IOSR Journal of Electrical and Electronics Engineering (IOSR-JEEE) e-ISSN: 2278-1676 Volume 4, Issue 3 (Jan. - Feb. 2013), PP 58-65 www.iosrjournals.org

Compensation of Intrachannel Cross-phase Modulation (IXPM) Induced Phase perturbation in Dispersion Managed Transmission over Uncompensated Single Fiber Line Nitu Syed1, Tanjib Rubaiyat2 1

School of Engineering and Computer Science, Independent University Bangladesh (IUB), Dhaka, Bangladesh 2 Department of Electrical and Electronic Engineering, Bangladesh University of Engineering and Technology (BUET), Dhaka, Bangladesh

ABSTRACT: This paper analyzes the phase perturbation caused by intrachannel cross-phase modulation (IXPM) in 40Gbit/s optical RZ pulse for both periodically dispersion managed (DM) transmission and uncompensated single fiber line. Analytical estimation for phase fluctuation due to intra-channel effects has been deduced using variational analysis. Simulation results confirm significant reduction in the phase fluctuations due to IXPM by using dispersion managed line compared to uncompensated fiber line. As a result of using simple dispersion compensation technique IXPM induced phase fluctuation can be mitigated by proper adjustment of different parameters and the quality of existing transmission system is improved. Keywords: Dispersion management, duty cycle, intrachannel cross-phase modulation, uncompensated fiber, variational analysis

I.

INTRODUCTION

Nonlinear intrachannel effects occur especially in high bit rate return-to-zero (RZ) transmission, while pulses are transmitted over optical fibers. They base on the interplay between chromatic dispersion and the nonlinear Kerr effect and yield in amplitude and timing jitter, thus decreasing signal quality and maximum transmission distance [1]-[2]. Dispersion managed (DM) system has been an active research topic in the area of long-haul optical communication systems for some years [3]â€“[5]. A dispersion managed optical communication system is made of alternate segments of normal (positive) and anomalous (negative) dispersion fiber in a periodic manner. The combination of fiber segments with alternating normal and anomalous dispersions makes a unit cell of a DM link. Thus, in a unit cell, fiber dispersion becomes locally high, but the average dispersion of a cell remains low. In long distance transmission links above 100 km, high transmission powers are involved which give rise to nonlinear effects. In particular, in standard single mode fiber (SSMF) the high local dispersion leads to rapid pulse broadening over several bit slots, and the overlapping neighboring pulses interact through intra-channel cross phase modulation and intra-channel four wave mixing (IFWM) in a single channel system [6]. In comparison to the combined effect of IXPM and ISPM induced non-linear phase noise (NLPN), IFWM effect is considered insigniďŹ cant for highly dispersive fiber [7]. On the other hand, IXPM distortion directly contaminates the pulse phase. Recently some research on IXPM have been conducting [8]-[10] but the basic study with overall performance analyses due to IXPM distortion are still under research. So among these nonlinearities IXPM is our concern as the impact of IXPM on fiber-optic transmission system has yet to be address completely. The objective of this paper is to study & investigate the phase fluctuations due to IXPM on RZ pulse in details for both uncompensated line and DM system. We have analyzed the phase perturbation using variational analysis [11]. We have obtained several dynamical equations for various pulse parameters. The phase fluctuation is obtained by solving these equations using Runge-Kutta method. Next the effects of various parameters (such as transmission distance, input power, duty cycle) on phase shift have been investigated for both systems. The simulation results show that lower phase fluctuation is achieved by using DM technique and pulse distortion is significantly reduced compared to uncompensated single fiber transmission line. Finally split step Fourier method (SSMF) is used in some cases to validate the analytical results of dispersion management scheme. Phase fluctuation is calculated by detecting pulse peak power and the position of pulse peak in axis of time. This paper is organized as follows: variational analysis presuming IXPM as a perturbation has been presented in section 2. Section 3 gives the system description and results of uncompensated single fiber transmission. The simulation results for a DM model are described in Section 4. Finally the summary and conclusion of work is stated in Section 5.

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Compensation of Intrachannel Cross-phase Modulation (IXPM) Induced Phase perturbation in Dispersion

II.

ANALYSIS OF IXPM INDUCED PHASE FLUCTUATION IN RZ PULSE

Optical pulse propagation in a fiber with dispersion management can be described by dimensionless nonlinear Schrödinger equation (NLSE): i

U j Z

2

b Uj 2 T

S ( z) U

2

2

Uj

j

Rj,

(1)

Where U (Z, T), b(z), S(z), T and Z represent normalized envelop of electric field, dispersion parameter, nonlinear coefficients, normalized retarded time and propagation distance respectively. We assume that Aj, pj , Cj, κj, τj and θj represent the j-th pulse’s amplitude, reciprocal of pulse width, linear chirp, central frequency, central time position and the phase of the pulse, respectively. Then the solution of Eq. (1) can be approximated by a Gaussian pulse which is associated with linear chirp as:

2 j U j ( Z , T ) A j ( Z ) exp exp( i j ), 2 Assuming IXPM as the sole perturbation, Rj is can be defined as 2 2 R j 2S Z U 3 j U j 2S Z A32 j Aj exp 32 j exp j exp i j 2 The dynamical equations with perturbation can be written for two pulses (j = 1, 2) as: dp j b Z p 3j C j R p j dZ dC j S Z 2 b Z p 2j 1 C 2j Aj RC j dZ 2

d j

R j dZ dT j b Z j RT j dZ d j b Z 2 5S Z 2 j p 2j Aj R j dZ 2 4 2

(2) (3) (4) (5) (6)

where

Rp j

pj

Aj

Im R j e

i j

2 1 2 2j exp j d 2

(7)

2 C j Im R j ei j 1 2 2j exp j d 2 2 2pj i i R j Re R j e j C j Im R j e j j exp j d 2 Aj 2 2 i RT j Im R j e j j exp j d 2 Aj p j RC j

2 Aj

Re R j e

i j

(8)

(9)

(10)

2j . i j i j 2 (11) p j Re R j e 3 2 j 4 j Im R j e j exp 2 d Here Re R j ei j and Im R j ei j represent the real and imaginary parts of R j ei j , respectively, and can given as 2 i Re R j e j 2S Z A32 j Aj exp 32 j exp j 2 i j Im R j e 0. 1 R j 2 Aj p j

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Compensation of Intrachannel Cross-phase Modulation (IXPM) Induced Phase perturbation in Dispersion 2

Now applying variational method and E j U j dT A2j p j which represents constant pulse energy of

Uj, Eqs. (2) – (6) can be deduced as: dp j b( Z ) p 3j C j dZ dC j dZ

2

Ejpj

2

b( Z ) p j (1 C j ) S ( Z )

d ( )

(12)

2

2

4 E 3 j p 3 j P

2

2( )

2

K

(13)

4( E1 E 2 ) p1 p 2 P ( ) K 2

(14)

dZ 2 d ( ) b( Z ){ p 2j C j p1 p 2 } dZ j 1

d j dZ

(15)

5E j b( Z ) 2 4 2 2 2 j p 2j S ( Z ) p j E3 j 2 P p 3 j P 2( ) K 2 4 2

2

(16)

2

Where 1 2 , P ( p1 p 2 )

K

S ( Z ) p1 p 2

P

5

j (Z ) = j (0) Z

2 and 1 (0) 2 (0) 0 . The pulse phase is evaluated by P

exp 5E j 4 2

E 3 j 2 P p 3 j P 2( ) 4

2

2

Z

z 0 S ( ) p d b( )( j p j ) d j

2

2

2

0

K ( )d

(17)

0

The phase shift observed at any pulse is deduced as 2 1 , where θ2 is the observed phase when two pulses are transmitted and θ1 is the phase when single pulse is transmitted. Applying Runge-Kutta method, we can evaluate phase shift due to IXPM using (12) to (17). III.

SYSTEM DESCRIPTION AND RESULTS OF UNCOMPENSATED SINGLE FIBER TRANSMISSION

We model a single channel system and a single fiber transmission line with highly dispersive fibers like standard single mode fiber (SSMF) and Non-zero dispersion–shifted fiber (NZDSF) as shown in Fig. 1 for two different systems. We consider the total transmission period of around 100 km. Model parameters for SSMF is taken as dispersion parameter 17ps/nm/km, effective core area 80µm 2 and nonlinear index coefficient 2.5×10-20 m2/W. In another system, we use NZDSF in place of SSMF. It has fiber parameters as following: dispersion 4ps/nm/km, effective core area 50µm2 and nonlinear index coefficient 1.5×10-20 m2/W. The minimum pulse width (FWHM) is taken as 10ps for each pulse and the pulses have a difference in time domain of 25ps.

Fig. 1. Uncompensated Single Fiber Transmission System using SSMF or NZDSF

1.1

Results We numerically simulate the Gaussian pulse evolution in single fiber transmission system for a transmission period of 100 km. We show pulse evolution along SSMF in the absence of noise in Fig. 2. It is evident from Fig. 2 that each pulse is spreading out as it propagates down the ﬁber. Under the inﬂuence of dispersion and nonlinearities each pulse is taking a distorted and broader shape only for 100km propagation.

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Compensation of Intrachannel Cross-phase Modulation (IXPM) Induced Phase perturbation in Dispersion

Fig. 2. Pulse dynamics within uncompensated SSMF system with full numerical simulation Fig. 3 shows the IXPM induced phase fluctuation as a function of transmission distance for SSMF and NZDSF. The simulation is done for 50km propagation at 40% duty cycle with a peak power of 1mW. We can see from Fig. 3 that phase fluctuation increases linearly with the transmission distance. The reason for higher phase fluctuations in NZDSF transmission is the smaller effective area of NZDSF. The effective core area of NZDSF is less (50µm2) compared to SSMF (80µm2). It is evident from Eq.(17) that the non-linear effects that occur in optical fiber are proportional to power density. On the other hand, power density is inversely proportional to the effective area of the fiber.

Fig. 3. Phase shift versus transmission distance for uncompensated single fiber transmission Fig. 4 shows that the phase shift is increasing for both types of uncompensated fiber lines with increasing duty cycle d. The phase shift is highest when duty cycle is nearly 100%. It indicates the rapid increase of pulse to pulse interaction in the region 0 < d ≤ 1. It is clear from Fig. 4 that SSMF shows lower phase variation compared to NZDSF.

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Compensation of Intrachannel Cross-phase Modulation (IXPM) Induced Phase perturbation in Dispersion

Fig. 4. Maximum phase fluctuation versus duty cycle for 50km propagation The change in phase shifts while propagating through SSMF and NZDSF with the variation of power is shown in Fig. 5. The analytical result shows that phase shift increases rapidly with the increase of peak power. The nonlinear refractive index causes an induced phase shift that is proportional to the intensity of pulse. Again we can see that SSMF yields lower phase fluctuation compared to NZDSF. So it can be said from the above results that SSMF shows better performance than NZDSF.

Fig. 5. Phase shift versus initial peak power for uncompensated single line propagation From the above results we can predict that fiber chromatic dispersion and nonlinearity cause severe distortion in the pulse shape only for 100km propagation. It is very evident that for uncompensated long-haul transmission (more than 1000km) the optical pulse can disperse, or spread, over a distance, which clearly can confuse the light detector at the far end of the fiber. A common method for overcoming this problem is dispersion management technique. III. SYSTEM DESCRIPTION AND RESULTS OF DM SYSTEM We assume a two step periodic dispersion map for DM transmission line. We consider a periodic dispersion model which has a period span of L1+ L2 =50km. It is repeated 20 times to cover the total transmission of around 1000km.Amplifiers are assumed to be noise free in our studies, as we focus on perturbations by nonlinear intrachannel effects only. For the DM model SSMF is followed by dispersion www.iosrjournals.org

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Compensation of Intrachannel Cross-phase Modulation (IXPM) Induced Phase perturbation in Dispersion compensating fiber (DCF) in each period where the length of SSMF is L1= 43km and length of DCF is L2=7km as shown in Fig. 6. The fiber parameters for SSMF are taken as dispersion 17ps/nm/km, fiber core area 80μm², nonlinear index coefficient 2.5×10-20 m²/W, and loss 0.21 dB/km when these are -100ps/nm/km, 20 μm², 3×10-20 m²/W, and 0.5 dB/km for DCF.

Fig. 6. Transmission line models for a DM system We numerically simulate the Gaussian pulse evolution in DM transmission system for the total transmission length of 1000 km. The numerical simulations have been carried out by directly solving Eq. (1) using split-step Fourier method (SSFM). We show pulse evolution along the periodic DM system for two DM map periods in Fig.7. We observe stationary pulse propagation for a single pulse in a dispersion managed system. The figure shows that the pulse can keep its robustness during propagation which is enviable for long haul transmission system.

Fig. 7. Single Pulse dynamics within the DM system with full numerical simulation The change in phase shift with the variation of distance and power are shown in Fig. 8 and Fig. 9 respectively while propagating through a DM system. The simulation is done for 1000km propagation with a peak power of 1mW and 40% duty cycle. It can be said, path length introduces a fundamental limit to long-haul fiber communications. The analytical result shows that phase shift increases rapidly with the increase of peak power for dispersion managed scheme which is also approved by the numerical result. But it is evident from all the results that phase fluctuation in the dispersion managed system is much lower compared to the uncompensated single SSMF or NZDSF fiber. So to realize a long haul transmission, dispersion compensation is essential to avoid nonlinear signal distortion instead of using single uncompensated fiber. The agreement between the analytical estimation and numerical simulation results is fairly satisfactory.

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Compensation of Intrachannel Cross-phase Modulation (IXPM) Induced Phase perturbation in Dispersion

Fig. 8. Phase shift versus transmission distance for DM system

Fig. 9. Phase shift versus initial peak power for dispersion managed line Next we explore the change of maximum phase shift as a function of duty cycle d for DM system in Fig. 10. Here duty cycle is varied from (0-100) %. Similar to the uncompensated line transmission the phase fluctuation shows a rapid increase in the region 0 < d â‰¤ 1. But it is evident that in a dispersion managed line the optical pulses show lower phase variation compared to uncompensated line.

Fig. 10. Phase shift versus duty cycle d for dispersion managed line

IV.

CONCLUSION www.iosrjournals.org

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Compensation of Intrachannel Cross-phase Modulation (IXPM) Induced Phase perturbation in Dispersion This work has been devoted to the investigation of phase fluctuations in different optical fiber transmission systems in order to obtain long-haul high capacity optical communication networks. The effects of IXPM induced phase distortion at 40Gbit/s in SSMF and NZDSF are investigated in this paper. The influences of various parameters (such as transmission distance, input power, duty cycle) on phase shift have been explored. But in ﬁber optic communication systems, information is transmitted over an optical ﬁber for more than 1000km. Several phenomena limit the transmission performance of long-haul optical transmission systems including fiber nonlinearities, dispersion, and noise. So, the effect of using dispersion managed system is also investigated for practical communication system and simulation results show that phase fluctuation is greatly reduced in DM system. Nonlinear phase fluctuation is compensated dramatically using combinations of SSMF and DCF. The analytical prediction is supported by the numerical results also. We can say, phase fluctuations can be considerably mitigated by properly choosing DM model with due adjustment in different pulse parameters. Further DM modeling could be checked to attain lower IXPM-induced phase shift. Fiber Bragg gratings can also be considered for DM system instead of DCF. In order to obtain a complete real picture, experimental investigation can be done taking the combined effect of all other major effects including ASE noise, IFWM, stimulated Raman scattering and residual dispersion. REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]

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