We propose a novel wideband chaos generation scheme by using an external-cavity semiconductor laser (ECSL) subject to optical-electronic hybrid feedback. In this scheme, the output of ECSL is photo-detected and used to modulate the output of a continuous wave laser by an electro-optical phase modulator, the constant-amplitude self-phase-modulated light is then injected back into the ECSL. The experimental results indicate that, compared with the chaos generation with conventional optical feedback (COF), significant bandwidth enhancement is achieved in the proposed scheme. The effective bandwidth of generated chaos is increased from a few GHz to over 20 GHz, and moreover, the spectrum flatness and the complexity of generated chaos are also considerably improved. Furthermore, we propose a wideband chaos synchronization system based on the proposed chaos generation scheme. It is experimentally demonstrated that high-quality synchronization between two wideband chaos signals with an effective bandwidth greater than 20 GHz is achieved. This work simultaneously achieves the generation and the synchronization of wideband chaos, which shows valuable potential in chaos-based secure communication, such as enhancing the transmission capacity and improving the security.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Chaotic systems have attracted much attention in the last two decades, because of their advantages including noise-like waveform, unpredictability and wide-spectrum characteristics [1,2]. In particular, chaotic signal has been considered as a good candidate for providing physical layer security, and extensively investigated in secure optical communication [3–8]. For example, Argyris et al. demonstrated the first field experiment of optical chaos communication with a data rate of 2.4 Gb/s and a transmission distance of 120 km in the metropolitan area network of Athens . Larger et al. reported the first field trial of 10-Gb/s chaos communication in a 100-km optical fiber link . Yi et al. experimentally demonstrated 30-Gb/s secure transmission over 100 km standard optical fiber, using a chaotic carrier with a bandwidth of 10 GHz .
In optical chaos communication systems, the message is encrypted into chaotic carrier at transmitter end and decrypted at the receiver on the basis of the synchronization of chaotic carriers. As that in conventional communication systems, the transmission capacity of chaos-based secure communication is limited by the bandwidth of chaotic carrier. The wider the bandwidth of chaotic carrier, the higher transmission rate it supports. In addition, the bandwidth enhancement of chaotic signal also determines the performance of its applications in the physical random number generation [9–11] and secure key distribution [12,13]. To enhance the bandwidth of chaos, several methods have been reported in recent years, in virtue of optical injection [14,15], mutual injection , fiber propagation , feedback with parallel-coupling ring resonators , heterodyning couplings [19,20], and self-phase-modulated feedback with microsphere resonator or delay-interference [21,22]. Nevertheless, these works mainly focused on the bandwidth enhancement of chaos, there are few experimental demonstrations of synchronization of wideband chaos with a bandwidth beyond 20 GHz so far.
In this paper, we propose and demonstrate a new wideband chaos generation scheme using an external-cavity semiconductor laser (ECSL) subject to constant-amplitude self-phase-modulated optical injection originated from a continuous-wave laser (CWL), and demonstrate a wideband chaos synchronization system on the basis of the proposed chaos generation scheme. The generation and synchronization of wideband chaos with an effective bandwidth exceeding 20 GHz are experimentally achieved simultaneously.
2. Experimental setup
Figure 1(a) illustrates the experiment setup of the proposed wideband chaos generation scheme. The output of an ECSL is split into two parts by a 50:50 fiber coupler (FC). One part of the tapped light is converted as an electronic signal by a photodetector (PD1), and then amplified by a radio frequency (RF) amplifier. Subsequently, the electronic signal is used as the driving signal of a phase modulator (PM), to modulate the output of a CWL. The constant-amplitude phase-modulated light is then injected into the ECSL via an optical circulator (OC). The injected optical power is tuned by a variable optical attenuator (VOA1), and the polarization state of the injection light is adjusted by a polarization controller (PC). The other part of the tapped light is used as the output of the proposed wideband chaos generation system after detected by PD2. We also compare the proposed wideband chaos generation system with a conventional chaos generation system, in which an ECSL is subjected to conventional optical feedback (COF) [2,3]. The experimental setup of the COF scenario is illustrated in Fig. 1(b). The output of an ECSL is divided into two parts by a 20:80 FC. Twenty percent of the tapped light is sent back to the ECSL through an OC, while the other 80% is detected by a PD for the analyses of time series and power spectra. A VOA is utilized to adjust the feedback strength which is defined as the power ratio of the feedback light to the ECSL output, and a PC is used to control the polarization state of the feedback light. Here the feedback strength is fixed at a typical value of −15 dB [21,22]. In Figs. 1(a) and 1(b), the ECSLs are a same distributed-feedback (DFB) laser, and its bias current and temperature are monitored by a current-temperature controller. The threshold current of the DFB laser is 8.8 mA, and the bias current is set as 15.2 mA. The central wavelengths of the ECSL and CWL are set to 1549.6 nm and 1549.66 nm, respectively. The injected power from the CWL is −3 dBm. The bandwidths and responsivities of all the PDs are 30 GHz and 1200 V/W, respectively. The maximum power gain of the RF amplifier is 35 dB with an operation voltage of 15V. The bandwidth of PM is 20 GHz, and its half-wave voltage is 3.8 V. All the electronic signals are measured and recorded by a digital oscilloscope with a bandwidth of 25 GHz and a real-time sampling rate of 100 GS/s.
3. Experimental results and discussions
Figure 2 presents the temporal waveforms and power spectra of the chaos generated by the COF scenario (first row), and the proposed chaos generation scheme (second row). Here, the effective bandwidth is adopted to quantify the bandwidth of chaotic signals, which is defined as the span between the direct current (DC) component and the frequency where 80% of energy is contained in the power spectrum [14–20]. In the experiment, the peak-to-peak amplitude of the PM driving signal is approximately 6.8 V, thus the corresponding maximum modulation depth is about 1.8. For the chaos obtained by the COF scenario, as shown in Fig. 2(b), because of the relaxation oscillation effect of ECSL, the power spectrum is obviously uneven and degrades rapidly with the increase of frequency. The corresponding effective bandwidth of this chaotic signal is 8.1 GHz only. Comparatively, for the chaotic signal generated by the proposed scheme, the results in both of the time and frequency domains are significantly improved. The temporal waveform in Fig. 2(c) is significantly denser than that of Fig. 2(a), and it shows a typical chaotic state with a random distribution of large amplitude values. Moreover, as shown in Fig. 2(d), the power spectrum is greatly broadened and becomes much flatter in comparison with that in Fig. 2(b). As a consequence, the corresponding effective bandwidth is enhanced up to 24.3 GHz, which is greater than three times that of the COF-generated chaos. The reason for the achievement of bandwidth enhancement is attributed to that, the chaotic phase modulation induces significant spectrum-expansion effect as demonstrated in our previous works [22,23], and then the low-filtering effect of ECSL converts the phase-modulation into the intensity-modulation [12,24]. It is noteworthy that, since the bandwidth of the oscilloscope used in the experiment is 25 GHz, the calculated effective bandwidth actually reaches the maximum value of the measurement. In addition, since the security of chaotic system is affected by the complexity of chaos, we also compare the complexities between the generated chaotic signals, which are quantified by permutation entropy (PE) as reported in [14,25]. Here, 2×105 data points are used to calculate the PE with an embedding dimension of 6. The closer the PE value is to 1, the higher the complexity of chaos is. The PE of the COF-generated chaos is calculated to be 0.85, while that of the chaos obtained in the proposed scheme is as high as 0.98. The above comparisons indicate that the significant bandwidth enhancement and the complexity enhancement of chaos are simultaneously achieved in the proposed chaos generation scheme.
To further investigate the bandwidth characteristic, Figs. 3(a) and 3(b) present the influences of two critical parameters in the proposed chaos generation scheme on the effective bandwidth: one is the injected optical power of the ECSL (refer to Fig. 1(a)), and the other is the modulation depth of the PM. Here, the variation of PM modulation depth is reflected and achieved by adjusting the attenuation of VOA2, the modulation depth decreases with the increase of the attenuation. As depicted in Fig. 3(a), the effective bandwidth gradually increases from 10.82 GHz, and reaches to a stable level at approximately 24.3 GHz, as the injected power increases from −13 dBm to −3 dBm. The evolution trend in Fig. 3(b) is opposite to that in Fig. 3(a): the effective bandwidth decreases gradually from 24.3 GHz to 12.1 GHz with increasing the attenuation of VOA2. We also investigate the influence of the wavelength detuning between the CWL and ECSL on the effective bandwidth, as shown in Fig. 3(c). The effective bandwidth is larger than 24 GHz when the wavelength detuning is controlled in the range of −0.03 nm to 0.06 nm. The results indicate that, the proposed scheme can easily obtain wideband chaotic signal with an effective bandwidth larger than 20 GHz by properly choosing the parameters.
Next, we turn to investigate the synchronization performance of the generated wideband chaos. The experimental setup of the proposed chaos synchronization system is illustrated in Fig. 4. At the transmitter (Alice), the wideband chaotic signal is generated by ECSL1 which is subjected to the constant-amplitude self-phase-modulated optical injection originated from CWL1. Then after split by a 50:50 FC1, a portion of the ECSL1 output is sent to the receiver (Bob), where it is converted into an electronic chaotic signal by PD3 and amplified by RF2. Then the electronic chaotic signal is used as the driving signal of PM2. The phase-modulated light is injected into ECSL2, while VOA4 and PC2 are used to match the optical power and the polarization state of the injection light of ECSL2 to those of ECSL1. The outputs of ECSL1 and ECSL2 are detected by PDs, and then recorded by the oscilloscope for analyzing the synchronization performance. To eliminate the impact of the high-frequency noise of experimental electronic devices, the obtained chaotic signals are filtered by a digital low-pass four-order Butterworth filter with a cut-off frequency of 25 GHz (corresponding to the bandwidth of the oscilloscope). In the experiment, the devices used at the receiver (PDs, PM2 and RF2) are the same with those used at the transmitter. The central wavelengths of CWL1 and CWL2 are set to 1549.66 nm, and those of ECSL1 and ECSL2 are set to 1549.6 nm.
Figure 5 presents the synchronization performance of the chaotic outputs of Alice and Bob. As illustrated in Figs. 5(a) and 5(b), it can be seen that the temporal waveforms of the outputs of ECSL1 and ECSL2 show apparently similar fluctuations, which indicates that these two ECSLs are well synchronized with each other. In addition, the corresponding power spectra of these two chaotic signals are illustrated in Figs. 5(c) and 5(d), respectively. Both of the two power spectra are broad and very flat in a wide frequency range over 20 GHz. The effective bandwidths of these two chaotic signals are 22.1 GHz and 21.7 GHz, respectively. In order to exhibit the synchronization performance more intuitively, we adopt the frequently used cross-correlation (CC) coefficient to evaluate the synchronization quality, which is defined as [5–7,26,27]:
In practice, a mismatch of the parameters is inevitable, which would induce a degradation of the synchronization performance. The sensitivity of parameters mismatch is also highly related to the security of chaotic systems. In Fig. 6, we investigate the sensitivity of two parameters, the injected optical power of the ECSL and the PM modulation depth, by fixing these parameters of Alice and changing those of Bob. Here, the injected power of ECSL1 at the transmitter is fixed to −3 dBm, and the variation of modulation depth mismatch is reflected by adjusting the attenuation mismatch between VOA2 and VOA3. Similar phenomenon can be observed in Figs. 6(a) and 6(b): the CC value quickly decreases with increasing the mismatch value, while high-quality synchronization with a CC value of 0.95 can be achieved when the parameter mismatch is controlled in a minimal range. It is indicated that the synchronization performance is sensitive to the parameters mismatch, which is beneficial to improve the security of chaotic system .
In conclusion, a novel wideband chaos generation scheme has been proposed and experimentally demonstrated, in which an ECSL is subject to a constant-amplitude self-phase-modulated optical injection originated by a CWL. The experiment results indicate that, the proposed scheme can produce bandwidth-enhanced chaos with an effective bandwidth over 20 GHz, which is three times larger than the effective bandwidth of the COF-generated chaos. The spectrum flatness and the complexity of generated chaos are also improved. Furthermore, a wideband chaos synchronization system has been experimentally demonstrated based on the proposed chaos generation scheme. Synchronization of wideband chaos with an effective bandwidth larger than 20 GHz is achieved. The synchronization performance is sensitive to the mismatch of parameters, including the injected optical power of the ECSL and the PM modulation depth, while high-quality synchronization with a CC coefficient of 0.95 can be observed within a minimal parameters mismatch. We believe the proposed chaos generation and synchronization scheme has great potential to enhance the transmission capacity and the security of optical chaos communication in the future.
National Natural Science Foundation of China (61671119); Fundamental Research Funds for the Central Universities (ZYGX2019J003).
The authors declare no conflicts of interest.
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