Wavelength division multiplexing of chaotic secure and fiber-optic communications References and...

Wavelength division multiplexing of chaotic secure and fiber-optic communications

Jian-Zhong Zhang, An-Bang Wang, Juan-Fen Wang , and Yun-Cai Wang∗

Department of Physics, College of Science, Taiyuan University of Technology,

Taiyuan 030024, China

∗Corresponding author: [email protected]

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

OCIS codes: (140.5960) Semiconductor lasers; (060.2330) Fiber optics communications;

(060.4230) Mutiplexing.

References and links

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1111. 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 λC. In COC system, transmitter (LDT) and receiver

(LDR), both of which are composed of a single-mode semiconductor laser with an external

reflector, have the same configuration. Transmitter laser (LDT) 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 LD1, LD2, … , LDN 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.

Fig. 1. Schematic diagram of COC and CFOC WDM transmission.

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]:

T,R

T,R T,R T,R T,R inj ext

P

d ( ) 1 1(1 )[ ( ) ] ( ) ( ) exp( ) ( )

d 2

E ti G t E t k E t i k E t

tα τ ωτ

τ= + − + − − + (1)

2T,R T,R

T,R T,R T,R

n

d ( ) 1( ) ( ) ( )

d

N t IN t G t E t

t qV τ= − − (2)

T,R 0

T,R 2

T,R

[ ( ) ]

( )1 ( )

,G N t N

G tE tε

−=

+ (3)

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 Eext is the input signal at the receiver and I is the pump current density of the

semiconductor laser.

The feedback coefficient kT,R of the semiconductor lasers with optical feedback and the

injection coefficient kinj from the transmitter to the receiver are defined as follows:

2

0 T ,R

T ,R

in 0

(1 )1 r rk

rτ

−= (4)

2

0 in j

in j

in 0

(1 )1 r rk

rτ

−= , (5)



where τin is the round-trip time in the laser cavity, r0 and rT,R represent amplitude reflectivity

of the laser exit facet and the external reflector respectively, rinj 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]. 2

2 2

2 2( 2 )

2 2

j j

j j k j

k j

A AiA i A A A

z T

αβ γ

≠

∂ ∂+ + = +

∂ ∂∑ . (6)

Here j, k is chosen to be 1, or 2. Aj 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，β2，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, β2=5.1ps2/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.

Fig. 2. Optical spectra for COC and CFOC WDM system with 2 channels and 0.8nm channel

spacing.

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 10log10(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

[ ][ ]

[ ] [ ]

T T R R

2 2

T T R R

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

P t P t P t P t

P t P t P t P t

ρ− −

=

− −

, (7)

where PT(t) and PR(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 LD1 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

ChebyshevⅠfilter 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.



Fig. 3. COC numerical realization (a) chaotic carrier (b) chaotic carrier encoding the message

(c) pseudorandom NRZ bit sequence at 1Gb/s (d) decoded message after filtering.

Fig. 4. CFOC numerical realization (a) pseudorandom NRZ sequence at the OC-192 standard

bit rate of 10Gb/s (b) the received pseudorandom signal (c) after filtering.

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.



Fig. 5. Output chaotic carriers from (a) transmitter (b), (c) 80-km-long fiber without

and with the crosstalk of CFOC, respectively.

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.

Fig. 6. Correlation coefficient of COC system as a function of transmission distance under

the crosstalk of digital optical signals of CFOC. (Solid curve denotes no crosstalk; Dotted,

dash-dotted, and dashed curves denote the cases of the crosstalk with digital optical signals of

peak power, 8, 14, and 17dBm, respectively.)

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.

Fig. 7. Eye diagrams of the received NRZ digital signal at 10Gb/s with the crosstalk of COC

for transmission distance of 20, 80, and 160km, respectively.

Fig. 8. EOP of the received 10-Gb/s NRZ sequence with peak power of 8dBm as a function

of transmission distance. (Solid curve denotes no crosstalk; Dotted and dash-dotted curves

denote the cases of the crosstalk with COC channel and the other CFOC channel, respectively.)



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 ChebyshevⅠfilters. 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.

Fig. 9. Correlation coefficient of COC system as a function of channel spacing for an

80-km-long two-channel WDM system.

Fig. 10. EOP of CFOC system as a function of channel spacing for an 80-km-long two-channel

WDM system.

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.

Fig. 11. Correlation coefficient of COC system is plotted as a function of transmission distance

for a four- and a six-channel system with100GHz channel spacing for different value of the

peak power of CFOC.

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.



Wavelength division multiplexing of chaotic secure and fiber-optic communications References and...

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