Opt. Lett. 32(4), 403–405 (2007). [CrossRef]   [PubMed]  

12. X. Porte, M. C. Soriano, D. Brunner, and I. Fischer, “Bidirectional private key exchange using delay-coupled semiconductor lasers,” Opt. Lett. 41(12), 2871–2874 (2016). [CrossRef]   [PubMed]  

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

14. B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, “Robustness of optimal synchronization in real networks,” Phys. Rev. Lett. 107(3), 034102 (2011). [CrossRef]   [PubMed]  

15. J. Tiana-Alsina, K. Hicke, X. Porte, M. C. Soriano, M. C. Torrent, J. García-Ojalvo, and I. Fischer, “Zero-lag synchronization and bubbling in delay-coupled lasers,” Phys. Rev. E 85(2), 026209 (2012). [CrossRef]   [PubMed]  

16. M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Controlling Synchronization in Large Laser Networks,” Phys. Rev. Lett. 108(21), 214101 (2012). [CrossRef]   [PubMed]  

17. J. Ohtsubo, R. Ozawa, and M. Nanbu, “Synchrony of small nonlinear networks in chaotic semiconductor lasers,” Jpn. J. Appl. Phys. 54(7), 072702 (2015). [CrossRef]  

18. F. Böhm, A. Zakharova, E. Schöll, and K. Lüdge, “Amplitude-phase coupling drives chimera states in globally coupled laser networks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(4), 040901 (2015). [CrossRef]   [PubMed]  

19. A. Argyris, M. Bourmpos, and D. Syvridis, “Experimental synchrony of semiconductor lasers in coupled networks,” Opt. Express 24(5), 5600–5614 (2016). [CrossRef]   [PubMed]  

20. J. Ohtsubo, Semiconductor Lasers, Stability, Instability and Chaos, 4th ed. (Springer-Verlag, 2017).

21. R. Toral, C. R. Mirasso, E. Hernandez-Garcia, and O. Piro, “Analytical and numerical studies of noise-induced synchronization of chaotic systems,” Chaos 11(3), 665–673 (2001). [CrossRef]   [PubMed]  

22. C. Zhou and J. Kurths, “Noise-induced phase synchronization and synchronization transitions in chaotic oscillators,” Phys. Rev. Lett. 88(23), 230602 (2002). [CrossRef]   [PubMed]  

23. J. N. Teramae and D. Tanaka, “Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators,” Phys. Rev. Lett. 93(20), 204103 (2004). [CrossRef]   [PubMed]  

24. H. Nakao, K. Arai, and Y. Kawamura, “Noise-induced synchronization and clustering in ensembles of uncoupled limit-cycle oscillators,” Phys. Rev. Lett. 98(18), 184101 (2007). [CrossRef]   [PubMed]  

25. K. Yoshimura, I. Valiusaityte, and P. Davis, “Synchronization induced by common colored noise in limit cycle and chaotic systems,” Phys. Rev. E 75(2), 026208 (2007). [CrossRef]   [PubMed]  

26. K. Yoshimura, J. Muramatsu, and P. Davis, “Conditions for common-noise-induced synchronization in time delay systems,” Physica D 237(23), 3146–3152 (2008). [CrossRef]  

27. T. Yamamoto, I. Oowada, H. Yip, A. Uchida, S. Yoshimori, K. Yoshimura, J. Muramatsu, S. I. Goto, and P. Davis, “Common-chaotic-signal induced synchronization in semiconductor lasers,” Opt. Express 15(7), 3974–3980 (2007). [CrossRef]   [PubMed]  

28. S. Goto, P. Davis, K. Yoshimura, and A. Uchida, “Synchronization of chaotic semiconductor lasers by optical injection with random phase modulation,” Opt. Quantum Electron. 41(3), 137–149 (2009). [CrossRef]  

29. I. Oowada, H. Ariizumi, M. Li, S. Yoshimori, A. Uchida, K. Yoshimura, and P. Davis, “Synchronization by injection of common chaotic signal in semiconductor lasers with optical feedback,” Opt. Express 17(12), 10025–10034 (2009). [CrossRef]   [PubMed]  

30. H. Aida, M. Arahata, H. Okumura, H. Koizumi, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Experiment on synchronization of semiconductor lasers by common injection of constant-amplitude random-phase light,” Opt. Express 20(11), 11813–11829 (2012). [CrossRef]   [PubMed]  

31. J. Muramatsu, K. Yoshimura, and P. Davis, “Information theoretic security based on bounded observability,” Lect. Notes Comput. Sci. 5973, 128–139 (2010). [CrossRef]  

32. J. Muramatsu, K. Yoshimura, P. Davis, A. Uchida, and T. Harayama, “Secret-key distribution based on bounded observability,” Proc. IEEE 103(10), 1762–1780 (2015). [CrossRef]  

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

34. H. Koizumi, S. Morikatsu, H. Aida, T. Nozawa, I. Kakesu, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Information-theoretic secure key distribution based on common random-signal induced synchronization in unidirectionally-coupled cascades of semiconductor lasers,” Opt. Express 21(15), 17869–17893 (2013). [CrossRef]   [PubMed]  

35. T. Sasaki, I. Kakesu, Y. Mitsui, D. Rontani, A. Uchida, S. Sunada, K. Yoshimura, and M. Inubushi, “Common-signal-induced synchronization in photonic integrated circuits and its application to secure key distribution,” Opt. Express 25(21), 26029–26044 (2017). [CrossRef]   [PubMed]  

36. T. Ito, H. Koizumi, N. Suzuki, I. Kakesu, K. Iwakawa, A. Uchida, T. Koshiba, J. Muramatsu, K. Yoshimura, M. Inubushi, and P. Davis, “Physical implementation of oblivious transfer using optical correlated randomness,” Sci. Rep. 7(1), 8444 (2017). [CrossRef]   [PubMed]  

37. N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics 4(4), 248–254 (2010). [CrossRef]  

38. S. Sunada, K. Arai, K. Yoshimura, and M. Adachi, “Optical phase synchronization by injection of common broadband low-coherent light,” Phys. Rev. Lett. 112(20), 204101 (2014). [CrossRef]  

39. K. Arai, K. Yoshimura, S. Sunada, and A. Uchida, “Synchronization induced by common ASE noise in semiconductor lasers,” in Proc. 2014 International Symposium on Nonlinear Theory and Its Applications (NOLTA2014) (2014), pp. 472–477.

40. K. Yoshimura, J. Muramatsu, A. Uchida, and P. Davis, “Spectral characteristics of consistency of a single-mode semiconductor laser injected with broadband random light,” in Proc. 2014 International Symposium on Nonlinear Theory and Its Applications (NOLTA2014) (2014), pp. 545–548.

41. K. Yoshimura, M. Inubushi, and A. Uchida, “Principal frequency band of cascaded single-mode semiconductor lasers injected with broadband random light,” in Proc. 2015 International Symposium on Nonlinear Theory and Its Applications (NOLTA2015) (2015), pp. 257–260.

42. N. Suzuki, T. Hida, M. Tomiyama, A. Uchida, K. Yoshimura, K. Arai, and M. Inubushi, “Common-signal-induced synchronization in semiconductor lasers with broadband optical noise signal,” IEEE J. Select. Top. Quantum Electron. 23(6), 1800810 (2017).

43. A. Uchida, Y. Liu, I. Fischer, P. Davis, and T. Aida, “Chaotic antiphase dynamics and synchronization in multimode semiconductor lasers,” Phys. Rev. A 64(2), 023801 (2001). [CrossRef]  

44. J. M. Buldú, J. García-Ojalvo, and M. C. Torrent, “Multimode synchronization and communication using unidirectionally coupled semiconductor lasers,” IEEE J. Quantum Electron. 40(6), 640–650 (2004). [CrossRef]  

References

  • View by:
  • |
  • |
  • |

  1. G. D. VanWiggeren and R. Roy, “Communication with chaotic lasers,” Science 279(5354), 1198–1200 (1998).
    [Crossref] [PubMed]
  2. J.-P. Goedgebuer, L. Larger, and H. Porte, “Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode,” Phys. Rev. Lett. 80(10), 2249–2252 (1998).
    [Crossref]
  3. A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
    [Crossref] [PubMed]
  4. A. Uchida, Optical Communication with Chaotic Lasers, Applications of Nonlinear Dynamics and Synchronization (Wiley-VCH, 2012).
  5. A. Uchida, P. Davis, and S. Itaya, “Generation of information theoretic secure keys using a chaotic semiconductor laser,” Appl. Phys. Lett. 83(15), 3213–3215 (2003).
    [Crossref]
  6. J. Scheuer and A. Yariv, “Giant fiber lasers: A new paradigm for secure key distribution,” Phys. Rev. Lett. 97(14), 140502 (2006).
    [Crossref] [PubMed]
  7. A. Zadok, J. Scheuer, J. Sendowski, and A. Yariv, “Secure key generation using an ultra-long fiber laser: transient analysis and experiment,” Opt. Express 16(21), 16680–16690 (2008).
    [Crossref] [PubMed]
  8. D. Bar-Lev and J. Scheuer, “Enhanced key-establishing rates and efficiencies in fiber laser key distribution systems,” Phys. Lett. A 373(46), 4287–4296 (2009).
    [Crossref]
  9. E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E 74(4), 046201 (2006).
    [Crossref] [PubMed]
  10. I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18(17), 18292–18302 (2010).
    [Crossref] [PubMed]
  11. R. Vicente, C. R. Mirasso, and I. Fischer, “Simultaneous bidirectional message transmission in a chaos-based communication scheme,” Opt. Lett. 32(4), 403–405 (2007).
    [Crossref] [PubMed]
  12. X. Porte, M. C. Soriano, D. Brunner, and I. Fischer, “Bidirectional private key exchange using delay-coupled semiconductor lasers,” Opt. Lett. 41(12), 2871–2874 (2016).
    [Crossref] [PubMed]
  13. C. Xue, N. Jiang, K. Qiu, and Y. Lv, “Key distribution based on synchronization in bandwidth-enhanced random bit generators with dynamic post-processing,” Opt. Express 23(11), 14510–14519 (2015).
    [Crossref] [PubMed]
  14. B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, “Robustness of optimal synchronization in real networks,” Phys. Rev. Lett. 107(3), 034102 (2011).
    [Crossref] [PubMed]
  15. J. Tiana-Alsina, K. Hicke, X. Porte, M. C. Soriano, M. C. Torrent, J. García-Ojalvo, and I. Fischer, “Zero-lag synchronization and bubbling in delay-coupled lasers,” Phys. Rev. E 85(2), 026209 (2012).
    [Crossref] [PubMed]
  16. M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Controlling Synchronization in Large Laser Networks,” Phys. Rev. Lett. 108(21), 214101 (2012).
    [Crossref] [PubMed]
  17. J. Ohtsubo, R. Ozawa, and M. Nanbu, “Synchrony of small nonlinear networks in chaotic semiconductor lasers,” Jpn. J. Appl. Phys. 54(7), 072702 (2015).
    [Crossref]
  18. F. Böhm, A. Zakharova, E. Schöll, and K. Lüdge, “Amplitude-phase coupling drives chimera states in globally coupled laser networks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(4), 040901 (2015).
    [Crossref] [PubMed]
  19. A. Argyris, M. Bourmpos, and D. Syvridis, “Experimental synchrony of semiconductor lasers in coupled networks,” Opt. Express 24(5), 5600–5614 (2016).
    [Crossref] [PubMed]
  20. J. Ohtsubo, Semiconductor Lasers, Stability, Instability and Chaos, 4th ed. (Springer-Verlag, 2017).
  21. R. Toral, C. R. Mirasso, E. Hernandez-Garcia, and O. Piro, “Analytical and numerical studies of noise-induced synchronization of chaotic systems,” Chaos 11(3), 665–673 (2001).
    [Crossref] [PubMed]
  22. C. Zhou and J. Kurths, “Noise-induced phase synchronization and synchronization transitions in chaotic oscillators,” Phys. Rev. Lett. 88(23), 230602 (2002).
    [Crossref] [PubMed]
  23. J. N. Teramae and D. Tanaka, “Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators,” Phys. Rev. Lett. 93(20), 204103 (2004).
    [Crossref] [PubMed]
  24. H. Nakao, K. Arai, and Y. Kawamura, “Noise-induced synchronization and clustering in ensembles of uncoupled limit-cycle oscillators,” Phys. Rev. Lett. 98(18), 184101 (2007).
    [Crossref] [PubMed]
  25. K. Yoshimura, I. Valiusaityte, and P. Davis, “Synchronization induced by common colored noise in limit cycle and chaotic systems,” Phys. Rev. E 75(2), 026208 (2007).
    [Crossref] [PubMed]
  26. K. Yoshimura, J. Muramatsu, and P. Davis, “Conditions for common-noise-induced synchronization in time delay systems,” Physica D 237(23), 3146–3152 (2008).
    [Crossref]
  27. T. Yamamoto, I. Oowada, H. Yip, A. Uchida, S. Yoshimori, K. Yoshimura, J. Muramatsu, S. I. Goto, and P. Davis, “Common-chaotic-signal induced synchronization in semiconductor lasers,” Opt. Express 15(7), 3974–3980 (2007).
    [Crossref] [PubMed]
  28. S. Goto, P. Davis, K. Yoshimura, and A. Uchida, “Synchronization of chaotic semiconductor lasers by optical injection with random phase modulation,” Opt. Quantum Electron. 41(3), 137–149 (2009).
    [Crossref]
  29. I. Oowada, H. Ariizumi, M. Li, S. Yoshimori, A. Uchida, K. Yoshimura, and P. Davis, “Synchronization by injection of common chaotic signal in semiconductor lasers with optical feedback,” Opt. Express 17(12), 10025–10034 (2009).
    [Crossref] [PubMed]
  30. H. Aida, M. Arahata, H. Okumura, H. Koizumi, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Experiment on synchronization of semiconductor lasers by common injection of constant-amplitude random-phase light,” Opt. Express 20(11), 11813–11829 (2012).
    [Crossref] [PubMed]
  31. J. Muramatsu, K. Yoshimura, and P. Davis, “Information theoretic security based on bounded observability,” Lect. Notes Comput. Sci. 5973, 128–139 (2010).
    [Crossref]
  32. J. Muramatsu, K. Yoshimura, P. Davis, A. Uchida, and T. Harayama, “Secret-key distribution based on bounded observability,” Proc. IEEE 103(10), 1762–1780 (2015).
    [Crossref]
  33. K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
    [Crossref] [PubMed]
  34. H. Koizumi, S. Morikatsu, H. Aida, T. Nozawa, I. Kakesu, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Information-theoretic secure key distribution based on common random-signal induced synchronization in unidirectionally-coupled cascades of semiconductor lasers,” Opt. Express 21(15), 17869–17893 (2013).
    [Crossref] [PubMed]
  35. T. Sasaki, I. Kakesu, Y. Mitsui, D. Rontani, A. Uchida, S. Sunada, K. Yoshimura, and M. Inubushi, “Common-signal-induced synchronization in photonic integrated circuits and its application to secure key distribution,” Opt. Express 25(21), 26029–26044 (2017).
    [Crossref] [PubMed]
  36. T. Ito, H. Koizumi, N. Suzuki, I. Kakesu, K. Iwakawa, A. Uchida, T. Koshiba, J. Muramatsu, K. Yoshimura, M. Inubushi, and P. Davis, “Physical implementation of oblivious transfer using optical correlated randomness,” Sci. Rep. 7(1), 8444 (2017).
    [Crossref] [PubMed]
  37. N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics 4(4), 248–254 (2010).
    [Crossref]
  38. S. Sunada, K. Arai, K. Yoshimura, and M. Adachi, “Optical phase synchronization by injection of common broadband low-coherent light,” Phys. Rev. Lett. 112(20), 204101 (2014).
    [Crossref]
  39. K. Arai, K. Yoshimura, S. Sunada, and A. Uchida, “Synchronization induced by common ASE noise in semiconductor lasers,” in Proc. 2014 International Symposium on Nonlinear Theory and Its Applications (NOLTA2014) (2014), pp. 472–477.
  40. K. Yoshimura, J. Muramatsu, A. Uchida, and P. Davis, “Spectral characteristics of consistency of a single-mode semiconductor laser injected with broadband random light,” in Proc. 2014 International Symposium on Nonlinear Theory and Its Applications (NOLTA2014) (2014), pp. 545–548.
  41. K. Yoshimura, M. Inubushi, and A. Uchida, “Principal frequency band of cascaded single-mode semiconductor lasers injected with broadband random light,” in Proc. 2015 International Symposium on Nonlinear Theory and Its Applications (NOLTA2015) (2015), pp. 257–260.
  42. N. Suzuki, T. Hida, M. Tomiyama, A. Uchida, K. Yoshimura, K. Arai, and M. Inubushi, “Common-signal-induced synchronization in semiconductor lasers with broadband optical noise signal,” IEEE J. Select. Top. Quantum Electron. 23(6), 1800810 (2017).
  43. A. Uchida, Y. Liu, I. Fischer, P. Davis, and T. Aida, “Chaotic antiphase dynamics and synchronization in multimode semiconductor lasers,” Phys. Rev. A 64(2), 023801 (2001).
    [Crossref]
  44. J. M. Buldú, J. García-Ojalvo, and M. C. Torrent, “Multimode synchronization and communication using unidirectionally coupled semiconductor lasers,” IEEE J. Quantum Electron. 40(6), 640–650 (2004).
    [Crossref]

2017 (3)

T. Sasaki, I. Kakesu, Y. Mitsui, D. Rontani, A. Uchida, S. Sunada, K. Yoshimura, and M. Inubushi, “Common-signal-induced synchronization in photonic integrated circuits and its application to secure key distribution,” Opt. Express 25(21), 26029–26044 (2017).
[Crossref] [PubMed]

T. Ito, H. Koizumi, N. Suzuki, I. Kakesu, K. Iwakawa, A. Uchida, T. Koshiba, J. Muramatsu, K. Yoshimura, M. Inubushi, and P. Davis, “Physical implementation of oblivious transfer using optical correlated randomness,” Sci. Rep. 7(1), 8444 (2017).
[Crossref] [PubMed]

N. Suzuki, T. Hida, M. Tomiyama, A. Uchida, K. Yoshimura, K. Arai, and M. Inubushi, “Common-signal-induced synchronization in semiconductor lasers with broadband optical noise signal,” IEEE J. Select. Top. Quantum Electron. 23(6), 1800810 (2017).

2016 (2)

2015 (4)

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

J. Ohtsubo, R. Ozawa, and M. Nanbu, “Synchrony of small nonlinear networks in chaotic semiconductor lasers,” Jpn. J. Appl. Phys. 54(7), 072702 (2015).
[Crossref]

F. Böhm, A. Zakharova, E. Schöll, and K. Lüdge, “Amplitude-phase coupling drives chimera states in globally coupled laser networks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(4), 040901 (2015).
[Crossref] [PubMed]

J. Muramatsu, K. Yoshimura, P. Davis, A. Uchida, and T. Harayama, “Secret-key distribution based on bounded observability,” Proc. IEEE 103(10), 1762–1780 (2015).
[Crossref]

2014 (1)

S. Sunada, K. Arai, K. Yoshimura, and M. Adachi, “Optical phase synchronization by injection of common broadband low-coherent light,” Phys. Rev. Lett. 112(20), 204101 (2014).
[Crossref]

2013 (1)

2012 (4)

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

H. Aida, M. Arahata, H. Okumura, H. Koizumi, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Experiment on synchronization of semiconductor lasers by common injection of constant-amplitude random-phase light,” Opt. Express 20(11), 11813–11829 (2012).
[Crossref] [PubMed]

J. Tiana-Alsina, K. Hicke, X. Porte, M. C. Soriano, M. C. Torrent, J. García-Ojalvo, and I. Fischer, “Zero-lag synchronization and bubbling in delay-coupled lasers,” Phys. Rev. E 85(2), 026209 (2012).
[Crossref] [PubMed]

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Controlling Synchronization in Large Laser Networks,” Phys. Rev. Lett. 108(21), 214101 (2012).
[Crossref] [PubMed]

2011 (1)

B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, “Robustness of optimal synchronization in real networks,” Phys. Rev. Lett. 107(3), 034102 (2011).
[Crossref] [PubMed]

2010 (3)

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18(17), 18292–18302 (2010).
[Crossref] [PubMed]

J. Muramatsu, K. Yoshimura, and P. Davis, “Information theoretic security based on bounded observability,” Lect. Notes Comput. Sci. 5973, 128–139 (2010).
[Crossref]

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics 4(4), 248–254 (2010).
[Crossref]

2009 (3)

S. Goto, P. Davis, K. Yoshimura, and A. Uchida, “Synchronization of chaotic semiconductor lasers by optical injection with random phase modulation,” Opt. Quantum Electron. 41(3), 137–149 (2009).
[Crossref]

I. Oowada, H. Ariizumi, M. Li, S. Yoshimori, A. Uchida, K. Yoshimura, and P. Davis, “Synchronization by injection of common chaotic signal in semiconductor lasers with optical feedback,” Opt. Express 17(12), 10025–10034 (2009).
[Crossref] [PubMed]

D. Bar-Lev and J. Scheuer, “Enhanced key-establishing rates and efficiencies in fiber laser key distribution systems,” Phys. Lett. A 373(46), 4287–4296 (2009).
[Crossref]

2008 (2)

A. Zadok, J. Scheuer, J. Sendowski, and A. Yariv, “Secure key generation using an ultra-long fiber laser: transient analysis and experiment,” Opt. Express 16(21), 16680–16690 (2008).
[Crossref] [PubMed]

K. Yoshimura, J. Muramatsu, and P. Davis, “Conditions for common-noise-induced synchronization in time delay systems,” Physica D 237(23), 3146–3152 (2008).
[Crossref]

2007 (4)

T. Yamamoto, I. Oowada, H. Yip, A. Uchida, S. Yoshimori, K. Yoshimura, J. Muramatsu, S. I. Goto, and P. Davis, “Common-chaotic-signal induced synchronization in semiconductor lasers,” Opt. Express 15(7), 3974–3980 (2007).
[Crossref] [PubMed]

H. Nakao, K. Arai, and Y. Kawamura, “Noise-induced synchronization and clustering in ensembles of uncoupled limit-cycle oscillators,” Phys. Rev. Lett. 98(18), 184101 (2007).
[Crossref] [PubMed]

K. Yoshimura, I. Valiusaityte, and P. Davis, “Synchronization induced by common colored noise in limit cycle and chaotic systems,” Phys. Rev. E 75(2), 026208 (2007).
[Crossref] [PubMed]

R. Vicente, C. R. Mirasso, and I. Fischer, “Simultaneous bidirectional message transmission in a chaos-based communication scheme,” Opt. Lett. 32(4), 403–405 (2007).
[Crossref] [PubMed]

2006 (2)

J. Scheuer and A. Yariv, “Giant fiber lasers: A new paradigm for secure key distribution,” Phys. Rev. Lett. 97(14), 140502 (2006).
[Crossref] [PubMed]

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E 74(4), 046201 (2006).
[Crossref] [PubMed]

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] [PubMed]

2004 (2)

J. N. Teramae and D. Tanaka, “Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators,” Phys. Rev. Lett. 93(20), 204103 (2004).
[Crossref] [PubMed]

J. M. Buldú, J. García-Ojalvo, and M. C. Torrent, “Multimode synchronization and communication using unidirectionally coupled semiconductor lasers,” IEEE J. Quantum Electron. 40(6), 640–650 (2004).
[Crossref]

2003 (1)

A. Uchida, P. Davis, and S. Itaya, “Generation of information theoretic secure keys using a chaotic semiconductor laser,” Appl. Phys. Lett. 83(15), 3213–3215 (2003).
[Crossref]

2002 (1)

C. Zhou and J. Kurths, “Noise-induced phase synchronization and synchronization transitions in chaotic oscillators,” Phys. Rev. Lett. 88(23), 230602 (2002).
[Crossref] [PubMed]

2001 (2)

R. Toral, C. R. Mirasso, E. Hernandez-Garcia, and O. Piro, “Analytical and numerical studies of noise-induced synchronization of chaotic systems,” Chaos 11(3), 665–673 (2001).
[Crossref] [PubMed]

A. Uchida, Y. Liu, I. Fischer, P. Davis, and T. Aida, “Chaotic antiphase dynamics and synchronization in multimode semiconductor lasers,” Phys. Rev. A 64(2), 023801 (2001).
[Crossref]

1998 (2)

G. D. VanWiggeren and R. Roy, “Communication with chaotic lasers,” Science 279(5354), 1198–1200 (1998).
[Crossref] [PubMed]

J.-P. Goedgebuer, L. Larger, and H. Porte, “Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode,” Phys. Rev. Lett. 80(10), 2249–2252 (1998).
[Crossref]

Adachi, M.

S. Sunada, K. Arai, K. Yoshimura, and M. Adachi, “Optical phase synchronization by injection of common broadband low-coherent light,” Phys. Rev. Lett. 112(20), 204101 (2014).
[Crossref]

Aida, H.

Aida, T.

A. Uchida, Y. Liu, I. Fischer, P. Davis, and T. Aida, “Chaotic antiphase dynamics and synchronization in multimode semiconductor lasers,” Phys. Rev. A 64(2), 023801 (2001).
[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] [PubMed]

Arahata, M.

Arai, K.

N. Suzuki, T. Hida, M. Tomiyama, A. Uchida, K. Yoshimura, K. Arai, and M. Inubushi, “Common-signal-induced synchronization in semiconductor lasers with broadband optical noise signal,” IEEE J. Select. Top. Quantum Electron. 23(6), 1800810 (2017).

S. Sunada, K. Arai, K. Yoshimura, and M. Adachi, “Optical phase synchronization by injection of common broadband low-coherent light,” Phys. Rev. Lett. 112(20), 204101 (2014).
[Crossref]

H. Nakao, K. Arai, and Y. Kawamura, “Noise-induced synchronization and clustering in ensembles of uncoupled limit-cycle oscillators,” Phys. Rev. Lett. 98(18), 184101 (2007).
[Crossref] [PubMed]

K. Arai, K. Yoshimura, S. Sunada, and A. Uchida, “Synchronization induced by common ASE noise in semiconductor lasers,” in Proc. 2014 International Symposium on Nonlinear Theory and Its Applications (NOLTA2014) (2014), pp. 472–477.

Argyris, A.

A. Argyris, M. Bourmpos, and D. Syvridis, “Experimental synchrony of semiconductor lasers in coupled networks,” Opt. Express 24(5), 5600–5614 (2016).
[Crossref] [PubMed]

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

Ariizumi, H.

Aviad, Y.

Bar-Lev, D.

D. Bar-Lev and J. Scheuer, “Enhanced key-establishing rates and efficiencies in fiber laser key distribution systems,” Phys. Lett. A 373(46), 4287–4296 (2009).
[Crossref]

Böhm, F.

F. Böhm, A. Zakharova, E. Schöll, and K. Lüdge, “Amplitude-phase coupling drives chimera states in globally coupled laser networks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(4), 040901 (2015).
[Crossref] [PubMed]

Bourmpos, M.

Brunner, D.

Buldú, J. M.

J. M. Buldú, J. García-Ojalvo, and M. C. Torrent, “Multimode synchronization and communication using unidirectionally coupled semiconductor lasers,” IEEE J. Quantum Electron. 40(6), 640–650 (2004).
[Crossref]

Butkovski, M.

Cohen, A. B.

B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, “Robustness of optimal synchronization in real networks,” Phys. Rev. Lett. 107(3), 034102 (2011).
[Crossref] [PubMed]

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] [PubMed]

Davidson, N.

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Controlling Synchronization in Large Laser Networks,” Phys. Rev. Lett. 108(21), 214101 (2012).
[Crossref] [PubMed]

Davis, P.

T. Ito, H. Koizumi, N. Suzuki, I. Kakesu, K. Iwakawa, A. Uchida, T. Koshiba, J. Muramatsu, K. Yoshimura, M. Inubushi, and P. Davis, “Physical implementation of oblivious transfer using optical correlated randomness,” Sci. Rep. 7(1), 8444 (2017).
[Crossref] [PubMed]

J. Muramatsu, K. Yoshimura, P. Davis, A. Uchida, and T. Harayama, “Secret-key distribution based on bounded observability,” Proc. IEEE 103(10), 1762–1780 (2015).
[Crossref]

H. Koizumi, S. Morikatsu, H. Aida, T. Nozawa, I. Kakesu, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Information-theoretic secure key distribution based on common random-signal induced synchronization in unidirectionally-coupled cascades of semiconductor lasers,” Opt. Express 21(15), 17869–17893 (2013).
[Crossref] [PubMed]

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

H. Aida, M. Arahata, H. Okumura, H. Koizumi, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Experiment on synchronization of semiconductor lasers by common injection of constant-amplitude random-phase light,” Opt. Express 20(11), 11813–11829 (2012).
[Crossref] [PubMed]

J. Muramatsu, K. Yoshimura, and P. Davis, “Information theoretic security based on bounded observability,” Lect. Notes Comput. Sci. 5973, 128–139 (2010).
[Crossref]

I. Oowada, H. Ariizumi, M. Li, S. Yoshimori, A. Uchida, K. Yoshimura, and P. Davis, “Synchronization by injection of common chaotic signal in semiconductor lasers with optical feedback,” Opt. Express 17(12), 10025–10034 (2009).
[Crossref] [PubMed]

S. Goto, P. Davis, K. Yoshimura, and A. Uchida, “Synchronization of chaotic semiconductor lasers by optical injection with random phase modulation,” Opt. Quantum Electron. 41(3), 137–149 (2009).
[Crossref]

K. Yoshimura, J. Muramatsu, and P. Davis, “Conditions for common-noise-induced synchronization in time delay systems,” Physica D 237(23), 3146–3152 (2008).
[Crossref]

K. Yoshimura, I. Valiusaityte, and P. Davis, “Synchronization induced by common colored noise in limit cycle and chaotic systems,” Phys. Rev. E 75(2), 026208 (2007).
[Crossref] [PubMed]

T. Yamamoto, I. Oowada, H. Yip, A. Uchida, S. Yoshimori, K. Yoshimura, J. Muramatsu, S. I. Goto, and P. Davis, “Common-chaotic-signal induced synchronization in semiconductor lasers,” Opt. Express 15(7), 3974–3980 (2007).
[Crossref] [PubMed]

A. Uchida, P. Davis, and S. Itaya, “Generation of information theoretic secure keys using a chaotic semiconductor laser,” Appl. Phys. Lett. 83(15), 3213–3215 (2003).
[Crossref]

A. Uchida, Y. Liu, I. Fischer, P. Davis, and T. Aida, “Chaotic antiphase dynamics and synchronization in multimode semiconductor lasers,” Phys. Rev. A 64(2), 023801 (2001).
[Crossref]

K. Yoshimura, J. Muramatsu, A. Uchida, and P. Davis, “Spectral characteristics of consistency of a single-mode semiconductor laser injected with broadband random light,” in Proc. 2014 International Symposium on Nonlinear Theory and Its Applications (NOLTA2014) (2014), pp. 545–548.

Fischer, I.

X. Porte, M. C. Soriano, D. Brunner, and I. Fischer, “Bidirectional private key exchange using delay-coupled semiconductor lasers,” Opt. Lett. 41(12), 2871–2874 (2016).
[Crossref] [PubMed]

J. Tiana-Alsina, K. Hicke, X. Porte, M. C. Soriano, M. C. Torrent, J. García-Ojalvo, and I. Fischer, “Zero-lag synchronization and bubbling in delay-coupled lasers,” Phys. Rev. E 85(2), 026209 (2012).
[Crossref] [PubMed]

R. Vicente, C. R. Mirasso, and I. Fischer, “Simultaneous bidirectional message transmission in a chaos-based communication scheme,” Opt. Lett. 32(4), 403–405 (2007).
[Crossref] [PubMed]

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

A. Uchida, Y. Liu, I. Fischer, P. Davis, and T. Aida, “Chaotic antiphase dynamics and synchronization in multimode semiconductor lasers,” Phys. Rev. A 64(2), 023801 (2001).
[Crossref]

Fontaine, N. K.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics 4(4), 248–254 (2010).
[Crossref]

Fridman, M.

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Controlling Synchronization in Large Laser Networks,” Phys. Rev. Lett. 108(21), 214101 (2012).
[Crossref] [PubMed]

Friesem, A. A.

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Controlling Synchronization in Large Laser Networks,” Phys. Rev. Lett. 108(21), 214101 (2012).
[Crossref] [PubMed]

García-Ojalvo, J.

J. Tiana-Alsina, K. Hicke, X. Porte, M. C. Soriano, M. C. Torrent, J. García-Ojalvo, and I. Fischer, “Zero-lag synchronization and bubbling in delay-coupled lasers,” Phys. Rev. E 85(2), 026209 (2012).
[Crossref] [PubMed]

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

J. M. Buldú, J. García-Ojalvo, and M. C. Torrent, “Multimode synchronization and communication using unidirectionally coupled semiconductor lasers,” IEEE J. Quantum Electron. 40(6), 640–650 (2004).
[Crossref]

Goedgebuer, J.-P.

J.-P. Goedgebuer, L. Larger, and H. Porte, “Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode,” Phys. Rev. Lett. 80(10), 2249–2252 (1998).
[Crossref]

Goto, S.

S. Goto, P. Davis, K. Yoshimura, and A. Uchida, “Synchronization of chaotic semiconductor lasers by optical injection with random phase modulation,” Opt. Quantum Electron. 41(3), 137–149 (2009).
[Crossref]

Goto, S. I.

Gross, N.

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E 74(4), 046201 (2006).
[Crossref] [PubMed]

Harayama, T.

J. Muramatsu, K. Yoshimura, P. Davis, A. Uchida, and T. Harayama, “Secret-key distribution based on bounded observability,” Proc. IEEE 103(10), 1762–1780 (2015).
[Crossref]

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

Heritage, J. P.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics 4(4), 248–254 (2010).
[Crossref]

Hernandez-Garcia, E.

R. Toral, C. R. Mirasso, E. Hernandez-Garcia, and O. Piro, “Analytical and numerical studies of noise-induced synchronization of chaotic systems,” Chaos 11(3), 665–673 (2001).
[Crossref] [PubMed]

Hicke, K.

J. Tiana-Alsina, K. Hicke, X. Porte, M. C. Soriano, M. C. Torrent, J. García-Ojalvo, and I. Fischer, “Zero-lag synchronization and bubbling in delay-coupled lasers,” Phys. Rev. E 85(2), 026209 (2012).
[Crossref] [PubMed]

Hida, T.

N. Suzuki, T. Hida, M. Tomiyama, A. Uchida, K. Yoshimura, K. Arai, and M. Inubushi, “Common-signal-induced synchronization in semiconductor lasers with broadband optical noise signal,” IEEE J. Select. Top. Quantum Electron. 23(6), 1800810 (2017).

Inubushi, M.

N. Suzuki, T. Hida, M. Tomiyama, A. Uchida, K. Yoshimura, K. Arai, and M. Inubushi, “Common-signal-induced synchronization in semiconductor lasers with broadband optical noise signal,” IEEE J. Select. Top. Quantum Electron. 23(6), 1800810 (2017).

T. Ito, H. Koizumi, N. Suzuki, I. Kakesu, K. Iwakawa, A. Uchida, T. Koshiba, J. Muramatsu, K. Yoshimura, M. Inubushi, and P. Davis, “Physical implementation of oblivious transfer using optical correlated randomness,” Sci. Rep. 7(1), 8444 (2017).
[Crossref] [PubMed]

T. Sasaki, I. Kakesu, Y. Mitsui, D. Rontani, A. Uchida, S. Sunada, K. Yoshimura, and M. Inubushi, “Common-signal-induced synchronization in photonic integrated circuits and its application to secure key distribution,” Opt. Express 25(21), 26029–26044 (2017).
[Crossref] [PubMed]

K. Yoshimura, M. Inubushi, and A. Uchida, “Principal frequency band of cascaded single-mode semiconductor lasers injected with broadband random light,” in Proc. 2015 International Symposium on Nonlinear Theory and Its Applications (NOLTA2015) (2015), pp. 257–260.

Itaya, S.

A. Uchida, P. Davis, and S. Itaya, “Generation of information theoretic secure keys using a chaotic semiconductor laser,” Appl. Phys. Lett. 83(15), 3213–3215 (2003).
[Crossref]

Ito, T.

T. Ito, H. Koizumi, N. Suzuki, I. Kakesu, K. Iwakawa, A. Uchida, T. Koshiba, J. Muramatsu, K. Yoshimura, M. Inubushi, and P. Davis, “Physical implementation of oblivious transfer using optical correlated randomness,” Sci. Rep. 7(1), 8444 (2017).
[Crossref] [PubMed]

Iwakawa, K.

T. Ito, H. Koizumi, N. Suzuki, I. Kakesu, K. Iwakawa, A. Uchida, T. Koshiba, J. Muramatsu, K. Yoshimura, M. Inubushi, and P. Davis, “Physical implementation of oblivious transfer using optical correlated randomness,” Sci. Rep. 7(1), 8444 (2017).
[Crossref] [PubMed]

Jiang, N.

Kakesu, I.

Kanter, I.

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Controlling Synchronization in Large Laser Networks,” Phys. Rev. Lett. 108(21), 214101 (2012).
[Crossref] [PubMed]

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18(17), 18292–18302 (2010).
[Crossref] [PubMed]

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E 74(4), 046201 (2006).
[Crossref] [PubMed]

Kawamura, Y.

H. Nakao, K. Arai, and Y. Kawamura, “Noise-induced synchronization and clustering in ensembles of uncoupled limit-cycle oscillators,” Phys. Rev. Lett. 98(18), 184101 (2007).
[Crossref] [PubMed]

Khaykovich, L.

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E 74(4), 046201 (2006).
[Crossref] [PubMed]

Kinzel, W.

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18(17), 18292–18302 (2010).
[Crossref] [PubMed]

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E 74(4), 046201 (2006).
[Crossref] [PubMed]

Klein, E.

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E 74(4), 046201 (2006).
[Crossref] [PubMed]

Koizumi, H.

Kopelowitz, E.

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E 74(4), 046201 (2006).
[Crossref] [PubMed]

Koshiba, T.

T. Ito, H. Koizumi, N. Suzuki, I. Kakesu, K. Iwakawa, A. Uchida, T. Koshiba, J. Muramatsu, K. Yoshimura, M. Inubushi, and P. Davis, “Physical implementation of oblivious transfer using optical correlated randomness,” Sci. Rep. 7(1), 8444 (2017).
[Crossref] [PubMed]

Kurths, J.

C. Zhou and J. Kurths, “Noise-induced phase synchronization and synchronization transitions in chaotic oscillators,” Phys. Rev. Lett. 88(23), 230602 (2002).
[Crossref] [PubMed]

Larger, 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] [PubMed]

J.-P. Goedgebuer, L. Larger, and H. Porte, “Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode,” Phys. Rev. Lett. 80(10), 2249–2252 (1998).
[Crossref]

Li, M.

Liu, Y.

A. Uchida, Y. Liu, I. Fischer, P. Davis, and T. Aida, “Chaotic antiphase dynamics and synchronization in multimode semiconductor lasers,” Phys. Rev. A 64(2), 023801 (2001).
[Crossref]

Lüdge, K.

F. Böhm, A. Zakharova, E. Schöll, and K. Lüdge, “Amplitude-phase coupling drives chimera states in globally coupled laser networks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(4), 040901 (2015).
[Crossref] [PubMed]

Lv, Y.

Mirasso, C. R.

R. Vicente, C. R. Mirasso, and I. Fischer, “Simultaneous bidirectional message transmission in a chaos-based communication scheme,” Opt. Lett. 32(4), 403–405 (2007).
[Crossref] [PubMed]

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

R. Toral, C. R. Mirasso, E. Hernandez-Garcia, and O. Piro, “Analytical and numerical studies of noise-induced synchronization of chaotic systems,” Chaos 11(3), 665–673 (2001).
[Crossref] [PubMed]

Mitsui, Y.

Morikatsu, S.

H. Koizumi, S. Morikatsu, H. Aida, T. Nozawa, I. Kakesu, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Information-theoretic secure key distribution based on common random-signal induced synchronization in unidirectionally-coupled cascades of semiconductor lasers,” Opt. Express 21(15), 17869–17893 (2013).
[Crossref] [PubMed]

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

Motter, A. E.

B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, “Robustness of optimal synchronization in real networks,” Phys. Rev. Lett. 107(3), 034102 (2011).
[Crossref] [PubMed]

Muramatsu, J.

T. Ito, H. Koizumi, N. Suzuki, I. Kakesu, K. Iwakawa, A. Uchida, T. Koshiba, J. Muramatsu, K. Yoshimura, M. Inubushi, and P. Davis, “Physical implementation of oblivious transfer using optical correlated randomness,” Sci. Rep. 7(1), 8444 (2017).
[Crossref] [PubMed]

J. Muramatsu, K. Yoshimura, P. Davis, A. Uchida, and T. Harayama, “Secret-key distribution based on bounded observability,” Proc. IEEE 103(10), 1762–1780 (2015).
[Crossref]

H. Koizumi, S. Morikatsu, H. Aida, T. Nozawa, I. Kakesu, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Information-theoretic secure key distribution based on common random-signal induced synchronization in unidirectionally-coupled cascades of semiconductor lasers,” Opt. Express 21(15), 17869–17893 (2013).
[Crossref] [PubMed]

H. Aida, M. Arahata, H. Okumura, H. Koizumi, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Experiment on synchronization of semiconductor lasers by common injection of constant-amplitude random-phase light,” Opt. Express 20(11), 11813–11829 (2012).
[Crossref] [PubMed]

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

J. Muramatsu, K. Yoshimura, and P. Davis, “Information theoretic security based on bounded observability,” Lect. Notes Comput. Sci. 5973, 128–139 (2010).
[Crossref]

K. Yoshimura, J. Muramatsu, and P. Davis, “Conditions for common-noise-induced synchronization in time delay systems,” Physica D 237(23), 3146–3152 (2008).
[Crossref]

T. Yamamoto, I. Oowada, H. Yip, A. Uchida, S. Yoshimori, K. Yoshimura, J. Muramatsu, S. I. Goto, and P. Davis, “Common-chaotic-signal induced synchronization in semiconductor lasers,” Opt. Express 15(7), 3974–3980 (2007).
[Crossref] [PubMed]

K. Yoshimura, J. Muramatsu, A. Uchida, and P. Davis, “Spectral characteristics of consistency of a single-mode semiconductor laser injected with broadband random light,” in Proc. 2014 International Symposium on Nonlinear Theory and Its Applications (NOLTA2014) (2014), pp. 545–548.

Murphy, T. E.

B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, “Robustness of optimal synchronization in real networks,” Phys. Rev. Lett. 107(3), 034102 (2011).
[Crossref] [PubMed]

Nakao, H.

H. Nakao, K. Arai, and Y. Kawamura, “Noise-induced synchronization and clustering in ensembles of uncoupled limit-cycle oscillators,” Phys. Rev. Lett. 98(18), 184101 (2007).
[Crossref] [PubMed]

Nanbu, M.

J. Ohtsubo, R. Ozawa, and M. Nanbu, “Synchrony of small nonlinear networks in chaotic semiconductor lasers,” Jpn. J. Appl. Phys. 54(7), 072702 (2015).
[Crossref]

Nixon, M.

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Controlling Synchronization in Large Laser Networks,” Phys. Rev. Lett. 108(21), 214101 (2012).
[Crossref] [PubMed]

Nozawa, T.

Ohtsubo, J.

J. Ohtsubo, R. Ozawa, and M. Nanbu, “Synchrony of small nonlinear networks in chaotic semiconductor lasers,” Jpn. J. Appl. Phys. 54(7), 072702 (2015).
[Crossref]

Okumura, H.

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

H. Aida, M. Arahata, H. Okumura, H. Koizumi, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Experiment on synchronization of semiconductor lasers by common injection of constant-amplitude random-phase light,” Opt. Express 20(11), 11813–11829 (2012).
[Crossref] [PubMed]

Oowada, I.

Ozawa, R.

J. Ohtsubo, R. Ozawa, and M. Nanbu, “Synchrony of small nonlinear networks in chaotic semiconductor lasers,” Jpn. J. Appl. Phys. 54(7), 072702 (2015).
[Crossref]

Peleg, Y.

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] [PubMed]

Piro, O.

R. Toral, C. R. Mirasso, E. Hernandez-Garcia, and O. Piro, “Analytical and numerical studies of noise-induced synchronization of chaotic systems,” Chaos 11(3), 665–673 (2001).
[Crossref] [PubMed]

Porte, H.

J.-P. Goedgebuer, L. Larger, and H. Porte, “Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode,” Phys. Rev. Lett. 80(10), 2249–2252 (1998).
[Crossref]

Porte, X.

X. Porte, M. C. Soriano, D. Brunner, and I. Fischer, “Bidirectional private key exchange using delay-coupled semiconductor lasers,” Opt. Lett. 41(12), 2871–2874 (2016).
[Crossref] [PubMed]

J. Tiana-Alsina, K. Hicke, X. Porte, M. C. Soriano, M. C. Torrent, J. García-Ojalvo, and I. Fischer, “Zero-lag synchronization and bubbling in delay-coupled lasers,” Phys. Rev. E 85(2), 026209 (2012).
[Crossref] [PubMed]

Qiu, K.

Ravoori, B.

B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, “Robustness of optimal synchronization in real networks,” Phys. Rev. Lett. 107(3), 034102 (2011).
[Crossref] [PubMed]

Reidler, I.

Ronen, E.

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Controlling Synchronization in Large Laser Networks,” Phys. Rev. Lett. 108(21), 214101 (2012).
[Crossref] [PubMed]

Rontani, D.

Rosenbluh, M.

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18(17), 18292–18302 (2010).
[Crossref] [PubMed]

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E 74(4), 046201 (2006).
[Crossref] [PubMed]

Roy, R.

B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, “Robustness of optimal synchronization in real networks,” Phys. Rev. Lett. 107(3), 034102 (2011).
[Crossref] [PubMed]

G. D. VanWiggeren and R. Roy, “Communication with chaotic lasers,” Science 279(5354), 1198–1200 (1998).
[Crossref] [PubMed]

Sasaki, T.

Scheuer, J.

D. Bar-Lev and J. Scheuer, “Enhanced key-establishing rates and efficiencies in fiber laser key distribution systems,” Phys. Lett. A 373(46), 4287–4296 (2009).
[Crossref]

A. Zadok, J. Scheuer, J. Sendowski, and A. Yariv, “Secure key generation using an ultra-long fiber laser: transient analysis and experiment,” Opt. Express 16(21), 16680–16690 (2008).
[Crossref] [PubMed]

J. Scheuer and A. Yariv, “Giant fiber lasers: A new paradigm for secure key distribution,” Phys. Rev. Lett. 97(14), 140502 (2006).
[Crossref] [PubMed]

Schöll, E.

F. Böhm, A. Zakharova, E. Schöll, and K. Lüdge, “Amplitude-phase coupling drives chimera states in globally coupled laser networks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(4), 040901 (2015).
[Crossref] [PubMed]

Scott, R. P.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics 4(4), 248–254 (2010).
[Crossref]

Sendowski, J.

Shore, K. A.

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

Soares, F. M.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics 4(4), 248–254 (2010).
[Crossref]

Soriano, M. C.

X. Porte, M. C. Soriano, D. Brunner, and I. Fischer, “Bidirectional private key exchange using delay-coupled semiconductor lasers,” Opt. Lett. 41(12), 2871–2874 (2016).
[Crossref] [PubMed]

J. Tiana-Alsina, K. Hicke, X. Porte, M. C. Soriano, M. C. Torrent, J. García-Ojalvo, and I. Fischer, “Zero-lag synchronization and bubbling in delay-coupled lasers,” Phys. Rev. E 85(2), 026209 (2012).
[Crossref] [PubMed]

Sun, J.

B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, “Robustness of optimal synchronization in real networks,” Phys. Rev. Lett. 107(3), 034102 (2011).
[Crossref] [PubMed]

Sunada, S.

T. Sasaki, I. Kakesu, Y. Mitsui, D. Rontani, A. Uchida, S. Sunada, K. Yoshimura, and M. Inubushi, “Common-signal-induced synchronization in photonic integrated circuits and its application to secure key distribution,” Opt. Express 25(21), 26029–26044 (2017).
[Crossref] [PubMed]

S. Sunada, K. Arai, K. Yoshimura, and M. Adachi, “Optical phase synchronization by injection of common broadband low-coherent light,” Phys. Rev. Lett. 112(20), 204101 (2014).
[Crossref]

K. Arai, K. Yoshimura, S. Sunada, and A. Uchida, “Synchronization induced by common ASE noise in semiconductor lasers,” in Proc. 2014 International Symposium on Nonlinear Theory and Its Applications (NOLTA2014) (2014), pp. 472–477.

Suzuki, N.

N. Suzuki, T. Hida, M. Tomiyama, A. Uchida, K. Yoshimura, K. Arai, and M. Inubushi, “Common-signal-induced synchronization in semiconductor lasers with broadband optical noise signal,” IEEE J. Select. Top. Quantum Electron. 23(6), 1800810 (2017).

T. Ito, H. Koizumi, N. Suzuki, I. Kakesu, K. Iwakawa, A. Uchida, T. Koshiba, J. Muramatsu, K. Yoshimura, M. Inubushi, and P. Davis, “Physical implementation of oblivious transfer using optical correlated randomness,” Sci. Rep. 7(1), 8444 (2017).
[Crossref] [PubMed]

Syvridis, D.

A. Argyris, M. Bourmpos, and D. Syvridis, “Experimental synchrony of semiconductor lasers in coupled networks,” Opt. Express 24(5), 5600–5614 (2016).
[Crossref] [PubMed]

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

Tanaka, D.

J. N. Teramae and D. Tanaka, “Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators,” Phys. Rev. Lett. 93(20), 204103 (2004).
[Crossref] [PubMed]

Teramae, J. N.

J. N. Teramae and D. Tanaka, “Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators,” Phys. Rev. Lett. 93(20), 204103 (2004).
[Crossref] [PubMed]

Tiana-Alsina, J.

J. Tiana-Alsina, K. Hicke, X. Porte, M. C. Soriano, M. C. Torrent, J. García-Ojalvo, and I. Fischer, “Zero-lag synchronization and bubbling in delay-coupled lasers,” Phys. Rev. E 85(2), 026209 (2012).
[Crossref] [PubMed]

Tomiyama, M.

N. Suzuki, T. Hida, M. Tomiyama, A. Uchida, K. Yoshimura, K. Arai, and M. Inubushi, “Common-signal-induced synchronization in semiconductor lasers with broadband optical noise signal,” IEEE J. Select. Top. Quantum Electron. 23(6), 1800810 (2017).

Toral, R.

R. Toral, C. R. Mirasso, E. Hernandez-Garcia, and O. Piro, “Analytical and numerical studies of noise-induced synchronization of chaotic systems,” Chaos 11(3), 665–673 (2001).
[Crossref] [PubMed]

Torrent, M. C.

J. Tiana-Alsina, K. Hicke, X. Porte, M. C. Soriano, M. C. Torrent, J. García-Ojalvo, and I. Fischer, “Zero-lag synchronization and bubbling in delay-coupled lasers,” Phys. Rev. E 85(2), 026209 (2012).
[Crossref] [PubMed]

J. M. Buldú, J. García-Ojalvo, and M. C. Torrent, “Multimode synchronization and communication using unidirectionally coupled semiconductor lasers,” IEEE J. Quantum Electron. 40(6), 640–650 (2004).
[Crossref]

Uchida, A.

N. Suzuki, T. Hida, M. Tomiyama, A. Uchida, K. Yoshimura, K. Arai, and M. Inubushi, “Common-signal-induced synchronization in semiconductor lasers with broadband optical noise signal,” IEEE J. Select. Top. Quantum Electron. 23(6), 1800810 (2017).

T. Sasaki, I. Kakesu, Y. Mitsui, D. Rontani, A. Uchida, S. Sunada, K. Yoshimura, and M. Inubushi, “Common-signal-induced synchronization in photonic integrated circuits and its application to secure key distribution,” Opt. Express 25(21), 26029–26044 (2017).
[Crossref] [PubMed]

T. Ito, H. Koizumi, N. Suzuki, I. Kakesu, K. Iwakawa, A. Uchida, T. Koshiba, J. Muramatsu, K. Yoshimura, M. Inubushi, and P. Davis, “Physical implementation of oblivious transfer using optical correlated randomness,” Sci. Rep. 7(1), 8444 (2017).
[Crossref] [PubMed]

J. Muramatsu, K. Yoshimura, P. Davis, A. Uchida, and T. Harayama, “Secret-key distribution based on bounded observability,” Proc. IEEE 103(10), 1762–1780 (2015).
[Crossref]

H. Koizumi, S. Morikatsu, H. Aida, T. Nozawa, I. Kakesu, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Information-theoretic secure key distribution based on common random-signal induced synchronization in unidirectionally-coupled cascades of semiconductor lasers,” Opt. Express 21(15), 17869–17893 (2013).
[Crossref] [PubMed]

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

H. Aida, M. Arahata, H. Okumura, H. Koizumi, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Experiment on synchronization of semiconductor lasers by common injection of constant-amplitude random-phase light,” Opt. Express 20(11), 11813–11829 (2012).
[Crossref] [PubMed]

I. Oowada, H. Ariizumi, M. Li, S. Yoshimori, A. Uchida, K. Yoshimura, and P. Davis, “Synchronization by injection of common chaotic signal in semiconductor lasers with optical feedback,” Opt. Express 17(12), 10025–10034 (2009).
[Crossref] [PubMed]

S. Goto, P. Davis, K. Yoshimura, and A. Uchida, “Synchronization of chaotic semiconductor lasers by optical injection with random phase modulation,” Opt. Quantum Electron. 41(3), 137–149 (2009).
[Crossref]

T. Yamamoto, I. Oowada, H. Yip, A. Uchida, S. Yoshimori, K. Yoshimura, J. Muramatsu, S. I. Goto, and P. Davis, “Common-chaotic-signal induced synchronization in semiconductor lasers,” Opt. Express 15(7), 3974–3980 (2007).
[Crossref] [PubMed]

A. Uchida, P. Davis, and S. Itaya, “Generation of information theoretic secure keys using a chaotic semiconductor laser,” Appl. Phys. Lett. 83(15), 3213–3215 (2003).
[Crossref]

A. Uchida, Y. Liu, I. Fischer, P. Davis, and T. Aida, “Chaotic antiphase dynamics and synchronization in multimode semiconductor lasers,” Phys. Rev. A 64(2), 023801 (2001).
[Crossref]

K. Yoshimura, M. Inubushi, and A. Uchida, “Principal frequency band of cascaded single-mode semiconductor lasers injected with broadband random light,” in Proc. 2015 International Symposium on Nonlinear Theory and Its Applications (NOLTA2015) (2015), pp. 257–260.

K. Arai, K. Yoshimura, S. Sunada, and A. Uchida, “Synchronization induced by common ASE noise in semiconductor lasers,” in Proc. 2014 International Symposium on Nonlinear Theory and Its Applications (NOLTA2014) (2014), pp. 472–477.

K. Yoshimura, J. Muramatsu, A. Uchida, and P. Davis, “Spectral characteristics of consistency of a single-mode semiconductor laser injected with broadband random light,” in Proc. 2014 International Symposium on Nonlinear Theory and Its Applications (NOLTA2014) (2014), pp. 545–548.

Valiusaityte, I.

K. Yoshimura, I. Valiusaityte, and P. Davis, “Synchronization induced by common colored noise in limit cycle and chaotic systems,” Phys. Rev. E 75(2), 026208 (2007).
[Crossref] [PubMed]

VanWiggeren, G. D.

G. D. VanWiggeren and R. Roy, “Communication with chaotic lasers,” Science 279(5354), 1198–1200 (1998).
[Crossref] [PubMed]

Vicente, R.

Xue, C.

Yamamoto, T.

Yariv, A.

Yip, H.

Yoo, S. J. B.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics 4(4), 248–254 (2010).
[Crossref]

Yoshimori, S.

Yoshimura, K.

T. Ito, H. Koizumi, N. Suzuki, I. Kakesu, K. Iwakawa, A. Uchida, T. Koshiba, J. Muramatsu, K. Yoshimura, M. Inubushi, and P. Davis, “Physical implementation of oblivious transfer using optical correlated randomness,” Sci. Rep. 7(1), 8444 (2017).
[Crossref] [PubMed]

T. Sasaki, I. Kakesu, Y. Mitsui, D. Rontani, A. Uchida, S. Sunada, K. Yoshimura, and M. Inubushi, “Common-signal-induced synchronization in photonic integrated circuits and its application to secure key distribution,” Opt. Express 25(21), 26029–26044 (2017).
[Crossref] [PubMed]

N. Suzuki, T. Hida, M. Tomiyama, A. Uchida, K. Yoshimura, K. Arai, and M. Inubushi, “Common-signal-induced synchronization in semiconductor lasers with broadband optical noise signal,” IEEE J. Select. Top. Quantum Electron. 23(6), 1800810 (2017).

J. Muramatsu, K. Yoshimura, P. Davis, A. Uchida, and T. Harayama, “Secret-key distribution based on bounded observability,” Proc. IEEE 103(10), 1762–1780 (2015).
[Crossref]

S. Sunada, K. Arai, K. Yoshimura, and M. Adachi, “Optical phase synchronization by injection of common broadband low-coherent light,” Phys. Rev. Lett. 112(20), 204101 (2014).
[Crossref]

H. Koizumi, S. Morikatsu, H. Aida, T. Nozawa, I. Kakesu, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Information-theoretic secure key distribution based on common random-signal induced synchronization in unidirectionally-coupled cascades of semiconductor lasers,” Opt. Express 21(15), 17869–17893 (2013).
[Crossref] [PubMed]

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

H. Aida, M. Arahata, H. Okumura, H. Koizumi, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Experiment on synchronization of semiconductor lasers by common injection of constant-amplitude random-phase light,” Opt. Express 20(11), 11813–11829 (2012).
[Crossref] [PubMed]

J. Muramatsu, K. Yoshimura, and P. Davis, “Information theoretic security based on bounded observability,” Lect. Notes Comput. Sci. 5973, 128–139 (2010).
[Crossref]

I. Oowada, H. Ariizumi, M. Li, S. Yoshimori, A. Uchida, K. Yoshimura, and P. Davis, “Synchronization by injection of common chaotic signal in semiconductor lasers with optical feedback,” Opt. Express 17(12), 10025–10034 (2009).
[Crossref] [PubMed]

S. Goto, P. Davis, K. Yoshimura, and A. Uchida, “Synchronization of chaotic semiconductor lasers by optical injection with random phase modulation,” Opt. Quantum Electron. 41(3), 137–149 (2009).
[Crossref]

K. Yoshimura, J. Muramatsu, and P. Davis, “Conditions for common-noise-induced synchronization in time delay systems,” Physica D 237(23), 3146–3152 (2008).
[Crossref]

K. Yoshimura, I. Valiusaityte, and P. Davis, “Synchronization induced by common colored noise in limit cycle and chaotic systems,” Phys. Rev. E 75(2), 026208 (2007).
[Crossref] [PubMed]

T. Yamamoto, I. Oowada, H. Yip, A. Uchida, S. Yoshimori, K. Yoshimura, J. Muramatsu, S. I. Goto, and P. Davis, “Common-chaotic-signal induced synchronization in semiconductor lasers,” Opt. Express 15(7), 3974–3980 (2007).
[Crossref] [PubMed]

K. Yoshimura, M. Inubushi, and A. Uchida, “Principal frequency band of cascaded single-mode semiconductor lasers injected with broadband random light,” in Proc. 2015 International Symposium on Nonlinear Theory and Its Applications (NOLTA2015) (2015), pp. 257–260.

K. Yoshimura, J. Muramatsu, A. Uchida, and P. Davis, “Spectral characteristics of consistency of a single-mode semiconductor laser injected with broadband random light,” in Proc. 2014 International Symposium on Nonlinear Theory and Its Applications (NOLTA2014) (2014), pp. 545–548.

K. Arai, K. Yoshimura, S. Sunada, and A. Uchida, “Synchronization induced by common ASE noise in semiconductor lasers,” in Proc. 2014 International Symposium on Nonlinear Theory and Its Applications (NOLTA2014) (2014), pp. 472–477.

Zadok, A.

Zakharova, A.

F. Böhm, A. Zakharova, E. Schöll, and K. Lüdge, “Amplitude-phase coupling drives chimera states in globally coupled laser networks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(4), 040901 (2015).
[Crossref] [PubMed]

Zhou, C.

C. Zhou and J. Kurths, “Noise-induced phase synchronization and synchronization transitions in chaotic oscillators,” Phys. Rev. Lett. 88(23), 230602 (2002).
[Crossref] [PubMed]

Zhou, L.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics 4(4), 248–254 (2010).
[Crossref]

Zigzag, M.

Appl. Phys. Lett. (1)

A. Uchida, P. Davis, and S. Itaya, “Generation of information theoretic secure keys using a chaotic semiconductor laser,” Appl. Phys. Lett. 83(15), 3213–3215 (2003).
[Crossref]

Chaos (1)

R. Toral, C. R. Mirasso, E. Hernandez-Garcia, and O. Piro, “Analytical and numerical studies of noise-induced synchronization of chaotic systems,” Chaos 11(3), 665–673 (2001).
[Crossref] [PubMed]

IEEE J. Quantum Electron. (1)

J. M. Buldú, J. García-Ojalvo, and M. C. Torrent, “Multimode synchronization and communication using unidirectionally coupled semiconductor lasers,” IEEE J. Quantum Electron. 40(6), 640–650 (2004).
[Crossref]

IEEE J. Select. Top. Quantum Electron. (1)

N. Suzuki, T. Hida, M. Tomiyama, A. Uchida, K. Yoshimura, K. Arai, and M. Inubushi, “Common-signal-induced synchronization in semiconductor lasers with broadband optical noise signal,” IEEE J. Select. Top. Quantum Electron. 23(6), 1800810 (2017).

Jpn. J. Appl. Phys. (1)

J. Ohtsubo, R. Ozawa, and M. Nanbu, “Synchrony of small nonlinear networks in chaotic semiconductor lasers,” Jpn. J. Appl. Phys. 54(7), 072702 (2015).
[Crossref]

Lect. Notes Comput. Sci. (1)

J. Muramatsu, K. Yoshimura, and P. Davis, “Information theoretic security based on bounded observability,” Lect. Notes Comput. Sci. 5973, 128–139 (2010).
[Crossref]

Nat. Photonics (1)

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics 4(4), 248–254 (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] [PubMed]

Opt. Express (9)

A. Zadok, J. Scheuer, J. Sendowski, and A. Yariv, “Secure key generation using an ultra-long fiber laser: transient analysis and experiment,” Opt. Express 16(21), 16680–16690 (2008).
[Crossref] [PubMed]

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18(17), 18292–18302 (2010).
[Crossref] [PubMed]

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

H. Koizumi, S. Morikatsu, H. Aida, T. Nozawa, I. Kakesu, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Information-theoretic secure key distribution based on common random-signal induced synchronization in unidirectionally-coupled cascades of semiconductor lasers,” Opt. Express 21(15), 17869–17893 (2013).
[Crossref] [PubMed]

T. Sasaki, I. Kakesu, Y. Mitsui, D. Rontani, A. Uchida, S. Sunada, K. Yoshimura, and M. Inubushi, “Common-signal-induced synchronization in photonic integrated circuits and its application to secure key distribution,” Opt. Express 25(21), 26029–26044 (2017).
[Crossref] [PubMed]

T. Yamamoto, I. Oowada, H. Yip, A. Uchida, S. Yoshimori, K. Yoshimura, J. Muramatsu, S. I. Goto, and P. Davis, “Common-chaotic-signal induced synchronization in semiconductor lasers,” Opt. Express 15(7), 3974–3980 (2007).
[Crossref] [PubMed]

I. Oowada, H. Ariizumi, M. Li, S. Yoshimori, A. Uchida, K. Yoshimura, and P. Davis, “Synchronization by injection of common chaotic signal in semiconductor lasers with optical feedback,” Opt. Express 17(12), 10025–10034 (2009).
[Crossref] [PubMed]

H. Aida, M. Arahata, H. Okumura, H. Koizumi, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Experiment on synchronization of semiconductor lasers by common injection of constant-amplitude random-phase light,” Opt. Express 20(11), 11813–11829 (2012).
[Crossref] [PubMed]

A. Argyris, M. Bourmpos, and D. Syvridis, “Experimental synchrony of semiconductor lasers in coupled networks,” Opt. Express 24(5), 5600–5614 (2016).
[Crossref] [PubMed]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

S. Goto, P. Davis, K. Yoshimura, and A. Uchida, “Synchronization of chaotic semiconductor lasers by optical injection with random phase modulation,” Opt. Quantum Electron. 41(3), 137–149 (2009).
[Crossref]

Phys. Lett. A (1)

D. Bar-Lev and J. Scheuer, “Enhanced key-establishing rates and efficiencies in fiber laser key distribution systems,” Phys. Lett. A 373(46), 4287–4296 (2009).
[Crossref]

Phys. Rev. A (1)

A. Uchida, Y. Liu, I. Fischer, P. Davis, and T. Aida, “Chaotic antiphase dynamics and synchronization in multimode semiconductor lasers,” Phys. Rev. A 64(2), 023801 (2001).
[Crossref]

Phys. Rev. E (3)

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E 74(4), 046201 (2006).
[Crossref] [PubMed]

J. Tiana-Alsina, K. Hicke, X. Porte, M. C. Soriano, M. C. Torrent, J. García-Ojalvo, and I. Fischer, “Zero-lag synchronization and bubbling in delay-coupled lasers,” Phys. Rev. E 85(2), 026209 (2012).
[Crossref] [PubMed]

K. Yoshimura, I. Valiusaityte, and P. Davis, “Synchronization induced by common colored noise in limit cycle and chaotic systems,” Phys. Rev. E 75(2), 026208 (2007).
[Crossref] [PubMed]

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

F. Böhm, A. Zakharova, E. Schöll, and K. Lüdge, “Amplitude-phase coupling drives chimera states in globally coupled laser networks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(4), 040901 (2015).
[Crossref] [PubMed]

Phys. Rev. Lett. (9)

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Controlling Synchronization in Large Laser Networks,” Phys. Rev. Lett. 108(21), 214101 (2012).
[Crossref] [PubMed]

B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, “Robustness of optimal synchronization in real networks,” Phys. Rev. Lett. 107(3), 034102 (2011).
[Crossref] [PubMed]

J. Scheuer and A. Yariv, “Giant fiber lasers: A new paradigm for secure key distribution,” Phys. Rev. Lett. 97(14), 140502 (2006).
[Crossref] [PubMed]

J.-P. Goedgebuer, L. Larger, and H. Porte, “Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode,” Phys. Rev. Lett. 80(10), 2249–2252 (1998).
[Crossref]

C. Zhou and J. Kurths, “Noise-induced phase synchronization and synchronization transitions in chaotic oscillators,” Phys. Rev. Lett. 88(23), 230602 (2002).
[Crossref] [PubMed]

J. N. Teramae and D. Tanaka, “Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators,” Phys. Rev. Lett. 93(20), 204103 (2004).
[Crossref] [PubMed]

H. Nakao, K. Arai, and Y. Kawamura, “Noise-induced synchronization and clustering in ensembles of uncoupled limit-cycle oscillators,” Phys. Rev. Lett. 98(18), 184101 (2007).
[Crossref] [PubMed]

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

S. Sunada, K. Arai, K. Yoshimura, and M. Adachi, “Optical phase synchronization by injection of common broadband low-coherent light,” Phys. Rev. Lett. 112(20), 204101 (2014).
[Crossref]

Physica D (1)

K. Yoshimura, J. Muramatsu, and P. Davis, “Conditions for common-noise-induced synchronization in time delay systems,” Physica D 237(23), 3146–3152 (2008).
[Crossref]

Proc. IEEE (1)

J. Muramatsu, K. Yoshimura, P. Davis, A. Uchida, and T. Harayama, “Secret-key distribution based on bounded observability,” Proc. IEEE 103(10), 1762–1780 (2015).
[Crossref]

Sci. Rep. (1)

T. Ito, H. Koizumi, N. Suzuki, I. Kakesu, K. Iwakawa, A. Uchida, T. Koshiba, J. Muramatsu, K. Yoshimura, M. Inubushi, and P. Davis, “Physical implementation of oblivious transfer using optical correlated randomness,” Sci. Rep. 7(1), 8444 (2017).
[Crossref] [PubMed]

Science (1)

G. D. VanWiggeren and R. Roy, “Communication with chaotic lasers,” Science 279(5354), 1198–1200 (1998).
[Crossref] [PubMed]

Other (5)

A. Uchida, Optical Communication with Chaotic Lasers, Applications of Nonlinear Dynamics and Synchronization (Wiley-VCH, 2012).

J. Ohtsubo, Semiconductor Lasers, Stability, Instability and Chaos, 4th ed. (Springer-Verlag, 2017).

K. Arai, K. Yoshimura, S. Sunada, and A. Uchida, “Synchronization induced by common ASE noise in semiconductor lasers,” in Proc. 2014 International Symposium on Nonlinear Theory and Its Applications (NOLTA2014) (2014), pp. 472–477.

K. Yoshimura, J. Muramatsu, A. Uchida, and P. Davis, “Spectral characteristics of consistency of a single-mode semiconductor laser injected with broadband random light,” in Proc. 2014 International Symposium on Nonlinear Theory and Its Applications (NOLTA2014) (2014), pp. 545–548.

K. Yoshimura, M. Inubushi, and A. Uchida, “Principal frequency band of cascaded single-mode semiconductor lasers injected with broadband random light,” in Proc. 2015 International Symposium on Nonlinear Theory and Its Applications (NOLTA2015) (2015), pp. 257–260.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1 Experimental setup for common-signal-induced synchronization subject to a bandwidth-limited optical noise signal. Amp, electronic amplifier; ATT, optical attenuator; EDFA, erbium-doped fiber amplifier; FC, fiber coupler; Filter, variable wavelength filter; ISO, optical isolator; PC, polarization controller; PD, photodetector; SLD, super-luminescent diode.
Fig. 2
Fig. 2 Optical spectra of the noise drive signal and the two response laser outputs when the noise drive signal is filtered out with a bandwidth of 14.4 nm. By injecting the noise drive signal, 50 longitudinal modes are excited in the two response lasers. (a), (b) Matching condition of peak wavelengths. (c), (d) Mismatching condition of peak wavelengths. (b), (d) Enlarged views of (a) and (c).
Fig. 3
Fig. 3 (a), (c) Temporal waveforms of the two response laser outputs and (b), (d) their correlation plots when the peak wavelengths of the two response lasers are (a), (b) matched and (c), (d) mismatched.
Fig. 4
Fig. 4 RF spectra of response lasers 1 and 2 when the peak wavelengths of the two response lasers are (a) matched and (b) mismatched.
Fig. 5
Fig. 5 (a) Temporal waveforms of the drive-injection signal and the response 1 laser output and (b) its correlation plot.
Fig. 6
Fig. 6 Cross-correlation values between the two response laser outputs when the numbers of longitudinal modes of the two response lasers are changed simultaneously. (a) Optical injection power varies as the bandwidth of the noise drive signal is changed. (b) Optical injection power is fixed for different numbers of modes by adjusting the gain of the EDFAs as the bandwidths of the noise drive signals are changed simultaneously.
Fig. 7
Fig. 7 Cross-correlation values between the two response lasers as the injection powers of the noise drive signals for the two response lasers are changed simultaneously under the wavelength-matching condition. The ratio of the injection power between the two response lasers is maintained. Only the injection power for the response 1 laser is plotted on the horizontal axis.
Fig. 8
Fig. 8 Optical spectra of the response 1 and 2 lasers when the three peak wavelengths are matched and shifted. (a) All the three peak wavelengths are matched. (b) Two of the three peak wavelengths are matched.
Fig. 9
Fig. 9 Cross-correlation values when the peak wavelengths are changed continuously for the case of (a) three longitudinal modes and (b) 50, six, three, and one longitudinal mode. The curve for the three modes in (a) is replotted in (b) for comparison. The injection power is changed as the bandwidths of the noise drive signals (the numbers of modes in the response lasers) are changed.
Fig. 10
Fig. 10 Cross-correlation values as the number of longitudinal modes for only the response 2 laser is changed, with that of the response 1 laser fixed at 50 modes. The correlation values for 50 modes differ from those in Figs. 3(b) and 3(d) owing to the different injection power.
Fig. 11
Fig. 11 (a), (c) Optical spectra and (b), (d) correlation plots between the response 1 and 2 lasers. (a), (b) Comparison between the outputs of the 50-mode response 1 laser and the three-mode response 2 laser. (c), (d) Comparison between the output of the three-mode response 1 laser selected from 50 modes obtained using the wavelength filter and the output of the three-mode response 2 laser.
Fig. 12
Fig. 12 Cross-correlation values obtained when the eavesdropper changes the bandwidth of the wavelength filter for the noise drive signal and changes the number of longitudinal modes in the laser of the eavesdropper to reproduce the outputs of the lasers of the legitimate users by using synchronization (the blue line). The correlation values between the two legitimate users (the red dotted line) and between the noise drive signal and the legitimate users (the green line) are also shown. The correlation value between the two legitimate users is constant because the number of modes in the laser of the eavesdropper is changed.

Metrics