Optics Communications 222 (2003) 169–178

www.elsevier.com/locate/optcom

Long-haul WDM system through conventional singlemode optical fiber with dispersion compensation by

chirped fiber Bragg grating

Pei Li*, Jian Shuisheng, Yan fengping, Ning Tigang, Wang Zhi

Institute of Light-wave Technology, Northern Jiaotong University, Beijing 100044, China

Received 17 September 2002; received in revised form 12 May 2003; accepted 13 May 2003

Abstract

By optimizing the fabrication process of the chirped optical fiber Bragg grating (FBG), we have obtained the ripple

coefficient of reflectivity and time delay smaller than 0.2 dB and 12 ps, respectively. We have implemented dispersion

compensation with FBG in two conventional single mode optical fiber (G.652) systems (4� 10 Gb/s, 400 km, and 4� 10

Gb/s, 800 km), with a power penalty less than 2 dB per-channel. Our results show that the properties of the 4� 10 Gb/s,

800 km transmission system are better than the criterion of the international telecommunication union-telecommuni-

cation standardization sector (ITU-T). We monitored the polarization mode dispersion (PMD) of the 4� 10 Gb/s, 800

km transmission systems for several months, our results show that the PMD compensation is not necessary for a 10 Gb/s

system.

� 2003 Elsevier Science B.V. All rights reserved.

Keywords: Long-haul WDM system; Optical fiber grating; Dispersion compensation; PMD

1. The dispersion compensation of optical fiber

With rapid increasing of information industry

throughout the world, more and more attention is

attracted on the communication networks with

high speed and larger capacity. The optical fiber

communication system is an important part in

modern communication networks. Usually, thereare three key problems associated with the optical

* Corresponding author. Tel.: +86-10-51688016; fax: +86-10-

51683625.

E-mail address: peilip@sina.com (P. Li).

0030-4018/03/$ - see front matter � 2003 Elsevier Science B.V. All r

doi:10.1016/S0030-4018(03)01556-6

fiber communication system, that is, the trans-

mission loss, dispersion, and the nonlinear effect

[1–3]. The transmission loss is now not a main

problem due to the invention of Erbium doped

fiber amplifier (EDFA) [4], the nonlinear effect can

also be suppressed by introducing some dispersion.

Therefore, the dispersion becomes the major ob-

stacle of improvement of the optical fiber com-munication system. For example, there is about

17 ps/nm km dispersion at wavelength 1.55 lm in

G.652 fiber, this dispersion expands the pulse se-

riously and causes inter-symbol interference, and

results in an optical fiber communication system

with lower speed.

ights reserved.

Fig. 1. The residual dispersion of 80 km fiber compensated by

DCF (kD¼0 � 1545 nm).

170 P. Li et al. / Optics Communications 222 (2003) 169–178

In order to reduce the effect of dispersion, many

fiber structures have been proposed. At first, the

zero dispersion point was shifted to wavelength at

1.55 lm to obtain the so-called dispersion-shifted

fiber (DSF). But this kind of fiber is not efficient in

wavelength division multiplex (WDM) system dueto nonlinear effect. Then, the compromise struc-

tures considered both the dispersion and nonlinear

effect were studied. This kind of fiber is called

G.655 fiber [5–8], and has about 2–6 ps/nm km

dispersion at 1.55 lm wavelength window. How-

ever, the dispersion is still a problem of G.655 fiber

system, especially for long distance and high-speed

transmission system and the dispersion compen-sation is still necessary in G.655 fiber system. In

addition, because G.655 fiber has small dispersion,

nonlinear effect prevents it from building the

WDM system with channel spacing of 50 GHz.

However, G.652 fiber has high dispersion at

wavelength 1.55 lm, so the nonlinear effect can be

suppressed effectively, so, using dispersion com-

pensation technique, it is easy to establish a WDMsystem with the channel spacing of 50 GHz on

G.652 fiber.

Among different dispersion compensation

techniques [9,10], there are two methods which are

very useful; one is of using the dispersion com-

pensation fiber (DCF), the other is of using the

fiber bragg grating (FBG) [11]. However, by

comparison, the DCF have following disadvan-tages: first, it is very expensive. Second, EDFA is

often necessary to compensate the insertion loss of

DCF, and introduce an extra cost. Third, the

dispersion slope of DCF (Lucent Type DK-60)

does not match those of G.652 (Corning SMF-28)

and G.655 fiber (Leaf). For instance, the disper-

sion slopes of G.652 and G.655 fibers at bands of

S, C and L are 0.09404, 0.0922, 0.0901, and 0.0931,0.1055, 0.1013 ps/nm2 km, respectively, but the

dispersion slopes of DCF are )0.33457, )0.3986,)0.3049 ps/nm2 km. Taking 80 km as an elemen-

tary cable section, when the dispersions at the

center wavelengths of S, C or L band are com-

pletely compensated, the residual dispersions at

the lower and higher wavelengths are still very

high, even reaches 150 ps/nm. The residual dis-persion of C band is given in Fig. 1. If the trans-

mission distance increases, the whole residual

dispersion would even go up to thousands of ps/

nm. All these disadvantages prevent DCF from

being used in WDM system. The FBG, however, is

compatible very well with most of present optical

fiber communication systems. It has low trans-

mission and insertion losses, and its refractive

modulation can be controlled in exposure processeasily. The most attractive advantage of using

FBG is that the dispersion and dispersion slope

can be compensated and matched simultaneously.

This is very important, because, in DWDM sys-

tem, the dispersion and dispersion slope of each

channel are different and must be compensated by

different FBGs. Now, the dispersion compensation

of FBG is considered as the best scheme, andhopefully has wide application foreground.

In this paper, the coupled mode theory of FBG

is studied. The FBGs are made by double lens and

scanning stage with phase mask, respectively. The

fabrication process of FBG is optimized to obtain

the high performance FBGs with the wavelengths

P. Li et al. / Optics Communications 222 (2003) 169–178 171

satisfying the ITU-T criterion. The 4� 10 Gb/s 400

km and 4� 10 Gb/s 800 km transmission systems

on G.652 fibers with dispersion compensated by

FBGs are implemented. The power penalty in each

channel is less than 2 dB and even negative at best

point. The PMD of 4� 10 Gb/s 800 km trans-mission system is monitored in a very long time

period at the first time. The result shows that in the

10 Gb/s-transmission system, the PMD dispersion

compensation is not necessary.

2. Theory of FBG dispersion compensation

In chirped FBG, different wavelength compo-

nent involved in a light is reflected at different lo-

cation and result in different time delay. This

property makes FBG useful in dispersion com-

pensation. The characteristics of chirped FBG can

be analyzed by coupled mode theory [12–14].

We define the effective refractive indexs of LP01mode and cladding modes obtained from disper-sion equation as ncoeff andn

cleff , and assume that the

fiber is of single cladding and step-index, and the

radius and refractive index of the core and clad-

ding are a1, n1 and a2, n2, respectively. Then the

electrical fields of the LP01 mode and cladding

mode in the core region can be expressed as:

Ecor � iEco

01J0ðVffiffiffiffiffiffiffiffiffiffiffi1� b

pr=a1Þ

� expðiuÞ expðiðbz� xtÞÞ;Eco

u � � Eco01J0ðV

ffiffiffiffiffiffiffiffiffiffiffi1� b

pr=a1Þ

� expðiuÞ expðiðbz� xtÞÞ;

ð1Þ

Eclr � iEcl

1v

u12

J2ðu1rÞ�

þ J0ðu1rÞ �r2n0n21

� ½J2ðu1rÞ � J0ðu1rÞ�expðiuÞ expðiðbz�xtÞÞ;

Eclu � Ecl

1v

u12

J2ðu1rÞ�

� J0ðu1rÞ �r2n0n21

� ½J2ðu1rÞ þ J0ðu1rÞ�expðiuÞ expðiðbz�xtÞÞ;

Eclz � Ecl

1v

u12

u21r2n0n21b

J1ðu1rÞ expðiuÞ expðiðbz�xtÞÞ;

ð2Þ

where JmðxÞ is the Bessel function of mth order. Eco01

and Ecl1v are the normalized constants. v is the

cladding-mode number, and n0 is the formula for

dispersion relation. Other variables are:

b ¼ ðncoeffÞ2 � n22

n21 � n22; V ¼ 2p

ka1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffin21 � n22

q;

b ¼ 2pkncoeff ; r2 ¼ incleff

ffiffiffiffiffiffiffiffiffiffiffil0=e0

p;

u1 ¼2pk

� � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðn21 � ncl

2

effÞq

:

ð3Þ

From the fields distribution, the coupling con-

stants for core-mode–core-mode coupling and

core-mode–cladding-mode coupling can be

obtained, we defined them as jco–co01–01 and jcl–cl

1v–01.

Third, the coupled mode equations of the LP01mode and cladding modes will be solved by the

numerical method. The slowly changed amplitudes

of the modes that transmit along the +z and �zdirections are Bþ

1 ðzÞ and B�j ðzÞ, respectively. The

subscript j denotes the jth mode. We define:

B�j ðzÞ¼SjðzÞexp

�� i

Z z

0

pK

��1

2ðbjþb1Þþ/ðnÞ

�dn

;

Bþ1 ðzÞ¼RðzÞexp i

Z z

0

pK

���1

2ðbjþb1Þþ/ðnÞ

�dn

;

ð4Þ

where K is the period of FBG, and /ðzÞ is the

slowly changed function along the fiber axis. Then,

the coupled mode equations of FBG are:

R0ðzÞ þ iajðzÞRðzÞ ¼ iXj

K t1jðzÞSjðzÞ;

S0jðzÞ � iajðzÞSjðzÞ ¼ �iK t

1jðzÞRðzÞ;ð5Þ

where jtkj and jz

kj are the transverse and longitu-dinal coupling coefficients between modes k and j,respectively. ajðzÞ are the mismatch of phase be-

tween the forward and backward fundamental

modes. If the length of the FBG is L, then

Rð�L=2Þ ¼ 1; SjðL=2Þ ¼ 0: ð6ÞThe local refractive coefficient is

f ðzÞ ¼ SðzÞRðzÞ : ð7Þ

We can obtain the Riccati differential equation

f 0ðzÞ ¼ �ijt1jf ðzÞ

2 � 2iajðzÞf ðzÞ � ijt1j;

f ðL=2Þ ¼ 0;ð8Þ

172 P. Li et al. / Optics Communications 222 (2003) 169–178

the response of the FBG would be

R0 ¼ f ð�L=2Þ � f �ð�L=2Þ: ð9Þ

From (8), the reflectivity, dispersion and the time

delay of the FBG can be obtained. Fig. 2 gives the

reflectivity and time delay of FBGs with lengthL ¼ 4 cm, The modulation of refractive index is

1� 10�4, and the chirp parameters of the FBGs are

C1 ¼ 1� 10�4, C2 ¼ 7� 10�4, C3 ¼ 1� 10�3.

It can be seen that when the FBG length is

fixed, large dispersion can be obtained with less

chirp of the FBG, but the bandwidth is narrower.

In order to get an optimum FBG dispersion

compensator, it must be certain that the FBG hasthe compromise combination between the disper-

sion, bandwidth and reflectivity, and the ripple

coefficient of reflectivity and time delay should be

as small as possible.

Fig. 3 gives the transmission spectrum of three

cases: (a) n3 ¼ n2, Dn ¼ 5� 10�4, (b) n3 ¼ 0:99n2,Dn ¼ 5� 10�4 (c) n3 ¼ 0:99n2, Dn ¼ 7� 10�4,

Fig. 2. The reflectivity (a) and

Fig. 3. The influence o

where Dn is the modulation of refractive index, n2and n3 are the refractive index of cladding and

outside cladding, respectively. Fig. 3 shows that

there is power penalty at the short wavelength

caused by cladding mode, and this influence will be

increasing with Dn.By analyzing the reflectivity and time delay of

FBG, we find the key problems for the break-

through of the fabrication, they are the stability of

temperature, the flatness of reflectivity, the ripple

of time delay, the PMD, etc.

We had explored and optimized the fabrication

process of FBG. By comparing the PMD of FBGs

made by different kinds of photosensitive fibers,we found that if the fibers are rotated, the FBGs

made by the hydrogen-loaded fibers will have the

smallest PMD. By this experience, we first de-

signed a high-pressure hydrogen loading device,

this device can control the loading time accurately.

Then, we designed the program controlled scan-

ning stage with high accuracy, the length and the

time delay (b) of FBG.

f cladding mode.

P. Li et al. / Optics Communications 222 (2003) 169–178 173

refractive index modulation of the FBGs can be

easily controlled by this stage. We analyzed and

got the diverse optimized programs for various

FBGs. By the optimized process of fabrication,

FBGs with good apodization can be made, and the

ripple coefficient of the power and time delay canbe very small. After the fabrication, the FBGs

were annealed for 7 h at 140 �C, the temperature iscontrolled by program to prevent the characteris-

tics of the FBGs from changing. Finally, the FBGs

were packaged by special materials.

Now, the FBGs with the wavelengths satisfying

the ITU-T criterion can be made. The ripple of

time delay of the optimal designed FBG is lessthan 20 ps, some even less than 12 ps. The cladding

mode loss is less than 0.5 dB. The temperature

coefficient is less than 0.0005 nm/�C. And the

PMD is less than 1 ps.

Fig. 4 shows the reflectivity and time delay of

one of the FBGs fabricated by above technique. Its

center wavelength is 1547.76 nm, and the ripple

Fig. 5. Transmission system of 4� 10 Gb

Fig. 4. The reflectivity (a) and

coefficient of reflectivity and time delay are less

than 0.2 dB and 14 ps, respectively.

3. 4� 10 Gb/s 400 km transmission system on G.652

fiber

3.1. Transmission system structure

As shown in Fig. 5, after multiplex, the 10 Gb/s

signal is amplified, the fiber length is 400 km with

80 km span. In each span, a FBG is used for dis-

persion compensation. At the same time, the ASE

noise of EDFA can be filtered by the FBG. SixEDFAs had been used for power compensation.

3.2. The reflectivity and time delay of FBG

The FBGs used in the system are made by using

the double lens exposure stage and phase mask.

After 400 km transmission, the reflectivity of the

/s 400 km dispersion compensation.

time delay (b) of FBG.

Fig. 6. The reflectivity and time delay of the whole FBGs after

400 km transmission.

174 P. Li et al. / Optics Communications 222 (2003) 169–178

whole FBGs are shown in Fig. 6. We can see thatthe time delay slope is zero, this means a fully

compensation of the dispersion. The center wave-

lengths of each channel are 1549.322, 1550.842,

1552.544 and 1554.136 nm, respectively. The 3 dB

bandwidths are 0.350, 0.348, 0.353 and 0.331 nm,

respectively. The channel spacing is about 1.6 nm,

and the wavelengths fit for the ITU-T wavelength

criterion.

Fig. 7. The eye diagram of back-to-back.

Fig. 8. The eye diagrams of 10 Gb/s signal after transmi

3.3. The eye diagram of 400 km G.652 fiber

transmission after dispersion compensation

The eye diagram of back-to-back is shown in

Fig. 7. The eye diagrams after transmission anddispersion compensation in 4� 10 Gb/s 400 km

system on G.652 fiber is shown in Fig. 8. We can

see that the pulse width has been recovered, and

the eyes open well, this means that the signal-to-

noise ratio (SNR) is good.

3.4. The measurement of BER

The BER of 10 Gb/s signal in each channel after

demultiplexing is measured. When the BER is

10�10 and the bit error is zero, the power penalties

of transmission in each channel are 1.2, 1.98, )0.9and 0.4 dB. As shown in Fig. 9, the power penalty

in channel 2# is larger, this is because that a dif-

ferent package material is used. After changing the

package material, the power penalty has beenimproved to be 0.9 dB.

4. 4� 10 Gb/s 800 km transmission system on G.652

fiber

4.1. Transmission system structure

As shown in Fig. 10, the dispersion of the 4� 10

Gb/s 800 km transmission system is compensated

by FBGs that are fabricated by using the scanning

stage and phase mask, and the FBGs have similar

characteristics by controlling the exposure UV

power and the scanning process. The center

wavelengths of the four channels are 1547.709,

1549.338, 1550.936 and 1552.578 nm, respectively.The space is about 1.6 nm, and the wavelength fit

ssion and compensation in 400 km G.652 fiber.

Fig. 12. The reflectivity and time delay of whole FBGj1 (j ¼ 1–

5) after 800 km transmission.

Fig. 9. The BER of 4� 10 Gb/s, 400 km FBG dispersion

compensation.

Fig. 11. The reflectivity, time delay of FBG11.

P. Li et al. / Optics Communications 222 (2003) 169–178 175

for the ITU-T wavelength criterion. In this system,11 EDFAs are used for the power compensation.

4.2. The reflectivity and time delay of FBG

Figs. 11 and 12 give the experimental results of

channel 1# (kC ¼ 1547:709 nm). Fig. 11 shows thereflectivity and time delay of FBG11. Its center

wavelength is 1547.786 nm and its 3 dB bandwidthis 0.430 nm; Fig. 12 shows the reflectivity and time

delay of whole FBGj1 (j ¼ 1–5) after 800 km

transmission. The center wavelength is 1547.709

nm and its 3dB bandwidth is 0.362 nm.

By comparing Figs. 11 and 12 and the same

measurement results of the other three channels,

we can see that after 800 km transmission, the

Fig. 10. 4� 10 Gb/s 800 km transmission syste

bandwidth of the FBG becomes narrower and the

center wavelength changes a little, this is due to

the error accumulation of 5 FBGs. The reflectivity

m with dispersion compensated by FBG.

176 P. Li et al. / Optics Communications 222 (2003) 169–178

of FBG is still flatness and the time delay slope is

zero, this means that the dispersion is fully com-

pensated.

4.3. The measurement of BER

After 800 km transmission, we measured the

BER of each channel, and get the BER curves as

shown in Fig. 13. When the BER is 10�10 and the

bit error is zero, the power penalty in four chan-

nels are 1.36, 0.89, 1.67 or 1.32 dB.

5. The PMD of FBG dispersion compensationsystem

With the development of optical communica-

tion system, the PMD of the system can�t be ne-

glected. ITU-T had suggested interferometer

method and Jones Matrix Eigen analysis method

as the basic method of measuring the PMD. But

the latter method seems better for the PMD mea-surement of FBG [15].

Fig. 14 is the measurement structure. Through

the polarization adjustor, the light source from the

tunable laser is launched into FBG by fixed step

Fig. 13. The BER of 4� 10 Gb/s, 800 km FBG dispersion

compensation.

Fig. 14. The experiment unit for FBG�s PMD measure

spacing, and signal is analyzed by the polarization

analyzer. Finally, the result will be displayed after

the data had been processed by computer.

5.1. The tolerance of PMD

To the first order, PMD is a group-velocity

difference between two orthogonal states of po-

larization. These orthogonal states are called the

principal states of polarization (PSP�s), and the

difference in arrival time between both axes is

called the differential group delay (DGD). PMD is

a statistical process in optical fibers. Owing to

variation of the local birefringence, the DGD andthe PSP�s vary with time. The mean value of the

DGD is also called PMD.

According to the worst condition design model,

there is a maxim tolerant DGD exist in each

transmission system, and its value is decided by the

bit rate and transmission haul of the system. If the

difference in arrival time between both axes is Ds,then in a data transmission system, when thepower loss caused by PMD is 1 dB, Ds is equal to30% of the bit duration of the optical pulse, and it

is defined as the normative value of the maxim

tolerant DGD. As DGD vary with time, a safety

actor should be considered which means that the

maxim tolerant DGD must less than 10% of the bit

duration of the optical pulse. Under such condi-

tion, the probability of the <1dB power loss thatcaused by PMD is 99.994%, so we can get

PMDMaxðps=ffiffiffiffiffiffiffikm

pÞ ¼ 100 ðB L1=2Þ�1; ð10Þ

where B is the bit rate of the system, L is the

transmission distance. The maxim tolerant DGD

of different transmission rate is shown in Fig. 15. It

can be seen that in the 10 Gb/s-transmission sys-

tem, when the power loss caused by PMD is 1dB,the maxim tolerant DGD is 10 ps. When the

ment with Jones Matrix Eigen analysis method.

Fig. 15. The maxim tolerant DGD of different transmission

rate.

P. Li et al. / Optics Communications 222 (2003) 169–178 177

transmission rate is increased, the tolerant DGDdecreased very quickly. For example, when the

rate is 40 Gb/s, tolerant DGD is only 2.5 ps.

5.2. The PMD measurement of 4� 10 Gb/s 800 kmtransmission system

Measurements had been done on the above

4� 10 Gb/s 800 km transmission system. The re-sults show that the PMD of each channel is less

than 10 ps, which means that the power loss

caused by PMD is less than 1dB. Fig. 16 shows a

team of statistical results, the PMD is measured

within two days, and we choose the results of 10

time spots for measurement. At each time, we

measured the PMD three times, and took the av-

erage as the PMD at this time. We had also donethe similar measurements for the 10 Gb/s, 1000 km

transmission system and the PMD is still less than

10 ps.

Fig. 16. The PMD of the 4� 10 Gb/s 800 km transmission

system.

From these results, we can see that in the 10 Gb/

s long distance transmission system with FBG

dispersion compensation, the PMD has little in-

fluence on the system, and the compensation is not

necessary.

6. Conclusions

By optimizing the fabrication process of FBG,

four difficult problems have been solved, that is,

the temperature excursion of the center wave-

length, the PMD affection, the ripple of time delay,

and the large loss due to cladding mode. Now, theFBGs with the wavelengths satisfying the ITU-T

criterion can be made with ripple of time delay less

than 20 ps, in some cases even less than 12 ps, the

PMD is less than 1 ps. The cladding mode loss and

the temperature coefficient are less than 0.5 dB and

0.0005 nm/�C, respectively.The 4� 10 Gb/s 400 km transmission systems

on G.652 fibers with dispersion compensated byFBGs are implemented, the power penalty in each

channel is less than 2 dB, and even negative at the

best point. These results are in advance in the

world. And the negative power penalty shows that

the sensitivity of the receiver is increased compared

to that of the back-to back one.

By far, the 4� 10 Gb/s 800 km transmission

system is the longest system on G.652 fibers withdispersion compensated completely by FBGs.

(Now, in our laboratory, we successfully imple-

mented the 2� 10 Gb/s 1000 km transmission

systems on G.652 fiber with dispersion compen-

sated by FBGs, the power penalty in each channel

is less than 1 dB.) And the PMD of this system was

monitored during a very long time period at first

time. The result shows that in the 10 Gb/s-trans-mission system, the PMD dispersion compensa-

tion is not necessary.

Because of its large communication capacity

and cheap building outlay, the optical fiber com-

munication system provides an infinite bandwidth

communication platform, and its developing trend

is towards the direction of all optical network.

Now, attention is attracted on the problem ofsolving the dispersion on G.652 fiber. The

achievement of the two transmission systems

178 P. Li et al. / Optics Communications 222 (2003) 169–178

means that it is feasible for the dispersion com-

pensation scheme by FBG. We can expect that the

chirped FBG will plays a very important role in

the future�s optical fiber communication system.

Acknowledgements

This work is jointly supported by the national

‘‘863’’ project, the national natural science foun-

dation of China and the Pandeng foundation of

Northern Jiaotong University.

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