a1350_1.pdf JTuA122.pdf
Real-Time PMD monitoring Using a DOP Ellipsoid Based on PSO Technique Xiaoguang Zhang1,2, Lixia Xi1,2, Gaoyan Duan1,2, and Bojun Yang1,2 P
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1. Department of Physics, Beijing University of Posts and Telecommunications, Beijing 100876, China. 2 . The Key Laboratory of Optical Communications and Lightwave Technologies, Ministry of Education, Beijing 100876, China.
[email protected]
Abstract: DOP ellipsoid can be used as PMD monitoring signal for automatic PMD compensation. We introduced the particle swarm optimization algorithm into obtaining real-time DOP ellipsoid with high precision only by 100 sampling SOP data. ©2007 Optical Society of America
OCIS code: (060.2330) Fiber optics communications; (260.5430) Polarization; (260.2030) Dispersion.
1. Introduction The PMD monitoring technique is critical for an automatic PMD compensator. An ideal PMD monitoring technique can reveal PMD vector with much more details, such as both differential group delay (DGD) and principal states of polarization (PSPs). Degree of polarization (DOP) ellipsoid obtained by using a polarization scrambler can determine both DGD and PSP orientation by its three radii and orientation angle of ellipsoid [1]. In this paper we introduce the particle swarm optimization (PSO) as a powerful data fitting algorithm for getting a precise analytical DOP ellipsoid equation from 100 measured SOP (state of polarization) samples with fast speed, and getting real-time characteristic features of PMD such as DGD and PSP. 2. PSO technique used as getting real-time DOP ellipsoid DOP ellipsoid is a good PMD monitoring technique, from which we can read out detailed information of PMD. It is important to find a good algorithm to get the analytical ellipsoid equation from measured output SOP data, in order to obtain the information such as the three radii of ellipsoid rmax , rmid , rmin and its orientation angles α, β, γ, as shown in Fig.1. This algorithm is required to get right ellipsoid with high precision from as fewer samples of data as possible for the speed request of PMD compensation. The PSO algorithm, proposed by Kennedy and Eberhart [2], has proved to be very effective in solving global optimization for multi-dimensional problem in static, noisy, and continuously changing environment. The implementation of the PSO algorithm can be described as a procedure to find the global maximum/minimum of a function in a multi-dimensional hyperspace by adjusting multi-control parameters, without being trapped into local sub-optima. In order to obtain a exact DOP ellipsoid from SOP samples, We firstly get the normal ellipsoid without tilt in principal axis coordinate through three rotations by the angles −α, −β, −γ from original data samples. Secondly, we endlessly adjust 6-dimensional parameters (r1, r2, r3, α, β, γ) until minimizing following function: B
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⎛ N S12n S22n S32n ⎞ + 2 + 2 −1 ⎟ ⎜ ∑ 2 ⎟ ( r1 , r2 , r3 ,α , β ,γ ) ⎜ r2 r3 ⎝ n =1 r1 ⎠ MIN
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where S1, S2, S3 are the Stokes parameters in Stokes space, and N is the number of sampling data used for ellipsoid data fitting. As long as the function in the parenthesis is close enough to zero, the corresponding r1, r2, r3, α, β, γ are the right parameters to be found for the DOP ellipsoid equation. B
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Fig. 1. The orientation of DOP ellipsoid in Stokes space.
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Fig. 2. Experimental setup for DOP ellipsoid collection
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a1350_1.pdf JTuA122.pdf
3. Experiment and results Fig. 2 shows the experimental setup for obtaining DOP ellipsoid. The laser pulses in linear polarization state were generated by a fiber ring laser. The pulsewidth is 7-ps, and central wavelength is 1560.5-nm. A polarization controller controlled with the computer was used as a polarization scrambler to randomly transform the SOPs of the laser output to be uniformly distributed on entire Poincaré sphere. A computer controlled air gap time delay line was acted as the first-order PMD emulator. A polarimeter detected the SOPs of the output optical signals, and fed them into computer through 4-channel A/D. The computer program with PSO algorithm made the data fitting from sampling data and obtaining the right DOP ellipsoid equation and its information, such as rmax, rmid, rmin and α, β, γ. B
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DGD=4ps
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DGD=10ps
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Fig. 3. 8000 sampling output SOPs recorded with various DGD values
Fig. 3 shows the 8000 sampling SOPs of the output optical signals with various DGD values in the experiment. It can be seen that, all the output SOPs form a ball sphere in Stokes space with zero DGD (Fig.3(a)), and a needle-like spheroid is formed with larger DGD (Fig.3(c)). The larger DGD is, the smaller value of minimum radius of ellipsoid is. Furthermore, the PSP’s orientation of the PMD vector does not change for the first-order. Therefore we see that the longest radius of ellipsoid remains oriented in the same direction in spite of various DGD (Fig.3(b) and Fig.3(c)). In the experiment, getting 8000 sampling data will suffer from a long time that can not be endured for rapid PMD compensation. We need 4-channel A/D for obtaining each SOP. In order to get the right PMD information in a real-time manner, It is required to obtain a precise analytical ellipsoid equation to get three radii rmax, rmid, rmin and its orientation angles α, β, γ through data fitting from as fewer sampling data as possible. We made the data fitting from only 100 sampling data using PSO algorithm, and obtained the DOP ellipsoids shown in Fig. 4. B
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Fig. 4. DOP ellipsoids obtained with PSO technique from only 100 sampling SOPs.
By comparison between Fig. 3 and Fig. 4, we can see that, the ellipsoids obtained from 100 samplings, with high precision, nearly fit close to the ellipsoids formed by 8000 sampling points. We conclude that the PSO algorithm is a powerful one to do the job of data fitting with multi-adjusting parameters. The whole procedure that involved 100 points sampling and ellipsoid data fitting using PSO algorithm took a time within 1ms if the speed of hardwares used were fast enough. 4. Acknowledgements This work was supported partly by the National Natural Science Foundation of China (No. 60577046), and Corporative Building Project of Beijing Educational Committee (No. XK100130637). 5. References [1] H. Rosenfeldt et al., “Automatic PMD compensation at 40Gbit/s and 80Gbit/s using a 3-dimentional DOP evaluation for feedback,” in OFC 2001, PD27-1. [2] J. Kennedy et al., “Particle swarm optimization,” in Proc. IEEE ICNN’95, (Piscataway, NJ, 1995), pp. 1942.
