Effect of Chromatic Dispersion on Four-Wave Mixing in WDM ... · S. M. A. Islam IMCT University...

(IJIDCS) International Journal on Internet and Distributed Computing Systems. Vol: 1 No: 2, 2011 62

Effect of Chromatic Dispersion on Four-Wave Mixing in WDM Optical Transmission System

M. Z. Rahman Research Support and

Publication University Grants

Commission, Bangladesh [email protected]

M. S. Islam IICT

Bangladesh University of Engineering and Technology,

Bangladesh [email protected]

T. Rahman IMCT

University Grants Commission (UGC)


S. M. A. Islam IMCT

University Grants Commission (UGC)


Abstract— Crosstalk due to four-wave mixing (FWM) is the dominant nonlinear effect in long-haul multi-channel optical communication systems which can severely limit system performance. In this paper, we have simulated the effect of chromatic dispersion on FWM using equal and unequal channel spacing in terms input/output spectrum, eye diagram and bit error rate. Results show that the effect of FWM reduces with the increasing dispersion coefficient, but the reduction is more effective for unequal channel spacing than equal channel spacing. But since, such a fiber is difficult to build, it is suggested that the FWM effect can be suppressed with increased flatter dispersion slope and unequal signal space. Keywords— Four-Wave Mixing, Wavelength-Division Multiplexing, Optical Communication, Chromatic Dispersion, BER, Q-factor and Eye diagram.

I. INTRODUCTION Very high-capacity, long-haul optical communication

systems are made possible by the extremely wide bandwidth of optical fibers, which is best exploited by wavelength-division multiplexing (WDM) [1]. The performance of long-distance optical communication systems is limited, however, by chromatic dispersion and nonlinear effects of fiber, which interact and accumulate along the length of the optical link. Chromatic dispersion, which broadens the pulses, can be reduced by using dispersion-shifted fibers at the 1550-nm wavelength range, but low chromatic dispersion enhances some nonlinear effects of fiber, especially four-wave mixing (FWM) [2-3]. FWM is of particular concern on account of its relatively low threshold power and rises very quickly as the number of channels increased. The number of FWM product with channel number is shown in Fig. 1. The efficiency of FWM crosstalk generation can be reduced by increasing the frequency separation between the various channels [4], increased channel separation would preclude dense WDM systems. To suppress FWM-induced crosstalk in WDM systems in dispersion-shifted fiber (DSF), the unequal channel-spacing scheme was proposed and worked quite well for most cases since it avoids generating FWM products to fall on to any channels [5-6]. However, the newly produced FWM products can mix with channel signals or themselves to produce higher-order FWM products which can overlap with channels and result in crosstalk [7-8].

FIG. 1: NUMBER OF FWM PRODUCTS

In this paper, we have simulated the effect of FWM products in an intensity-modulated direct-detection (IM-DD) WDM environment by varying the chromatic dispersion parameter for equal and unequal channel spacing. It is observed that the effect of FWM is maximum channel the chromatic dispersion coefficient is zero.

II. BACKGROUND Optical fibres in telecommunication systems now carry

more channels and higher optical powers than ever before. Systems are operating in which the fibre carries such a high optical power density that signals can modify the transmission properties of the fibre. An optical channel can then affect how it and other channels propagate through the fibre - leading to nonlinear effects. By the term nonlinear, we mean that the optical signal leaving the fibre at a given wavelength no longer increases linearly with the input power at that wavelength. Nonlinearity in optical fibre essentially leads to the conversion of power from one wavelength to another. The system implications of this wavelength conversion depend on the type of channel or channels used to carry the data.

Nonlinear effects have become much more important since the development of the optical fibre amplifier. These amplifiers can boost the power in a number of channels at different wavelengths simultaneously rather than having a

(IJIDCS) International Journal on Internet and Distributed Computing Systems. Vol: 1 No: 2, 2011 63 separate repeater for each channel. This allows many more channels to be multiplexed into a single fibre than was economically viable with optoelectronic repeaters. Although the individual power in each channel may be below that needed to produce nonlinearities, the combined effects of all channels can quickly become significant. The combination of high total optical power and a large number of channels at closely spaced wavelengths is ideal for many kinds of nonlinear effects, including:

• Cross-Phase Modulation (XPM) • Four-Wave Mixing (FWM) • Stimulated Brillouin Scattering (SBS) • Stimulated Raman Scattering (SRS)

The non-linear effects of the fibers play a detrimental role in the light propagation. Nonlinear Kerr effect is the dependence of refractive index of the fiber on the power that is propagating through it. Both XPM and FWM cause interference between channels of different wavelengths resulting in an upper power limit for each WDM channel .The most severe problems are imposed by Four-wave mixing (FWM), also known as four-photon mixing, is a parametric interaction among optical waves, which is analogous to inter modulation distortion in electrical systems. In a multi-channel system, the beating between two or more channels causes generation of one or more new frequencies at the expense of power depletion of the original channels. Since these mixing products can fall directly on signal channels, proper FWM suppression is required to avoid significant interference between signal channels and FWM frequency components. The power of FWM product is inversely proportional to the square of the channel spacing.

The performance of an optical wavelength-division multiplexed system is analyzed taking the four-wave mixing (FWM) effect into account. The efficiency of FWM generation is observed to greatly reduce if the spacing between channels is made unequal. However, the scheme requires an increased bandwidth, which can further be reduced by utilizing another scheme called repeated unequal channel spacing. Also the FWM efficiency is found to reduce in the presence of chromatic dispersion. Use of non-uniform chromatic dispersion along the fiber length, which reduces the FWM effect while maintaining a low value of dispersion is investigated. Various other dispersion management mechanisms are also considered in addition to different channel spacing schemes to achieve a comparative study as to which scheme gives the best solution to the FWM problem [9].

III. MAJOR PROBLEMS

Fiber nonlinearity is the main destructive phenomena in high data rate optical communication systems. Because of limited low loss optical spectrum, DWDM is an efficient technique to increase spectral efficiency. To have more channels in the low loss optical spectrum, the channel spacing must decrease. As channel spacing decrease the fiber nonlinearity effects increase and cause to performance degradation of optical system. This degradation even is more critical for the long haul transmission where we need to

supply high level of power to the fiber. Feeding the high power to the fiber not only increase the XPM and FWM effect but also cause to activate the effect of other fiber nonlinearity phenomena like SRS and SBS. In multi-channel systems, FWM in optical fibers induces channel crosstalk and possibly degrades system performance. In this research, we investigate this issue, and our focus is on FWM effect as a fiber most dominant nonlinear effect in zero dispersion fiber.

Fiber nonlinearity is another technical challenge which limits the number of channel in WDM. The fiber nonlinearity causes to high interference and channel cross-talk between WDM channels. Therefore, Extra channel spacing is essential. In addition, the simplest approach to avoid fiber nonlinearity effects is keeping the light intensity low. This action nonetheless, is detrimental due to decreasing the system SNR.

IV. THEORITICAL ANALYSIS

In multi-mode fibers, intermodal dispersion is the dominant contributor of signal waveform distortion. Although intermodal dispersion is eliminated in single mode fibers, different frequency component of optical signal carried by the fundamental mode still travel in slightly different speed giving rise to a wavelength-dependent group delay. As group delay depends on wavelength, different amount of time is taken for the different spectral components to reach a certain distance. Due to this effect the optical signal with a certain spectral width spreads with time when it travels through the fiber. This pulse spreading is important and needs to be determined. Dispersion can also be measured by adding the material and waveguide dispersion together unless a very precise value is needed. Thus material dispersion and waveguide dispersion can be calculated separately and summing up these values will gives the dispersion value.

FWM is a nonlinear process in optical fibers in which generally three signal frequencies combine and produce several mixing products. It originates from the weak dependence of the fiber refractive index on the intensity of the optical wave propagating along the fiber through the third order nonlinear susceptibility. If three signal waves’ three frequencies cba fandff , are incident at the fiber input, new waves generated whose frequencies are , f abc = f a + f b - f c where, ( 3,2,1,, =cba ) (1)

The number of the side bands use to the FWM increases geometrically, and is given by,

⎟⎟⎠

⎞⎜⎜⎝

⎛ −=

2

23 NNM (2)

Where, N is the number of channels and M is the number of newly generated side bands. For example, eight (8) channels produce 224 side bands. The Fig.1 shows the FWM products due to the channels increases.

If we assume that the input channels are not depleted

by the generation of mixing products, the power of the new optical signal generated at frequency exiting the fiber is given by [1],


ηχ

λπ αL

cbaeff

effFWM ePPP

ALD

cnP −

⎥⎥⎦

⎤

⎢⎢⎣

⎡=

2111

224

21024 (3)

Where, n is refractive index, λ is the wavelength, ba PP , and

cP are the input power of three waves, D is the degeneracy factor. 111χ is nonlinear susceptibility and

esu15111 104 −×=χ and η is the mixing efficiency, effA is the

effective area of the fiber and effL is the effective length of fiber. The FWM mixing efficiency η is given by [1],

( )( ) ⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛

−+

+=

−

−

2

2

22

2

1

2/sin41L

L

e

eα

α βΔβΔα

αη (4)

Where, βΔ is the propagation constant difference, can be written as abcabc βββββΔ −−+= (5) Here, β indicates the propagation constant. Efficiency η takes the maximum value of 1 for βΔ =0. In this situation the phase matching condition is satisfied. And the probability of error or bit error rate (BER) is given by, ][5.0)( SNRerfcPBER e = (6) where, signal- to- noise ratio is,

2

)(σ

sIrSNR = (7)

where, )(rPRI sds = and, FWMshotth PPP ++=σ thP is the thermal noise, shotP is the shot noise.

V. SIMULATION SETUP AND DESCRIPTION In this work, we have used the OptSim simulator that gives

us the environment almost the exact physical realization of a fiber-optic transmission system. OptSim provides the users with laser diodes, filters, modulators and all the components which are essential to build an optical network.

The simulation setup for a pump-probe configuration for a NRZ modulated WDM system is shown in Fig. 2. This simulation is carried out to observe the effect of FWM in a WDM configuration in presence of CD.

A. Transmitter section

The transmitter consists of a PRBS generator, which generates pseudo random bit sequences at the rate of 10 Gbps with 27 –1 bits. This bit sequence is fed to the NRZ coder that produces an electrical NRZ coded signal. Three channels are used in this simulation.

B. Fiber section The combined optical signal is fed into the fiber which is a single mode fiber. The fiber model in OptSim takes into account the unidirectional signal flow, stimulated and spontaneous Raman scattering, Kerr nonlinearity and dispersion. Here, we can set the length, dispersion parameters, attenuation, nonlinear index, core area of the fiber and FWM options. At the output of the fiber, the probe signal would have undergone the FWM effects and the waveform at the output will be distorted. C. Receiver section At the output of the trapezoidal optical filter (for the probe channel), a photodiode converts the optical signal into an electrical signal. An electrical low pass Bessel filter follows the avalanche photodiode. This has a cut-off frequency determined by the type of the waveform used for modulation and in our case 193.125 THz. Finally at the output of the low pass filter, OptSim provides a visualization tool called Scope. It is an optical or electrical oscilloscope with numerous data processing options, eye display and BER estimation features. If the eye opening is very wide and there is no crosstalk. Eye diagrams can be used to effectively analyze the performance of an optical system

Fig. 2: Simulation set up diagram of 3-channel WDM system


VI. RESULT AND DISCUSSION Here, we investigate the effect of XPM on WDM optical

transmission system in terms of eye diagram, BER, input pump and probe power etc. The channels are modulated at 10 Gbps data rate using NRZ format and separated by 0.4 nm, the distance between the in-line optical EDFA fiber amplifiers is 100 km (span length). The fiber dispersion value is varied from 0 to 6 ps/nm-km through several parametric runs. The three signals are launched at 193.025 THz, 193.075 THz and 193.125 THz respectively, so that they have 0.05 THz uniform spacing. The fourth signal FWM is studied to investigate the effect of FWM using optical power meter with a center frequency, estimated in Equation-1 (192.975 THz). The simulation parameters are given in Table I.

TABLE I SIMULATION PARAMETER AND THEIR VALUES

Parameter (unit) Values Pump frequency ( THz) 193.025-193.125 Probe frequency (THz) 193.075 Channel separation (GHz) 50 Pump power (dBm) -10 to 4 Reference bit rate ( Gbit/s) 10 Attenuation (dB/km) 0.2 Fiber length (km) 100 Dispersion coefficient (ps/nm-km) 0-6 Booster amplifier gain (dBm) 6 Preamplifier gain (dB) 25

For equal channel spacing, the optical spectrum for

input signals shown in Fig. 3. The output spectrum of the signals for D= 0 ps/nm-km and D=6.0 ps/nm-km are shown in Fig. 4 and Fig. 5 respectively. The output signal spectrums show that with the increase of dispersion the peak of the FWM effect decreases. For example, at zero dispersion co-efficient the effect becomes significant and it generated other wavelengths of significant amplitude which are taking power from its parent signal.

Fig.3: Input signals of 3-channels with equal channel spacing

Fig.4: Output spectrum of 3-chs. with equal channel spacing (D=0)

Fig. 5: Output spectrum of 3-chs. with equal channel spacing (D=6)

On the other hand, at Fig. 5 at dispersion co-efficient (D) of 6 ps/nm-km generated other wavelengths amplitude significantly small.

Fig. 6: Input signals of 3-channels with unequal channel spacing

Fig. 7: Pout Vs Dispersion with unequal channel spacing


For unequal channel spacing, the optical spectrum for input signals shown in Fig. 6. At the output power meter measure the output power in corresponds shown in Fig. 7. The variation shows that the three signals are transmitted whereas the FWM signal is suppressed as the dispersion is increased. The performance of the probe channel is also monitored at the receiver end by observing the eye diagram formation for equal as well as unequal channel spacing by varying the dispersion parameter. Fig. 8 and Fig. 9 show the effect of zero dispersion for equal and unequal channel spacing respectively. We found that the link performance of unequal channel spacing is better than equal channel spacing.

Fig. 8: Eye diagram for equal channel spacing at D=0

Fig. 9: Eye diagram for unequal channel spacing at D=0

Bit error rate (BER) is a more accurate metric to evaluate the performance of an optical transmission system. We have observed BER performance of both equal and unequal channel spacing by varying the dispersion coefficient. The plots of BER versus chromatic dispersion are presented in Fig. 10 and Fig. 11 for equal and unequal channel spacing respectively. From Fig. 10, it is seen that at D= 3.5 ps/nm-km the BER is about 10-10 for equal channel spacing on the contrary from Fig. 11 BER is about 10-20 for the same of dispersion coefficient. Thus we can say that the fibers which has higher dispersion are good enough than the zero dispersion fiber for a WDM fiber-optic transmission system.

Fig. 10: BER Vs Dispersion coefficient for equal channel spacing

Fig. 11: BER Vs Dispersion coefficient for unequal channel spacing In this paper, we have considered these FWM products and shown that these products could become a serious problem when channel power became large or channel spacing became narrow. The influence of fiber four-wave mixing (FWM) on multi-wavelength systems have been studied, which causes unexpected signal i.e. noise and degrades system performance. In this paper, bit error rate (BER), Q factor and eye diagram are analyzed for optimum result by the using simulation.

VII. POSSIBLE APPLICATIONS

WDM systems send data through an optical fibre using a number of channels (typically 16 or 32) - each with its own designated frequency. If two or more channels interact with each other through four-wave mixing, optical power will be generated at new frequencies at the cost of reduced power in the original channels. This power loss makes it more difficult to correctly detect the digital data in these channels - making errors more likely and reducing the information bandwidth of the system.

However, four-wave mixing is not just a detrimental effect. Possible applications for FWM in fibre include:

• High-speed, all-optical frequency conversion • Dispersion compensation in long-haul optical fibre

links • Distributed measurements of dispersion and

nonlinear parameters in fibres


Millimetre wave generation for microcellular mobile communications

VIII. CONCLUSION In this paper we have demonstrated the impact of

dispersion coefficient on FWM in a WDM system for equal and unequal channel spacing for 3-copropagrting channel at a bit rate of 10 Gbps. The FWM effect has been illustrated through computer simulations. It has been shown that FWM effect can be suppressed by increasing dispersion in the fiber. There is less FWM effect it unequal channels are considered. We also found that FWM crosstalk generation and its effect is maximum at zero dispersion. The number of FWM component increases dramatically and it causes to transfer energy from the main component to new component. Also most of these components are overlapped directly with original channel and causes high level of interferences and performance degradation. In addition, the nonlinearity effect of optical fiber causes phase shifting on both sidebands of each channel. And because the frequency of each sideband is different, the phase delay of each sideband might be different. The results of our simulation have important consequences for understanding multi-channel WDM systems that suffer signal degradation by FWM or use FWM for wavelength conversion.

REFERENCES

[1] G. P. Agrawal, Fiber-Optic Communication Systems, 3rd Ed., Wiley, New York, 2002.

[2] G. P. Agrawal, Nonlinear Fiber Optics, 3rd Ed., Academic Press, San Diego, CA, 2001.

[3] A. R. Chraplyvy, Limitations on lightwave communications imposed by optical-fiber nonlinearities, IEEE J. Lightwave Technology, pp. iw-1557, 1990, vol. 8.

[4] R. G. Waarts and R. P. Braun, System limitations due to four-wave mixing in single-mode optical fibers, Electron. Letts., pp. 873-875, 1986, vol. 22.

[5] S. Shuxian, Higher-order four-wave mixing and its effect in WDM systems, Optical Society of America, pp 166-171, 2000, vol. 7, no. 4.

[6] K. Inoue, Experimental Study on Channel Crosstalk Due to Fiber Four- Wave Mixing Around the Zero-Dispersion Wavelength, IEEE Journal of Lightwave Technology, pp 1023-1028, 1994, vol. 12.

[7] N. Shibata, R. P. Braun, and R. G. Waarts, Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a singlemode optical fiber, IEEE J. Quantum Electron, pp. 1205-1210, 1987, vol. 7.

[8] F. Forghieri, R.W. Tkach, A.R. Carplyvy, and D. Marcause, Reduction of four-wave mixing crosstalk in WDM systems using unequally spaced channels, IEEE Photonics Technology Letters, 1994, vol. 6.

[9] M. F. Uddin, A. B. M. N. Doulah, A. B. M. I. Hossain, M. Z. Alam and M. N. Islam, Reduction of four-wave mixing effect in an optical wavelength-division multiplexed system by utilizing different channel spacing and chromatic dispersion schemes, Opt. Eng. 42, 2761 ,2003.

Engr. Z. Rahman is currently working at the University Grants Commission of Bangladesh, as an Senior Assistant Director in Research Support and Publication Division. Also he is studying in PhD program at BUET. He received his M.Sc in Electrical and Electronic Engineering from BUET, Bangladesh and his B.Sc in Electrical and Electronic Engineering from Islamic University of Technology (IUT), Bangladesh. He received a number of prizes in his

academic period. He was a Faculty Member at the Institute of Scientific Instrumentation and some private universities. Previously he was also an Assistant Programmer at the Prime Minister’s Office and Project Engineer at a private consulting company. He is a member of the IEB, BCS, and IEEE.

Effect of Chromatic Dispersion on Four-Wave Mixing in WDM ... · S. M. A. Islam IMCT University...

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