- Email: [email protected]
Effect of self-phase modulation on a dispersion compensated link employing a dispersion-compensating fiber
I5 November 1997
OPTICS
COMMUNICATIONS ELSEVIER
Optics Communications
143 ( 1997) 203-208
Effect of self-phase modulation on a dispersion compensated link employing a dispersion-compensating fiber P. Palai, K. Thyagarajan
’
Depurtment of PhyCcs, Indian Institute of Technology New Delhi 110 016. India Received 14 April 1997: revised 23 June 1997; accepted
I
July 1997
Abstract A study of the effect of self phase modulation (SPMI on a fiber link consisting of a non-dispersion shifted fiber (NDSF) and a dispersion compensating fiber (DCF) operating at 1550 nm has been carried out. The characteristics of signal pulse transmission through the fiber combination of NDSF followed by DCF (post-compensation) and DCF followed by NDSF (pre-compensation) are obtained by numerical simulation. It is found that though in the linear regime there can be exact compensation of dispersion for either combinations of NDSF + DCF and DCF + NDSF, in the nonlinear regime of transmission the two combinations behave very differently. For the case of NDSF + DCF the pulse width increases and attains a maximum value before decreasing with the input signal power, whereas for the combination of DCF + NDSF the pulse undergoes compression. It is also shown that when the linear dispersion in NDSF is slightly under compensated by DCF, the pulse width in the DCF + NDSF combination does not change appreciably for a large range of input signal power. 0 1997 Elsevier Science B.V.
1. Introduction Recently, there has been a growing interest in high data rate repeaterless optical fiber communication systems using practical erbium doped fiber amplifiers (EDFAs). With the advent of EDFAs, the preferred wavelength for optical communication has been shifted to 1550 nm. More than 70 million kilometers of non-dispersion-shifted fibers (NDSFSI with very low value of chromatic dispersion (D) at 1310 nm. have already been laid through out the world. Unfortunately, these fibers have a large dispersion coefficient (D - + I8 ps/(kmnm)) at 1550 nm which will limit the data rate. This large dispersion could be compensated by using one of the various schemes of dispersion compensation wherein the accumulated dispersion of the NDSF is cancelled by passing the dispersed pulses through a suitable optical device so as to have a net zero chromatic dispersion before it is received. Amongst various schemes of
’ Corresponding author. E-mail: [email protected].
dispersion compensation, use of dispersion compensating fibers (DCFS) has been found to be very practical and convenient [l-3]. These DCFs have a large negative D at 1550 nm so that a relatively short length of the DCF with the NDSF could lead to a net zero dispersion in the link. Generally, dispersion compensated fiber links employing DCFs are designed to have a net zero dispersion value at a particular wavelength. In these designs, the signal power is assumed to be small enough not to induce any nonlinear effects such as self-phase modulation @PM), cross-phase modulation (CPM), four wave mixing (FWMI, etc., in the fiber link. These nonlinear effects may arise in the presence of optical amplifiers in the fiber link and can modify various physical properties such as shape, frequency components. etc., of the signal pulse along the length of the link leading to impairment in signal transmission [4]. Hence alleviation of the impairments by managing dispersion and nonlinearity in the transmission link has become a vital issue in the field of optical fiber communications systems. In view of this, various schemes such as optimal dispersion compensation, various formats of time domain multiplexed data, dispersion-allocated soliton
0030-4018/97/S 17.00 0 1997 Elsevier Science B.V. All rights reserved. PfI SOO30-4018(97)00370-2
204
P. P&i.
K. Thyqarajan/
Optics Communications 143 (IYY7J 203-208
transmission systems, etc., have been proposed. In the optimal dispersion compensation scheme, it has been shown that it may be advantageous to slightly under compensate the chromatic dispersion in the fiber link. as it can support more input signal power [5,6]. The detrimental effects of the dispersion and nonlinearity can also be controlled by modulating the signal in a particular format so as to cancel the effect of dispersion with that due to nonlinearity such as SPM [7,8]. Another interesting scheme is to use the dispersion-allocated solitons in a dispersion compensated system where the net dispersion is slightly anomalous but dispersion at any point is large. These systems are shown to have negligible distortion even at very high powers [9- 111. In all the above mentioned schemes, either nonlinearity is assumed to be confined only to the NDSF or performance of the system under nonlinear regime with pre-compensation (DCF followed by NDSF) or post-compensation (NDSF followed by DCF) has not been analyzed. It is quite clear that, in the linear regime, pre- and post-compensation schemes will result in exact dispersion compensation, whereas in the nonlinear regime they may not compensate dispersion exactly. In addition, due to the fiber nonlinearity, the overall system response may depend on whether the DCF follows NDSF or vice versa. This is primarily due to the fact that DCFs have very different characteristics as compared to NDSF such as having a higher nonlinear coefficient (y). and a large negative D and also a different length; these parameters play major roles in pulse evolution in the nonlinear regime. In view of this it is necessary to study the total response of the NDSF-DCF combination in the nonlinear regime. Some preliminary experimental work has been reported on the nonlinear response of NDSF-DCF combinations [12], but no adequate theoretical explanation was provided for the specific results obtained. In this paper we present a numerical study of the pulse propagation in the presence of SPM in the NDSF + DCF (post-compensation) and DCF + NDSF (pre-compensation) combinations to evaluate their relative performances in a fiber transmission link. We show that the total response of the link is significantly different in the two combinations. Indeed in the latter case we show the possibility of pulse compression. Our results are shown to explain some of the results obtained in Ref. [ 121. Also. we show that by using the DCF + NDSF combination with the DCF over-compensating the dispersion of NDSF. it is possible to use a large range of input signal power without affecting the output pulse shape.
2. Modelling Fig. 1 shows a simple typical point to point link consisting of NDSF and DCF. The signal at 1550 nm wavelength from the transmitter may be amplified by an optical amplifier such as EDFA and then propagates
Fig. I. Schematic of a typical point to point fiber link showing transmitter CT, ), fiber combination F, and F2. and receiver CR, ).
through combination of fibers F, and FZ. As the signal is attenuated in the fiber combination, it may again be amplified by another optical amplifier before it reaches the receiver. The combination of the fibers F, and F> is such that either F, is NDSF and FZ is DCF or vice versa. The lengths of the NDSF and DCF are chosen so that the net accumulated linear dispersion from the transmitter to receiver end is zero. Thus exact dispersion compensation will take place for low signal peak power ( P,), where the linear regime of transmission is valid. The evolution of an optical pulse through a fiber is described by the well-known nonlinear Schradinger equation (NLSE) given by [ 131: au
iZ
I fJ’U - 2 sgn( &)T + N’ 1~1’~ = - i r u.
(1)
where u( 5,~) is the normalized pulse amplitude, 5 = z/L, is the normalized length, 7 = T/T, is the normalized time, L, = Ti/l & is the dispersion length, L,, = I/yP, is r= (ff/2)L,, T,, is the nonhnear length, N 2 = Lo/L,,. the input pulse width, pZ = -(A’/27rc)D, y = 2rn2/AA,, is the nonlinear coefficient, P,, is the peak power of the pulse, A,, is the effective core area of the fiber, LY is the loss coefficient of the fiber. In Eq. (I ), sgn( &) = f 1 depending on whether the group velocity dispersion (GVD) is normal ( & > 0) or anomalous ( & < 0). Eq. (I) describes pulse propagation in the presence of self phase modulation (SPM) only. As in our case T, u 22 ps, all other higher order nonlinear effects can be neglected [131. There are various techniques available for solving the NLSE. We have used the split-step Fourier transform method to solve the NLSE for the simulation of pulse propagation through the NDSF-DCF combination. Various structural parameters of the NDSF and DCF which are used for the numerical simulation are shown in Table I. These values have been chosen to correspond
Table 1 Structural
parameters
of the fibers
Parameters
NDSF
DCF
A,,, _..(I.LI~‘) D (ps/(kmnm)) II: (m’/W) LY(dB/km) .-. (km)
79.2 18 3 60x 10~“’ _. 0.20 75.6
26.4 - 63.65 3.80X IO-“’ 0.60 21.4
P. Palai. K. Thyagarajan / Optics Communications
approximately to those mentioned in Ref. [12]. For the fiber parameters not given in Ref. [ 121, we have used typical parameter values from Ref. [ 141. It should be noted that the nonlinear refractive index coefficient (n,) of the DCF is higher than that of the NDSF and further. the effective area (A,,) of the DCF is smaller than that of the NDSF leading to a value of (nz/A,ff> almost four times larger for the DCF. Thus in the DCF, nonlinear effects, which depend on (n/A,,-) are more prevalent than in NDSF. Furthermore, DCF also has very large negative D whose magnitude is almost four to five times larger than for the NDSF.
3. Numerical
143 (IYY7) 203-208
205
ciently weak so that the propagation in the second fiber is almost linear. This observation is valid even for the combination of DCF + NDSF.
O,rtput of YDSF
(4
160 120 P” (1nW)
=
results and discussions 160
In order to show the dependence of the output optical pulses on the position of the DCF with respect to NDSF in the link, we have obtained the time and frequency spectrum evolution of the optical pulse after the first as well as the second fiber. We have assumed the input pulse to be of secant hyperbolic type in shape. Also, to show that the length of the DCF can play a significant role in the nonlinear regime of transmission, three different cases are considered namely (i) perject compensation in which case the length of the DCF is chosen such that the DCF exactly compensates the dispersion of the NDSF in the link under linear regime. (ii) OIXYcompensation where the length of the DCF is more than that required for perfect compensation, (iii) under compensation where the length of the DCF is shorter than that required for perfect compensation. 3. I. Perfect
120 80
Pi, (mW]
-10 0
compensation
For the values of the parameters of NDSF and DCF given in Table I. the length of the DCF required for 75.6 km of NDSF is 21.4 km. We first consider the pulse propagation in the NDSF + DCF combination for different input peak powers P,. We have checked that for P,, I 5 mW the linear regime of pulse transmission is maintained through the combination, i.e., the shape and the spectrum of the pulse at the output of the combination are independent of P, and are exactly equal to the input pulse. Figs. 2(a) and 2(b) show the temporal evolution of the pulse after the first fiber (NDSF) and the second fiber (DCF), respectively for different values of P,. Figs. 2(c) and 2(d) show the corresponding frequency spectrum evolution. Fig. 2(c) shows that the frequency spectrum broadens with increasing PO as new frequencies are generated in the first fiber (NDSF) due to SPM. Fig. 2(d) which represents the frequency spectrum at the output of DCF, shows that the second fiber (DCF) does not change the frequency spectrum of the pulse. This implies that the second fiber behaves as a linear element only. This can be explained by the fact that the total loss suffered by the input pulse in traversing the first fiber (_ I6 dB) makes the pulse suffi-
a-&
160
*
120
*
80
&
#)
_+_-I
-100
-,jn
0
50
P” (m\V)
loo0
Fig. 2. (a) Temporal evolution of the input pulse (dashed curve) with the input signal peak power (P,,) at the output of the NDSF in the NDSF + DCF combination for exact dispersion compensation. Various values of the fiber parameters are given in Table I. The pulse is normalized to its maximum value. (b) Temporal evolution of the pulse at the output of the DCF in the NDSF+DCF combination with the input signal peak power (PO) for exact dispersion compensation. The pulse is normalized to its maximum value. (c) Frequency spectrum evolution of the input pulse (dashed curve) with the input signal peak power (PO) at the output of the NDSF in the NDSF+ DCF combination for exact dispersion compensation. The pulse is normalized to its maximum value. (d) Frequency spectrum evolution of the pulse at the output of the DCF in the NDSF+DCF combination with the input signal peak power (PO) for exact dispersion compensation. The pulse is normalized to its maximum value.
206
P. Palai, K. Thyagarajan/Optics
For low powers, the linear regime of transmission is maintained in the NDSF and the frequency chirping introduced by the anomalous group velocity dispersion (GVD) of the NDSF broadens the pulse. When this broadened pulse enters the DCF, which operates in the normal GVD regime, it experiences a frequency chirping opposite to the one in the anomalous regime. Thus, when the dispersion compensation is exact there is no net chirping in the pulse and the pulse retains its original shape at the output of the NDSF + DCF combination. As the input power PO is increased, nonlinear effect due to SPM introduces a frequency chirping which is in the opposite direction to that introduced by the anomalous GVD in the NDSF. This leads to a reduction in the net frequency chirping and the pulse in the NDSF does not broaden as rapidly as it does in the linear regime (see Fig. 2(a)). As the net chirping of the pulse which enters the DCF has decreased, the DCF which operates only in the linear regime over compensates the chirping in the pulse and hence, the pulse at the output of the combination broadens. The maximum broadening of the pulse occurs for PO _ 80 mW. As the input P, is increased further, pulse shaping takes place in the NDSF and is further modified by the DCF. Though for P,, N 160 mW the central portion of the pulse approaches towards the input pulse shape, it is accompanied by side lobes and hence is unsuitable for further amplification and transmission. The above discussion can also be verified from the following facts. The dispersion length Lo of the NDSF is 2 1.17km. For P,, = 5 mW, the nonlinear length L,, = 150 km leading to N = 0.37. This shows that, for P, 5 5 mW, pulse transmission in the NDSF is predominantly influenced by chromatic dispersion only. Beyond this power, as the L,, goes on decreasing SPM in the NDSF becomes more and more effective. When P,, = 100 mW, then N = 1.67 and hence the combined effect of dispersion and SPM leads to soliton like pulse shaping in the NDSF (see Fig. 2(a)). Figs. 3(a) and 3(b) show the time evolution of the DCF + NDSF combination after the first and second fiber, respectively, and Figs. 3(c) and 3(d) show the corresponding frequency spectrum evolution. As in the previous combination the second fiber (NDSF) here behaves as a linear element only. For small input Pa, the transmission of the pulse is in the linear regime where the pulse width in the first fiber (DCF) increases due to the normal GVD which is then compensated to its original width at the output of the combination due to the anomalous GVD of the second fiber (NDSF). In the nonlinear regime of transmission, SPM in the DCF introduces a frequency chirping which is in the same direction as that introduced by the normal GVD in the DCF. Hence, as seen from Fig. 3(a) the pulse in the DCF broadens much more rapidly as compared to the previous case (Fig. 2(a)). In the anomalous GVD regime of the NDSF the broadened pulse experiences net
Communications 143 (1997) 203-208
reduction of frequency chirping output pulse gets compressed very much similar to the all [ 151, where pulse compression
Outpllt
(4
and in the time domain the (Fig. 3(b)). This effect is fiber compression scheme is achieved by passing the
of DCF 160 120 80
fi (mU’)
40 ”
(b)
Output of DCF+NDSF 160
-15
-III
-5
0 TIT,
.5
10
15 ”
Spectrum after DCF
(d)
Spwtrnmaftrr
DCF+KDSF
fi (mW
Fig. 3. (a) Temporal evolution of the input pulse (dashed curve) with the input signal peak power (P,) at the output of the DCF in the DCF + NDSF combination for exact dispersion compensation. The pulse is normalized to its maximum value. (b) Temporal evolution of the pulse at the output of the NDSF in the DCF+ NDSF combination with the input signal peak power (P,) for exact dispersion compensation. The pulse is normalized to its maximum value. (c) Frequency spectrum evolution of the input pulse (dashed curve) with the input signal peak power (f’s) at the output of the DCF in the DCF+NDSF combination for exact dispersion compensation, The pulse is normalized to its maximum value. (d) Frequency spectrum evolution of the pulse at the output of the NDSF in the DCF+ NDSF combination with the input signal peak power (P,,) for exact dispersion compensation. The pulse is normalized to its maximum value.
207
P. Palai. K. Thyagarajan / Optics Communications 143 (1997) 203-208
---
NDSF+DCF DCF+NDSF
1 ------.__________ -x_ 0 8 -
=..
. ..\ L\
0.6 -
*\ ‘\\\ 0.8
1
’
“,,,,I
10
“....’
100
“”
1000
P”(rn\V)
Fig. 4. Variation of the output rms pulse width normalized to that of the input pulse ((~/u~o) with input signal power PO for exact compensation (DCF length = 21.4 km). Solid and dashed curves correspond to NDSF + DCF and DCF + NDSF. respectively.
pulse first through a fiber with a normal GVD in the nonlinear regime and through a fiber with anomalous GVD in the linear regime. The amount of pulse compression increases with increasing P,. For the DCF, the dispersion length Lo turns out to be 5.98 km because of its high D value. In the case of DCF, the nonlinear coefficient y is approximately four times greater and the nonlinear length L,, is about four times smaller than those of the NDSF. Thus N of the DCF is of the same order of magnitude as that of the NDSF. For P, = 5 mW, the DCF has N = 0.41. Hence, for P, I 5 mW, the DCF operates in the linear regime, where only dispersion is effective. As PO goes on increasing the L,, goes on decreasing and the combination of dispersion and nonlinearity affects the pulse propagation. In comparison to the earlier case, no soliton like pulse compression is encountered as the DCF operates in the normal regime of GVD. Fig. 4 shows the variation of the root-mean-square (rms) pulse width (a) of the output pulse normalized with respect to that of the input pulse cc,,,) with PO. As discussed earlier, in the nonlinear regime (P,, 2 5 mW) as P, increases the output pulse width for the combination NDSF + DCF first increases and after attaining a maximum value starts to decrease. In contrast, g/u0 for the combination DCF + NDSF shows a decrease in pulse width with P,.
Fig. 5. Variation of the output rms pulse width normalized to that of the input pulse (o/a,) with input signal power PO for over compensation. Solid and dashed curves correspond to NDSF+ DCF for small (DCF length = 23.55 km) and large (DCF length = 25.8 km) over compensation, respectively. Dotted and dashdotted curves correspond to DCF + NDSF for small and large over compensation. respectively.
case of exact compensation. For the combination DCF + NDSF as the accumulation of dispersion is larger in the DCF, SPM is less effective and this leads to a reduction of the amount of pulse compression compared to the case of exact compensation. Fig. 5 shows that for the case of smaller over compensation, r/a0 decreases from 1.02 to 0.85 for a significant range of P,. This particular configuration may thus be advantageous to use in a system since the pulse width changes only slightly over a range of input power levels. For the case of higher over compensation where the DCF length is 25.8 km the pulse width increases with PO. This increase in rms pulse width with increasing PO for this combination of DCF and NDSF is similar to that observed in Ref. [4]. Thus perhaps the DCF length in the experimental results reported in Ref. [4] is slightly longer than that required for exact compensation.
12
t
/
\
-I
1
NDSF+DCF DCF+NDSF
-.-
NDSF+DCF D;F+N;i
3.2. Over compensation In order to show the effect of over compensation for a fixed length of NDSF (75.6 km), we have considered two lengths of the DCF, 23.55 and 25.8 km, for which the amount of over compensation is relatively small and large, respectively. In Fig. 5 we have plotted the variation of a/a, with P, for both the combinations NDSF + DCF and DCF + NDSF. It can be observed that for the combination NDSF + DCF, both small and large over compensation lead to an increase of the pulse width compared to the
Fig. 6. Variation of the output rrns pulse width normalized to that of the input pulse (a/~~,) with input signal power P, for under compensation. Solid and dashed curves correspond to NDSF+ DCF for small (DCF length = 19.25 km) and large (DCF length = 17.0 km) under compensation, respectively. Dotted and dashdotted curves correspond to DCF+NDSF for small and large under compensation, respectively.
208
P. Palai, K. Thyagarajan / Optics Communications 143 (19971203-208
3.3. Under compensation We finally consider the case where the length of the DCF used in the link along with the NDSF is shorter than that required for an exact dispersion compensation. In this case the magnitude of total linear dispersion in the NDSF will be more than the total linear dispersion of the DCF. As in the previous case, we have considered two lengths, 19.25 and 17.0 km. of DCF for a fixed length of 75.6 km of NDSF in the link corresponding to a relatively small and large value of under compensation. Fig. 6 shows the variation of o/u,, with Pa for the combinations NDSF + DCF and DCF + NDSF, respectively. For the smaller under compensation configuration the results are not very different from those obtained from exact compensation. The large under compensation configuration is limited by a large variation of the pulse width with P,, for both fiber combinations. Although the results presented here are for a specific case. we have verified the general conclusions of the study for different lengths of NDSF and DCF.
4. Conclusion In conclusion, we have numerically investigated signal pulse propagation through the combination of NDSF followed by DCF and DCF followed by NDSF. We have shown that for small powers there can be exact linear dispersion compensation of NDSF by a suitable length of DCF by either combinations of fibers. As the input power increases linear dispersion compensation may not be exact as the combinations behave very differently in the nonlinear regime of transmission. In the combination NDSF + DCF the pulse width increases before decreasing with the input signal power, whereas for the combination DCF + NDSF the pulse undergoes compression. We have also considered two different cases where the dispersion in the NDSF is under compensated and over compensated by the DCF. It is found that it may be advantageous to use a
small value of under compensation for the DCF + NDSF combination as the pulse does not change appreciably for a relatively large range of input signal power.
Acknowledgements The authors would like to thank Dr. Vishnu Priye of the Indian Institute of Technology, Delhi, for his valuable discussions and suggestions.
References [I] B. Jopsons. A. &auk, IEEE Commun. Mag. (June 1995) 96. 121H. Izadpanah, C. Lin, J.L. Gimlett, A.J. Antos. D.W. Hall, D.S. Smith, Electron. Lett. 28 (1992) 1469. [3] R.W. Tkach. R.M. Derosier, A.H. Gnauck, A.M. Vengsarkar, D.W. Peckham, J.L. Zyskind, J.W. Sulhoff, A.R. Chraplyvy, IEEE Photon. Technol. Lett. 7 (1995) 1369. [4] A. Chraplyvy, IEEE J. Lightwave Technol. 8 (1990) 1548. [51 A. Naka. S. Saito. IEEE J. Lightwave Technol. 13 (1995) 862. [6] R.J. Nuyts. Y.K. Park, P. Gallion, IEEE J. Lightwave Technol. 15 (1997) 31. [7] F. Matera, M. Settembre. IEEE J. Lightwave Technol. 14 (1996) 1. [8] D. Breuer, K. Petermann. IEEE Photon. Technol. Lett. 9 ( 1997) 398. [9] F.M. Knox, W. Forysiak, N.J. Doran, IEEE J. Lightwave Technol. 13 (1995) 1955. [IO] J.M. Jacob, E.A. Golovchenko. A.N. Pilipetskii, G.M. Carter, CR. Menyuk, IEEE Photon. Technol. Lett. 9 (1997) 130. [I I] E. Yamada. H. Kubota. T. Yamamoto, A. Sahara, M. Nakazawa. Electron. Lett. 33 (1997) 602. [ I21 F. Niedermaier. A. Mattheus, R. Ries, COST Workshop 94, Optical Telecommunications, Nice. 1994, p. 45. [ 131 G.P. Agrawal. Nonlinear Fiber Optics (Academic, New York, 1989). [ 141 M. Kakui. T. Kato, T. Kashiwada, K. Nakazato, C. Fukuda, M. Onishi, M. Nishimura, Opt. Fiber Technol. I (1995) 312. [IS] K.J. Blow, N.J. Doran, B.P. Nelson, Optics Lett. 10 (1985) 393.
OPTICS
COMMUNICATIONS ELSEVIER
Optics Communications
143 ( 1997) 203-208
Effect of self-phase modulation on a dispersion compensated link employing a dispersion-compensating fiber P. Palai, K. Thyagarajan
’
Depurtment of PhyCcs, Indian Institute of Technology New Delhi 110 016. India Received 14 April 1997: revised 23 June 1997; accepted
I
July 1997
Abstract A study of the effect of self phase modulation (SPMI on a fiber link consisting of a non-dispersion shifted fiber (NDSF) and a dispersion compensating fiber (DCF) operating at 1550 nm has been carried out. The characteristics of signal pulse transmission through the fiber combination of NDSF followed by DCF (post-compensation) and DCF followed by NDSF (pre-compensation) are obtained by numerical simulation. It is found that though in the linear regime there can be exact compensation of dispersion for either combinations of NDSF + DCF and DCF + NDSF, in the nonlinear regime of transmission the two combinations behave very differently. For the case of NDSF + DCF the pulse width increases and attains a maximum value before decreasing with the input signal power, whereas for the combination of DCF + NDSF the pulse undergoes compression. It is also shown that when the linear dispersion in NDSF is slightly under compensated by DCF, the pulse width in the DCF + NDSF combination does not change appreciably for a large range of input signal power. 0 1997 Elsevier Science B.V.
1. Introduction Recently, there has been a growing interest in high data rate repeaterless optical fiber communication systems using practical erbium doped fiber amplifiers (EDFAs). With the advent of EDFAs, the preferred wavelength for optical communication has been shifted to 1550 nm. More than 70 million kilometers of non-dispersion-shifted fibers (NDSFSI with very low value of chromatic dispersion (D) at 1310 nm. have already been laid through out the world. Unfortunately, these fibers have a large dispersion coefficient (D - + I8 ps/(kmnm)) at 1550 nm which will limit the data rate. This large dispersion could be compensated by using one of the various schemes of dispersion compensation wherein the accumulated dispersion of the NDSF is cancelled by passing the dispersed pulses through a suitable optical device so as to have a net zero chromatic dispersion before it is received. Amongst various schemes of
’ Corresponding author. E-mail: [email protected].
dispersion compensation, use of dispersion compensating fibers (DCFS) has been found to be very practical and convenient [l-3]. These DCFs have a large negative D at 1550 nm so that a relatively short length of the DCF with the NDSF could lead to a net zero dispersion in the link. Generally, dispersion compensated fiber links employing DCFs are designed to have a net zero dispersion value at a particular wavelength. In these designs, the signal power is assumed to be small enough not to induce any nonlinear effects such as self-phase modulation @PM), cross-phase modulation (CPM), four wave mixing (FWMI, etc., in the fiber link. These nonlinear effects may arise in the presence of optical amplifiers in the fiber link and can modify various physical properties such as shape, frequency components. etc., of the signal pulse along the length of the link leading to impairment in signal transmission [4]. Hence alleviation of the impairments by managing dispersion and nonlinearity in the transmission link has become a vital issue in the field of optical fiber communications systems. In view of this, various schemes such as optimal dispersion compensation, various formats of time domain multiplexed data, dispersion-allocated soliton
0030-4018/97/S 17.00 0 1997 Elsevier Science B.V. All rights reserved. PfI SOO30-4018(97)00370-2
204
P. P&i.
K. Thyqarajan/
Optics Communications 143 (IYY7J 203-208
transmission systems, etc., have been proposed. In the optimal dispersion compensation scheme, it has been shown that it may be advantageous to slightly under compensate the chromatic dispersion in the fiber link. as it can support more input signal power [5,6]. The detrimental effects of the dispersion and nonlinearity can also be controlled by modulating the signal in a particular format so as to cancel the effect of dispersion with that due to nonlinearity such as SPM [7,8]. Another interesting scheme is to use the dispersion-allocated solitons in a dispersion compensated system where the net dispersion is slightly anomalous but dispersion at any point is large. These systems are shown to have negligible distortion even at very high powers [9- 111. In all the above mentioned schemes, either nonlinearity is assumed to be confined only to the NDSF or performance of the system under nonlinear regime with pre-compensation (DCF followed by NDSF) or post-compensation (NDSF followed by DCF) has not been analyzed. It is quite clear that, in the linear regime, pre- and post-compensation schemes will result in exact dispersion compensation, whereas in the nonlinear regime they may not compensate dispersion exactly. In addition, due to the fiber nonlinearity, the overall system response may depend on whether the DCF follows NDSF or vice versa. This is primarily due to the fact that DCFs have very different characteristics as compared to NDSF such as having a higher nonlinear coefficient (y). and a large negative D and also a different length; these parameters play major roles in pulse evolution in the nonlinear regime. In view of this it is necessary to study the total response of the NDSF-DCF combination in the nonlinear regime. Some preliminary experimental work has been reported on the nonlinear response of NDSF-DCF combinations [12], but no adequate theoretical explanation was provided for the specific results obtained. In this paper we present a numerical study of the pulse propagation in the presence of SPM in the NDSF + DCF (post-compensation) and DCF + NDSF (pre-compensation) combinations to evaluate their relative performances in a fiber transmission link. We show that the total response of the link is significantly different in the two combinations. Indeed in the latter case we show the possibility of pulse compression. Our results are shown to explain some of the results obtained in Ref. [ 121. Also. we show that by using the DCF + NDSF combination with the DCF over-compensating the dispersion of NDSF. it is possible to use a large range of input signal power without affecting the output pulse shape.
2. Modelling Fig. 1 shows a simple typical point to point link consisting of NDSF and DCF. The signal at 1550 nm wavelength from the transmitter may be amplified by an optical amplifier such as EDFA and then propagates
Fig. I. Schematic of a typical point to point fiber link showing transmitter CT, ), fiber combination F, and F2. and receiver CR, ).
through combination of fibers F, and FZ. As the signal is attenuated in the fiber combination, it may again be amplified by another optical amplifier before it reaches the receiver. The combination of the fibers F, and F> is such that either F, is NDSF and FZ is DCF or vice versa. The lengths of the NDSF and DCF are chosen so that the net accumulated linear dispersion from the transmitter to receiver end is zero. Thus exact dispersion compensation will take place for low signal peak power ( P,), where the linear regime of transmission is valid. The evolution of an optical pulse through a fiber is described by the well-known nonlinear Schradinger equation (NLSE) given by [ 131: au
iZ
I fJ’U - 2 sgn( &)T + N’ 1~1’~ = - i r u.
(1)
where u( 5,~) is the normalized pulse amplitude, 5 = z/L, is the normalized length, 7 = T/T, is the normalized time, L, = Ti/l & is the dispersion length, L,, = I/yP, is r= (ff/2)L,, T,, is the nonhnear length, N 2 = Lo/L,,. the input pulse width, pZ = -(A’/27rc)D, y = 2rn2/AA,, is the nonlinear coefficient, P,, is the peak power of the pulse, A,, is the effective core area of the fiber, LY is the loss coefficient of the fiber. In Eq. (I ), sgn( &) = f 1 depending on whether the group velocity dispersion (GVD) is normal ( & > 0) or anomalous ( & < 0). Eq. (I) describes pulse propagation in the presence of self phase modulation (SPM) only. As in our case T, u 22 ps, all other higher order nonlinear effects can be neglected [131. There are various techniques available for solving the NLSE. We have used the split-step Fourier transform method to solve the NLSE for the simulation of pulse propagation through the NDSF-DCF combination. Various structural parameters of the NDSF and DCF which are used for the numerical simulation are shown in Table I. These values have been chosen to correspond
Table 1 Structural
parameters
of the fibers
Parameters
NDSF
DCF
A,,, _..(I.LI~‘) D (ps/(kmnm)) II: (m’/W) LY(dB/km) .-. (km)
79.2 18 3 60x 10~“’ _. 0.20 75.6
26.4 - 63.65 3.80X IO-“’ 0.60 21.4
P. Palai. K. Thyagarajan / Optics Communications
approximately to those mentioned in Ref. [12]. For the fiber parameters not given in Ref. [ 121, we have used typical parameter values from Ref. [ 141. It should be noted that the nonlinear refractive index coefficient (n,) of the DCF is higher than that of the NDSF and further. the effective area (A,,) of the DCF is smaller than that of the NDSF leading to a value of (nz/A,ff> almost four times larger for the DCF. Thus in the DCF, nonlinear effects, which depend on (n/A,,-) are more prevalent than in NDSF. Furthermore, DCF also has very large negative D whose magnitude is almost four to five times larger than for the NDSF.
3. Numerical
143 (IYY7) 203-208
205
ciently weak so that the propagation in the second fiber is almost linear. This observation is valid even for the combination of DCF + NDSF.
O,rtput of YDSF
(4
160 120 P” (1nW)
=
results and discussions 160
In order to show the dependence of the output optical pulses on the position of the DCF with respect to NDSF in the link, we have obtained the time and frequency spectrum evolution of the optical pulse after the first as well as the second fiber. We have assumed the input pulse to be of secant hyperbolic type in shape. Also, to show that the length of the DCF can play a significant role in the nonlinear regime of transmission, three different cases are considered namely (i) perject compensation in which case the length of the DCF is chosen such that the DCF exactly compensates the dispersion of the NDSF in the link under linear regime. (ii) OIXYcompensation where the length of the DCF is more than that required for perfect compensation, (iii) under compensation where the length of the DCF is shorter than that required for perfect compensation. 3. I. Perfect
120 80
Pi, (mW]
-10 0
compensation
For the values of the parameters of NDSF and DCF given in Table I. the length of the DCF required for 75.6 km of NDSF is 21.4 km. We first consider the pulse propagation in the NDSF + DCF combination for different input peak powers P,. We have checked that for P,, I 5 mW the linear regime of pulse transmission is maintained through the combination, i.e., the shape and the spectrum of the pulse at the output of the combination are independent of P, and are exactly equal to the input pulse. Figs. 2(a) and 2(b) show the temporal evolution of the pulse after the first fiber (NDSF) and the second fiber (DCF), respectively for different values of P,. Figs. 2(c) and 2(d) show the corresponding frequency spectrum evolution. Fig. 2(c) shows that the frequency spectrum broadens with increasing PO as new frequencies are generated in the first fiber (NDSF) due to SPM. Fig. 2(d) which represents the frequency spectrum at the output of DCF, shows that the second fiber (DCF) does not change the frequency spectrum of the pulse. This implies that the second fiber behaves as a linear element only. This can be explained by the fact that the total loss suffered by the input pulse in traversing the first fiber (_ I6 dB) makes the pulse suffi-
a-&
160
*
120
*
80
&
#)
_+_-I
-100
-,jn
0
50
P” (m\V)
loo0
Fig. 2. (a) Temporal evolution of the input pulse (dashed curve) with the input signal peak power (P,,) at the output of the NDSF in the NDSF + DCF combination for exact dispersion compensation. Various values of the fiber parameters are given in Table I. The pulse is normalized to its maximum value. (b) Temporal evolution of the pulse at the output of the DCF in the NDSF+DCF combination with the input signal peak power (PO) for exact dispersion compensation. The pulse is normalized to its maximum value. (c) Frequency spectrum evolution of the input pulse (dashed curve) with the input signal peak power (PO) at the output of the NDSF in the NDSF+ DCF combination for exact dispersion compensation. The pulse is normalized to its maximum value. (d) Frequency spectrum evolution of the pulse at the output of the DCF in the NDSF+DCF combination with the input signal peak power (PO) for exact dispersion compensation. The pulse is normalized to its maximum value.
206
P. Palai, K. Thyagarajan/Optics
For low powers, the linear regime of transmission is maintained in the NDSF and the frequency chirping introduced by the anomalous group velocity dispersion (GVD) of the NDSF broadens the pulse. When this broadened pulse enters the DCF, which operates in the normal GVD regime, it experiences a frequency chirping opposite to the one in the anomalous regime. Thus, when the dispersion compensation is exact there is no net chirping in the pulse and the pulse retains its original shape at the output of the NDSF + DCF combination. As the input power PO is increased, nonlinear effect due to SPM introduces a frequency chirping which is in the opposite direction to that introduced by the anomalous GVD in the NDSF. This leads to a reduction in the net frequency chirping and the pulse in the NDSF does not broaden as rapidly as it does in the linear regime (see Fig. 2(a)). As the net chirping of the pulse which enters the DCF has decreased, the DCF which operates only in the linear regime over compensates the chirping in the pulse and hence, the pulse at the output of the combination broadens. The maximum broadening of the pulse occurs for PO _ 80 mW. As the input P, is increased further, pulse shaping takes place in the NDSF and is further modified by the DCF. Though for P,, N 160 mW the central portion of the pulse approaches towards the input pulse shape, it is accompanied by side lobes and hence is unsuitable for further amplification and transmission. The above discussion can also be verified from the following facts. The dispersion length Lo of the NDSF is 2 1.17km. For P,, = 5 mW, the nonlinear length L,, = 150 km leading to N = 0.37. This shows that, for P, 5 5 mW, pulse transmission in the NDSF is predominantly influenced by chromatic dispersion only. Beyond this power, as the L,, goes on decreasing SPM in the NDSF becomes more and more effective. When P,, = 100 mW, then N = 1.67 and hence the combined effect of dispersion and SPM leads to soliton like pulse shaping in the NDSF (see Fig. 2(a)). Figs. 3(a) and 3(b) show the time evolution of the DCF + NDSF combination after the first and second fiber, respectively, and Figs. 3(c) and 3(d) show the corresponding frequency spectrum evolution. As in the previous combination the second fiber (NDSF) here behaves as a linear element only. For small input Pa, the transmission of the pulse is in the linear regime where the pulse width in the first fiber (DCF) increases due to the normal GVD which is then compensated to its original width at the output of the combination due to the anomalous GVD of the second fiber (NDSF). In the nonlinear regime of transmission, SPM in the DCF introduces a frequency chirping which is in the same direction as that introduced by the normal GVD in the DCF. Hence, as seen from Fig. 3(a) the pulse in the DCF broadens much more rapidly as compared to the previous case (Fig. 2(a)). In the anomalous GVD regime of the NDSF the broadened pulse experiences net
Communications 143 (1997) 203-208
reduction of frequency chirping output pulse gets compressed very much similar to the all [ 151, where pulse compression
Outpllt
(4
and in the time domain the (Fig. 3(b)). This effect is fiber compression scheme is achieved by passing the
of DCF 160 120 80
fi (mU’)
40 ”
(b)
Output of DCF+NDSF 160
-15
-III
-5
0 TIT,
.5
10
15 ”
Spectrum after DCF
(d)
Spwtrnmaftrr
DCF+KDSF
fi (mW
Fig. 3. (a) Temporal evolution of the input pulse (dashed curve) with the input signal peak power (P,) at the output of the DCF in the DCF + NDSF combination for exact dispersion compensation. The pulse is normalized to its maximum value. (b) Temporal evolution of the pulse at the output of the NDSF in the DCF+ NDSF combination with the input signal peak power (P,) for exact dispersion compensation. The pulse is normalized to its maximum value. (c) Frequency spectrum evolution of the input pulse (dashed curve) with the input signal peak power (f’s) at the output of the DCF in the DCF+NDSF combination for exact dispersion compensation, The pulse is normalized to its maximum value. (d) Frequency spectrum evolution of the pulse at the output of the NDSF in the DCF+ NDSF combination with the input signal peak power (P,,) for exact dispersion compensation. The pulse is normalized to its maximum value.
207
P. Palai. K. Thyagarajan / Optics Communications 143 (1997) 203-208
---
NDSF+DCF DCF+NDSF
1 ------.__________ -x_ 0 8 -
=..
. ..\ L\
0.6 -
*\ ‘\\\ 0.8
1
’
“,,,,I
10
“....’
100
“”
1000
P”(rn\V)
Fig. 4. Variation of the output rms pulse width normalized to that of the input pulse ((~/u~o) with input signal power PO for exact compensation (DCF length = 21.4 km). Solid and dashed curves correspond to NDSF + DCF and DCF + NDSF. respectively.
pulse first through a fiber with a normal GVD in the nonlinear regime and through a fiber with anomalous GVD in the linear regime. The amount of pulse compression increases with increasing P,. For the DCF, the dispersion length Lo turns out to be 5.98 km because of its high D value. In the case of DCF, the nonlinear coefficient y is approximately four times greater and the nonlinear length L,, is about four times smaller than those of the NDSF. Thus N of the DCF is of the same order of magnitude as that of the NDSF. For P, = 5 mW, the DCF has N = 0.41. Hence, for P, I 5 mW, the DCF operates in the linear regime, where only dispersion is effective. As PO goes on increasing the L,, goes on decreasing and the combination of dispersion and nonlinearity affects the pulse propagation. In comparison to the earlier case, no soliton like pulse compression is encountered as the DCF operates in the normal regime of GVD. Fig. 4 shows the variation of the root-mean-square (rms) pulse width (a) of the output pulse normalized with respect to that of the input pulse cc,,,) with PO. As discussed earlier, in the nonlinear regime (P,, 2 5 mW) as P, increases the output pulse width for the combination NDSF + DCF first increases and after attaining a maximum value starts to decrease. In contrast, g/u0 for the combination DCF + NDSF shows a decrease in pulse width with P,.
Fig. 5. Variation of the output rms pulse width normalized to that of the input pulse (o/a,) with input signal power PO for over compensation. Solid and dashed curves correspond to NDSF+ DCF for small (DCF length = 23.55 km) and large (DCF length = 25.8 km) over compensation, respectively. Dotted and dashdotted curves correspond to DCF + NDSF for small and large over compensation. respectively.
case of exact compensation. For the combination DCF + NDSF as the accumulation of dispersion is larger in the DCF, SPM is less effective and this leads to a reduction of the amount of pulse compression compared to the case of exact compensation. Fig. 5 shows that for the case of smaller over compensation, r/a0 decreases from 1.02 to 0.85 for a significant range of P,. This particular configuration may thus be advantageous to use in a system since the pulse width changes only slightly over a range of input power levels. For the case of higher over compensation where the DCF length is 25.8 km the pulse width increases with PO. This increase in rms pulse width with increasing PO for this combination of DCF and NDSF is similar to that observed in Ref. [4]. Thus perhaps the DCF length in the experimental results reported in Ref. [4] is slightly longer than that required for exact compensation.
12
t
/
\
-I
1
NDSF+DCF DCF+NDSF
-.-
NDSF+DCF D;F+N;i
3.2. Over compensation In order to show the effect of over compensation for a fixed length of NDSF (75.6 km), we have considered two lengths of the DCF, 23.55 and 25.8 km, for which the amount of over compensation is relatively small and large, respectively. In Fig. 5 we have plotted the variation of a/a, with P, for both the combinations NDSF + DCF and DCF + NDSF. It can be observed that for the combination NDSF + DCF, both small and large over compensation lead to an increase of the pulse width compared to the
Fig. 6. Variation of the output rrns pulse width normalized to that of the input pulse (a/~~,) with input signal power P, for under compensation. Solid and dashed curves correspond to NDSF+ DCF for small (DCF length = 19.25 km) and large (DCF length = 17.0 km) under compensation, respectively. Dotted and dashdotted curves correspond to DCF+NDSF for small and large under compensation, respectively.
208
P. Palai, K. Thyagarajan / Optics Communications 143 (19971203-208
3.3. Under compensation We finally consider the case where the length of the DCF used in the link along with the NDSF is shorter than that required for an exact dispersion compensation. In this case the magnitude of total linear dispersion in the NDSF will be more than the total linear dispersion of the DCF. As in the previous case, we have considered two lengths, 19.25 and 17.0 km. of DCF for a fixed length of 75.6 km of NDSF in the link corresponding to a relatively small and large value of under compensation. Fig. 6 shows the variation of o/u,, with Pa for the combinations NDSF + DCF and DCF + NDSF, respectively. For the smaller under compensation configuration the results are not very different from those obtained from exact compensation. The large under compensation configuration is limited by a large variation of the pulse width with P,, for both fiber combinations. Although the results presented here are for a specific case. we have verified the general conclusions of the study for different lengths of NDSF and DCF.
4. Conclusion In conclusion, we have numerically investigated signal pulse propagation through the combination of NDSF followed by DCF and DCF followed by NDSF. We have shown that for small powers there can be exact linear dispersion compensation of NDSF by a suitable length of DCF by either combinations of fibers. As the input power increases linear dispersion compensation may not be exact as the combinations behave very differently in the nonlinear regime of transmission. In the combination NDSF + DCF the pulse width increases before decreasing with the input signal power, whereas for the combination DCF + NDSF the pulse undergoes compression. We have also considered two different cases where the dispersion in the NDSF is under compensated and over compensated by the DCF. It is found that it may be advantageous to use a
small value of under compensation for the DCF + NDSF combination as the pulse does not change appreciably for a relatively large range of input signal power.
Acknowledgements The authors would like to thank Dr. Vishnu Priye of the Indian Institute of Technology, Delhi, for his valuable discussions and suggestions.
References [I] B. Jopsons. A. &auk, IEEE Commun. Mag. (June 1995) 96. 121H. Izadpanah, C. Lin, J.L. Gimlett, A.J. Antos. D.W. Hall, D.S. Smith, Electron. Lett. 28 (1992) 1469. [3] R.W. Tkach. R.M. Derosier, A.H. Gnauck, A.M. Vengsarkar, D.W. Peckham, J.L. Zyskind, J.W. Sulhoff, A.R. Chraplyvy, IEEE Photon. Technol. Lett. 7 (1995) 1369. [4] A. Chraplyvy, IEEE J. Lightwave Technol. 8 (1990) 1548. [51 A. Naka. S. Saito. IEEE J. Lightwave Technol. 13 (1995) 862. [6] R.J. Nuyts. Y.K. Park, P. Gallion, IEEE J. Lightwave Technol. 15 (1997) 31. [7] F. Matera, M. Settembre. IEEE J. Lightwave Technol. 14 (1996) 1. [8] D. Breuer, K. Petermann. IEEE Photon. Technol. Lett. 9 ( 1997) 398. [9] F.M. Knox, W. Forysiak, N.J. Doran, IEEE J. Lightwave Technol. 13 (1995) 1955. [IO] J.M. Jacob, E.A. Golovchenko. A.N. Pilipetskii, G.M. Carter, CR. Menyuk, IEEE Photon. Technol. Lett. 9 (1997) 130. [I I] E. Yamada. H. Kubota. T. Yamamoto, A. Sahara, M. Nakazawa. Electron. Lett. 33 (1997) 602. [ I21 F. Niedermaier. A. Mattheus, R. Ries, COST Workshop 94, Optical Telecommunications, Nice. 1994, p. 45. [ 131 G.P. Agrawal. Nonlinear Fiber Optics (Academic, New York, 1989). [ 141 M. Kakui. T. Kato, T. Kashiwada, K. Nakazato, C. Fukuda, M. Onishi, M. Nishimura, Opt. Fiber Technol. I (1995) 312. [IS] K.J. Blow, N.J. Doran, B.P. Nelson, Optics Lett. 10 (1985) 393.