[3] Neokosmidis Techniques for FWM Suppresion

7/30/2019 [3] Neokosmidis Techniques for FWM Suppresion

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New Techniques for the Suppression of the Four

Wave Mixing-Induced Distortion in Non-Zero

Dispersion Fiber WDM Systems

I . Neokosmidis, T. Kamalakis, A. Chipouras and T. Sphicopoulos

Department of Informatics and Telecommunications, University of Athens

Panepistimiopolis Ilissia, Athens, Greece, GR-15784

[email protected]

Abstract: The performance of a Wavelength Division Multiplexing (WDM) optical

network can be severely degraded due to fiber nonlinear effects. In the case where

Non-Zero Dispersion (NZD) fibers are employed, the Four Wave Mixing (FWM)

effect sets an upper limit on the input power especially in the case of narrow channel

spacing. In order to reduce FWM-induced distortion two new techniques, the hybrid

ASK/FSK modulation and the use of pre-chirped pulses, are investigated. It is shown

that both techniques can greatly improve the Q factor in a 10Gb/s WDM system. This

happens even for very high input powers (~10dBm) where the degradation of the

conventional WDM system is prohibitively strong. The proposed methods are also

applied and tested in higher bit rates (40Gbps). It is deduced that although the hybrid

ASK/FSK modulation technique marginally improves the system performance, the

optical pre-chirp technique can still be used to greatly increase the maximum

allowable input power of the system.

Index Terms: Chirp, nonlinear optics, optical crosstalk, optical fiber

communications, wavelength division multiplexing.


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I. INTRODUCTION

Wavelength Division Multiplexing (WDM) is widely being adopted as a

means to increase the capacity of optical networks. However, the rapid growth in the

number of Internet users and the need for provision of new broadband services is

expected to significantly increase the traffic volume. There is thus a tendency to

develop larger WDM networks with narrower channel spacing and higher channel

capacity. Furthermore, a significant decrease of the overall cost can be accomplished

by reducing the number of optical amplifiers used in the links which leading to the

use of higher input power at the transmitter. However, this increase in the optical

power results to signal degradation due to fiber nonlinear effects, including Four

Wave Mixing (FWM), Cross Phase Modulation (XPM) and Self Phase Modulation

(SPM).

Both XPM and FWM introduce intensity fluctuations that are dependent on

the neighboring channels, resulting into interchannel interference throughout the fiber

length. SPM is generally considered negligible compared to XPM, since even for a

system of two optical channels XPM is twice as effective as SPM for the same

intensity [1, p. 262]. However, in WDM systems employing Non-zero Dispersion

(NZD) fibers the main nonlinear induced penalty arises from FWM. This is especially

true in systems with dispersion compensation in which the XPM induced distortion is

diminished [2]-[3].

In recent years, several FWM suppression techniques have been proposed.

Since the power of the FWM products decreases quickly as the fiber dispersion

increases, one solution is to use standard single mode fibers. This however, results in

a large dispersion accumulation at the receiver and necessitates the use of long

dispersion compensating fibers in each network node. Another approach is to use


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optical multiplexers and demultiplexers with the combination of delay lines [4], bit-

phase arranged RZ (BARZ) signals [5], hybrid WDM/TDM technique [6],

polarization-division multiplexing [7] and unequal channel spacing [8]-[10]. The

above techniques come at the expense of less channel efficiency or / and more

network complexity. For example, the use of unequal channel spacing requires the

design of optical multiplexers and demultiplexers with central wavelengths not

compatible with the ITU grid.

In this paper, two new methods based on a hybrid ASK/FSK modulation and

pulse pre-chirping are proposed for the suppression of the FWM effect. The basic

ideas behind these methods are summarized as follows. FWM is a nonlinear process

in which three waves of frequenciesfi,fj andfk(ki, j) interact through the third-order

electric susceptibility of the optical fiber to generate a product wave at frequency

fijk=fi+fj-fk. In a WDM system, a product is generated for every possible combination

of channels. Therefore, even if the system has only ten channels, hundreds of new

components are generated. If the channels are assumed to be in-phase and equally

spaced then the efficiency of the FWM process is high and most of the generated

components will be located at the channel frequencies. By FSK modulating the WDM

channels, the spectral position of the FWM components is altered and hence less

products fall near the central frequency of the WDM channels. Hence the

accumulation of the FWM noise is reduced. On the other hand the optical pre-chirping

increases the phase mismatch by randomizing the phases of the input signals. Since

the efficiency of the FWM process is inversely proportional to the phase mismatch it

follows that optical pre-chirping can suppress the FWM noise.

The effectiveness of the new methods is studied by numerically solving the

basic nonlinear propagation equation with the Split Step Fourier Method (SSFM) [1].


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Simulations show that both techniques can provide a significant improvement on the

Q factor obtained at the receiver. The maximum allowable input power is

significantly increased and a power gain that can be as high as 3dB may be obtained

for 10Gb/s WDM systems. The effectiveness of the two techniques is also tested for

higher transmission rates. It is shown that the hybrid ASK/FSK modulation can only

marginally improve the performance of a 40Gb/s WDM system. Optical pre-chirping

on the other hand, offers a significant improvement even for these high bit rates.

The paper is organized as follows: The system configuration is shown in

section II. The transmission model used to study the system under consideration is

described in section III. In section IV, the importance of the FWM-induced distortion

in a conventional WDM system is discussed. The basic concepts of the proposed

compensation techniques are illustrated in section V. The results obtained by the

application of the two methods are presented and discussed in section VI. Some

concluding remarks are given in section VII.

I I . SYSTEM CONFIGURATION

A conventional WDM link is shown in figure 1. The WDM channel are ASK

modulated and multiplexed in a single WDM signal. The WDM signal is then

launched into a Non-Zero Dispersion Fiber. As the signal propagates through the

fiber, nonlinear effects can cause interchannel interference and degrade its quality. At

the receiver the signals are dispersion compensated and demultiplexed. Each signal is

then detected using a direct detection receiver. The receiver may consist of a

photodiode, an electrical amplifier and an electrical filter. After the filter the signal is

sampled and a decision threshold device is used to detect whether a 1 or a 0 is

received.


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In this paper, the input optical power waveform representing a single 1-bit,

p1(t) is specified within the time interval [0, (1+b)Tp] as [11]:

[ ] [ ]{ }[ ]

+

+=

ppin

ppp

pp

pin

TTbtP

TbTandTbt

TT

btTbPtp

,,

)1(,,0,22)1(sin1)(1

(1)

wherePin denotes the peak input power, Tp represents the bit duration and b specifies

the pulse shape. Varying b from 1 to 0, the pulse changes from cos2(t)-like to

rectangular. To estimate the performance of the system, the input channels will be

assumed modulated by a 28

-1 pseudorandom bit streams of the above shape.

Throughout this work NRZ pulses are used with a value ofb=0.4. Finally, the bit

duration Tp was taken to be 100ps for bit rateR=10Gbps and Tp=25ps forR=40Gbps.

The central channel of the WDM system is assumed to be located around 0=1.55m.

The NZD transmission fiber is assumed to have a chromatic dispersion

coefficient D=2ps/nm/km, an optical loss coefficient adB=0.2dB/Km and a nonlinear

coefficient =2(Watt x km)-1. The Dispersion Compensating Fiber (DCF) used at the

receiver has D=-200ps/nm/km, adB=0.5dB/km and =4.5(Watt x km)-1. The total

length of the optical link is L=160Km. At its ith output port, the WDM demultiplexer

is assumed to have a Gaussian transfer function,

( )( )

2

2

2 c

i

f

ff

i efH

= (2)

where

)10ln(2

Bfc

= (3)

In the above equations, B is the 40dB bandwidth of the demultiplexer and fi is the

central frequency of each channel. The Gaussian transfer function is often

encountered in many practical demultiplexers (i.e. Arrayed Waveguide Gratings [12]).


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I I I. THE TRANSMISSION MODEL

In order to test the performance of the system, the fibers propagation equation

can be numerically solved using the Split Step Fourier Method (SSFM) [1, pp. 51-53].

The basic propagation equation is written as:

AAjAt

Aj

z

A 22

2

222

+

=

(4)

where A=A(t,z) is the slowly varying complex envelope of the optical field at time t

and positionzalong the fiber, 2 is the Group Velocity Dispersion (GVD) parameter,

=adB/4.343 is the fiber loss coefficient and is the nonlinear coefficient of the fiber.

In a WDM system consisting ofN channels, the input signal (z=0) can be

written as:

=

=N

i

tfj

iietAtA

1

2)0,()0,(

(5)

whereAi(t,0) and fi are the slowly varying envelope and the central frequency of the

i-th channel respectively. Equation (4) under the initial condition (5) can be used to

describe the signal propagation taking into account the optical losses, chromatic

dispersion and the three Kerr-induced nonlinear phenomena namely the SPM, XPM

and FWM effects.

All channels are assumed aligned in time at the input (synchronous WDM

system) and equally spaced. Under these conditions the strength of FWM effect is

maximized. In order to investigate the performance of a WDM system, the Q factor

can be calculated from the eye diagrams at the receiver. The Q factor is a commonly

used parameter in telecommunications and it is expressed as:

o

oPPQ

+

=

1

1 (6)


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where and are the average optical power of bits 1 and 0 respectively

and 1 and o are the corresponding standard deviations of the noise.

IV. IMPORTANCE OF THE FWM INDUCED DISTORTION

As WDM channels become denser, the power limitations imposed by

nonlinear effects, become more pronounced. FWM introduces intensity fluctuations in

a WDM channel due to the existence of the other channels. The power of these

fluctuations increases with decreasing channel spacing and causes interchannel

interference at the receiver.

Before discussing the FWM compensation techniques, it will be useful to

compare the FWM contribution to system degradation with that induced by XPM and

SPM effects. In order to accomplish this comparison, the effect of SPM and XPM can

be isolated from the effect of FWM by numerically solving the set of coupled

propagation equations (7)

i

il

liii

ii

ii AAAjA

a

t

Aj

t

A

z

A

+=+

+

+

22

2

2

21 222

(7)

instead of equation (4), where Ni 1 andAi=Ai(t,z) is the envelope of the i channel

as above. Also 1i is the inverse of the group velocity at the frequency fi and 2i is the

GVD parameter at the same frequency. Note that in the above system of equations the

SPM effect is described by the j|Ai|2 on the right hand side of (7) while the XPM

effect is described by the sum 2jAili|Al|2. Since the FWM is not taken into account

in (7), a comparison between the solutions of (4) and (7) can be used to estimate the

importance of the FWM-induced distortion in the WDM link.

In order to ascertain that the FWM is indeed the dominant noise source, the

eye diagrams of the central channel are plotted in figure 2, in the case where a) Only


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SPM is assumed (i.e. only the central WDM channel is on), b) only SPM and XPM

are assumed, c) FWM, XPM and SPM are assumed. An 8 channel 10Gb/s WDM

system is assumed with a channel spacing of 50GHz. As seen by the eye diagrams of

figure 2, the degradation induced by SPM and XPM is much lower than that of FWM

and hence, in a WDM link with NZDF, the FWM imposes the severest limitations.

The results of figure 2 can also be justified theoretically. In [13], it is shown

that the XPM intensity fluctuations depend on the accumulated dispersion of the span.

When dispersion compensation is used, the XPM-induced intensity distortion is

greatly diminished. On the other hand the FWM-induced intensity distortion rests

almost unaffected from dispersion compensation. Also as shown in [13] the FWM-

induced intensity distortion decreases as 1/2 and as 1/|2|, while the XPM distortion

decreases much slower. It is therefore not surprising that in the dense WDM system

considered, the FWM-induced intensity distortion dominates over the XPM effect.

V. DESCRIPTION OF THE FWM COMPENSATION SCHEMES

A. Hybrid FSK/ASK Modulation Technique

In order to explain the effectiveness of the hybrid ASK/FSK technique, we

first consider 3 CW waves at frequencies f1, f2 and f3. The FWM products, will be

located at frequenciesfpqr=fp+fq-fr, wherep,q,rtake the values 1,2 or 3.As mentioned

in the introduction, if the channels are equally spaced, the central frequency of the

products will coincide with some of the central frequencies of the channels. In order

to reduce the number of FWM products that coincide with the WDM channels, one

solution is to modulate the WDM signals using a special kind of FSK modulation. In

the context of this special scheme, the WDM channels are divided into pairs and on

each pair the channels follow the same FSK modulation. The FSK modulation of two


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adjacent pairs is opposite, i.e. if the channels in a pair are detuned + away from their

central frequency, the channels of the adjacent pair are inversely detuned and so

on as shown in figure 3. Note that a similar (but constant) channel detuning scheme is

also used in the unequal channel spacing technique [10]. The hybrid ASK/FSK

system structure is depicted in figure 4a.

Figure 4b, depicts the optical spectrum of a hybrid ASK/FSK signal with a

10Gb/s ASK rate and a 1Gb/s FSK rate. The peak optical power of the ASK signal is

Pin=10dBm and a =5GHz detuning. The modulation of the FSK signal is 1,0,1,0,

,0,1. From figure 4b one can notice the two peaks caused by the FSK modulation.

B. Optical Pre-chirp

In this section optical pre-chirping is proposed as another solution for the

reduction of the effect of the FWM induced distortion. Since the efficiency of the

FWM products are inversely proportional to the phase mismatch, it follows that

reducing the phase coherence may reduce the power of the FWM noise. One way to

reduce this coherence is through pulse pre-chirping. Note that a similar technique is

used in the suppression of the XPM induced distortion in systems employing standard

fibers [14]-[15]. In the case of NZD fibers, where the FWM effect dominates as

discussed in section IV, optical pre-chirping will be shown to greatly improve the Q

factor by suppressing the FWM effect.

There are several methods to produce a pre-chirped signal such as cascading

intensity and phase modulators or using dispersion-compensating devices like chirped

fiber gratings and DCFs. In this work, the latter technique was chosen due to its ease

of implementation. The optimal length of the DCF fiber used at the transmitter, in

order to pre-chirp the optical pulses was evaluated through iterative simulations that


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aimed to maximize the performance of the system. The system configuration is shown

in figure 5. Note a DCF is also used at the receiver in order to compensate the

remaining accumulated dispersion of the signal. In this configuration, Pin designates

the power at the end of the transmitter DCF.

VI . EFFECTIVENESS OF THE PROPOSED METHODS

In order to investigate the performance improvement of the two techniques, a

series of simulations were performed using the SSFM method. The 40dB bandwidth

B of the optical demultiplexer was optimized at the receiver in order to achieve the

highest Q factor value for the different values of the input powerPin.

In figure 6, the eye diagrams for the 5th channel (central channel) of a single

span eight-channel WDM system in the case when a) none of the two methods is

applied (conventional WDM system), b) the hybrid ASK/FSK modulation is applied

and c) when the pre-chirped pulses are used. A 10Gb/s WDM system is assumed with

channel spacing equal to 50GHz. The channel detuning of the hybrid ASK/FSK

system is =5GHz and the FSK modulation rate is 1Gb/s. A 225m DCF fiber was

used for optical pre-chirping, with parameters as given in section II. This figure

provides a first indication of the performance improvement of the two techniques. As

shown in the figure, the eye-diagram of the uncompensated system is closed due to

the effect of the FWM induced distortion. The Q factor in this case is 3.4 resulting in

a high error probability. If the FWM is assumed to follow Gaussian distribution, this

Q factor corresponds to an error probability of erfc(Q/ 2 )/23x10-4. However,

adopting the hybrid ASK/FSK modulation technique, the quality of the link is

significantly improved as shown by the second eye-diagram. The Q factor in this case

is 7.5, implying an error probability of the order 10-14. The results are even better for


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the case of optical pre-chirping in which case the Q factor is 10.8 and the

corresponding error probability is even lower. Hence, the effectiveness of the

proposed methods on reducing the FWM noise is clearly seen even for input powers

as high as ~10dBm where the degradation of the conventional WDM system is

prohibitively high.

To further illustrate the effectiveness of the proposed methods and gain a more

quantitative aspect at the performance of each compensation scheme, the Q factor was

evaluated for various values of the input power. Figure 7 depicts the Q factor of the

central channel (worst case) as a function of the input powerPin assuming a 10Gb/s

WDM system with a) N=8 channels and a channel spacing fch=50GHz, b) N=8

channels and a fch=100GHz, c) N=16 channels and fch=50GHz and d) N=16

channels and a fch=100GHz spacing. The FSK modulation rate for the hybrid

ASK/FSK is 1Gb/s and a =5GHz frequency detuning is used. The DCF fiber used in

the above cases is 225m, 150m, 48.5m and 19.4m for figures 7(a), 7(b), 7(c) and 7(d)

respectively. As shown by the figures, both techniques greatly improve the Q factor in

all cases. For example, in the case of a N=16 WDM channel system with 100GHz

channel spacing (figure 7d), the obtained Q factor forPin=14dBm was approximately

5.3 for the uncompensated system and 8.8 for the hybrid ASK/FSK modulation at the

transmitter. These values correspond to a Q factor improvement of 2.2dB. It can also

be seen that while a Q factorQ=10 is achieved forPin=12.3dBm for the conventional

system, the same Q factor value is achieved forPin=13.8dBm in the case of the hybrid

ASK/FSK modulation technique. This corresponds to a power gain of 1.5dB.

The results obtained from the optical pre-chirping technique are even better. In

this case the Q factor is Q=15.1 forPin=14dBm. It is understood that the improvement

of the Q factor is 4.55dB. In order to obtain Q factor equal to 10 the input power can


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be as high as 15dBm, and this translates to a power gain greater than 2.5dB. Note that

this power gain of 2.5dB can be used to increase the tolerance of the system or

increase the span length by 2.5/0.2=12.5Km. Similar results can also be observed for

the other cases considered in the figure. It is therefore evident that both techniques

offer a significant improvement in the performance of the system.

In all cases the Q factor is reduced as the input power increases. This is not

surprising, since it is well known that the power of the produced components is

proportional to Pin3. Hence, these results demonstrate again the strong dependence of

the FWM noise and consequently of the Q factor on the input power. However, the

improvement of the proposed techniques is significant even for high input powers.

In figure 8, the performance improvement of the two techniques in the case of

a 8 channel 40Gb/s WDM system is investigated. The channels are assumed to have

200GHz spacing while the rest of the parameters are the same as those of the 10Gb/s

WDM system considered earlier. The FSK modulation rate for the hybrid ASK/FSK

is 1Gb/s and a =5GHz frequency detuning is used. The DCF fiber used in the above

case is 193.9m. The hybrid ASK/FSK modulation technique only marginally

improves the system performance. On the other hand the use of optical pre-chirped

pulses significantly improves the value of the Q factor. ForPin=14dBm the Q factors

of the conventional and the prechirped system is approximately equal to 8.0 and 16.0

implying a 3dB improvement. Also a power gain as high as 2.5dB is obtained for

Q=12.

It seems therefore that pre-chirping the optical channels can be used in order

to reduce the FWM-induced distortion for a 40Gb/s WDM system as well. Although

40Gb/s WDM systems are presently not used in commercial networks, they may

constitute an option for future all-optical backbone networks. It should also be noticed


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that the optical pre-chirping can be implemented with greater ease than the hybrid

ASK/FSK modulation technique. A single DCF at the receiver can be used to

simultaneously pre-chirp all the WDM signals. On the other hand, the hybrid

ASK/FSK technique may prove more amenable for integration with the WDM

multiplexer on a single chip.

In addition, both methods seem to present significant advantages compared to

other suppression techniques since they overcome some problems. For example, the

use of unequally channel spacing [8]-[10] comes at the expense of increased

multiplexer / demultiplexer design complexity. In [10] the BER is improved by one

order of magnitude while, as shown in this section, the proposed techniques achieve

many orders of magnitude improvement. Unlike the hybrid TDM/WDM technique

[6], these methods do not require the allocation of time slots and the generation of RZ

pulses. The optical delay line technique [4] is applicable only when zero dispersion

fibers are used. It is also interesting to note that the methods proposed in this paper

employ NRZ modulation which is more easily implemented than the RZ modulation.

VII. CONCLUSIONS

In this paper, two techniques, hybrid ASK/FSK modulation and pre-chirping

the optical pulses, are applied to suppress the FWM-induced distortion which can

pose important limitation on the input power of a WDM system. The effectiveness of

the two methods is numerically demonstrated using the Split Step Fourier Method

(SSFM) to simulate the WDM signal propagation. From the obtained results, it is

shown that both techniques greatly improve the performance of the system, providing

a power gain that can be as high as 2.5dB in the case of a 10Gbps WDM system. Pre-

chirping the optical pulses can also be used for the reduction of the FWM-induced


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distortion for a higher bit rate (40Gb/s) system as well and seems to be more easily

implemented than the hybrid ASK/FSK modulation technique.

REFERENCES

[1] G. P. Agrawal,Nonlinear Fiber Optics, 2nd ed. New York: Academic, 1995.

[2] A. V. T. Cartaxo, Cross-Phase Modulation in Intensity Modulation- Direct

Detection WDM Systems with Multiple Optical Amplifiers and Dispersion

Compensators, J. Lightwave Technol., vol. 17, No. 2, pp. 178-190, February 1999.

[3] R. Hui, K. R. Demarest and C. T. Allen, Cross-Phase Modulation in Multispan

WDM Optical Fiber Systems, J. Lightwave Technol., vol. 17, No. 6, pp. 1018-1026,

June 1999.

[4] K. Inoue, Suppression Technique for Fiber Four-Wave Mixing Using Optical

Multi-/Demultiplexers and a Delay Line, J. Lightwave Technol., vol. 11, No. 3, pp.

455-461, March 1993.

[5] K. Sekine, N. Kikuchi, S. Sasaki and H. Ikeda, FWM crosstalk reduction using

bit-phase arranged RZ (BARZ) signals in WDM systems, in Proc. Optoelectronics

and Communications Conf. (OECC) 96, 1996, pp. 114-115, paper 17B2-4.

[6] A. Okada, V. Curri, S. M. Gemelos and L. G. Kazovsky, Reduction of Four-

Wave Mixing crosstalk using a novel hybrid WDM/TDM technique, ECOC98,

1998, pp. 289-290.

[7] K. Sekine, S. Sasaki and N. Kikuchi, 10Gbit/s four-channel wavelength- and

polarization-division multiplexing transmission over 340km with 0.5nm channel

spacing, Electron. Lett., vol. 31, pp. 49-50, 1995.


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[8] F. Forghieri, R. Tkach, A. Chraplyvy and D. Marcuse, Reduction of four-wave

mixing crosstalk in WDM systems using unequally spaced channels, IEEE Photon.

Technol. Lett., vol. 6, pp. 754-756, 1994.

[9] H. Suzuki, S. Ohteru and N. Takachio, 22 x 10 Gb/s WDM transmission based on

extended method of unequally channel allocation around the zero-dispersion

wavelength region, IEEE Photon. Technol. Lett., vol. 11, pp. 1677-1679, 1999.

[10] A. Boskovic, S. Ten and V. L. da Silva, FWM penalty reduction in dense WDM

systems through channel detuning, ECOC98, 1998, pp. 163-164.

[11] P. J. Winzer, M. Pfennigbauer, M. M. Strasser and W. R. Leeb, Optimum Filter

Bandwidths for Optically Preamplified NRZ Recievers, J. Lightwave Technol., vol.

19, No. 9, pp. 1263-1273, September 2001.

[12] M. K. Smit and C. Dam, PHASAR-Based WDM-Devices: Principles and

Applications,IEEE J. Selected Topics in Quant. Elec. Vol. 2, No. 2, June 1996, pp.

236-250.

[13] B. Xu and M. Brandt-Pearce, Comparison of FWM- and XPM-Induced

Crosstalk Using the Volterra Series Transfer Function Method, J. Lightwave

Technol., vol. 21, No. 1, pp. 40-53, January 2003.

[14] A.Sano, Y. Miyamoto, S. kuwahara and H. Toba, A 40Gb/s/ch WDM

transmission with SPM/XPM suppression through prechirping and dispersion

management, J. Lightwave Technol., vol. 18, pp. 1519-1527, 2000.

[15] A. Sano and Y. Miyamoto, Performance evaluation of prechirped RZ and CS-

RZ formats in high-speed transmission systems with dispersion management, J.

Lightwave Technol., vol. 19, No. 12, pp. 1864-1871, December 2001.


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Figure 1


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Figure 2


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Figure 3


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Figure 4

(a)


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Figure 6


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22

5 6 7 8 9 100

4

8

12

16

20

2428

32

36

40

44

(a)

Qf

actor

Pin(dBm)

Uncompensated system

With FSK

With pre-chirp

5th channel

10 11 12 13 14 154

8

12

16

20

24

28

32

36

40

(b)

Qf

actor

Pin(dBm)


With FSK

With pre-chirp

5th channel

4 5 6 7 8 94

8

12

16

20

24

28

32

36

40

(c)

Qf

actor

Pin(dBm)


With FSK

With pre-chirp

8th channel


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10 11 12 13 14 154

8

12

16

20

2428

32

36

40

(d)

Qf

actor

Pin(dBm)


With FSK

With pre-chirp

8th channel

Figure 7


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10 11 12 13 14 154

8

12

16

20

24

28

32

36

Qf

actor

Pin(dBm)


With FSK

With pre-chirp

5th channel

Figure 8


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Figure Captions

Fig. 1: System structure.

Fig. 2: Comparison of the SPM, XPM and FWM effect when Pin=10dBm. a) SPM

effect, b) SPM and XPM effects, c) SPM, XPM and FWM effects

Fig. 3: The FSK modulation scheme used in the proposed system

Fig. 4: a) the hybrid ASK/FSK WDM system configuration and b) the power spectral

density of a hybrid ASK/FSK modulated signal forPin=10dBm. The ASK and FSK

modulation rates are 10Gb/s and 1Gb/s respectively and the channel detuning is

=5GHz.

Fig. 5: System configuration of the pre-chirped optical WDM system.

Fig. 6: Eye diagrams for the central channel of a single span eight-channel WDM

system: a) conventional WDM system, b) application of the hybrid ASK/FSK

modulation and c) WDM with pre-chirped pulses. The transmission rate is 10Gb/s, the

channel spacing is 50GHz and the input power is 10dBm.

Fig. 7: Q factor of the central channel as a function of the input powerPin for a

10Gbps system of a) 8 channels and 50GHz channel spacing, b) 8 channels and

100GHz channel spacing, c) 16 channels and 50GHz channel spacing and d) 16

channels and 100GHz channel spacing


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Fig. 8:Q factor vs. input power for a single span eight-channel 40Gbps system

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[3] Neokosmidis Techniques for FWM Suppresion