## Abstract

Wavelength division multiplexing (WDM) transmission of chaotic optical communication (COC) and conventional fiber-optic communication (CFOC) is numerically confirmed and analyzed. For an 80-km-long two-channel communication system, a 1-Gb/s secure message in COC channel and 10-Gb/s digital signal in CFOC channel are simultaneously achieved with 100GHz channel spacing. Our numerical simulations demonstrate that the COC and CFOC can realize no-crosstalk transmission of 80km when the peak power of CFOC channel is less than 8dBm. We also find that the crosstalk between COC and CFOC does not depend on channel spacing when the channel spacing exceeds 100GHz. Moreover, the crosstalk does not limit channel number by comparing the synchronization performance of COC in four- and six-channel WDM systems.

©2009 Optical Society of America

## 1. Introduction

Many researches have been devoted to achieving chaotic secure communications since the idea of synchronization between two chaotic oscillators was proposed in early 1990s [1]. Compared with electrical chaos, optical chaos generated from lasers offers higher dimension, broader bandwidth and thus has attracted extensive attention in recent years. Optical chaos synchronizations have been implemented in many laser systems: gas laser [2], fiber laser [3], solid laser [4], semiconductor laser [5-8], and so on. As the chaotic transmitter and receiver, semiconductor lasers with optical feedback [5, 6, 9, 10] or optical injection [7-8] have been enthusiastically studied because they are the main light sources in conventional optical communication systems.

Up to now, Chaotic optical communication (COC) based on semiconductor lasers has been successfully demonstrated in a back-to-back configuration [5, 7, 8, 11] or short fiber transmission [12].To extend the distance of transmission, COC through long-distance optical fiber using semiconductor lasers with optical feedback has been theoretically studied [13, 14]. The effects of fiber transmission characteristics, such as dispersion and nonlinearity, on the performance of COC system are further investigated by a numerical simulation [15]. Although a field COC system was successfully implemented in 120-km commercial fiber-optic channel for 1-Gb/s transmission rate [16], COC sharing the existing fiber networks with conventional fiber-optic communication (CFOC) to realize the wavelength division multiplexing (WDM) transmission has not been reported so far.

In this paper, we numerically realize WDM transmission of COC and CFOC in fiber link. In addition, we investigate the inter-channel crosstalk between COC and CFOC and the dependence of COC and CFOC WDM system on channel spacing and channel number.

## 2. Theoretical model

The schematic diagram of COC and CFOC WDM transmission in our study is shown in Fig. 1. Each channel, defined by the wavelength of its carrier wave, is coupled into the same optical fiber in its original data format. The chaos cryptography technique encrypts some important information at a given WDM channel *λ*
_{C}. In COC system, transmitter (LD_{T}) and receiver (LD_{R}), both of which are composed of a single-mode semiconductor laser with an external reflector, have the same configuration. Transmitter laser (LD_{T}) emits a chaotic carrier and an optical isolator (ISO) is used to ensure unidirectional transmission. The original message is superposed on chaotic carrier by chaos masking (CMS). The CMS method is implemented by simply adding the message to the output chaotic carrier. The chaotic carrier encoded by message and multiple digital optical signals from lasers LD_{1}, LD_{2}, …, LD_{N} are launched together into the fiber via a WDM multiplexer (MUX), and separated by a WDM demultiplexer (DMUX) after long-haul transmission. An erbium-doped fiber amplifier (EDFA) is placed at the end of the fiber to compensate the fiber loss. The demultiplexed chaotic light is divided into two beams by a beam splitter (BS). One beam is injected into the receiver laser to achieve chaos synchronization. The other beam, as well as the output from the receiver laser, is separately detected by two identical photodiodes. The message can be extracted from the subtraction of the two detected signals.

The dynamics of the transmitter and receiver in COC system can be described by the following Lang-Kobayashi rate equations with optical feedback and injection terms [17]:

where *E* and *N* are the slowly varying complex electrical field amplitude and the carrier density in the laser cavity. Subscripts T and R represent the transmitter and receiver, respectively. *ωτ* is the round-trip phase shift induced by the external feedback, where *ω* is the angular frequency of the free-running laser and *τ* is the external cavity round-trip time. The field *E*
_{ext} is the input signal at the receiver and *I* is the pump current density of the semiconductor laser.

The feedback coefficient *k*
_{T,R} of the semiconductor lasers with optical feedback and the injection coefficient *k*
_{inj} from the transmitter to the receiver are defined as follows:

where *τ*
_{in} is the round-trip time in the laser cavity, *r*
_{0} and *r*
_{T,R} represent amplitude reflectivity of the laser exit facet and the external reflector respectively, *r*
_{inj} represents the percentage of the transmitter’s output electrical field amplitude injected into the receiver laser cavity. All the involved laser parameters and their values used in our numerical model are from [18].

For COC and CFOC parallel transmission, we first consider a two-channel WDM system (each subscript denotes the channel number). The light propagation through the fiber is described in terms of the well-known nonlinear Schrödinger equation [19].

Here *j*, *k* is chosen to be 1, or 2. *A _{j}* is the slowly varying complex electrical field amplitude,

*z*is the propagation distance, and

*T*is the time measured in a reference frame moving at the group velocity.

*α*,

*β*

_{2},

*γ*are the fiber attenuation coefficient, the second-order dispersion parameter and the nonlinear coefficient, respectively. The two terms on the right-hand side of Eq. (6) are due to self-phase modulation (SPM) and cross-phase modulation (XPM), respectively. The factor of 2 shows that XPM is twice as effective as SPM for the same intensity. In our numerical simulations, we consider nonzero dispersion-shifted fiber (NZ-DSF) with typical values of

*α*=0.2dB/km,

*β*

_{2}=5.1ps

^{2}/km and

*γ*=1.5W

^{-1}/km as transmission link. The wavelengths of the emitted signals are set on the International Telecommunication Union (ITU) grid with a spacing of 0.8nm (100GHz). The channel,

*λ*=1550.12nm, is viewed as transmission channel of chaotic light, and the channel,

*λ*=1550.92nm, as transmission channel of conventional digital optical signal. The optical spectra corresponding to two channels are shown in Fig. 2. Optical spectrum of semiconductor laser is broadened owing to optical feedback. Thus, the linewidth of chaotic optical spectrum is as much as 11.8GHz. However, this value is still smaller than channel spacing, 100GHz.

## 3. Numerical results and discussions

We first evaluate the system performance of COC and CFOC WDM system. The quality of the recovered message can be quantitatively evaluated by the eye opening penalty (EOP) defined as 10log_{10}(a/b), where a and b are the maximum eye opening measured for the decoded message without and with transmission. Value of the EOP smaller than 3dB can be considered fairly good. The synchronization performance of COC system can be evaluated by introducing the correlation coefficient defined as

where *P*
_{T}(*t*) and *P*
_{R}(*t*) are the outputs of the transmitter and the receiver, respectively, and 〈〉
denotes the time average. The correlation coefficient is bounded as -1≤*ρ*≤1.A larger value of ∣*ρ*∣ indicates a higher synchronization quality.

#### 3.1 Numerical realization of COC and CFOC WDM

For COC and CFOC WDM transmission, two channels separately including COC and CFOC are launched at the transmitter end. Figure 3(a) shows the chaotic carrier with 4.2GHz bandwidth from the chaotic transmitter. Its correlation dimension is 6.37 according to Grassberger-Procaccia (G-P) algorithm [20], and the largest Lyapunov exponent is 3.6ns^{-1}. The mean optical power of the chaotic carrier is about 7dBm. A 1-Gb/s pseudorandom nonreturn-to-zero (NRZ) bit sequence [Fig. 3(c)] is embedded into the output chaotic carrier by CMS method, as shown in Fig. 3(b). The amplitude of the NRZ sequence is set to 9% of the mean amplitude of chaotic carrier. This small value ensures security, and moreover alleviates destructive influence on the system synchronization. Figure 4(a) shows a pseudorandom NRZ sequence at the OC-192 standard bit rate of 10 Gb/s. The laser LD_{1} that functions as an emitter launches the optical carrier of wavelength λ=1550.92nm when the current of the laser is biased at 14.4mA. By using the 10-Gb/s NRZ bit stream chosen to encode the optical carrier, the digital optical signal with 8dBm peak power is obtained. Now, chaotic light encoding the message in COC channel and the digital optical signal in CFOC channel are multiplexed together into the fiber for 80-km-long WDM transmission. The fiber dispersion and nonlinearity effects distort chaotic carrier characteristics and degrade the synchronization performance between the transmitter and receiver. So, the decoded 1-Gb/s pseudorandom message of COC has high-frequency noises. Similarly, the received 10-Gb/s pseudorandom signal at the receiver end for CFOC takes on high-frequency noises due to the fiber dispersion and nonlinearity effects, shown in Fig. 4(b). However, the quality of the extracted messages can be effectively improved via a low-pass filter. For COC, a low-pass Chebyshev ☐ filter with 1.5GHz pass-band cut-off frequency is utilized to filter out the high-frequency temporal oscillations and the decoded message after filtering is shown in Fig. 3(d). The corresponding EOP is 2.5dB by calculation. For CFOC, the fast temporal oscillations can be effectively removed by a same type low-pass filter with 11.0 GHz pass-band cut-off frequency. The received signal after filtering is shown in Fig. 4(c). Obviously, the recovered signal at the receiving end is in good agreement with the encoded pseudorandom signal at the transmitter end except for the sharp fast oscillations. Moreover, the corresponding EOP is as low as 2.7dB. We can see that the high-quality pseudorandom messages are separately recovered at the receiver end for COC and CFOC WDM transmission. This indicates that COC and CFOC can simultaneously be realized within the same fiber link.

#### 3.2 Inter-channel crosstalk between COC and CFOC

When two-channel lights propagate simultaneously in a single fiber, the XPM-induced crosstalk can degrade the system performance. For COC and CFOC WDM system, if the chaotic carrier from the transmitter is directly fed into the receiver without propagating inside the fiber, the correlation coefficient between the transmitter and receiver outputs is as high as 0.93. If the chaotic carrier from the transmitter travels through 80-km-long fiber, the corresponding correlation coefficient decreases to 0.72. However, when the chaotic carrier travels not only through a fiber of 80km but also with the crosstalk of CFOC whose peak power is 14dBm, the corresponding correlation coefficient is as low as 0.64. Therefore, the interference of CFOC can further deteriorate the synchronization performance of COC system.

The main reason is that the accumulation of fiber dispersion and nonlinearity effects leads to the widening of chaotic carrier. Figures 5(a)-5(c) show the output chaotic carriers from the transmitter and an 80-km-long fiber without and with the crosstalk of CFOC, respectively. From Figs. 5(b) and 5(c), we can see that chaotic carriers are broadened through a length of fiber. Moreover, when CFOC and COC simultaneously propagate inside the fiber, the nonlinear phase shift of chaotic carrier is induced by another field of CFOC due to XPM effect. Thus, the XPM-induced frequency chirp interacts with the fiber dispersion-induced chirp, not only leading to the broadening of chaotic carrier but also producing the sharp oscillations at the leading and trailing edges of irregular pulses of chaotic carrier. Therefore, the synchronization performance of COC system is further degraded.

The crosstalk between COC and CFOC is mainly due to the fiber XPM effect. The influence of the XPM effect on system results from the power of optical pulses propagating inside the fiber and the transmission distance. Figure 6 shows that the correlation coefficient of COC system is plotted as a function of the propagation distance under the crosstalk of CFOC. The solid curve denotes the case without parallel transmission of CFOC. The dotted, dash-dotted and dashed curves denote the cases of the crosstalk with digital optical signals of peak power, 8, 14, and 17dBm, respectively. We can see that, regardless of whether or not the crosstalk of CFOC, the correlation coefficient decreases with the increase of the propagated distance due to the accumulation of fiber dispersion and nonlinearity effects. In Fig. 6, the interval between dashed and solid curves is wider than that between dash-dotted and solid curves. This indicates that as the peak power in CFOC channel is increased from 14 to 17dBm, the inter-channel crosstalk between COC and CFOC is enhanced. However, when the peak power of digital optical signal is as low as 8dBm, COC can realize no-crosstalk parallel transmission over the distance range of 80km.

As mentioned before, CFOC can affect COC due to fiber XPM effect. Similarly, COC can in turn have negative effects on CFOC. For investigating the crosstalk induced by COC on CFOC, digital optical signal with peak power of 8dBm and chaotic carrier with mean power of 7dBm are injected into a single fiber for the parallel transmission. Figure 7 shows the eye diagrams of the received NRZ digital signal at 10Gb/s under the crosstalk of COC when the propagated distance is 20, 80, and 160km, respectively. As the transmission distance is increased to 160km, the eye diagram is almost closed. Figure 8 illustrates the corresponding EOP of CFOC versus the transmission distance. The solid curve denotes the case without the crosstalk, and the dotted and dash-dotted curves denote the cases with the crosstalk of COC and the other CFOC channel, respectively. We can see that when the transmission distance is less than 80km, COC has almost no influence on CFOC. After the transmission distance extends beyond 80km, the effect of COC on CFOC increases with the increase of the propagated distance. Clearly, the influence of COC on CFOC is similar to that of CFOC on COC as previously mentioned. At the same time, we also compare the effects of the crosstalk between COC and the other CFOC channel on the given CFOC channel. For the other CFOC channel, it has the same transmission rate and peak power as the above-mentioned CFOC channel. Channel spacing of these two CFOC channels is still set to 100GHz. For a short transmission length of 80km, the crosstalk of COC on CFOC is similar to the influence of the other CFOC channel on CFOC, as shown in Fig. 8. CFOC can achieve no-crosstalk parallel propagation with COC or the other CFOC channel. However, for the comparatively long distance that exceeds 80km, the communication quality of CFOC under the crosstalk of COC degrades severely compared with the crosstalk of the other CFOC channel.

#### 3.3 Dependence on channel spacing and channel number

The channel separation is a very important parameter in WDM system. To investigate the dependence of COC and CFOC WDM transmission on channel separation, we still consider two channels with variable channel separation, that is, COC channel with 7dBm mean power and CFOC channel with 8dBm peak power. Figure 9 and Fig. 10 show that for the 80-km-long transmission distance the correlation coefficient of COC and EOP of CFOC are plotted as functions of channel spacing, respectively. Obviously, the synchronization performance of COC and the communication quality of CFOC increase with the increase of channel spacing. When two channels are closely spaced, the nonlinear crosstalk between COC and CFOC can be enhanced. Moreover, optical filters do not completely eliminate the power input of adjacent channel. On the demultiplexing of these two channels, COC channel is separated by an optical band-pass filter (BW=60GHz) and CFOC channel by another optical band-pass filter (BW=20GHz). Both filters are Chebyshev∣filters. So, the crosstalk induced by XPM effect and the filtering characteristics of optical filter can degrade the synchronization performance of COC and the communication quality of CFOC. However, when channel spacing exceeds 100GHz, the influence of channel spacing on COC and CFOC WDM system decreases the lowest level, and moreover, keeps unchangeable as the channel spacing increases.

In the previous sections, COC and CFOC WDM system with only two channels is investigated. Now the system performance of a four- and a six-channel WDM system with 100GHz channel spacing is further investigated when channel number is expanded to 4 and 6. Of these channels, one of the two innermost of four or six channels is chosen as the COC channel and other channels as the CFOC channels. Figure 11 shows that the correlation coefficient of COC system is plotted as a function of transmission distance for four- and six-channel WDM systems for the different peak power of CFOC. We can see that the degradation of the six-channel system is no more severe than that of the four-channel system when the peak power of each channel of CFOC is equal and as low as 8dBm. We attribute the similarity of performance of the six- and four-channel systems to the fact that only XPM from neighboring channels degrades the performance of a given channel for the lower peak power so that channels that are farther removed have little or no influence. However, when the peak power per channel for CFOC is increased to 11dBm, the performance of multichannel systems depends somewhat on the power that is carried by each channel. From Fig. 11, it is clear that when the transmission distance is less than 60km, the system performance of a four-channel system is almost similar to that of a six-channel system. However, when the transmission distance exceeds 60km, the synchronization quality of COC system for six-channel WDM system is significantly degraded compared with four-channel WDM system. So, more channels simultaneously travel inside a single fiber for COC and CFOC WDM system only if all channels carry low power signals.

## 4. Conclusions

In this paper, a theoretical model of COC and CFOC WDM system is proposed, and the parallel transmission of COC and CFOC is numerically confirmed. At the same time, the inter-channel crosstalk of COC and CFOC is further analyzed only considering the fiber XPM effect. The theoretical investigation indicates that for a two-channel WDM system with channel spacing of 100GHz, when the mean power of chaotic channel is 7dBm and the peak power of CFOC channel is less than 17dBm, the synchronization of COC system is very good within 80km. When COC system maintains the high-quality chaos synchronization, for achieving COC and CFOC WDM transmission, CFOC must simultaneously ensure a high communication quality. However, as the peak power of CFOC is set to 17dBm, the corresponding EOP of the received NRZ sequence is as high as 6.2dB at 80km. This value is far higher than 3dB. So, we need to degrade the peak power of digital optical signal of CFOC. The investigations suggest that CFOC with the peak power of 8dBm can realize high-quality parallel transmission together with COC in 80km. In addition, the dependence of COC and CFOC WDM system on channel spacing and channel number is investigated. When the channel spacing exceeds 100GHz, the inter-channel crosstalk between COC and CFOC decreases to the lowest level, and moreover, keeps unchangeable with the increase of channel spacing. We also find that when all channels carry low power signals, COC and CFOC WDM system can support simultaneous transmission of more channels. In our previous work, the influence of dispersion on COC system has been quantitatively investigated and a symmetrical dispersion compensation scheme has been proposed to improve the performance of COC system [21]. However, the COC and CFOC WDM system discussed above is investigated without carrying out dispersion compensation. If a dispersion compensation scheme is introduced, the transmission distance of COC and CFOC WDM can be further extended.

## Acknowledgments

This work is supported by the National Natural Science Foundation of China under Grant 60577019, 60777041 and the International Cooperation Project of Shanxi Province, China, under the project number 2007081019.

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