CHAOS synchronization has been a hot topic, since the pioneer

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1 1978 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 28, NO. 13, JULY 1, 2010 Chaos Synchronization and Communication in Mutually Coupled Semiconductor Lasers Driven by a Third Laser Ning Jiang, Wei Pan, Lianshan Yan, Senior Member, IEEE, Bin Luo, Weili Zhang, Shuiying Xiang, Lei Yang, and Di Zheng Abstract We numerically investigate the chaos synchronization and message transmission between two mutual coupling semiconductor lasers (MCSLs) subject to identical unidirectional injections (UIs) from an external cavity semiconductor laser (ECSL). The synchronization between the MCSLs is realized through injection locking in conjunction with symmetric operation. The simulation results show that stable isochronal synchronization between the MCSLs can be achieved under proper driving injections. This type of synchronization is robust to parameter mismatch up to tens of percentage and frequency detuning of several tens of gigahertz, which is much better than those of the MCSLs systems with self-feedback. Moreover, the investigations on the mutual chaos pass filtering effects and the message transmission indicate that the isochronal synchronization allows mutual message exchange with a bit rate higher than 10 Gb/s, when the chaos modulation technology is adopted. In addition, the MCSLs can synchronize with the ECSL for proper UI and MC, which provides an opportunity for array chaos synchronization and chaos communication networks. Finally, leader/laggard synchronization can also be achieved in the proposed system. Index Terms Chaos synchronization, mutual chaos pass filtering (CPF), Q-factor, semiconductor laser (SL). I. INTRODUCTION CHAOS synchronization has been a hot topic, since the pioneer work of Pecora and Carroll [1] for its potential applications in secure communications, neural networks, and public channel cryptography [2] [10]. In optical communication systems, semiconductor laser (SL) is a good candidate for optical chaos communication for its rich nonlinear dynamics and easy operation [4] [6], [11]. The advantages of optical chaotic carrier generated by SLs, include wide bandwidth, high security, and easy to implement. For instance, several methods, such as Manuscript received November 24, 2009; revised March 24, 2010, May 07, 2010; accepted May 13, Date of publication May 27, 2010; date of current version June 28, This work was supported in part by the National Natural Science Foundation of China under Grant , in part by the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant , and in part the Doctoral Innovation Talent Foundation of Southwest Jiaotong University (2009). N. Jiang, W. Pan, L. Yan, B. Luo, S. Xiang, L. Yang, and D. Zheng are with the Center for Information Photonics and Communications, Southwest Jiaotong University, Chengdu , China ( swjtu_nj@163.com; weipan80@sina.com). W. Zhang is with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore ( daduoer@126.com). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /JLT optical feedback, optical injection, and optoelectronic feedback, can be adopted to generate chaotic carrier [4] [6], [11] [13]. The general concept of message transmission based on the chaos synchronization is that a message is modulated onto or into the noise-like output of the chaotic transmitter laser, and recovered in virtue of chaos pass filtering (CPF) effect at the receiver end. Recent field experiment in Athens (Greece) has confirmed the feasibility and potential of this technique [12]. On the other hand, more and more studies are being conducted on mutual coupling SLs (MCSLs) systems and various phenomena have been reported [13] [22]. For the face-to-face MCSLs, it is difficult to get stable isochronal synchronization, and the well-defined leader/laggard synchronization needs some detuning between the MCSLs, which makes the bidirectional messages exchange more complicated [17]. Recently, Klein et al. demonstrated that stable isochronal synchronization can be achieved by adding individual self-feedback (SF) to each MCSL [18]. Chiang et al. theoretically demonstrated the general synchronization conditions for MCSLs systems with feedback, and experimentally verified them using an optoelectronic feedback scheme [19]. More recently, Vicente et al. proposed a leader/laggard synchronization scheme in two MCSLs with a partially transparent mirror in between, and discussed its potential application in simultaneous bidirectional message transmission [20]. The chaos synchronization in these schemes is based on the symmetric operation, which is different from the injection locking that is the physical mechanism of the generalized synchronization (GS) in the master slave chaos systems [12], [21]. Zhang et al.[22] provided a synchronization scheme in the face-to-face MCSLs system with the extremely unsymmetrical bidirectional injections. Moreover, chaos synchronization in MCSLs systems with cascade configuration has also been investigated based on the symmetric operation mechanism [23], [24]. Recently, Zhou and Roy proposed a stable isochronal synchronization scheme between two MC Ikeda ring oscillators, which are symmetrically driven by a third Ikeda oscillator [25]. In this type of MC system, the injection-locking mechanism is adopted additionally, and the isochronal synchronization can be achieved more stable. However, there has not been a thorough investigation on the synchronization-related issues for the SL configurations yet. Moreover, in this type of complicated SL configurations, several issues, such as synchronization conditions, synchronization types, and system encryption performances, motivate further investigation. In this paper, we systematically investigate the chaos synchronization and communication of two MCSLs driven by /$ IEEE 转载

2 JIANG et al.: MUTUALLY COUPLED SEMICONDUCTOR LASERS 1979 Fig. 1. (a) Schematic of the chaos communication in MCSLs subject to injections from a chaotic ECSL. SL: semiconductor laser, EM: external mirror, M: mirror, CA: coupling attenuator, OI: optical isolator, BS: beam splitter, m(t): message, m (t): decrypted message, and m: modulator. (b) Bifurcation diagrams of the output of SL1 versus the UI strength (k ) for four different MC strengths corresponding to the MC from weak to strong (the corresponding results of SL2 are similar). a chaotic ECSL. The outlines of the paper are as follows. Section II describes the theory and model of the chaotic system based on the Lang Kobayashi equations. In Section III, the characteristics of the chaos synchronization are demonstrated, and the influences of mismatch and detuning on the synchronization performance are also studied. Section IV investigates the CPF effects of the system, and presents the message transmission process. Section V offers a rudiment discussion of the synchronization between the MCSLs and the driver SL, and also, the achievement of leader/laggard synchronization is discussed. Finally, a basic conclusion is given in Section VI. II. SYSTEM MODEL AND RATE EQUATIONS The theoretical diagram is illustrated in Fig. 1(a). The system is consisted of two MCSLs (SL1 and SL2) and a driver SL (SL3). The output of SL3 is rendered chaotic by the reflection of an external mirror (EM), and the chaotic output is unidirectionally injected into SL1 and SL2 through a beam splitter (BS) which equally separates the injection light from SL3 into SL1 and SL2. Hence, the dynamics of the MCSLs are determined by the joint effects of their mutual interaction and the unidirectional injection (UI) from SL3. The coupling attenuator (CA) is used to control the MC strength between the MCSLs. With the symmetrical MCs and identical UI from the driver SL, the evolutions of the MCSLs are identical. Since the UI from SL3 is chaotic, the nonlinear dynamics of the MCSLs is enhanced, such that the MCSLs can readily operate in a chaotic regime, as shown in Fig. 1(b). It is worth noting that the outputs of the MCSLs are still chaotic, even when the UI and the MC are weak which guarantee the feasibility of the chaos-based communication in the proposed system. For numerical purposes the modeling of the MCSLs subject to external injections from SL3 is performed by the Lang- Kobayashi equations according to [20], [24, [26], which take into account the UI and MC terms. For SL1 and SL2, we have (1) (2) SL3 is a conventional ECSL, which is modeled as (6) (7) (8) (9) (10) (11) where the subscripts 1, 2, and 3 denote the SL1, SL2, and SL3, respectively. is the complex amplitude of the optical field, is the carrier number of inner cavity,, and are the UI phase from SL3 to SL1 (SL2), the MC phase between SL1 and SL2, and the SF phase of SL3, respectively. is the operation frequency, is the linewidth enhancement factor, is the photon lifetime, is the carrier lifetime, is the differential gain, is the gain suppression factor, is the carrier number at the transparency, and is the spontaneous emission rate. is the injection strength from SL3 to SL1 and SL2, and is the corresponding injection delay. is the MC strength from SL1 (SL2) to SL2 (SL1), and is the corresponding coupling delay. is the feedback strength of SL3, and is the external cavity round-trip time of SL3. is the detuning frequency between SL1 and SL2, is the detuning frequency between SL3 and SL1, and is the detuning frequency between SL3 and SL2. Besides, the spontaneous emission processes are considered by introducing independent Gaussian white noise sources with zero-mean and correlation [17]. With identical injections from SL3, the synchronization condition between SL1 and SL2 becomes (3) (4) (5) (12)

3 1980 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 28, NO. 13, JULY 1, 2010 This is the general condition for existence of synchronization solution in the system, which can be fulfilled if (13) (14) (15) To evaluate the synchronization quality, we define the crosscorrelation function (CCF) as [27] Fig. 2. (a) Maximum of the CCF between the MCSLs as a function of the MC and the UI strengths. (b) Influence of the MC and UI strengths on the lag time at which the maximum of the CCF of SL1 SL2 appears, wherein the symbol tc stands for the lag time 5 ns (or 05 ns). (16) where denotes the time averaging, the subscripts 1 and 2 represent SL1 and SL2, respectively, is the time that the output of SL1 is shifted with respect to that of SL2, and is the photon number, which is equals to. Next we use the fix-step fourth-order Rung Kutta method to handle the mathematical model (1) (4), to investigate the chaos synchronization performance and communications between the MCSLs. In our simulations, the initial conditions of the three SLs are chosen to be different to investigate if the synchronization solution is physically relevant. All parameters used in the simulations are chosen as Hz, ns, ps, ns ma, ns ns, ns, and ns [26], [28]. III. ISOCHRONAL SYNCHRONIZATION With the synchronization conditions presented in (12) (15), there is only isochronal synchronization solution for the system (1) (2). A. Performance of Chaos Synchronization First, we investigate the influences of the MC strength and the UI strength on the isochronal synchronization. Fig. 2(a) depicts the maximum of the CCF of SL1 SL2 in the MC strength and the UI strength space. High-quality isochronal synchronization can be achieved as long as the UI strength is properly large for each of the MC strength. The stronger the MC, the stronger UI is needed to achieve stable isochronal synchronization. Fig. 2(b) shows the lag time at which the maximum of CCF appears as a function of the MC strength and the UI strength. It is indicated that the maximum of the CCF does not always appear at zero-lag. For the case of weak UI, the maximum of the CCF appears at 5 ns or ns by chance, which is because that under this condition the proposed system is similar to the face-to-face configuration in [17]. Moreover, the values of cross correlation are relatively small, such that we cannot treat the outputs of the MCSLs as being synchronized. Therefore, under such a scenario the message transmission between SL1 and SL2 is not feasible. The physical mechanism of the isochronal synchronization is mainly based on the competition between the mutual interaction and injection-locking effect. In the face-to-face configuration, there is only mutual interaction between the MCSLs. Starting from different initial conditions, each SL continuously receives a different signal, then it is difficult to achieve stable isochronal synchronization without external driving motions [17]. However, in the proposed system each MCSL continuously receives identical injection from SL3, which attempts to drive the evolutions of the MCSLs approaching to that of SL3. When the MC is weak relative to the UI, the effect of injection locking is stronger than that of the mutual interaction, and the isochronal synchronization would be easily obtained [see the left part of Fig. 2(a)]. Conversely, if the MC is too strong relative to the UI, the effect of the mutual interaction is stronger than the injection-locking effect, which makes the MCSLs system similar to the conventional face-to-face configuration. Thus, the correlation between the MCSLs is weak [see the right part of Fig. 2(a)]. Nevertheless, the negative effect of the MC can be overcome as long as the UI is properly strong, and stable isochronal synchronization would be achieved. Previous studies have shown that stable isochronal synchronization in MCSLs with SF is available. In those systems, the isochronal synchronization requires that the values of the feedback parameters are in the vicinity of those of the MC [18], [27], which limits the operation regime of stable isochronal synchronization. However, in the present scheme, the synchronization conditions are relaxed. Isochronal synchronization can be achieved for any MC strength as long as the UI is properly strong. Furthermore, compared with the case, where the spontaneous emission noise is neglected, the isochronal synchronization is robust to the spontaneous emission noise. B. Influence of Mismatch and Detuning Since the parameter mismatch is unavoidable in practical applications, it is necessary to investigate the mismatch robustness of the isochronal synchronization between the MCSLs. In Fig. 3, the synchronization performance versus the variation of the mismatch between SL1 and SL2 is presented. Here, the mismatch is induced by increasing the, and parameters and decreasing the, and parameters of the SL2 by the same amount as in [29]. We discuss four different MC strengths corresponding to the MC from weak to strong. The UI strength is fixed to 60 ns to guarantee high-quality isochronal synchronization for each case of MC. Obviously, the isochronal synchronization can tolerate relatively large (tens of percentage) parameter mismatch, even though the synchronization quality

4 JIANG et al.: MUTUALLY COUPLED SEMICONDUCTOR LASERS 1981 Fig. 3. Influence of parameter mismatch between the MCSLs on the quality of the isochronal synchronization. The circle, diamond, square, and triangular curves denote the results for k = k =1ns ; k = k =10ns ; k = k = 20ns, and k = k = 30ns, respectively. The gray line stands for the result of the isochronal synchronization in MCSLs with SF, where the MC parameters (k ; ) and feedback parameters (k ; ) are chose as k = k =20ns and = =5ns. Fig. 4. Influence of the frequency detuning between the MCSLs. The solid curves denote the proposed scheme, and the dashed ones stand for the case with SF. Parameters: (a) k = k = 1ns ; k = k = 1ns ; (b) k = k =10ns ;k = k =10ns ; (c) k = k =20ns ;k = k = 20 ns ; and (d) k = k =30ns ;k = k =30ns. The UI strength is set to k =60ns. is degraded gradually as the increase of mismatch. Also, it is found that the stronger the MC is, the faster the degradation of synchronization quality is; in other words, the stronger the MC is, the narrower the mismatch robustness regime is. Moreover, compared with the mismatch robustness of the isochronal synchronization in MCSLs with SF (gray), it is found that the mismatch robustness in the proposed scheme has been enhanced greatly. The operation wavelength of SL is sensitive to temperature and external perturbations, which may also degrade the symmetry of the MCSLs. Thus, it is valuable to investigate the influence of frequency detuning on the isochronal synchronization. The influence of the frequency detuning between the MCSLs is shown in Fig. 4 (solid). It is indicated that the sensitivity of the isochronal synchronization to the frequency detuning is high because of the symmetry breaking. However, there is a slow degradation regime before that the isochronal synchronization is collapsed fastly. When the MC is weak, as shown in Fig. 4(a) and (b), the regime is wider than those of stronger MC cases shown in Fig. 4(c) and (d). On the other hand, the similar investigations for the scenario, where the SF is used to achieve stable isochronal synchronization are also demonstrated here (dashed). The MC parameters and the feedback parameters are chosen to be identical to achieve good synchronization [18], [28]. The comparison between these two cases indicates that the robustness of the isochronal synchronization in this paper is much better, especially when the MC is weak. We attribute the robustness enhancement to the injection-locking effect induced by the UI from SL3. With this injection-locking effect, some small symmetry breaking induced by the mismatch or detuning between the MCSLs can be compensated as that in common master slave systems [21], whereas in the SF case, the symmetry breaking continuously affects the evolutions of the MCSLs, which results in the fast degradation of the synchronization. Moreover, since the injection-locking properties depend on the frequency detuning between the MCSLs and SL3, we present the influence of this kind of frequency detuning in Fig. 5. Apparently, the isochronal synchronization can tolerate a frequency detuning of several tens of gigahertz. By comparing with the results when the spontaneous emission noise is ignored, we find that the synchronization degradation and fluctuations are attributed to the symmetry breaking induced by the spontaneous emission noise. In the noiseless simulations, we find the isochronal synchronization can be perfectly maintained in the overall range of values considered for this detuning, which is in line with the corresponding result of [22]. With the mismatch robustness and the detuning tolerance characteristics, the proposed system may be extended to achieve chaos synchronization of lasers array. A. Mutual CPF Effects IV. CPF AND MESSAGE EXCHANGE To implement secure message transmission successfully, only synchronization between the transmitter laser and receiver laser is not sufficient. The message transmission needs to meet another essential condition: the receiver is insensitive to small perturbations added on the chaotic carrier transmitted from the transmitter laser. This phenomenon is the so-called CPF effect. The stronger the CPF effect is, the easier the recovery of message is. Here, the perturbations are two small amplitude sinusoidal signals. They are added to the outputs of SL1 and SL2 through external modulation [22], which is described as mathematically, wherein stands for the modulated chaotic carrier (including the perturbation part), is the output of the SLs, is the modulation index, and is the modulation frequency. In Fig. 6, we plot the spectra

5 1982 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 28, NO. 13, JULY 1, 2010 Fig. 7. Illustrations of message exchange. (a) Decryption process at the end of SL1, wherein the dashed curve stands for the original message encrypted by SL2, and the solid one denotes the recovery message of SL1. (b) Decryption process at the end of SL2, wherein the dashed curve stands for the original message encrypted by SL1, and the solid one denotes the recovery message of SL1. The coupling parameters are identical to those of Fig. 6. Fig. 5. Influence of the frequency detuning between the MCSLs and SL3. Parameters: (a) k = k = 1ns ; (b) k = k = 10ns ; (c) k = k =20ns ; and (d) k = k =30ns. Fig. 6. Illustrations of CPF. (a) SL1 is transmitter. (b) SL2 is transmitter. (c) and (d) Both SL1 and SL2 are transmitters and receivers simultaneously. Coupling parameters: k = k =20ns and k =40ns. of power difference between the modulated carrier of transmitter and the output of receiver [ for three different cases: only SL1 is used as transmitter [see Fig. 6(a)], only SL2 is used as transmitter [see Fig. 6(b)], and both MCSLs are used as transmitters and receivers simultaneously [see Fig. 6(c) and (d)]. The modulation index is set to 0.07, and the frequencies of the sinusoidal signals modulating the outputs of SL1 and SL2 are GHz and GHz, respectively. It is obvious that no matter the number of transmitters is one or two, there is an apparent peak at in the spectra of output difference, i.e., the corresponding receiver is insensitive to the perturbation added on chaotic carrier of the transmitter, and the CPF effect is strong at the modulation frequency. Comparing Fig. 6(a) with (c), we find that the peak at the modulation frequency of SL1 is not greatly affected by the modulation of the SL2, and so does the case of SL2. Thus, the CPF of SL1 is independent with that of SL2, which means that bidirectional message transmission is achievable. This type of CPF is called as mutual chaos filtering (MCPF) effect [27], [30]. B. Message Transmission So far, we have observed high-quality isochronal synchronization and strong MCPF effects between the MCSLs. Next, we investigate the performance of message transmission by simulating the encryption/decryption process. Several encryption/ decryption schemes have been used in chaos communication applications, such as chaos masking (CMA), chaos modulation (CMO), chaos shift keying (CSK), and chaos phase-shift keying (CPSK) [20], [21], [29], [31] [33]. Here, we adopt the CMO scheme as the encryption/decryption scheme, which can provide better decryption performance, as proved in [34]. In such a scheme, the chaotic carrier (without message) is modulated by the message, and then, transmitted to the receiver laser. At the receiver end, the message recovery is realized by taking the difference between the chaotic carrier (without message) generated by the receiver and the injection (with message) from transmitter, as shown in Fig. 1(a). Fig. 7 shows the bidirectional encryption/decryption processes between SL1 and SL2. Here, the messages encrypted by SL1 and SL2 are two random binary sequences (RBSs) with bit rates Gb/s and Gb/s, respectively. The modulation index is set to 0.07, which guarantees that the messages are well hidden in the noise-like carriers, and the synchronization quality is not degraded (the cross-correlation coefficient ). Fig. 7(a) shows the original message coded by SL2 (dashed) and the corresponding recovery message at SL1 end (solid). The recovered message is filtered by a low-pass fifth-order Butterworth filter with a bandwidth of 0.6. Similarly, Fig. 7(b) presents the decryption process at the SL2 end. Apparently, each MCSL can decrypt the message transmitted from the counterpart laser successfully. To investigate the communication performance in a wider range of the bit rate, Fig. 8(a) presents the variations of Q-factor of the messages recovered by the two MCSLs versus the transmission rate (the circle and triangle curves). Here, the definition of Q-factor is identical to that in [35], and each point is the average of Q-factor values for three different pairs of RBSs transmissions. Obviously, acceptable decryption performance with Q-factor values greater than 5 can be maintained, when the bit rate is lower than 15 Gb/s, even though the Q-factor is degraded

6 JIANG et al.: MUTUALLY COUPLED SEMICONDUCTOR LASERS 1983 Fig. 8. (a) Estimation of Q-factor values of the decoded and encrypted messages for different bit rate. (b) (g) Eye diagrams of messages recovered by SL1 for (b) R =1Gb/s, (c) R =5Gb/s, (d) R =10Gb/s, (e) R =12Gb/s, (f) R =16Gb/s, and (g) R =20Gb/s. The inset shows the time traces of the encrypted message (black) and the corresponding original message (red) of SL1, when the bit rate is chosen as 2 Gb/s. The coupling parameters are identical to that of Fig. 6. Fig. 9. Illustrations of the spectrum of the output of SL1. The coupling parameters are identical to those of Fig. 8. [37], [38]. Therefore, high bit rate message transmission based on the proposed scheme is feasible. V. DISCUSSION gradually as the bit rate increases. Fig. 8(b) (g) present a set of eye diagrams of the messages recovered by SL1 for six different bit rates. The eyes close gradually as the bit rate increases, which qualitatively agree with the results shown in Fig. 8(a). The results are similar when recovered messages of SL2 are considered. Moreover, we find that a part of the messages can also be decrypted when the bit rate is greater than 15 Gb/s, but the bit error rate increases greatly, as shown in Fig. 8(f) and (g). On the other hand, we also present the encryption quality versus the bit rate (dashed curves) in Fig. 8(a). Here, the encryption quality is indicated by the Q-factor of the encrypted message after filtering the modulated carrier (combined signal of chaotic carrier and message), which is filtered with a fifth-order Butterworth filter with cutoff frequency equal to the bit rate, as in [36]. Obviously, the Q-factor of the encrypted message is rapidly degraded to a small value that corresponds to high-encryption quality as the bit rate increases. By investigating the time traces of the encrypted messages, we find that the filtered encrypted message is hardly distinguishable when the bit rate is higher than a limited bit rate [such as the inset of Fig. 8(a)]. Moreover, the Q-factor of the encrypted message is much smaller than that of the decoded message. Therefore, the system affords efficiently encrypted message transmission with high-decoding efficiency in a wide range of bit rates. In the proposed system, since the synchronization between the chaotic carriers is always maintained with the MCPF procedure, the maximum transmission rate is mainly restricted by the efficient bandwidths of the chaotic carriers for the CMO technique. Fig. 9 shows the fast Fourier transform (FFT) of the output of SL1 (the results is similar when the output of SL2 is considered). It is indicated that the efficient bandwidth is 15.1 GHz, which qualitatively agrees with the maximum transmission rate for acceptable decryption performance shown in Fig. 8(a). Here, the efficient bandwidth is defined as the low-frequency span between the dc and the frequency, where 80% of the energy is contained within [37]. The efficient bandwidth is much higher than the relaxation oscillation frequency of solitary SL at 3.08 GHz because of the enhancement of the external optical injections (including both UI and MC as mentioned earlier) A. Transition From Synchronization of the Two Lasers to Three Laser Case In the aforementioned sections, we only concentrate on the isochronal synchronization between the MCSLs, while the synchronization between the two MCSLs (SL1 and SL2) and the driver SL (SL3) is not investigated. Fig. 10 shows the maximum of the CCFs between SL1 and SL3 as a function of the UI strength (the results are similar when those of SL3 SL2 are studied). We consider four different MC cases corresponding to the MC from weak to strong. Comparing the results with that of Fig. 2, we find that the MCSLs have synchronized with each other before they synchronize to SL3 for an identical MC strength. Consequently, the synchronization between the MCSLs and SL3 is similar to that of the common master slave systems [4], [11]. For weak MC cases (dashed blue and solid blue), two types of synchronization, namely complete synchronization (CS) and GS, can be achieved through symmetric operation and injection locking, respectively. The CS occurs when the sum of the MC and UI strengths equal to the feedback strength of SL3, while the GS occurs when the UI is properly strong. For the strong MC cases (red and black), only GS is available through injection locking as the UI strength continues to increase. It is worth noting that when the MC is identical to the feedback of SL3, the GS would be achievable without the strong UI requirement, and the synchronization quality is improved with respect to the cases with. This is because under this condition the subsystem SL3 SL1 (or SL3 SL2) is similar to the close-loop configuration in [39], where the slave SL can be locked to the master laser with moderate injection. We name this type of synchronization as optimum GS (OGS). We have repeated the simulations with different MC strengths, and found that the OGS can be achieved when the MC strength is in the vicinity of the feedback strength of SL3. The insets present the temporal intensity traces of the three SLs for CS with ns ( ns ) and OGS with ns ( ns ). For the CS case, the output of SL3 is identical to those of SL1 and SL2. For the OGS case, SL3 leads the two MCSLs by 5 ns that equals to the UI delay. These phenomena qualitatively agree with those

7 1984 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 28, NO. 13, JULY 1, 2010 Fig. 11. (a) Temporal traces of the outputs of SL1 (black) and SL2 (gray). The trace of SL1 has been shifted vertically to distinguish from that of SL2. The inset shows the CCF between the outputs of the MCSLs. (b1) Original message coded by SL2 (dashed) and the recovered message of SL1 (solid). (b2) Original message coded by SL1 (dashed) and the recovered message of SL2 (solid). The messages are two RBSs with a bit rate of 1 Gb/s. Fig. 10. Maximum of the CCFs of SL1 SL3 for four different MC strengths: k = k = 1ns (blue dash), k = k = 5ns (blue solid), k = k = 20ns (red solid), and k = k = 30ns (black solid). Insets: (a) temporal traces for CS with k = k =1ns and k =19ns and (b) temporal traces for OGS with k = k =20ns and k =40ns, wherein the trace of SL3 has been shifted by 5 ns horizontally to compare with those of SL1 and SL2. In both insets, the traces of SL1 (black) and SL3 (red) have been shifted vertically to distinguish from that of SL2 (green). of common master slave systems in [4] and [11]. With the synchronization of the three lasers, the proposed system can be used to achieve chaos communication network. B. Leader/Laggard Synchronization As mentioned earlier, the isochronal synchronization is realized through the joint effects of injection-locking and symmetric operation, which requires that the UI strength and the corresponding delay from SL3 to SL1 should be identical to those from SL3 to SL2. In fact, even the UI delays are different, with the injection-locking effect of the UIs the evolutions of SL1 and SL2 would also asymptotically approach to that of SL3 in the manner of and, wherein is the UI delay from SL3 to SL1(SL2). Then, another type of synchronization, namely leader/laggard synchronization, would be achieved. Fig. 11(a) shows the temporal intensity traces of the MCSLs and the corresponding CCF between them for the leader/laggard synchronization. Here, the UI delays are chosen as ns and ns, while the UI strength and MC strength are set to ns and ns, respectively. The other parameters are identical to those mentioned earlier. Under such conditions, SL1 synchronize with SL2, and leads SL2 by 2 ns. Repeating simulations with different sets of UI delays have indicated that similar results can be obtained, and the lag time between the MCSLs is determined by, i.e., the MCSL closer to SL3 would lead its counterpart, and vice versa. Moreover, we find that the influence of the UI and MC strengths on the performance of this type of synchronization is similar to that of the isochronal synchronization shown in Fig. 2. However, because the UIs are asymmetrical under this scenario, the operation regime for stable leader/laggard synchronization is narrower than that of the isochronal synchronization. For an identical MC strength, the leader/laggard synchronization calls for stronger UI than the isochronal synchronization. Furthermore, the decryption process of the leader/laggard synchronization is more complex than that of the isochronal synchronization. The output of the leader SL needs to be delayed to guarantee the synchronization of carriers and message bits. The message, sent from SL1 to SL2, is recovered by SL2 via a mutual CPF procedure, in the manner of. Similarly, the message, sent from SL2 to SL1, is recovered by SL1 in virtue of. Fig. 11(b1) and (b2) presents the mutual message exchange process between the MCSLs, which shows that the leader laser (SL1) can recover the message transmitted from the laggard laser (SL2) in real time, whereas the laggard laser (SL2) recovers a delayed message [see Fig. 11(b2)]. VI. CONCLUSION We have demonstrated the synchronization and message transmission between two MCSLs driven by an ECSL with identical UIs. With the joint effects of the UI and the mutual interaction, the MCSLs synchronize with each other isochronally in a large operation regime. Moreover, the investigations on mismatch robustness and detuning tolerance show that the isochronal synchronization is robust to relatively large mismatch and detuning. Message transmissions between the MCSLs with the MCPF effect indicate that bidirectional message exchange with a bit rate higher than 10 Gb/s is achievable, when the chaos modulation is used as the encryption/decryption scheme. Furthermore, with proper selection of the UI and MC, the MCSLs can synchronize with the ECSL completely or laggardly through symmetric operation or injection locking. Also, leader/laggard synchronization and corresponding message transmission can be achieved when the UI delays are different. The demonstrated scheme has the potential to be used as a basic topology of chaos communication networks and array chaos synchronization system. REFERENCES [1] L. M. Pecora and T. L. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett., vol. 64, no. 8, pp , Feb

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Quantum Electron., vol. 38, no. 9, pp , Sep Ning Jiang was born in Sichuan, China, in He received the B.S. degree from the University of Electronic Science and Technology of China, Chengdu, China, in He is currently working toward the Ph.D. degree from the Southwest Jiaotong University, Chengdu. His dissertation work focuses on the nonlinear dynamics of semiconductor lasers and chaotic optical communication. Wei Pan was born in Hunan, China, in He received the Ph.D. degree in communication engineering from the Southwest Jiaotong University, Chengdu, China, in He is currently a Professor and the Dean of the School of Information Science and Technology, Southwest Jiaotong University. He has authored or coauthored more than 100 research papers. His research interests include semiconductor lasers, nonlinear systems, and optical communications. Prof. Pan is a member of the Optical Society of America and the Chinese Optical Society.

9 1986 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 28, NO. 13, JULY 1, 2010 Lianshan Yan (S 99 M 05 SM 06) received the B.E. degree from Zhejiang University, Hangzhou, China, and the Ph.D. degree from the University of Southern California, Los Angeles, CA. He is currently a Professor with the Southwest Jiaotong University, Chengdu, China, where he is the Chief of the Center for Information Photonics and Communications. Prof. Yan is a Senior Member of the IEEE Lasers and Electrooptics Society and a member of the Optical Society of America. Weili Zhang, biography not available at the time of publication. Shuiying Xiang, biography not available at the time of publication. Bin Luo was born in Hubei, China, in He received the Ph.D. degree in communication engineering from the Southwest Jiaotong University, Chengdu, China, in He is currently a Professor with the School of Information Science and Technology, Southwest Jiaotong University. He has authored or coauthored more than 80 papers. His research interests include semiconductor lasers, semiconductor optical amplifiers, and optical communications. Prof. Luo is a member of the Optical Society of America and the Chinese Optical Society. Lei Yang, biography not available at the time of publication. Di Zheng, biography not available at the time of publication.