Open Access
Add to BibSonomyAbstract
We analyzed the probability of errors in the measured optical signal-to-noise ratio (OSNR) by using the polarization-nulling method, when the amplified spontaneous emission noise (ASE) is partially polarized due to the polarization-dependent loss (PDL) in the transmission link.
©2006 Optical Society of America
1. Introduction
In the next-generation fiber-optic network, WDM channels are expected to be add/dropped or cross-connected directly in the optical layer. Thus, for the efficient operation of these networks, it is essential to monitor various optical parameters such as optical powers, wavelengths, and optical signal-to-noise ratios (OSNRs) [1]. However, in such a network, the OSNR cannot be monitored accurately by using the conventional technique based on the optical spectrum analysis. This is because each channel becomes to have different OSNR due to the different routing path and the non-uniform ASE spectrum caused by the optical filtering occurred at the optical add/drop multiplexers (OADMs) and optical cross-connects (OXCs). To solve this problem, it has been proposed to use the polarization-nulling method for the monitoring of OSNR [2]–[3]. This technique is based on the fact that the ASE noise is nearly unpolarized while the signal is highly polarized. Thus, the noise power can be measured right at the signal’s wavelength by separating the noise component from the signal simply by using a polarizer. However, it has been recently reported that this technique could be inaccurate if the ASE noise is partially polarized due to the polarization-dependent loss (PDL) [3]. In fact, the polarization-nulling method is bound to be erroneous if the ASE noise is highly polarized. However, it should be noted that the degree-of-polarization (DOP) of ASE noise has a random nature. Thus, to evaluate the effectiveness of the polarization-nulling technique, a rigorous analysis on the DOP statistics of ASE noise is needed. In this paper, we investigated the probability of errors (caused by the partially polarized ASE noise due to PDL) in the measured OSNR values by using the polarization-nulling method.
2. Theory
The polarization-nulling method estimates the power of ASE noise (within the signal’s wavelength) by measuring only the noise power in the polarization state orthogonal to the signal. However, if the ASE noise is partially polarized, the noise power in the orthogonal polarization state may no longer be identical to the noise power in the state parallel to the signal. Thus, it could cause an error in the measured OSNR using the polarization-nulling method. In case OSNR is much higher than 10 dB, this measurement error can be estimated by
where DOPASE is the DOP of ASE noise, ŝ and p̂ represent the normalized Stokes vectors of the signal and the ASE noise, respectively, and ŝ·p̂ represents their inner product [4]. Figure 1(a) shows the OSNR measurement errors calculated by using (1). For a given value of DOPASE, the OSNR error can be maximized when the signal and the partially polarized ASE noise are either co-polarized or cross-polarized (i.e., ŝ·p̂=±1). Thus, in this case, the effect of the partially polarized ASE noise cannot be neglected (i.e., OSNR error >±1 dB) unless the DOP of ASE noise is less than 0.25. On the other hand, this error can be reduced substantially, regardless of the DOP of ASE noise, when the noise powers in the parallel and orthogonal polarization states are nearly same (i.e., ŝ·p̂≈0). Thus, to investigate the effect of the partially polarized ASE noise on the polarization-nulling method, it is necessary to evaluate the probability of measurement errors by considering the statistics of the DOP of noise and ŝ·p̂.
Fig. 1. Errors in the OSNR values measured by using the polarization-nulling method (shown in dB scale) caused by the partially polarized ASE noise. ŝ·p̂ represents the inner product of the normalized Stokes vectors of the signal and ASE noise.
The DOP of ASE noise should have Maxwellian distribution, since the polarized portion of the ASE noise arisen from each amplifier due to PDL should be added randomly [5]. And, the average DOP of the ASE noise (after the transmission of n amplifier spans) can be described as
for n ≥2 and <DOP 1>=Γ [5]. The parameter Γ represents the magnitude of PDL vector of each span defined as (1-10-pdl_dB/10)/(1+10-pdl_dB/10), where pdl_dB represents PDL in dB. In (2), it is assumed that all the amplifier spans have the same PDL. Using this result, the probability that the error in the measured OSNR using the polarization-nulling method becomes larger than x dB can be obtained as
for <DOPn> << 1 and x <3. In (3), we assumed that ŝ·p̂ had a uniform PDF, and DOPASE and ŝ·p̂ were completely uncorrelated.
3. Experiment and results
Fig. 2. Experimental setup to measure the Stokes parameters of the signal and ASE noise in the transmission link consisted of 15 EDFA spans with PDL. The average value of the PDL/span was 0.57 dB. (Sw: optical switch, Att.: optical attenuator, Pol. Cont.: polarization controller, BPF: bandpass filter.)
Figure 2 shows the experimental setup used to verify the analyses described above. The outputs of 20 lasers were multiplexed and sent to the transmission link consisted of 15 spans. The first 10 channels (channel number: 1~10) operated in the range of 1547.3~1550.9 nm (channel spacing: 50 GHz), while the other channels (channel number: 11~20) operated in the range of 1556.2~1559.8 nm. An additional laser (reference laser) operating at 1553.8 nm was used with an optical switch to measure the Stokes parameters of the signal and the ASE noise at this wavelength. Each span consisted of an Erbium-doped fiber amplifier (EDFA), an optical attenuator, a polarization controller, and a PDL element made by using a polymer waveguide. The span loss was set to be 10 dB by using an optical attenuator in every span. We set the optical power of each channel to be -10 dBm at the input of EDFA. The PDL of each span was set to be about 0.57 dB by using PDL elements. The polarization controllers were used to randomize the polarization states of optical signals. The average OSNR was about 28 dB after 15 EDFA spans. After the transmission of 15 EDFA spans, we filtered the reference signal together with the ASE noise at 1553.8 nm by using two optical bandpass filters in cascade (bandwidth: ~0.3 nm). This cascaded filter had a negligible PDL (<0.1 dB) at the center wavelength. We first measured the Stokes parameters of the reference signal by using a polarization analyzer. Then, we turned off the optical switch to measure the Stokes parameters of the ASE noise at the same wavelength. We repeated these measurements 500 times, while randomly varying the polarization controllers. We then identified the optical powers, polarization states, and DOP of signal and ASE noise, respectively, by using these measured Stokes parameters. Using these values, we evaluated the accuracy of the polarization-nulling method by comparing the total noise power with the noise power in the polarization state orthogonal to the signal.
Fig. 3. (a) DOP distribution of the ASE noise measured after the transmission of 15 EDFA spans in comparison with the theoretically calculated Maxwellian curve. (b) Distribution of ŝ·p̂ measured after the transmission of 15 EDFA spans in comparison with the line indicating uniform distribution.
Figure 3(a) shows the DOP distribution of the ASE noise measured after the transmission of 15 EDFA spans. The measured data agreed well with the calculated Maxwellian curve. Figure 3(b) shows the distribution of ŝ·p̂. This figure shows that the PDF of ŝ·p̂ was not uniform, but slightly tilted. This was because, due to PDL, the polarization states of both signal and ASE noise were forced to rotate slightly toward the direction of the PDL vector. Figure 4(a) shows the measured cross-correlation between the DOP of ASE noise and ŝ·p̂.
The correlation between them was negligible (correlation coefficient: ~0.12). Figure 4(b) shows the cumulative probability of OSNR errors measured in the transmission link consisted of 15 EDFA spans (where the average PDL/span was 0.57 dB), in comparison with the calculated curve using the analysis described above. The measured data agreed well the calculated curve. A small discrepancy between the measured data and calculated curve was due to the slight tilt in the distribution of ŝ·p̂ shown in Fig. 3(b). For the transmission link used in our experiment, the probability that the errors in the measured OSNR (caused by the partially polarized ASE noise due to PDL) became larger than 1 dB was about 10-2. Figure 5 shows this probability (i.e., the probability that the error in the measured OSNR becomes larger than 1 dB) as a function of PDL/span and the number of spans. The result shows that, if the PDL/span is smaller than 0.2 dB (which is a typical value for current systems [6]), the effect of PDL on the measured OSNR using the polarization-nulling method is very small even for an ultra long-distance transmission system. For example, the probability that the error in the measured OSNR becomes larger than 1 dB is <10-4 in a 50-span transmission system, as long as the PDL/span is smaller than 0.2 dB. However, this probability increases rapidly as the PDL/span is increased. For example, if the PDL/span is increased to 0.3 dB, this probability could be increased to 2×10-3. Thus, in this case, the number of amplifier span should be reduced to 23 to maintain the error probability within 10-4.
Fig. 4. (a) Cross-correlation between the DOP of ASE noise and ŝ·p̂ measured after the transmission of 15 spans (average PDL/span=0.57 dB). (b) Cumulative probability of the errors in the OSNR values measured by using the polarization-nulling method (due to the partially polarized ASE noise) in a transmission link consisted of 15 spans (average PDL/span=0.57 dB) in comparison with the theoretically calculated curve obtained by using equations (3).
Fig. 5. Probability that the error in the OSNR measured by using the polarization-nulling method becomes larger than 1 dB (due to the partially polarized ASE noise caused by PDL).
4. Summary
We have investigated the effect of PDL on the OSNR measured by using the polarizationnulling method. The results show that, as long as the PDL/span is smaller than 0.2 dB, the OSNR can be estimated accurately by using the polarization-nulling method even in the ultra long-distance system. For example, when the PDL/span is 0.2 dB, the probability that the error in the measured OSNR becomes larger than 1 dB is 10-4 in a 50-span system. However, for the same probability, the maximum number of span could be reduced to 23, if the PDL/span is increased to 0.3 dB.
References and links
1. Y. C. Chung , “Performance monitoring in optical networks (Tutorial)”, in Proceedings of Asia-Pacific Optoelectronics Conferece, 5282-46, 2003. in Asia-Pacific Optical and Wireless Communications, S. J. Ben Yoo, K. W. Cheung, Y. C. Chung, and G. Li, eds., Proc. SPIE5282, 5282-46 (2003).
2. J. H. Lee and Y. C. Chung, “OSNR monitoring technique using polarization-nulling method,” IEEE Photon. Technol. Lett. 13, 88–90 (2001). [CrossRef]
3. J. H. Lee and Y. C. Chung, “Improved OSNR monitoring technique based on polarization-nulling method,” Electron. Lett. 37, 972–973 (2001). [CrossRef]
4. M. D. Feuer, “Measurement of OSNR in the presence of partially polarized ASE,” IEEE Photon. Technol. Lett. 17, 435–437 (2005). [CrossRef]
5. J. H. Lee, D. M. Yeo, and Y. C. Chung, “Effect of partially polarized amplified spontaneous Emission Noise on Q-factor estimation using optical Signal-to-Noise Ratio,” IEEE Photon. Technol. Lett. 18, 463–465 (2006). [CrossRef]
6. I. T. Lima, A. O. Lima, Y. Sun, H. Jiao, J. Zweck, C. R. Menyuk, and G. M. Carter, “A receiver model for optical fiber communication systems with arbitrarily polarized noise,” J. Lightwave Technol. 23, 1478–1490 (2005). [CrossRef]
