Abstract

We report a novel chaos semiconductor laser chip in which a distributed feedback (DFB) laser, two semiconductor optical amplifiers (SOAs) and a photodiode (PD) are monolithically integrated with a passive ring waveguide. The ring-type structure with the two separate SOAs achieves stronger delayed optical feedback compared to previous chaos laser chips which use linear waveguide and facet-reflection. The integrated PD allows efficient detection of the optical signal with low optical loss. A rich variety of dynamical behaviors and optical signals can be selectively generated via injection currents to the two separate SOAs. In particular, the strong optical feedback makes possible the generation of strong broadband optical chaos, with very flat spectrum of ±6.5 dB up to 10 GHz. The stability and quality of the chaotic mode is demonstrated using strict statistical tests of randomness applied to long binary sequences extracted by sampling the optical intensity signal.

© 2011 OSA

1. Introduction

Semiconductor lasers with optical feedback have been intensively studied due to the importance for both fundamental physics and practical applications [1, 2]. From the perspective of fundamental physics, their nonlinear dynamics has exhibited numerous intriguing behaviors, such as high-dimensional chaos and chaos synchronization, which are representative examples of complex dynamics in infinite-dimensional systems. Concerning practical applications, complex signals generated by chaotic laser devices are useful for various sensing and communication applications. Synchronization of chaotic lasers has been applied for secure optical communication [35]. It has recently been reported that chaotic semiconductor lasers can be applied to high-quality physical random bit generation [610]. They can generate random bit sequences at fast rates of over one gigabit per second, much faster than any other physical random bit generators. In these applications, the ability of the chaotic devices to generate high bandwidth random intensity oscillations is important.

In most of the experimental setups for lasers with delayed optical feedback, discrete optical components, such as optical fiber and spatial components, have been used. However, from the viewpoint of practical applications, such system configurations are inconvenient because of their large size. Therefore, it is important to make them much smaller by using the modern technology of photonic integrated circuits. Recently, chaos laser chips in which a distributed feedback (DFB) laser, a semiconductor optical amplifier (SOA), and a phase modulator (PM) are monolithically integrated with a straight passive waveguide have been fabricated [11]. High-reflective (HR) coating as well as facet mirror made by precise cleavage were necessary to achieve delayed optical feedback strong enough to obtain chaotic behaviors of the output laser light. It has recently been reported that they have been used for secure optical communication experiments [12]. More recently, it has been reported that they can also be used for fast physical random bit generation [13].

In this paper, we report a novel compact chaos laser chip with a ring type optical delayed feedback. The feedback loop is formed by a passive ring waveguide monolithically integrated with a single-frequency DFB laser, two SOAs, and a fast-response photodiode (PD). The advantage of the ring type configuration is that precise cleaved facet mirrors and HR coating are not needed for achieving strong optical feedback.

The overall size of the chip is within 3.5 mm × 3.5 mm. The delay time is much shorter than previous systems using bulk components (for example, see [1]) and similar to the short delay achieved in [11]. As the delay time is shorter, stronger optical feedback is needed for exhibiting chaotic dynamics [1]. Therefore, the ring type optical feedback waveguide is carefully designed for reducing the propagation loss and for achieving strong optical feedback. We confirmed that the ring device is able to generate broadband chaotic signals in a strong feedback regime, with flatter spectrum than previous chaos laser chip [1113]. It is also confirmed that the chaotic signals are sufficiently random to pass statistical tests of randomness.

This paper is organized as follows: In section 2, the design and the layer structure of the chaos laser chip with a ring type optical delayed feedback are reported. In section 3, we evaluate the optical feedback strength on the basis of gain and loss measurements. In section 4, it is shown that rich dynamical behaviors, including stable solution, limit cycle, and broadband chaotic dynamics, can be selectively generated by controlling the injection currents to the dual SOAs. In section 5, the quality of the broadband chaos signal is evaluated by applying strict statistical test suites of randomness to long binary sequences extracted from the chaos signal by digital sampling. Finally, the summary of this paper is provided in section 6.

2. Chaos laser chips

Figure 1 shows the fabricated chaos laser chip, which consists of a DFB laser, two SOAs (we call them SOA1 and SOA2), a PD and a passive ring waveguide realized with an active-passive butt-joint integration technology. The length of DFB, SOA1, SOA2, PD, and the passive ring waveguide are respectively 500 μm, 200 μm, 100 μm, 50 μm, and 11.43 mm, and the overall size of the chaos laser chip is within 3.5 mm × 3.5 mm. The design of the laser is based on a standard theory of single mode semiconductor lasers subject to delayed optical feedback, as described with the Lang-Kobayashi model. The DFB is designed so that it operates at a single longitudinal mode. The passive ring waveguide works as a delayed feedback loop; the laser light emitted from the DFB propagates in clockwise and counter-clockwise directions and is fed back to the DFB with time delay 0.1785 ns. The strength and phase of the optical feedback is controlled by the injection current to SOAs, and the intensity of the optical signal can be efficiently detected using the PD in the ring feedback loop. In order to study the dynamics of the device with large feedback, we did not include an optical output port, so that the feedback could be made as large as possible.

 

Fig. 1 Device structures. (a)A schematic and (b)a photograph of the chaos laser chip.

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The layer structures of the active region (DFB, SOAs, and PD) and the passive waveguide in the laser chip are shown in Fig. 2(a) and 2(b), respectively. DFB, SOAs, PD sections contain the strained InGaAs/InGaAsP multi-quantum well (MQW) active layer grown by using metal-organic vapor phase epitaxy on the n-InP substrate. The MQW is bounded by the non-doped InGaAsP separate-confinement-heterostructure layer for the efficient active-passive coupling. For the DFB laser, the grating with depth 30 nm and pitch 234 nm are fabricated so that the laser emits light around the wavelength λa = 1.55 μm. The passive region contains the intrinsic InP cladding layer and the non-doped InGaAsP waveguiding core layer with the bandgap corresponding to the wavelength λp = 1.3 μm, which is shorter than λa, to avoid light absorption. These layers are made by butt-joint selective growth.

 

Fig. 2 The layer structures of the cross section in (a)the active region (DFB, SOAs, PD), and (b)the passive region. The grating is fabricated only for DFB part. MQW, multi-quantum well; W, ridge width; H, ridge height.

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The passive ring waveguide is designed and fabricated so that the propagation loss is as small as possible. Here, it is important to note that there is a trade-off in determining the ridge height and the radius of the ring waveguide: Small height reduces the confinement of the propagating mode and enhances the bending loss while large height reduces bending loss but enhances light scattering loss. Thus, the height of the waveguide should be carefully tuned. We chose the radius R of the bending part of the ring waveguide and the ridge width W to be 1 mm and 2 μm, respectively, and fabricated multiple chaos laser chips of different ridge height H. We found that the bending loss is suddenly increased when the ridge height H is smaller than 1.7 μm, while the bending loss is almost not changed when the ridge height H is much larger than this value. The dependence of the bending loss on the ridge height is clearly seen in the light intensity vs. injection current (L-I) characteristics measured by the internal PD as shown in Fig. 3. In this measurement, the temperature of the laser chaos chip is kept at 25 degree. For H = 1.8 μm, the threshold for the injection current to the DFB laser can be clearly measured from the PD output to be around 13 mA, while for H = 1.7 μm, the PD output is weak and the lasing threshold cannot be observed. The light intensity at the PD is weak due to weak mode confinement and large bending loss. Consequently, we chose the ridge height H = 1.8 μm.

 

Fig. 3 L-I characteristics for ridge height 1.8 μm (the red curve) and 1.7μm (the blue curve). The threshold current Jth is estimated to be 13mA.

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3. Static property: estimation of the feedback power ratio

Next, we investigate how strong optical feedback can be achieved. We need to evaluate the passive waveguide loss, the active-passive coupling efficiency Tap, and the gain G of the SOA. The passive waveguide loss αp and the active-passive coupling efficiency Tap can be measured by the method reported in [14], and they were estimated to be Tap =0.55/facet (55%/facet) and αp =0.15 cm−1, respectively. As we have shown in the previous section, the bending loss of the ring waveguide becomes minimum when the ridge height is equal to 1.8 μm for the radius R=1 mm.

In order to evaluate the SOA gain, we fabricated multiple test device chips on the same wafer with the same DFB laser, SOA, passive waveguide and two PDs monolithically integrated by the same process but in a different configuration as shown in Fig. 4. In these chips, the DFB laser is used for the light source, and one of the two PDs is used for monitoring the input light power Pin to the SOA, that is, laser light emitted from DFB, while the other PD is used to detect the output power Pout amplified by the SOA. Then, the SOA gain G can be calculated using the ratio of the output power Pout to the input power Pin and the active-passive coupling efficiency Tap as

G=1Tap2PoutPin.
Figure 5(a) and 5(b) show the biasing current dependences of the gain of the SOAs 200 and 100 μm long, measured by using these test device chips. The DFB injection current is fixed at 22 mA that is about 1.7 Jth where the threshold current Jth = 13 mA. The gain of the SOA 200 μm long is changed in the range from −3 dB to 4 dB as the SOA biasing current is increased up to 20 mA, while the gain of the SOA 100 μm long is changed from −2 dB to 2.5 dB when the current is increased up to 10 mA. The gain saturation can be observed for high biasing current regime in both cases.

 

Fig. 4 Schematic of a test device used for the gain measurement. DFB, SOA, and two PDs (PD1 and PD2) are monolithically integrated with a passive waveguide (Passive WG), and the width of the waveguide is the same as that of the chaos laser chip.

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Fig. 5 Biasing current dependences of the gain for 200μm-long SOA (a) and 100μm-long SOA (b). DFB current is fixed at 22mA (about 1.7times of the threshold current).

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From the results of the waveguide loss and SOA gain measurement explained above, we can finally obtain the optical delayed feedback power ratio Pf, i.e., the ratio of the feedback light power after one-round trip to the input power, shown in Fig. 1 as follows,

Pf=G1G2Tap6exp(αpLpαpdLpd),
where G1 and G2 denote the gains of SOA1 and SOA2. (The bending loss of the ring waveguide is negligible due to the optimum ridge height.) In Eq. (2), Tap = 0.55 is the active-passive coupling efficiency, αp = 0.15 cm−1 is the ring waveguide loss, Lp = 11.43 mm is the waveguide length, αpd = 1.44 × 10−3 μm−1 is the absorption loss of the PD, and Lpd = 50 μm is the PD length. The absorption loss αpd of the PD is given as a gain value for biasing current 0 mA. Figure 6 shows the dependences of the optical delayed feedback power ratio Pf on the currents injected to SOA1 when the currents JSOA2 injected to SOA2 are fixed to 0 mA, 3 mA, and 6 mA. One can see that the feedback power ratio can be controlled in a wide range from 0.8 (%) to about 11 (%). In particular, it is important to note that this ring-type laser chaos chip can achieve stronger optical feedback than the previously reported laser chaos chips with conventional linear-type delayed optical feedback [11, 13].

 

Fig. 6 Optical feedback power ratios vs. the injection currents to SOA1. The injection currents to SOA2 were fixed to 0 mA(blue curve), 3 mA(green curve), and 6 mA(red curve).

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4. Dynamical properties: generation of broadband chaos

In this section, we study the dynamical property of the ring-type chaos laser chip.

First, let us explain the experimental setup. As shown in Fig. 7, the chaos laser chip was soldered on a temperature controlled mount in a module package containing a microstripline, chip resistor and high-frequency connector. The operation temperature is kept at 25 degree with the stability ±0.01 degree, and the current is applied to the DFB laser and two SOAs via bonding pads with the stability ±0.01 mA. The high frequency electric signals oscillating at the order of giga hertz obtained from the PD are extracted from the module to the high-frequency connector via a microstripline with a 50-Ω chip register for impedance matching. Then, only the AC component of the electric signal is extracted by a bias-tee (Agilent, 11612A, 45MHz-26.5GHz) which is used as a high-pass filter, amplified by an electronic amplifier (New Focus 1422-LF, 20 GHz bandwidth), and finally sent to a 8-bit digital oscilloscope (Tektronix, DSA71254, 50GigaSamples/sec, bandwidth 12.5GHz).

 

Fig. 7 Experimental setup for measuring chaotic waveforms.

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Next we describe the characteristics of the time series of the AC component of the PD voltage corresponding to the dynamics of the output light intensity from the chaos laser chip of a ring type delayed optical feedback. First we consider the injection current to the DFB laser is relatively weak, just above threshold, and the relaxation oscillation frequency is much smaller than the inverse delay time (5.6 GHz). When the injection current to the DFB laser is just above the threshold, the dynamical behavior of the PD voltage sensitively depends on the injection currents to the dual SOAs. By gradually increasing the injection currents to the dual SOAs, we observed the transition of the dynamical behavior from a stable single mode oscillation to chaos via periodic limit cycle oscillations, and then back to stable single mode operation. Such a cyclic scenario was observed within a slight change of injection currents by a few tenths of milliamperes. The emergence of such a cyclic behavior in the regime of the small injection current is a characteristic for lasers with short-delayed optical feedback whose inverse delay time is much larger than the relaxation oscillation frequency [15, 16]. However, the chaotic regime of the injection current to the SOAs is too narrow to maintain the same chaotic state for a long time. Therefore, the generation of the chaotic signals in this regime is very unstable.

When the injection current to the DFB laser is 1.7 times larger than the threshold current and the relaxation oscillation frequency approaches the inverse delay time, the dependence on the SOA injection current becomes less sensitive: the route from a stable single mode oscillation to chaos is similar to the case that the injection current to the DFB laser is smaller, but the period of the cyclic behavior becomes longer, and the regime of strongly chaotic dynamics is more stable. In Fig. 8, an example of the transition from the stable single mode oscillation to the broadband chaos is given in a series of wave forms observed when increasing the injection current to SOA1. The radio-frequency (rf) spectra corresponding to the series of wave forms are shown in Fig. 9. Here the injection current JSOA1 to SOA1 is increased from 6 mA to 15 mA, while the injection current JDFB to the DFB laser and the injection current JSOA2 to the SOA2 are fixed at 22 mA (≈ 1.7 Jth) and 6 mA, respectively. In Fig. 9, a noise floor obtained in the case of JDFB = JSOA1 = JSOA2 = 0 mA is subtracted from each spectra in order to display the characteristics clearly. For JSOA1 = 6 mA, a stable laser oscillation with very small noise is observed as shown in Fig. 8(a). The rf spectrum has a small peak corresponding to the relaxation oscillation frequency (≈ 4.2 GHz) as shown in Fig. 9(a). The wave form and broad peak in the spectrum imply that the time series are stationary and do not contain a stable oscillation.

 

Fig. 8 The waveforms of the PD signals for JSOA1= (a)6 mA, (b)7 mA, (c)8 mA, (d)9 mA, (e)12 mA, (f)15 mA.

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Fig. 9 The radio-frequency spectra for JSOA1= (a)6 mA, (b)7 mA, (c)8 mA, (d)9 mA, (e)12 mA, (f)15 mA.

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As JSOA1 is increased to 7 mA, the wave form changes into the limit cycle oscillation shown in Fig. 8(b). The corresponding rf spectrum shown in Fig. 9(b) has sharp peaks at the relaxation oscillation frequency and its higher harmonics reflecting the nonlinear phenomena due to the delayed optical feedback.

For JSOA1=8 mA, a period-doubling bifurcation is observed as shown in Figs. 8(c) and 9(c). The regime in the SOA1 injection current where this periodic oscillation emerges is very narrow. For JSOA1=9 mA, the dynamics exhibits intermittent chaos, and the spectrum becomes broad as shown in Figs. 8(d) and 9(d). Further increasing JSOA1 causes more complicated chaotic oscillation state (see Figs. 8(e) and 8(f)), and the broadening of the spectrum becomes more advanced, as shown in Figs. 9(e) and 9(f). The transition to such a broadband chaotic state is similar with that described with a standard model of single mode semiconductor lasers subject to delayed optical feedback, the so-called Lang-Kobayashi model.

In this experiment, the flattest spectrum can be observed in a range of JSOA1 between 14 mA to 20 mA. The spectrum keeps almost the same structure throughout this region. The delayed optical feedback power ratio is estimated to be more than 9.5%. As seen in Fig. 9(f), the spectrum has smooth envelope, and the flatness is within ±6.5 dB up to 10 GHz. No sharp features associated with weakness of the instability are seen in the spectrum.

It is important to note that the spectrum is flatter than that of the chaos laser chips previously reported in [1113]. This flatness of the spectrum is achieved by the stronger feedback and better tunability by the use of dual SOAs. Moreover, the intensity is increased by more than about 40 dB compared to the noise spectrum of the stationary oscillation shown in Fig. 9(b), suggesting that the chaotic oscillation is robust with respect to the external electrical perturbations. Figure 10 shows the autocorrelation function corresponding to the spectrum of Fig. 9(f). The correlation has a peak around the relaxation oscillation period, and the peak rapidly decays over just a few periods due to the strongly chaotic dynamics. There are no significant peaks associated with the feedback delay time, unlike the chaotic laser systems with long feedback delay [6, 17].

 

Fig. 10 (a) Autocorrelation of the chaotic signals obtained for JDFB = 22 mA, JSOA1 = 15 mA, and JSOA2 = 6 mA. (b) Enlargement of the short-time autocorrelation.

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5. Randomness of the chaotic signals

In order to check the randomness and robustness of the generated chaotic signals, we convert them to binary signals and evaluate the statistical properties of the randomness. The conversion to the binary signals is carried out with a random bit generation scheme shown in Fig. 11. This is a similar method to that used for a previous demonstration of fast random bit generation [6,7]. First the chaotic signal is digitized at a sampling rate 1.56 GHz (the sampling interval; 0.64 ns). The most important point is that the autocorrelation of the chaotic signal has almost vanished at this time as shown in Fig. 10. The sampled signals are converted to binary signals (“1” and “0”) by comparing a threshold value, which is chosen so that the bit frequency ratio is as close as possible to 50%. In our experiment, the tunability of the threshold value is limited in precision due to the 8-bit precision of a digital oscilloscope. Therefore, two independent binary sequences are used to generate a single random bit sequences whose bit frequency ratio is made closer 50% by logical Exclusive-OR (XOR) operation, which is a simple and common way to reduce statistical bias. In this scheme, no other post-processing is used, and thus the statistical randomness of the generated bit sequences directly indicate the quality of the broadband chaotic signal.

 

Fig. 11 Schematic diagram for random bit generation.

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Statistical randomness is evaluated using the standard statistical test suites for random number generators provided by National Institute of Standard Technology (NIST), NIST Special Publication 800-22 (revision 1a) [18] and ”Diehard” tests [19]. The NIST test consists of 15 statistical tests as shown in Table 1, and each test was performed using 1000 instances of 1 Mbit sequences generated with sampling rate 1.56 GHz and the significance level α =0.01. To pass these tests, the proportion of the sequences satisfying condition for the p-value, p > α, should be in the range of 0.99 ± 0.0094392, and the P-value of the uniformity of the p-values should be larger than 0.0001. Diehard tests consist of 18 statistical tests as shown in Table 2. The tests were performed using 92 Mbit sequences and the same significance level α=0.01. The p-values of each test should be within [0.01,0.99]. As shown in Table 1 and 2, the bit sequences obtained in this experiment pass all tests of both the NIST and Diehard tests. These results show that the generated chaotic signals can be statistically regarded as random signals over 0.64 ns.

Tables Icon

Table 1. Results of NIST Special Publication 800-22(rev. 1a) statistical tests. The tests have been performed using 1000 samples of 1 Mbit data and significance level α = 0.01. For the tests which produce multiple P-values and proportions, the worst case is shown

Tables Icon

Table 2. Typical results of “Diehard” statistical test suite. KS - Kolmogorov-Smirnov test. Significance level “α = 0.01”. For tests with multiple p-value, the worst case is shown

6. Summary

We reported that novel compact chaos laser devices designed to achieve strong optical feedback for broadband chaos signal generation can be achieved without cleaved facet mirror and high-reflection coating. In this laser device, chaotic signals are generated by a ring-type delayed optical feedback configuration using a passive ring waveguide monolithically integrated with a single mode DFB laser, two SOAs, and a fast-response PD. The strength of the delayed optical feedback strength was evaluated based on measurements of the individual optical components,and it was shown that with strong optical feedback of 9.5%, it is possible to generate broadband chaotic signals whose spectra are flat with fluctuation less than ±6.5 dB up to 10 GHz. We demonstrated the quality and robustness of the generated chaotic signals by converting them to binary signals and testing their statistical randomness. It was shown that high quality random bit sequences passed standard statistical tests of randomness can be generated at fast rate up to 1.56 Gbps. It is expected that the ring type feedback configuration will be useful for broadband chaos signal generation devices with asuperior combination of performance, small size and low cost, which will be advantageous for applications in sensing, communication and signal processing applications.

Acknowledgments

The authors would like to thank the members of NTT Communication Science Laboratories for their support.

References and links

1. J. Otsubo, Semiconductor Lasers: Stability, Instability and Chaos (Springer-Verlag, 2006).

2. D. M. Kane and K. A. Shore, eds. Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers, (Wiley, 2005). [CrossRef]  

3. A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(17), 343–346 (2005). [CrossRef]   [PubMed]  

4. C. R. Mirasso, P. Colet, and P. Garcia-Fernandez, “Synchronization of chaotic semiconductor lasers: application to encoded communications,” IEEE Photon. Technol. Lett. 8(2), 299–301 (1996). [CrossRef]  

5. I. Fischer, Y. Liu, and P. Davis, “Synchronization of chaotic semiconductor laser dynamics on subnanosecond time scales and its potential for chaos communication,” Phys. Rev. A 62(1), 011801(R) (2000). [CrossRef]  

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

7. K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009). [CrossRef]  

8. K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010). [CrossRef]   [PubMed]  

9. I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102, (2009). [CrossRef]   [PubMed]  

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

11. A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos application in communications,” Phys. Rev. Lett. 100(19), 194101 (2008). [CrossRef]   [PubMed]  

12. A. Argyris, E. Grivas, M. Hamacher, A. Bogris, and D. Syvridis, “Chaos-on-a-chip secures data transmission in optical fiber links,” Opt. Express 18(5), 5188–5198 (2010). [CrossRef]   [PubMed]  

13. A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express 18(18), 18763–18768 (2010). [CrossRef]   [PubMed]  

14. M. Choi, T. Tanaka, S. Sunada, and T. Harayama, “Linewidth properties of active-passive coupled monolithic InGaAs semiconductor ring lasers,” Appl. Phys. Lett. 94(23), 231110 (2009). [CrossRef]  

15. T. Heil, I. Fischer, W. Elsässer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: bifurcation scenarios and mechanisms,” Phys. Rev. E 67(6), 066214 (2003). [CrossRef]  

16. M. Peil, I. Fischer, and W. Elsäszer, “Spectral broadband dynamics of semiconductor lasers with resonant short cavities,” Phys. Rev. A 73(13), 023805 (2006). [CrossRef]  

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

18. A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo,“A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Special Publication 800-22 Revision 1a, (2010). http://csrc.nist.gov/groups/ST/toolkit/rng/documents/SP800-22rev1a.pdf

19. G. Marsaglia, DIEHARD: A battery of tests of randomness, (1996). http://stat.fsu.edu/geo

References

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  1. J. Otsubo, Semiconductor Lasers: Stability, Instability and Chaos (Springer-Verlag, 2006).
  2. D. M. Kane and K. A. Shore, eds. Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers, (Wiley, 2005).
    [CrossRef]
  3. A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(17), 343–346 (2005).
    [CrossRef] [PubMed]
  4. C. R. Mirasso, P. Colet, and P. Garcia-Fernandez, “Synchronization of chaotic semiconductor lasers: application to encoded communications,” IEEE Photon. Technol. Lett. 8(2), 299–301 (1996).
    [CrossRef]
  5. I. Fischer, Y. Liu, and P. Davis, “Synchronization of chaotic semiconductor laser dynamics on subnanosecond time scales and its potential for chaos communication,” Phys. Rev. A 62(1), 011801(R) (2000).
    [CrossRef]
  6. A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
    [CrossRef]
  7. K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
    [CrossRef]
  8. K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
    [CrossRef] [PubMed]
  9. I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102, (2009).
    [CrossRef] [PubMed]
  10. I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61, (2010).
    [CrossRef]
  11. A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos application in communications,” Phys. Rev. Lett. 100(19), 194101 (2008).
    [CrossRef] [PubMed]
  12. A. Argyris, E. Grivas, M. Hamacher, A. Bogris, and D. Syvridis, “Chaos-on-a-chip secures data transmission in optical fiber links,” Opt. Express 18(5), 5188–5198 (2010).
    [CrossRef] [PubMed]
  13. A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express 18(18), 18763–18768 (2010).
    [CrossRef] [PubMed]
  14. M. Choi, T. Tanaka, S. Sunada, and T. Harayama, “Linewidth properties of active-passive coupled monolithic InGaAs semiconductor ring lasers,” Appl. Phys. Lett. 94(23), 231110 (2009).
    [CrossRef]
  15. T. Heil, I. Fischer, W. Elsässer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: bifurcation scenarios and mechanisms,” Phys. Rev. E 67(6), 066214 (2003).
    [CrossRef]
  16. M. Peil, I. Fischer, and W. Elsäszer, “Spectral broadband dynamics of semiconductor lasers with resonant short cavities,” Phys. Rev. A 73(13), 023805 (2006).
    [CrossRef]
  17. D. Rontani, A. Locquet, M. Schiamanna, David S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view,” IEEE J. Quantum Electron. 45(7), 879–891 (2009).
    [CrossRef]
  18. A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo,“A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Special Publication 800-22 Revision 1a, (2010). http://csrc.nist.gov/groups/ST/toolkit/rng/documents/SP800-22rev1a.pdf
  19. G. Marsaglia, DIEHARD: A battery of tests of randomness, (1996). http://stat.fsu.edu/geo

2010 (4)

2009 (4)

M. Choi, T. Tanaka, S. Sunada, and T. Harayama, “Linewidth properties of active-passive coupled monolithic InGaAs semiconductor ring lasers,” Appl. Phys. Lett. 94(23), 231110 (2009).
[CrossRef]

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

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[CrossRef]

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102, (2009).
[CrossRef] [PubMed]

2008 (2)

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos application in communications,” Phys. Rev. Lett. 100(19), 194101 (2008).
[CrossRef] [PubMed]

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

2006 (1)

M. Peil, I. Fischer, and W. Elsäszer, “Spectral broadband dynamics of semiconductor lasers with resonant short cavities,” Phys. Rev. A 73(13), 023805 (2006).
[CrossRef]

2005 (1)

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(17), 343–346 (2005).
[CrossRef] [PubMed]

2003 (1)

T. Heil, I. Fischer, W. Elsässer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: bifurcation scenarios and mechanisms,” Phys. Rev. E 67(6), 066214 (2003).
[CrossRef]

2000 (1)

I. Fischer, Y. Liu, and P. Davis, “Synchronization of chaotic semiconductor laser dynamics on subnanosecond time scales and its potential for chaos communication,” Phys. Rev. A 62(1), 011801(R) (2000).
[CrossRef]

1996 (1)

C. R. Mirasso, P. Colet, and P. Garcia-Fernandez, “Synchronization of chaotic semiconductor lasers: application to encoded communications,” IEEE Photon. Technol. Lett. 8(2), 299–301 (1996).
[CrossRef]

Aida, H.

Amano, K.

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[CrossRef]

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

Annovazzi-Lodi, V.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(17), 343–346 (2005).
[CrossRef] [PubMed]

Argyris, A.

A. Argyris, E. Grivas, M. Hamacher, A. Bogris, and D. Syvridis, “Chaos-on-a-chip secures data transmission in optical fiber links,” Opt. Express 18(5), 5188–5198 (2010).
[CrossRef] [PubMed]

A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express 18(18), 18763–18768 (2010).
[CrossRef] [PubMed]

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos application in communications,” Phys. Rev. Lett. 100(19), 194101 (2008).
[CrossRef] [PubMed]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(17), 343–346 (2005).
[CrossRef] [PubMed]

Aviad, Y.

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

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102, (2009).
[CrossRef] [PubMed]

Bogris, A.

Chlouverakis, K. E.

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos application in communications,” Phys. Rev. Lett. 100(19), 194101 (2008).
[CrossRef] [PubMed]

Choi, M.

M. Choi, T. Tanaka, S. Sunada, and T. Harayama, “Linewidth properties of active-passive coupled monolithic InGaAs semiconductor ring lasers,” Appl. Phys. Lett. 94(23), 231110 (2009).
[CrossRef]

Citrin, David S.

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

Cohen, E.

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

Colet, P.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(17), 343–346 (2005).
[CrossRef] [PubMed]

C. R. Mirasso, P. Colet, and P. Garcia-Fernandez, “Synchronization of chaotic semiconductor lasers: application to encoded communications,” IEEE Photon. Technol. Lett. 8(2), 299–301 (1996).
[CrossRef]

Davis, P.

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[CrossRef] [PubMed]

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[CrossRef]

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

I. Fischer, Y. Liu, and P. Davis, “Synchronization of chaotic semiconductor laser dynamics on subnanosecond time scales and its potential for chaos communication,” Phys. Rev. A 62(1), 011801(R) (2000).
[CrossRef]

Deligiannidis, S.

Elsässer, W.

T. Heil, I. Fischer, W. Elsässer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: bifurcation scenarios and mechanisms,” Phys. Rev. E 67(6), 066214 (2003).
[CrossRef]

Elsäszer, W.

M. Peil, I. Fischer, and W. Elsäszer, “Spectral broadband dynamics of semiconductor lasers with resonant short cavities,” Phys. Rev. A 73(13), 023805 (2006).
[CrossRef]

Fischer, I.

M. Peil, I. Fischer, and W. Elsäszer, “Spectral broadband dynamics of semiconductor lasers with resonant short cavities,” Phys. Rev. A 73(13), 023805 (2006).
[CrossRef]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(17), 343–346 (2005).
[CrossRef] [PubMed]

T. Heil, I. Fischer, W. Elsässer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: bifurcation scenarios and mechanisms,” Phys. Rev. E 67(6), 066214 (2003).
[CrossRef]

I. Fischer, Y. Liu, and P. Davis, “Synchronization of chaotic semiconductor laser dynamics on subnanosecond time scales and its potential for chaos communication,” Phys. Rev. A 62(1), 011801(R) (2000).
[CrossRef]

Garcia-Fernandez, P.

C. R. Mirasso, P. Colet, and P. Garcia-Fernandez, “Synchronization of chaotic semiconductor lasers: application to encoded communications,” IEEE Photon. Technol. Lett. 8(2), 299–301 (1996).
[CrossRef]

Garcia-Ojalvo, J.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(17), 343–346 (2005).
[CrossRef] [PubMed]

Gavrielides, A.

T. Heil, I. Fischer, W. Elsässer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: bifurcation scenarios and mechanisms,” Phys. Rev. E 67(6), 066214 (2003).
[CrossRef]

Green, K.

T. Heil, I. Fischer, W. Elsässer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: bifurcation scenarios and mechanisms,” Phys. Rev. E 67(6), 066214 (2003).
[CrossRef]

Grivas, E.

Hamacher, M.

A. Argyris, E. Grivas, M. Hamacher, A. Bogris, and D. Syvridis, “Chaos-on-a-chip secures data transmission in optical fiber links,” Opt. Express 18(5), 5188–5198 (2010).
[CrossRef] [PubMed]

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos application in communications,” Phys. Rev. Lett. 100(19), 194101 (2008).
[CrossRef] [PubMed]

Harayama, T.

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[CrossRef] [PubMed]

M. Choi, T. Tanaka, S. Sunada, and T. Harayama, “Linewidth properties of active-passive coupled monolithic InGaAs semiconductor ring lasers,” Appl. Phys. Lett. 94(23), 231110 (2009).
[CrossRef]

Heil, T.

T. Heil, I. Fischer, W. Elsässer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: bifurcation scenarios and mechanisms,” Phys. Rev. E 67(6), 066214 (2003).
[CrossRef]

Hirano, K.

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[CrossRef] [PubMed]

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[CrossRef]

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

Inoue, M.

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[CrossRef]

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

Kanter, I.

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

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102, (2009).
[CrossRef] [PubMed]

Karashige, T.

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

Krauskopf, B.

T. Heil, I. Fischer, W. Elsässer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: bifurcation scenarios and mechanisms,” Phys. Rev. E 67(6), 066214 (2003).
[CrossRef]

Larger, L.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(17), 343–346 (2005).
[CrossRef] [PubMed]

Liu, Y.

I. Fischer, Y. Liu, and P. Davis, “Synchronization of chaotic semiconductor laser dynamics on subnanosecond time scales and its potential for chaos communication,” Phys. Rev. A 62(1), 011801(R) (2000).
[CrossRef]

Locquet, A.

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

Mirasso, C. R.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(17), 343–346 (2005).
[CrossRef] [PubMed]

C. R. Mirasso, P. Colet, and P. Garcia-Fernandez, “Synchronization of chaotic semiconductor lasers: application to encoded communications,” IEEE Photon. Technol. Lett. 8(2), 299–301 (1996).
[CrossRef]

Morikatsu, S.

Naito, S.

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[CrossRef]

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

Okumura, H.

Oowada, I.

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

Ortin, S.

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

Otsubo, J.

J. Otsubo, Semiconductor Lasers: Stability, Instability and Chaos (Springer-Verlag, 2006).

Peil, M.

M. Peil, I. Fischer, and W. Elsäszer, “Spectral broadband dynamics of semiconductor lasers with resonant short cavities,” Phys. Rev. A 73(13), 023805 (2006).
[CrossRef]

Pesquera, L.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(17), 343–346 (2005).
[CrossRef] [PubMed]

Pikasis, E.

Reidler, I.

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

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102, (2009).
[CrossRef] [PubMed]

Rontani, D.

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

Rosenbluh, M.

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

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102, (2009).
[CrossRef] [PubMed]

Schiamanna, M.

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

Shiki, M.

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

Shore, K. A.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(17), 343–346 (2005).
[CrossRef] [PubMed]

Someya, H.

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

Sunada, S.

M. Choi, T. Tanaka, S. Sunada, and T. Harayama, “Linewidth properties of active-passive coupled monolithic InGaAs semiconductor ring lasers,” Appl. Phys. Lett. 94(23), 231110 (2009).
[CrossRef]

Syvridis, D.

A. Argyris, E. Grivas, M. Hamacher, A. Bogris, and D. Syvridis, “Chaos-on-a-chip secures data transmission in optical fiber links,” Opt. Express 18(5), 5188–5198 (2010).
[CrossRef] [PubMed]

A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express 18(18), 18763–18768 (2010).
[CrossRef] [PubMed]

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos application in communications,” Phys. Rev. Lett. 100(19), 194101 (2008).
[CrossRef] [PubMed]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(17), 343–346 (2005).
[CrossRef] [PubMed]

Tanaka, T.

M. Choi, T. Tanaka, S. Sunada, and T. Harayama, “Linewidth properties of active-passive coupled monolithic InGaAs semiconductor ring lasers,” Appl. Phys. Lett. 94(23), 231110 (2009).
[CrossRef]

Uchida, A.

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[CrossRef] [PubMed]

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[CrossRef]

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

Yamazaki, T.

Yoshimori, S.

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[CrossRef] [PubMed]

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[CrossRef]

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

Yoshimura, K.

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[CrossRef] [PubMed]

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Device structures. (a)A schematic and (b)a photograph of the chaos laser chip.

Fig. 2
Fig. 2

The layer structures of the cross section in (a)the active region (DFB, SOAs, PD), and (b)the passive region. The grating is fabricated only for DFB part. MQW, multi-quantum well; W, ridge width; H, ridge height.

Fig. 3
Fig. 3

L-I characteristics for ridge height 1.8 μm (the red curve) and 1.7μm (the blue curve). The threshold current Jth is estimated to be 13mA.

Fig. 4
Fig. 4

Schematic of a test device used for the gain measurement. DFB, SOA, and two PDs (PD1 and PD2) are monolithically integrated with a passive waveguide (Passive WG), and the width of the waveguide is the same as that of the chaos laser chip.

Fig. 5
Fig. 5

Biasing current dependences of the gain for 200μm-long SOA (a) and 100μm-long SOA (b). DFB current is fixed at 22mA (about 1.7times of the threshold current).

Fig. 6
Fig. 6

Optical feedback power ratios vs. the injection currents to SOA1. The injection currents to SOA2 were fixed to 0 mA(blue curve), 3 mA(green curve), and 6 mA(red curve).

Fig. 7
Fig. 7

Experimental setup for measuring chaotic waveforms.

Fig. 8
Fig. 8

The waveforms of the PD signals for JSOA1= (a)6 mA, (b)7 mA, (c)8 mA, (d)9 mA, (e)12 mA, (f)15 mA.

Fig. 9
Fig. 9

The radio-frequency spectra for JSOA1= (a)6 mA, (b)7 mA, (c)8 mA, (d)9 mA, (e)12 mA, (f)15 mA.

Fig. 10
Fig. 10

(a) Autocorrelation of the chaotic signals obtained for JDFB = 22 mA, JSOA1 = 15 mA, and JSOA2 = 6 mA. (b) Enlargement of the short-time autocorrelation.

Fig. 11
Fig. 11

Schematic diagram for random bit generation.

Tables (2)

Tables Icon

Table 1 Results of NIST Special Publication 800-22(rev. 1a) statistical tests. The tests have been performed using 1000 samples of 1 Mbit data and significance level α = 0.01. For the tests which produce multiple P-values and proportions, the worst case is shown

Tables Icon

Table 2 Typical results of “Diehard” statistical test suite. KS - Kolmogorov-Smirnov test. Significance level “α = 0.01”. For tests with multiple p-value, the worst case is shown

Equations (2)

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G = 1 T ap 2 P out P in .
P f = G 1 G 2 T ap 6 exp ( α p L p α pd L pd ) ,

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