1. INTRODUCTION ABSTRACT

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1 Theory and experiment of PMD compensation with DOP as feedback signal Chen Lin *a,duan Gao Yan b, Yan Bo Jun b, Zhang Ru b, Yu Li b,zhang Xiao Guang b, Zhen Yuan b, Zhou Guang Tao b,shen Yu b, a The school of science, Hangzhou Dianzi University, Hangzhou,310018, China b Beijing university of post and telecommunication, box#49 ZIP:100876,China ABSTRACT In this paper, the degradation of signal degree of polarization( DOP) by first and second order polarization mode dispersion(pmd) in 40Gb/s RZ and NRZ optical communication is analyzed by numerical simulation. The simulation results show that the degradation of signal DOP by first order PMD is monotony, but which is fluctuated by second order PMD. The influence of two components of second order PMD on DOP for NRZ code and RZ are also investigated by numerical simulation method. The results also show that the influence of the depolarization component and the PCD component on NRZ and RZ data formats are different. Those results will provide the theory basis for how to select proper compensation arithmetic. A compensation system is founded to compensate the first and high order PMD effectively by DOP as feedback signal and particle swarm optimizer(pso) as compensation arithmetic. Here, we introduce an intelligent method PSO as a searching algorithm to multi-dof (degree of freedom) PMD compensation, The PSO algorithm used here is described as: (1) Local neighborhood structure is employed to avoid being trapped into sub-optima. () 0 particles are employed. So 0 time units (less than 0 ms) are required in one iteration. (3) The maximum iteration number is set to 50.The experiment result show that the first and second PMD can be compensated at the same times for 10 Gb/s RZ and NRZ by using DOP as feedback signal and PSO as searching algorithm. Keywords: Optical fiber communication, Polarization mode dispersion (PMD), Adaptive PMD compensation, Feedback signal, Degree of Polarization(DOP), RZ code,nrz code, Differently Group Delay(DGD) 1. INTRODUCTION With increasing bit rates, polarization mode dispersion(pmd) is becoming a major system impairment. Recently, people research PMD and its compensation largely, and come out many kinds of projects of self-adapted PMD compensation. As a feedback signal to compensate PMD, feedback technique mainly has two kinds: the first one is electric power method [1], check a certain given radio power as feedback signal, but photo electricity detector that electric-power method uses is related with code speed, which is not benefit to upgrade system. The second one is the method of degree of polarization (DOP) [], which checks DOP of light pulse as feedback signal. DOP of signal is not related with code speed, thus using DOP as feedback signal is appropriate for systems with different code speed in order to update it in PMD compensation. Many articles have discussed DOP of optical signal,but they have not discussed influence of two components of second PMD on DOP of optical signal. In this paper, the degradation of signal DOP by first and second order PMD in 40Gb/s RZ and NRZ optical communication is analyzed by numerical simulation, Here, we introduce an intelligent method PSO as a searching algorithm to multi-dof (degree of freedom) PMD compensation, A compensation system is founded to compensate the first and high order PMD effectively by DOP as feedback signal and particle swarm optimizer (PSO) as compensation arithmetic. The PSO algorithm used here is described as: (1) Local neighborhood structure is employed to avoid being trapped into sub-optima. () 0 particles are employed. So 0 time units (less than 0 ms) are required in one iteration. (3) The maximum iteration number is set to 50.The experiment result show that the first and second PMD can be compensated at the same times for 40 Gb/s RZ and NRZ by using DOP as feedback signal and PSO as searching algorithm. * Author for correspondences: lililiu@sina.com Information Optics and Photonics Technology, edited by Guoguang Mu, Francis T. S. Yu, Suganda Jutamulia, Proceedings of SPIE Vol. 564 (SPIE, Bellingham, WA, 005) X/05/$15 doi: /

2 . THE THEORY OF DOP AS FEEDBACK SIGNAL OF PMD COMPENSATION.1 The expression of higher order PMD Under the assumption of the absence of polarization-dependent losses, the dispersion of fiber can be represented by a complex transfer matrix [] L j( ) L T( ) e e M( ) (1) where ( ) ( ( ) ( ))/ is the mean propagation constant, is the fiber attenuation,and M is a x y unitary matrix. In the three-dimensional Poincare representation, PMD is described by the dispersion vector : () Where = ˆq, ˆq is the direction of one of the two orthogonal eigenvectors of M ( ) which represent the principal state of polarization s ( PSP) of the fiber. In a first-order approximation, the PMD vector can be described by: ˆq 0 0 Where 0 is the differential group time delay(dgd) between two input signals polarized along the two principal state of polarizations (PSP) of the fiber which is called the first order PMD b In the second approximation, the PMD can be described by: (3) 0qˆ0 ( qˆ0 qˆ 0) where / qˆ qˆ/ 0 where q and are called second PMD, the first component is called depolarization, i.e. a change in the direction of the PSP, the second component is called polarization-dependent chromatic dispersion (PCD). The unitary matrix M ( ) can be written as: u1( ) u( ) M ( ) * * u ( ) u 1( ) (4) when only first order and second PMD are considered, M ( ) can be written by 1 M( ) R( ) D( ) R( ). Where D( ) take into account the different propagation speeds on the two PSP s: j e 0 D( ) j 0 e In the second-order approximation 0 and R( ) describe second order PMD : m n R ( ) n * m * where m cos( k), n sin( k) k ˆ q (5) (6). The influence of two components of second PMD on DOP of optical signal In stokes space, three Stokes parts of a single frequency light are (s1, s, s3), DOP is defined as [3] 576 Proc. of SPIE Vol. 564

3 DOP s1 s s3 s s s 0 0 (7) s 0 is the intensity of the light, for the fully polarized light, s=s 0 and DOP=1; for partly polarized light, DOP<1. In the fiber communications, a transmitted signal accounts for a certain frequency range. DOP in this range need be calculated to obtain the feedback signal of PMD compensators. In frequency field, GVD and loss aren t considered, and then common Jones matrix of fiber is expressed as [4] : Here M u condition ( ) u u = 1 u u 1 1 u 1. The signal frequency spectrum is defined as and meets unitary f d 1 ] T ( ) f. The SOP of input light is independent of the frequency, and its unitary component at two PSPs is[ a b, plurals a and b aren t related with the frequency and have the relationship a b (8) 1. T is expressed as transpose, after a signal passing the transmitted fiber, Jones matrix of two polarization directions is T T obtained Eox E oy = M( )[ a b] f ( ), and then output field is also acquired ox ( ) 1 ( ) E = au + bu f oy ( 1) ( ) E = au + bu f Stokes parameters [5] of the output field is averaged in the whole signal frequency domain, then: s1= ( Eox ( ) Eoy ( ) ) d= ( a b )( u1 u ) abuu 1 abuu + + f( ) 1 d (11) = Re ox ( ) oy ( ) ( )( ) ( ) ( ) ( ) s E E d = b a uu + uu + abuu u + ab u uu f d 3 = Im ox ( ) oy ( ) ( )( ) ( ) ( ) ( ) s E E d = j b a uu uu + ab u + uu abu + uu f d The module of the vector s s s 3 1 is DOP of a signal, then DOP of a signal is such: DOP of every frequency component in the frequency domain weights power spectrum average. So, the DOP of the signal is related with SOP, PMD and the frequency spectrum of the signal. We calculated DOP of the different SOPs with DGD increasing when the system has only the first-order PMD. As shown in Fig.1 (a) and Fig.1(c) for NRZ and RZ formats respectively. Iin the condition of the same DGD, the different powers of the fiber PSPs have different DOP. When the two PSPs have the same powers, split rate is 0.5 and DOP is minimal. The maximum DOP is corresponding to split rate that equals to 1, and polarization direction of the input signal is parallel to PSP. According to PSP theory as described in [1], when the input signal put into fiber along the direction of PSP, the system has no PMD and DOP is unchangeable. If SOP of an input signal is parallel to PSP of the fiber, DOP of the output signal decreases with DGD. So, input SOP should be adjusted to have the same power in the two PSPs. DOP change is described as Fig.1(b) and Fig.1(d) with NRZ and RZ format respectively of different pulse width based on the same power on the two PSPs, The wider the pulse width, the narrower the frequency spectrum is and the slower the DOP change is and vice versa. So, when there is only first-order PMD, DOP of a optical signal decrease monotonously with increasing PMD. (9) (10) (1) (13) Proc. of SPIE Vol

4 (a) (b) (c) (d) Fig.1 Simulated DOP as a function of DGD for 40Gb/s NRZ and RZ signal with only first PMD. (a) DOP as function of polarization spitting rate for NRZ format, (b) Different pulse width for NRZ format (c) DOP as function of polarization spitting rate for RZ format, (d) Different pulse width for RZ format Two-order PMD is divided into two parts: polarization state depolarization and polarization correlative dispersion (PCD) [6]. PSP change with optical frequency leads to polarization state depolarization which is decided by PSP rotate rate (PSPrr). We emulated the influence of PSPrr on DOP of RZ and NRZ formats using Jones matrix module given by the particle [8] as shown in Fig.. PSPrr changes from 4GHz to 40GHz. When DGD is small, DOP of two formats decreases with PSPrr increasing. However, DOP change is very obvious with increasing DGD. The DOP of NRZ format has a certain periodicity and the DOP of RZ is out-of-order. The reason is that DOP is the average of the entire frequency signal and the influence of PSPrr on NRZ with narrower frequency spectrum is less than on RZ format. The influence of PCD on DOP is also calculated as shown in Fig.3. When PCD increases from 4ps to 40ps, the DOP of NRZ keeps invariable. However, the DOP of RZ becomes disordered. When DGD is small, PCD increases and DOP becomes small. On the other hand, DOP enhances with DGD increasing. Results show that PCD has great influence on DOP of RZ and has little influence on that of NRZ format. 578 Proc. of SPIE Vol. 564

5 a (b) Fig. The DOP change with DGD considering PSPrr for NRZ and RZ (a) for NRZ format,(b) for RZ format DOP PCD=4-40ps^ NRZ DGD/ps 5 30 DOP PCD increase 3a (3b) Fig.3 The DOP change with DGD considering PCD for NRZ and RZ, (3a) for NRZ format,(3b) for RZ format PCD=4-40ps^ Pulse width=5ps PCD increase DGD/ps Two parts of two-order PMD are discussed respectively above to know the change of every part. The two parts lie in the factual fiber communication systems at the same time. So we use Jones matrix output by PMD emulators to calculate DOP. The emulator outputs 5000 sampling data and average PMD is 15ps. The change of DOP with DGD is shown in Fig.4. DOP of RZ has large change with same DGD and that of NRZ has small fluctuation, which shows that two-order PMD affects RZ greater that NRZ. In a word, the two-order PMD has large influence on DOP of RZ and the circus is more obvious when DGD is larger. So it is difficult for compensation algorithms to compensate large PMD because of many sub-maximums. Selected inapposite algorithm lead to DOP being trapped into local maximum and PMD can t be compensated. From simulated results, we know that RZ format with broad frequency spectrum induces more DOP sub-maximums. The compensation algorithm spent more time in the cross of searching the maximum. If the spectrum of RZ is suppressed with the filtering technique before compensating, the compensation effect will be improved markedly. Proc. of SPIE Vol

6 DOP DGD/ps DOP (4a) (4b) Fig.4 DOP change with DGD by the PMD emulator (4a) for NRZ format, (4b) for RZ format DGD/ps 3. A ADAPTIVE PMD COMPENSATION SYSTEM FOR PMD COMPENSATION In order to compensate DGD and second order PMD, our ground found a compensation experiment system as showed in figure 5. The PMD compensation system includes four modules: code resource which can generates RZ code and NRZ code, PMD emulator, PMD compensator and monitor. PMD compensator consists of two sections Polarization Maintaining Fiber PMF3, PMF4 and Polarization Controller PC3, PC4, as well as feedback control logic.at the output end of the experiment system, a oscilloscope enable us watching the output eye graph, and a BER analyzer enable us monitoring the BER. The PMD emulator consists of two sections Polarization Maintaining Fiber PMF1, PMF and Polarization Controller PC1, PC, which can generate PMD including first and depolarization component of second order. The feedback control logic provides the error signal to PMD compensator to change input voltage of PC3 and PC4 so as to compensate PMD. The error signals are coming from the polarimeter which sampling the degree of depolarization (DOP) of optical pulse in the fiber. If the optical power is equal on two PSP, the DOP is minimum value. Fig.6 gives the relationship between DOP and DGD for the two formats, where the DOP is monitored by polarimeter. The control logic of PMD compensator minimizes the signal distortion by continuously searching for the most appropriate control signal applied at the PC3 and PC4, for which the measured DOP is maximized. Here, we introduce an intelligent method PSO [11] it as a searching algorithm to multi-dof (degree of freedom) PMD compensation, The PSO algorithm used here is described as: (1) Local neighborhood structure [1] is employed to avoid being trapped into sub-optima. () 0 particles are employed. So 0 time units (less than 0 ms) are required in one iteration. (3) The maximum iteration number is set to 50. Fig.7 give the results of PMD for both NRZ and RZ formats. After compensation, we can see that first order and second order PMD can be compensated by two stages compensator in the same time. 580 Proc. of SPIE Vol. 564

7 'FFECBDL DPOUSPM MPHJD Fig.5 The PMD compensation experiment system with DOP as feedback signal fig.6 Measured DOP as function of DGD by experiment for both NRZ and RZ formats (a) (b) Proc. of SPIE Vol

8 (c) (d) Fig.7 The eye graph before compensation and after compensation for NRZ and RZ formats (a) before compensation for 10Gb/s NRZ format,(b) after compensation for 10Gb/s NRZ format (c) ) before compensation for 10Gb/s RZ format, (d) after compensation for 10Gb/s RZ format References 1 Takahashi T,Imai T,A iki M. Automatic compensation technique for time wise fluctuating polarization mode dispersion in in-line amplifer system.electronics Letters,1994,30(4): Poole, C. D., Wagner, R. E. 1IOP FFO NPH EDB J MBQS QBD P IU PQMB PJ[ SUJ BOPOJPO M HTHM J FNEF P GJ CS.Electron. F Lett. 109, Kikuchi N..Analysis of signal degree of polarization degradation used as contral signal for optical polarization mode dispersion compensation. Journal of light wave technology., Rasmussen J C,Isomura A,Ishikawa G. oautomatic compensation of polarization mode dispersion for 40 Gb/s transmission systems p.journal of light wave technology., Rasmussen J C,Akihiko Isomura,George Ishikawa. oautomatic Compensation of Polarization-Mode Dispersion for 40Gb/s Transmission Systems p.j.lightwave Technol.,,0 101, Kogelink h,nelson L E,Gordon J P. Emulation and Inversion of polarization-mode dispersion.journal of lightwave technology., J. P. Gordon, H. Kogelnik, PMD fundamentals: Polarization mode dispersion in optical fibers,proc. Nat. Acad. Sci , Foschini G J,Nelson L E,Logelnik H. Statistics of Second-Order PMD Depolarization.Journal of Lightwave Technology , Jopson R M., Nelson L E., and Kogelnik H. Measurement of Second-OrderPolarization-Mode Dispersion Vectors in Optical Fibers, IEEE PHOTONICS TECHNOLOGY LETTERS, , Forestieri E and Vincetti L Exact Evaluation of the Jones Matrix of a Fiber in the Presence of Polarization Mode Dispersion of Any Order,J.Lightwave Technol , R. Eberhart and J. Kennedy, A new optimizer using particle swarm theory, Proc. Sixth International Symposium on Micro Machine and Human Science, IEEE Service Center, Piscataway, NJ, 39, J. Kennedy and R. Mendes, Population structure and particle swarm performance, Proc. ICEC, 1671, Proc. of SPIE Vol. 564

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