Polarization scrambling characteristic analysis based on density of polarization states statistics Download: 589次
Polarization-induced penalties such as polarization mode dispersion (PMD) and polarization-dependent loss/gain (PDL/PDG), are crucial obstacles to fully realizing ultra-highspeed long-haul fiber-optic backbone transmission systems[1
Alternatively, a polarization scrambler made of a fiber squeezer can overcome all of the above shortcomings, since it has less IL, PDL, and a lower cost, showing great potential for practical applications. Taking advantages of such a scrambler, Yao et al. achieved quasi-uniform rate polarization scrambling at 752 krad/s[12]. To indicate the scrambling uniformity, they use the concept of degree-of-polarization (DOP). It is convenient to operate, but only gives global information, which omits all the local distribution nonuniformity. In addition, the geometric approach to characterize polarization effects has several applications, such as entropy and DOP for nonlinear optical waves[22], a correlation-based method to quantify the homogeneity of random fields[23,24], quantum polarization distributions[25], and self-polarization effects[26]. To deeply analyze the scrambling characteristics, we propose in this Letter a novel method based on density of polarization states (DPS) statistics[26], which can provide the uniformity of any part on the Poincaré sphere. Then we develop the experimental polarization scrambler made of three fiber squeezers, and demonstrate the effectivity of our method. Moreover, we further discuss its unique advantage by comparing with the Stokes components statistics[27]. Finally, by the employment of a commercial polarization scrambler, we show the perfect scrambling uniformity according to the appraisal strategy. The results are available for accurate analysis of any kind of polarization scrambler, and the quality evaluation of polarization controllers or other polarization devices.
In Stokes space, the SOPs at the input and output of a voltage -controlled fiber-squeezing scrambler are related by a Muller matrix [13]: where , are the input and output Stokes vectors.
An arbitrary small spherical crown, as shown in Fig.
Fig. 1. Schematic representation of the DPS statistics: (a) sampling a certain part of the Poincaré sphere for DPS statistics, , the distance between two center points of the sampling part and its cross section; (b) scrambling simulation results of 10,000 polarization states; (c) complete DPS distribution of the results in (b).
In polar coordinates, P can be described by a unit vector ,
Choosing suitable , , and values, we can get any part of the sphere surface whose scrambling uniformity is required to be evaluated.
Obviously, any output SOP () of the scrambler can be expressed by Eq. (
According to the model we previously proposed in Ref. [13], we simulate the polarization scrambling based on random voltage driving by using MATLAB, whose results are plotted in Fig.
To describe completely the scrambling uniformity of any parts on the Poincaré sphere, we make use of the DPS statistics. Given a certain spherical crown with an area of and the DPS as , its normalized average DPS can be expressed by where is the total amount of polarization states on the whole sphere’s surface. When completely covers the surface of the unitary sphere, one can find that .
By comparing the values between and , we can obtain the following conclusions for qualitatively describing the scrambling uniformity.
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Now we analyze the DPS of the data in Fig.
In general, when , if the average DPS deviates from less than 0.01 and for 200 samples, the polarization scrambler will possess outstanding scrambling uniformity and satisfy most of the engineering applications.
To demonstrate above results, we build the experimental polarization scrambling system shown in Fig.
Fig. 2. Experimental setup for polarization scrambling. PC: manual polarization controller, PZT: piezoelectric ceramics, PA: polarization analyzer.
To obtain enough data for uniformity analysis, we continuously record 10,000 output SOPs by the polarization analyzer. Figure
Fig. 3. (a) Experiment scrambling results of 10,000 polarization states; (b) normalized DPS statistics for ; (c1)–(c3) histograms obtained by the Stokes components analysis method.
To further confirm it, we use the Stokes components analysis method as adopted in Ref. [27], and plot the results in Figs.
In practical cases, it is necessary to accurately figure out the area with bad uniformity to improve the performance of a scrambler, and then the DPS statistics method will be a very useful tool. That cannot be realized by Stokes components or DOP analysis methods because both of them omit the local address information of the SOP distribution.
Let us consider a special case: when some driving parts of the polarization scrambling system are wrong, the output SOPs will distribute as shown in Fig.
Fig. 4. (a) SOP distribution on the Poincaré sphere for a defective polarization scrambling system , , ; , , ; (b) complete normalized DPS statistics for ; (c1)–(c3) accompanying histograms obtained by the Stokes components analysis method.
To make it clear, we use the DPS statistics method. As shown in Fig.
However, if using the Stokes components analysis method, we can still get the uniform distribution as illustrated in Figs.
Finally, we apply the DPS statistics method to analyze a high-performance commercial scrambler (PCD-104, General Photonics). The experimental setup is similar to that in Fig.
Fig. 5. (a) 10,000 SOPs distribution on the Poincaré sphere for a commercial scrambler; (b) complete normalized DPS statistics for ; (c1)–(c3) corresponding histograms of DPS statistics at different values of .
Furthermore, we analyze the relationship between the evaluation results and the parameter . Figures
In summary, we propose and demonstrate the novel DPS statistics method to evaluate the scrambling performance of polarization scramblers that can provide complete DPS distribution on the whole Poincaré sphere, so it is easy to accurately locate the nonuniform areas for improvement of a defective polarization scrambler, while any other methods cannot realize it. We have proved the advantages of our method compared with others by experiments. By application to a commercial scrambler, we further confirm the validity of the evaluation standard. Our results are available to accurately analyze and diagnose the scrambling uniformity of any polarization scrambler, and are also valid for quality evaluation of polarization controllers or other polarization devices.
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Shangchun Wang, Zhengyong Li. Polarization scrambling characteristic analysis based on density of polarization states statistics[J]. Chinese Optics Letters, 2020, 18(6): 060604.