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Adjusting the detection window to improve the soliton

communication system

Sien Chi

a,*

, Chuan-Yuan Kao

a

, Jeng-Cherng Dung

a

, Senfar Wen

b

aInstitute of Electro-Optical Engineering, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 300, Taiwan, ROC bDepartment of Electrical Engineering, Chung Hua University, Hsinchu 300, Taiwan, ROC

Received 7 March 2000; received in revised form 14 September 2000; accepted 13 October 2000

Abstract

The improvements of the Q factors of 10-Gb/s soliton systems detected by adjusting detection window are studied. We have found that the optimal width of the detection window depends on the induced timing jitter, noise-induced soliton energy ¯uctuation, ampli®er noise, dispersive wave, and soliton pulse width. Ó 2000 Elsevier Science B.V. All rights reserved.

Keywords: Solitons; Optical communication; Nonlinear optics

The performances of soliton transmission sys-tems were evaluated by considering the noise-induced timing jitter [1], the ¯uctuation of soliton amplitude [2,3], and the ¯uctuation of soliton energy. The most commonly used method of measuring the system performance in an optical transmission system is the decision circuit method of measuring Q factor [4]. The Q factor can be calculated by integrating its power over a bit slot [5], which is called the integration and dump method. The integration of soliton power over a bit slot is not an optimal design because soliton energy lies within a duration much smaller than a bit slot. It has been reported that the in-line optical gate in time domain could reduce ampli®ed

spon-taneous emission (ASE) noise [6]. The optical gate can be realized by a sinusoidal driven electroab-sorption modulator and the gate function is nearly square shaped [6±8]. Considering such an optical gate is placed before the photodiode of the re-ceiver, only the soliton power within the gate time is able to arrive at the photodiode. Then the re-ceived signal is integrated over a bit duration in the receiver. Therefore, the optical gate together with the receiver circuit function as an integrator which integrates the soliton power over a duration of the gate time. We call the gate time as detection win-dow. When the detection window is less than a bit slot, a fraction of noise energy can be excluded without the expense of signal energy. On the other hand, with too small a detection window like sampling the signal's amplitude at bit centrum, the system performance may su€er from the noise-induced timing jitter. The dependence of the sys-tem performance on detection window has not

Optics Communications 186 (2000) 99±103

www.elsevier.com/locate/optcom

*Corresponding author. Tel.: 5731824; fax:

+886-3-5716631.

E-mail address: schi@cc.nctu.edu.tw (S. Chi).

0030-4018/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S0030-4018(00)01062-2

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been considered in literatures. In this letter we will study the improvements of the Q factors of a sol-iton systems by adjusting the detection window.

The modi®ed nonlinear Schrodinger equation describing the soliton propagation in a ®ber is numerically solved. We take the carrier wave-length k ˆ 1:55 lm, the second-order ®ber

dis-persion b2ˆ ÿ0:25 ps2/km, the third-order ®ber

dispersion b3ˆ 0:14 ps3/km, the Kerr coecient

n2ˆ 2:7  10ÿ20 m2/W, the e€ective ®ber area

Aeffˆ 50 lm2, and the ®ber loss a ˆ 0:2 dB/km.

The soliton system of 10-Gb/s bit rate is

consid-ered and its bit slot Tbˆ 100 ps. The soliton pulse

width Ts(FWHM) and the transmission distance Lt

are varied. The soliton is ampli®ed every 50 km

and the spontaneous emission factor nsp of an

optical ampli®er is assumed to be 1.2. An in-line Fabry±Perot ®lter is inserted after every ampli®er to reduce the ASE noise and noise-induced timing jitter, where the ®lter bandwidth is optimized. A second-order Butterworth electric ®lter with a

narrower bandwidth Dmf in the receiver is used to

further reduce noise [9,10]. The accumulated ASE noise is detrimental for optical ampli®ed long links [2], and the shot noise and thermal noise in the receiver are negligible. For the cases shown in this

paper, Dmf is also optimized. The bit energy is

obtained by integrating the amplitude of the ®l-tered signal over a bit slot in which its centrum coincides with the bit centrum. The gate function of the detection window is modeled by a ®fth-order super-Gaussian function

G…T † ˆ exp " ÿ1 2 T Td  2m# ; …1†

where Td is the detection window and m ˆ 5. The

system performance can be evaluated by bit error rate (BER) which is given by [11]

BER ˆ1 4 erfc E1ÿ ED dE1  2 p    ‡ erfc EDÿ E0 dE0  2 p   ; …2† where erfc…x† ˆ 2=p Rp x1eÿy2

dy is the

comple-mentary error function. In Eq. (2), ED is the

decision threshold; E1 and E0 are the average

in-tegrated energies of 1 and 0 bits, respectively; dE1

and dE0 are the standard deviations of energies of

1 and 0 bits, respectively. The Q factor of the soliton system can be evaluated by BER, which

is Q ˆp2erfcÿ1…2BER†: For BER ˆ 10ÿ9, Q ˆ 6.

For a given detection window Td, the decision

threshold ED is optimized for the minimum BER

or the maximum Q. We use 1024 sample bits of equal probable 1 and 0 bits to calculate the Q factor.

Fig. 1 shows an output of two neighboring 1 and 0 bits for the case of transmission distance

Ltˆ 10000 km and soliton pulse width Tsˆ 10 ps.

In Fig. 1, the initial pulse shape and the output pulse shape without ASE noise are shown for comparison. One can see that, in the absence of ASE noise, soliton broadens and the displacement of the soliton is due to the third-order ®ber dis-persion and ®lters. In the presence of ASE noise, soliton further broadens and the displacement of the soliton is due to noise-induced timing jitter in addition to the third-order ®ber dispersion and ®lters. In the presence of ASE noise, the beating and the nonlinear interaction between ASE noise and soliton lead to the distortion of output pulse shape, especially on the pedestal of the soliton, and the ¯uctuation of integrated energy. There is sig-ni®cant dispersive wave radiated from the soliton owing to the nonlinear interaction. One can see that the output soliton energy with ASE noise

Fig. 1. An output pulse shape of two neighboring 1 and 0 bits at 10 000 km for the case of soliton pulse width Tsˆ 10 ps. The

initial pulse shape is shown by dotted line. The output pulse shapes with and without noise are shown by solid and dashed-dotted lines, respectively.

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is less than that without ASE noise. The noise-induced soliton energy ¯uctuation and timing jitter are the main origins of the BER of 1 bits. Because the power of dispersive wave is low and the non-linear interaction between ASE noise and disper-sive wave is weak, the beating between ASE noise and dispersive wave is the main origin of the BER of 0 bits and is also an origin of the BER of 1 bits

when detection window Td is large.

Fig. 2(a) shows the average integrated soliton

energy E1versus detection window Tdat 10 000 km

for the case of Tsˆ 10 ps. The data shown in the

®gure is normalized by the average energy within a bit slot E1U, i.e., E1U ˆ E1…Td ˆ Tb†. The dashed

line represents the case that the center of the de-tection window is at the soliton peak in order to exclude the e€ect of timing jitter. Solid line rep-resents the case that the center of the detection window is at bit centrum and the e€ect of timing

jitter is included. We can see that, when Tdis small,

the average integrated soliton energy E1 including

the timing jitter is less than that without the timing

jitter. When Tdis larger than about 25 ps, the e€ect

of timing jitter on the average soliton energy can

almost be neglected. Fig. 2(b) shows dE1and dE0

versus Tdfor the same case shown in Fig. 2(a). One

can see that dE0 slowly increases with Td. dE1

rapidly decreases as Td increases when Td is less

than about 20 ps mainly because of noise-induced timing jitter. This shows that the e€ect of timing jitter is more tolerable with larger detection win-dow. The noise-induced soliton energy ¯uctuation

also contributes to dE1, which can be observed by

comparing dE1 to dE01 shown in the ®gure by

da-shed-dotted line. dE0

1 is the standard deviation of

integrated energies of 1 bits calculated by taking the center of the detection window at the soli-ton peak in order to exclude the e€ect of timing

jitter. When Td is larger than 25 ps, dE1 increases

with Tdthat is due to the ASE noise and dispersive

wave.

For the integration and dump method, the

op-timal Tdrelates to soliton pulse width. Fig. 3 shows

the increase of average root-mean-square (rms)

pulse width Tr normalized by initial rms pulse

width Tri along the ®ber for the case of 10-ps

sol-iton. In Fig. 3 both cases with and without am-pli®er noise are shown. As is explained previously, ASE noise enhances soliton broadening. We

opti-mize Td along the transmission distances and the

results are shown in Fig. 4, where the corre-sponding Q are also shown. One can see that the

optimal Td increases with pulse width. A larger

pulse width requires a wider detection window in order to reduce the degradation of Q that is due to noise-induced timing jitter and soliton energy ¯uctuation.

Fig. 5 shows Q versus Td for Ltˆ 10000 km

and Tsˆ 10, 15, and 20 ps. The optimal Td ˆ 35,

Fig. 2. (a) The average integrated soliton energy E1; (b) the

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47, and 55 ps for Tsˆ 10, 15, and 20 ps,

respec-tively. For the considered cases, the optimal Tds

are about three times of the initial pulse widths.

One can see that the optimal Tf for the maximum

Q factor increases with initial soliton pulse width. For a small detection window, Q factor is mainly deteriorated by 1 bits that is due to noise-induced timing jitter and soliton energy ¯uctuation. When

Td is much less than the pulse width, the detection

method in fact becomes the sampling method in which the Q factor is calculated by sampling the signal's amplitude at bit centrum. The result shows that the sampling method is not the best detection method to obtain the maximum Q factor. For a

larger detection window (Td> 22 ps in the case of

Tsˆ 10 ps), Q is mainly degraded by 0 bits because

0 bits contain signi®cant dispersive waves which can be clearly observed in Fig. 1. Again, from the results shown in Fig. 5, the Q measured by sam-pling method are smaller than the maximum Q measured by the integration and dump method. With the integration and dump method, the maxi-mum Q is higher for shorter initial pulse width because the signal-to-noise ratio is higher for the soliton of shorter pulse width.

In conclusion, the improvements of the Q fac-tors of 10-Gb/s soliton systems detected by ad-justing detection window are studied. The optimal detection window depends on the noise-induced timing jitter, noise-induced soliton energy ¯uctu-ation, ASE noise, dispersive wave, and soliton pulse width. The contribution of BER from 1 bits is slightly larger than 0 bits with the optimal detection window. It is found that the optimal detection window by the integration and dump method is about three times of the initial soliton pulse width for the considered cases.

Fig. 3. Average rms pulse width Trnormalized by initial value

Trialong the ®ber for the case of 10-ps soliton. The cases with

and without ampli®er noise are shown by solid and dashed lines, respectively.

Fig. 4. Optimal detection window Tdand the corresponding Q

factor for di€erent transmission distances for the case of 10-ps soliton.

Fig. 5. Q factor versus detection window Tdfor 10-Gb/s bit rate

and 10 000-km transmission distance. The cases of the soliton pulse width Tsˆ 10, 15, and 20 ps are shown.

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Acknowledgements

This work is partially supported by the Na-tional Science Council, Republic of China, under contract NSC 88-2215-E-009-006.

References

[1] J.P. Gordon, H.A. Haus, Opt. Lett. 11 (1986) 665±667. [2] F. Matera, M. Settembre, J. Lightwave Technol. 14 (1996)

1±11.

[3] D.S. Govan, W. Forysiak, N.J. Doran, Opt. Lett. 23 (1998) 1523±1525.

[4] N.S. Bergano, F.W. Kerfoot, C.R. Davidson, IEEE Photon. Technol. Lett. 5 (1993) 304±306.

[5] D. Marcuse, J. Lightwave Technol. 9 (1991) 505±513. [6] M. Suzuki, H. Tanaka, N. Edagawa, Y. Matsushima,

J. Lightwave Technol. 10 (1992) 1912±1918.

[7] M. Suzuki, H. Tanaka, Y. Matsushima, Electron. Lett. 28 (1992) 934±935.

[8] M. Suzuki, N. Edagawa, I. Morita, S. Yamamoto, S. Akiba, J. Opt. Soc. Am. B 14 (1997) 2953±2959. [9] B. Malomed, F. Matera, M. Settembre, Opt. Commun. 143

(1997) 193±198.

[10] E. Laedke, N. Gober, T. Schaefer, K. Spatschek, S. Turitsyn, Electron. Lett. 35 (1999) 2131±2133.

[11] G.P. Agrawal, Fiber-Optic Communication Systems, sec-ond ed., Wiley, New York, 1997 (Chapter 4).

數據

Fig. 1 shows an output of two neighboring 1 and 0 bits for the case of transmission distance
Fig. 5 shows Q versus T d for L t ˆ 10000 km
Fig. 4. Optimal detection window T d and the corresponding Q

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