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Precise measurements and their analysis of GAWBS-induced depolarization noise in various optical fibers for digital coherent transmission

Masato Yoshida, Naoya Takefushi, Keisuke Kasai, Toshihiko Hirooka, and Masataka Nakazawa

Open Access Open Access

Abstract

We undertake precise measurements of guided acoustic wave Brillouin scattering (GAWBS) depolarization noise caused by the TR2,m mode (torsional and radial mode) in various fibers and analyze the results. And we describe the influence of the noise on digital coherent transmission. We first show that the TR2,m mode is distributed over a wider bandwidth when the effective core area Aeff of the fiber is smaller. We then describe the strong mode-number dependence of the depolarization power generated from the profile of the refractive index change induced by the TR2,m mode. We also use two methods to measure the polarization crosstalk (XT) induced by the depolarization, namely, a direct detection method with a photodiode and a conventional power detection method with an optical spectrum analyzer. The results of the two methods agree well, and the XT increase is inversely proportional to the fiber Aeff and proportional to fiber length. Finally, we evaluate the influence of the GAWBS-induced XT on the BER characteristics in a coherent QAM transmission, where we find that the influence of the TR2,m mode is much weaker than that of the R0,m mode (radial mode). That is, the error-free transmission distance in standard single-mode fiber is extended to 8600 km for 256 QAM signal assuming hard-decision FEC with a 7% overhead. This distance is seven times longer than that obtained with the R0,m mode.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Digital coherent optical transmission with a multilevel modulation format is an important technology that supports today’s information infrastructure. If we are to increase the transmission capacity by employing, for example, a QAM signal with a higher multiplicity, it is very important that we compensate precisely for signal impairments such as chromatic dispersion and Kerr effects. Recently, guided acoustic wave Brillouin scattering (GAWBS) [1,2] has been re-investigated as a new factor limiting high-multilevel QAM coherent transmission performance [3–8].

GAWBS has two important resonant modes called the R0,m and TR2,m modes [1,2]. The R0,m mode vibrates only in the radial direction and induces pure phase noise in the optical signal. On the other hand, the TR2,m mode vibrates in both the radial and torsional directions, which induces not only phase noise but also depolarization due to rotational vibration. It is well known that the scattering efficiency of the R0,m mode is generally more dominant than that of the TR2,m mode [9,10]. We first studied the GAWBS phase noise caused by the R0,m mode in various optical fibers and discussed its influence on digital coherent transmission [6]. We have also proposed GAWBS phase noise compensation methods with a pilot tone [3], where the GAWBS information is detected by a pilot tone and fed back into the optical phase of a signal. With this method, we successfully improved the bit error rate (BER) characteristics in 64 and 1024 QAM-160 km transmissions [3,8].

On the other hand, the depolarization noise induced by the TR2,m mode causes polarization crosstalk (XT) in a polarization-multiplexed transmission [1,2]. Several groups have already investigated the GAWBS depolarization noise in various fibers including polarization-maintaining fibers [11], photonic crystal fibers [12], hole-assisted fibers [13], tapered fibers [14], few-mode fibers [15], and highly nonlinear fibers [16].

However, there has been no report on the fiber structural dependence of GAWBS depolarization noise that focused on a digital coherent transmission. When we focus on an optical transmission, a multi-input multi-output (MIMO) technique can be successfully employed to reduce the XT. However, the MIMO response speed is insufficient to compensate for the GAWBS depolarization noise within a data bandwidth of approximately 500 MHz. Therefore, GAWBS depolarization has an unavoidable influence on a digital coherent transmission [17].

In this paper, we present detailed measurements and their analysis with respect to the fiber structural dependence of the GAWBS depolarization noise and its influence on a digital coherent transmission. First, we numerically calculated the depolarization noise spectrum in three types of optical fibers with different effective core areas Aeff, namely an ultra-large area fiber (ULAF), a standard single-mode fiber (SSMF), and a dispersion-shifted fiber (DSF). Here, we show that the mode dependence of the depolarization power is derived from the profile of the refractive index change induced by the TR2,m mode. We then measured the GAWBS depolarization noise spectrum and the GAWBS-induced XT in each fiber by using a direct detection method with a photodiode (PD). These results show that the XT increases in inverse proportion to the fiber Aeff and in proportion to fiber length. Furthermore, we measured the XT with a conventional power detection method by using an optical spectrum analyzer, which proved the validity of experimental results obtained with the direct detection method. Finally, we evaluated the influence of GAWBS-induced XT on the BER characteristics in a coherent QAM transmission, where the error-free transmission distance was compared with that caused by the GAWBS phase noise in the R0,m mode.

2. Theoretical analysis of GAWBS depolarization noise in various optical fibers

In this section, we describe the theoretical characteristics of GAWBS depolarization noise caused by the TR2,m mode. The present analysis is based on Ref. [2]. The refractive index changes Δnx and Δny for X and Y-polarized signals induced by the TR2,m mode are given by

$$\begin{aligned}\Delta n_x^{}(r,\theta ) &= \frac{{n_0^3}}{2}\{{({{P_{11}}{{\cos }^2}\theta + {P_{12}}{{\sin }^2}\theta } ){S_{rr}}(r,\theta ) + ({{P_{11}}{{\sin }^2}\theta + {P_{12}}{{\cos }^2}\theta } ){S_{\theta \theta }}(r,\theta )} \\ &\quad - {({{P_{11}} - {P_{12}}} )\cos \theta \sin \theta {S_{r\theta }}(r,\theta )} \}\textrm{ }, \end{aligned}$$
$$\begin{aligned}\Delta n_y^{}(r,\theta ) &= \frac{{n_0^3}}{2}\{{({{P_{12}}{{\cos }^2}\theta + {P_{11}}{{\sin }^2}\theta } ){S_{rr}}(r,\theta ) + ({{P_{12}}{{\sin }^2}\theta + {P_{11}}{{\cos }^2}\theta } ){S_{\theta \theta }}(r,\theta )} \\ &\quad +{({{P_{11}} - {P_{12}}} )\cos \theta \sin \theta {S_{r\theta }}(r,\theta )} \}\textrm{ }. \end{aligned}$$

Here, P11(=0.121) and P12(=0.270) are the photo-elastic coefficients of quartz glass [2], n0 is the refractive index of the fiber core, and Srr(r,θ), Sθθ(r,θ) and Srθ(r,θ) are the strain components induced by the TR2,m mode in the fiber cross-section, which are given by

$$\begin{aligned} {S_{rr}}(r,\theta ) &= \frac{{{C_m}}}{a}\left\{ {{A_2}\left[ {\frac{{ - 2}}{{{{(r/a)}^2}}}{J_2}\left( {\frac{{\alpha {y_m}r}}{a}} \right) + \frac{{5\alpha {y_m}}}{{(r/a)}}{J_3}\left( {\frac{{\alpha {y_m}r}}{a}} \right) - {{(\alpha {y_m})}^2}{J_4}\left( {\frac{{\alpha {y_m}r}}{a}} \right)} \right]} \right.\\ & \left. { + {A_1}\left[ {\frac{2}{{{{(r/a)}^2}}}{J_2}\left( {\frac{{{y_m}r}}{a}} \right) - \frac{{2{y_m}}}{{(r/a)}}{J_3}\left( {\frac{{{y_m}r}}{a}} \right)} \right]} \right\}\cos 2\theta \\ &= S^{\prime}_{rr}(r)\cos 2\theta , \end{aligned}$$
$$\begin{aligned}{S_{\theta \theta }}(r,\theta ) &= \frac{{{C_m}}}{a}\left\{ {{A_2}\left[ {\frac{2}{{{{(r/a)}^2}}}{J_2}\left( {\frac{{\alpha {y_m}r}}{a}} \right) + \frac{{\alpha {y_m}}}{{(r/a)}}{J_3}\left( {\frac{{\alpha {y_m}r}}{a}} \right)} \right]} \right.\\ &\textrm{ }\left. { + {A_1}\left[ {\frac{{ - 2}}{{{{(r/a)}^2}}}{J_2}\left( {\frac{{{y_m}r}}{a}} \right) + \frac{{2{y_m}}}{{(r/a)}}{J_3}\left( {\frac{{{y_m}r}}{a}} \right)} \right]} \right\}\cos 2\theta \\ &= S^{\prime}_{\theta \theta }(r)\cos 2\theta , \end{aligned}$$
$$\begin{aligned} {S_{r\theta }}(r,\theta ) &= \frac{{{C_m}}}{a}\left\{ {{A_2}\left[ {\frac{4}{{{{(r/a)}^2}}}{J_2}\left( {\frac{{\alpha {y_m}r}}{a}} \right) - \frac{{4\alpha {y_m}}}{{(r/a)}}{J_3}\left( {\frac{{\alpha {y_m}r}}{a}} \right)} \right]} \right.\\ &\quad \textrm{ }\left. { + {A_1}\left[ {\frac{{ - 4}}{{{{(r/a)}^2}}}{J_2}\left( {\frac{{{y_m}r}}{a}} \right) + \frac{{4{y_m}}}{{(r/a)}}{J_3}\left( {\frac{{{y_m}r}}{a}} \right) - y_m^2{J_4}\left( {\frac{{{y_m}r}}{a}} \right)} \right]} \right\}\sin 2\theta \\ &= S^{\prime}_{r\theta }(r)\sin 2\theta , \end{aligned}$$
where
$${A_1} = ({6 - y_m^2} ){J_2}({\alpha {y_m}} ),\textrm{ }{A_2} = \left( {6 - \frac{{y_m^2}}{2}} \right){J_2}({{y_m}} )- 3{y_m}{J_3}({{y_m}} )\textrm{ }.$$

Here, Cm is the amplitude of the acoustic wave [18], Jn(y) is an n-th order Bessel function, ym is the m-th solution of the boundary condition for the TR2,m mode [18], α (=Vs/ Vd) is the ratio of the transverse sonic velocity Vs ( = 3740 m/s) to the longitudinal sonic velocity Vd ( = 5996 m/s) in quartz glass [2], and S′rr, S′θθ and S′rθ represent the radial dependence of the strain components of the TR2,m mode.

Figure 1 shows examples of the refractive index changes Δnx and Δny for the TR2,1, TR2,4, and TR2,7 modes. The vertical axis is normalized by the maximum value of each refractive index change. As seen in Fig. 1, the profiles have two resonant vibrations in the rotation direction, and the number of radial vibrations increases as the mode number m increases. Furthermore, there is an orthogonal relationship between Δnx and Δny, which causes a birefringence in the fiber. This results in depolarization.

 figure: Fig. 1.

Fig. 1. Refractive index changes induced by the TR2,1, TR2,4, and TR2,7 modes. (a-1)-(a-3) For X polarization, (b-1)-(b-3) for Y polarization.

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Since the polarization of the signal changes randomly in the fiber, the effective values of the refractive index changes are given by averaging Eqs. (1-1) and (1-2) in the θ direction as follows

$$\begin{aligned} \overline {\Delta n_x(r)} &= \frac{1}{{2\pi }}\int_0^{2\pi } {\Delta n_x(r,\theta )d\theta } \\ & = \frac{{n_0^3}}{8}({{P_{11}} - {P_{12}}} )[{{{S^{\prime}}_{rr}}(r) - {{S^{\prime}}_{\theta \theta }}(r) - {{S^{\prime}}_{r\theta }}(r)} ]\textrm{ }, \end{aligned}$$
$$\begin{aligned} \overline {\Delta n_y(r)} &= \frac{1}{{2\pi }}\int_0^{2\pi } {\Delta n_y(r,\theta )d\theta } \\ &= \frac{{n_0^3}}{8}({{P_{12}} - {P_{11}}} )[{{{S^{\prime}}_{rr}}(r) - {{S^{\prime}}_{\theta \theta }}(r) - {{S^{\prime}}_{r\theta }}(r)} ]={-} \overline {\Delta n_x(r)} \textrm{ }. \end{aligned}$$

These refractive index changes cause optical phase shifts in each polarization axis, which can be expressed as

$$\delta {\varphi _x} = kl\int_0^{2\pi } {\int_0^a {\overline {\Delta n_x(r)} \cdot E(r)rdrd\theta } } ={-} \delta {\varphi _y}, $$
Where
$$E(r) = \frac{1}{{\pi {w^2}}}\exp \left[ { - {{\left( {\frac{r}{w}} \right)}^2}} \right],\,w = \sqrt {\frac{{{\textrm{A}_{\textrm{eff}}}}}{\pi }}, $$

Here, k is a propagation constant, l is the fiber length, and w is the mode field radius, where the mode field is approximated as a Gaussian profile. In our analysis, we calculated the GAWBS noise generated in three types of optical fibers, namely, ULAF, SSMF, and DSF, whose Aeff values were 153, 80, and 45 µm2, respectively. The magnitude of depolarization, d, can then be calculated from the difference between the phase shifts of the two polarizations in the form.

$$d = {\sin ^2}\left( {\frac{{\delta {\varphi_x} - \delta {\varphi_y}}}{2}} \right) = {\sin ^2}(\delta {\varphi _x}) \approx \delta \varphi _x^2$$

Figure 2 shows the refractive index changes for X-polarization signals (red curve) induced by the TR2,7, TR2,10 and TR2,13 modes, which are calculated by substituting θ = 0 in Eq. (1-1). The vertical axis is normalized by each maximum value. Here, the mode profiles of the optical fields E(r) of ULAF and DSF are also plotted by black curves. The magnitude of the depolarization increases when the E(r) and refractive index changes are closer.

 figure: Fig. 2.

Fig. 2. Comparison of overlaps between the optical electric field and the refractive index changes of the TR2,7, TR2,10, and TR2,13 modes. (a-1)-(a-3) ULAF, (b-1)-(b-3) DSF.

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Figure 3 shows the changes in the power of the GAWBS depolarization noise spectrum induced by each TR2,m mode, which is calculated with Eq. (7). The vertical axis is normalized by the power level of the depolarization noise induced in the ULAF (TR2,7 mode). As Aeff becomes smaller, the resonant mode of the GAWBS is distributed over a wider bandwidth, which is the same relationship as that observed in the R0,m mode [6]. On the other hand, the noise power has a large mode-number dependence, which is different from the R0,m mode. For example, the noise power of the TR2,6 mode (126 MHz) is an order of magnitude lower than those of the TR2,5 mode (108 MHz) and TR2,7 mode (140 MHz). Since the refractive index change is expressed as the sum of the 2nd to 4th order Bessel functions as given by Eqs. (2-1)–(2-3), the profile depends strongly on the mode number. Figures 4(a)–4(c) show the refractive index changes induced by the TR2,5, TR2,6, and TR2,7 modes, respectively, which are also calculated by substituting θ = 0 in Eq. (1-1). Although the profiles for the TR2,5 and TR2,7 modes shown in Figs. 4(a) and 4(c) have their maximum values at the center, the TR2,6 mode has a local minimum at the center. As a result, the depolarization noise powers for each TR2,m mode differ greatly.

 figure: Fig. 3.

Fig. 3. The power of the GAWBS depolarization noise spectrum induced by each TR2m mode. (a) ULAF (Aeff = 153μm2), (b) SSMF (Aeff = 80 μm2), (c) DSF (Aeff = 45 μm2). The vertical axis is normalized by the power level of ULAF (TR2,7 mode).

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 figure: Fig. 4.

Fig. 4. Refractive index changes of the (a) TR2,5, (b) TR2,6, and (c) TR2,7 modes. The optical electric fields in SSMF are also shown for reference.

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3. Experimental analysis of GAWBS depolarization noise in various optical fibers

In this section, we describe our experimental analysis of GAWBS depolarization noise. First, we measured the noise spectrum with a direct detection method [17] and compared the results with the analytical results presented in section 2. We then evaluated the GAWBS-induced XT values from the data obtained with the direct detection method, where the validity of the estimation was also proven by comparing with the results obtained with a conventional power detection method.

Figure 5 shows the direct detection setup that we adopted to observe the GAWBS depolarization noise [17]. We prepared three types of 150∼160 km optical fibers, namely, ULAF, SSMF and DSF, whose optical loss and cut-off wavelength values were 0.20, 0.21, 0.18 dB/km and 1260, 1270, 1530 nm, respectively. We launched a CW signal from the transmitter at 0 dBm, which is below the stimulated Brillouin scattering threshold. The transmission loss was compensated for by using both EDFAs and Raman amplifiers, resulting in an OSNR of more than 40 dB after the transmission. Although the pump wavelength of the Raman amplifier (around 1440 nm) was shorter than the cut-off wavelength of the ULAF, a 10 dB Raman gain was obtained for the ULAF transmission line. At the receiver, the transmitted signal was coupled to an analyzer, which converted the polarization noise into intensity noise. We detected the intensity noise with a PD.

 figure: Fig. 5.

Fig. 5. Experimental setup for observing GAWBS depolarization noise generated in three types of optical fibers.

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Figure 6 shows the transmittivity of the analyzer when a linearly polarized signal is coupled to it at an angle of θA [deg.] with respect to the analyzer axis. The intensity I of the signal passed through the analyzer and the angle θA are related as follows

$$I = {\cos ^2}{\theta _A} = \frac{1}{2}({1 + \cos 2{\theta_A}} )\textrm{ }.$$

Here, the maximum value of the intensity is normalized to 1. In Fig. 6, when θA is set at 45 degrees, the slope is -1, so the polarization noise δθ(t) caused by the TR2,m mode can be linearly converted into the intensity noise δI(t). We analyzed the GAWBS depolarization noise spectrum by Fourier transforming δI(t), which is detected with a PD. On the other hand, the amount of XT is defined by the leaked signal intensity from the analyzer when θA is set at 90 degrees, which is given by

$$I(t) = {\sin ^2}\delta \theta (t) \approx \delta {\theta ^2}(t). $$

 figure: Fig. 6.

Fig. 6. Relationship between the rotation angle and the transmittivity of the analyzer.

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Therefore, the XT can be calculated by squaring δθ(t) measured with the condition θA = 45 degrees. This method helps to reduce the influence of the background noise of the photodetector.

The RF spectra of the measured depolarization noise for a 160 km ULAF, a 160 km SSMF, and a 150 km DSF are shown in Figs. 7(a)–7(c), respectively. For comparison, we also plot the calculated depolarization power results shown in Fig. 3. The vertical axes of all the calculated plots are normalized by the power level of the depolarization noise component in a 160 km ULAF (TR2,7 mode). As seen in these figures, the powers of the measured depolarization components agree well with the calculated results. These results indicate that the GAWBS depolarization noise can be precisely measured with the direct detection method. It should be noted that there are a few modes whose measured values are lower than the calculated values. This may be because the acoustic mode leaks into the polymer jacket material surrounding the fiber cladding [18]. On the other hand, disturbances such as pressure and stress from outside the fiber might change the mode profile of the thermal acoustic wave in the fiber cross section, which may affect the GAWBS depolarization noise. Such disturbances may be another reason for the slight mismatch between the measured and calculated values in Fig. 7.

 figure: Fig. 7.

Fig. 7. Experimentally measured GAWBS depolarization noise spectra observed after transmission. (a) 160 km ULAF, (b) 160 km SSMF, and (c) 150 km DSF. The calculated results shown in Fig. 3 are also plotted as filled circles.

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Figure 8 shows the temporal intensity noise of the direct detection signal corresponding to Fig. 7. To extract only the GAWBS components, we removed the DC component and the background white noise in the frequency domain by using digital signal processing. The vertical axis is normalized by the DC level, namely, the waveform shown in Fig. 8 corresponds to -δθ(t) defined in Fig. 6 with θA = 45 degrees. With these waveforms, we estimated the GAWBS-induced XT by using Eq. (9). The calculated XT values were -44.3, -41.0, and -39.9 dB for 160 km ULAF, 160 km SSMF, and 150 km DSF, respectively. Figure 8 shows that the XT increase is inversely proportional to the fiber Aeff.

 figure: Fig. 8.

Fig. 8. Temporal intensity noise caused by GAWBS depolarization noise after transmission. (a) 160 km ULAF, (b) 160 km SSMF, and (c) 150 km DSF. The vertical axis is normalized by the DC level.

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Next, we evaluated the dependence of the GAWBS depolarization noise on the transmission distance. Figure 9 shows the measured temporal intensity noise of the direct detection signal as a function of transmission distance when we used SSMF. The estimated XT values are also shown in Fig. 9, where we can see that the XT increased in proportion to the transmission distance.

 figure: Fig. 9.

Fig. 9. Measurement results for temporal intensity noise caused by GAWBS depolarization noise as a function of transmission distance. (a) 80 km, (b) 160 km, (c) 240 km, (d) 320 km, and (e) 400 km SSMF. The vertical axis is normalized by the DC level.

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To prove the validity of the XT values obtained with the direct detection method, we also measured the XT in a different way with a conventional power detection method. In the experimental setup shown in Fig. 5, we used a QAM modulated signal (3 Gbaud, 1024 QAM) as a probe light since a non-modulated signal caused an interference error in the power measurement. At the receiver, the optical signal that leaked from the analyzer, whose angle was set at θA = 0, was detected in the XT measurement. Here, we used an optical spectrum analyzer as a power monitor to separate the signal and ASE noise with a high resolution of 0.01 nm. Figure 10 shows the measured optical spectra of the output signal as a function of transmission distance. Here, the XT was defined by the ratio of the spectrum peak powers obtained at θA = 0° and 90°. The measured XT values are shown in Fig. 10, which agreed well with those obtained with the direct detection method and shown in Fig. 9. This indicates that both the noise spectrum and the GAWBS-induced XT values can be precisely and simultaneously obtained with the direct detection method.

 figure: Fig. 10.

Fig. 10. Measurement optical spectra obtained for θA = 0 and 90 degrees as a function of transmission distance. (a) 80 km, (b) 160 km, (c) 240 km, (d) 320 km, and (e) 400 km SSMF.

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Finally, we describe the influence of the GAWBS depolarization noise on digital coherent transmission. We numerically estimated the XT tolerance for 256, 1024, and 4096 QAM signals, and Fig. 11(a) shows a schematic diagram of the numerical model. The BER of a polarization-multiplexed QAM signal was counted after it had passed through an analyzer with a detuning angle of θA from θA = 0. We adjusted the magnitude of the XT applied to the QAM signal by changing θA. Figure 11(b) shows the relationship between the XT and BER for 256, 1024, and 4096 QAM signals. Numerically speaking, to achieve an error-free performance for 256, 1024, and 4096 QAM signals with a 7% overhead FEC (threshold: 2 × 10−3), the XT values have to be below -24.0, -30.0, and -36.3 dB, respectively. In our previous work [6], we studied the influence of GAWBS induced “phase” noise on a digital coherent transmission, where we calculated the error-free distances for 256, 1024, and 4096 QAM signals with a 7% overhead FEC. To allow comparison with our previous results, we assumed the same signal multiplicity and FEC condition in the present analysis.

 figure: Fig. 11.

Fig. 11. Numerical estimation of XT tolerance for 256, 1024, and 4096 QAM signals. a) Diagram of numerical analysis model. (b) Numerical results of BER as a function of the XT applied to the QAM signal.

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In Fig. 12, the measured XT values seen in Figs. 8 and 9 are plotted as a function of the transmission distance. The orange, blue, and green plots correspond to ULAF, SSMF, and DSF, respectively. The broken lines in the figure show the estimated XT values, which increase in proportion to the transmission distance. It can be seen that the measured and estimated XT values obtained for SSMF agree well. This is because the GAWBS noise power essentially increases in proportion to the transmission distance. The XT tolerances for 256, 1024 and 4096 QAM signals are also shown with solid red lines. The intersections between the estimated XT lines and the XT tolerance lines correspond to the maximum error-free transmission distance with FEC. Table 1 shows error-free transmission distances for 256, 1024, 4096 QAM signals in each fiber. As shown in the table, the error-free distances in SSMF are 8600, 2000, and 480 km, respectively, for 256,1024 and 4096 QAM transmissions. In our previous work [6], we obtained an error-free transmission distance of 1200 km for a 256 QAM signal due to the GAWBS phase noise induced by the R0,m mode. Therefore, the influence of the GAWBS depolarization noise on a digital coherent transmission was about one-seventh that of the GAWBS phase noise. Although the noise caused by the TR2,m mode is weak, the GAWBS-induced XT has an unavoidable influence since the response speed of MIMO signal processing is insufficient. Therefore, the GAWBS depolarization noise should be fully considered as we approach transoceanic transmission distances. Table 1 also shows that the error-free transmission distance can be doubled by replacing SSMF with ULAF.

 figure: Fig. 12.

Fig. 12. Measured XT values in Figs. 8 and 9 as a function of transmission distance. The orange, blue, and green plots correspond to ULAF, SSMF, and DSF, respectively.

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Tables Icon

Table 1. Estimated transmission distance tolerant of GAWBS depolarization noise for 256, 1024, 4096 QAM signals in three fibers with 7% overhead FEC. ( ) indicates corresponding transmission distances with GAWBS phase noise.

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Impairments such as ASE noise and nonlinear phase modulation degrade the BER performance during fiber transmission. To reduce these impairments, an all-Raman amplified low-loss ultra-large-area fiber (ULAF) transmission line has been employed for a long-haul transmission, where an OSNR of 21.1 dB including XT was obtained after a 6,000 km transmission [19]. On the other hand, the polarization XT induced by GAWBS depolarization after a 6,000 km transmission is estimated as -28 dB from Fig. 12. The XT value is approximately 7 dB lower than the ASE noise level reported in Ref. [19]. However, unlike the ASE noise, the XT component contains a data pattern and has a stronger influence on the BER performance depending on the peak to average power ratio (PAPR) of the pattern. A multi-level QAM signal with a roll-off factor of less than 0.1, which is typically used for a highly spectrally efficient transmission, has a PAPR of more than 7 dB [20]. Therefore, the influence of the polarization XT cannot be ignored in a long-haul transmission.

4. Conclusion

We performed detailed measurements of the GAWBS depolarization noise caused by the TR2,m mode in three types of fibers, namely, ULAF, SSMF, and DSF and analyzed the results. We showed that the GAWBS depolarization noise depends strongly on the fiber Aeff as with the GAWBS phase noise induced by the R0,m mode. We also pointed out that the mode number depends strongly on the depolarization power generated from the profile of the refractive index change caused by the TR2,m mode. The polarization XT caused by the depolarization was measured with two methods, namely, a direction detection method with a photodiode and a conventional power detection method with an optical spectrum analyzer, where we found that the XT increased in inverse proportion to the fiber Aeff and in proportion to the fiber length. Finally, we numerically investigated the influence of the GAWBS depolarization noise on the BER characteristics in a coherent QAM transmission and evaluated the limitation imposed on the transmission distances in three types of fibers. These results provide useful insights as regards the impairments in a long-haul high-multilevel digital QAM coherent transmission.

Funding

Ministry of Internal Affairs and Communications (JPMI00316).

Disclosures

The authors declare no conflicts of interest.

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Figures (12)
Fig. 1.
Fig. 1. Refractive index changes induced by the TR2,1, TR2,4, and TR2,7 modes. (a-1)-(a-3) For X polarization, (b-1)-(b-3) for Y polarization.

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Fig. 2.
Fig. 2. Comparison of overlaps between the optical electric field and the refractive index changes of the TR2,7, TR2,10, and TR2,13 modes. (a-1)-(a-3) ULAF, (b-1)-(b-3) DSF.

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Fig. 3.
Fig. 3. The power of the GAWBS depolarization noise spectrum induced by each TR2m mode. (a) ULAF (Aeff = 153μm2), (b) SSMF (Aeff = 80 μm2), (c) DSF (Aeff = 45 μm2). The vertical axis is normalized by the power level of ULAF (TR2,7 mode).

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Fig. 4.
Fig. 4. Refractive index changes of the (a) TR2,5, (b) TR2,6, and (c) TR2,7 modes. The optical electric fields in SSMF are also shown for reference.

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Fig. 5.
Fig. 5. Experimental setup for observing GAWBS depolarization noise generated in three types of optical fibers.

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Fig. 6.
Fig. 6. Relationship between the rotation angle and the transmittivity of the analyzer.

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Fig. 7.
Fig. 7. Experimentally measured GAWBS depolarization noise spectra observed after transmission. (a) 160 km ULAF, (b) 160 km SSMF, and (c) 150 km DSF. The calculated results shown in Fig. 3 are also plotted as filled circles.

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Fig. 8.
Fig. 8. Temporal intensity noise caused by GAWBS depolarization noise after transmission. (a) 160 km ULAF, (b) 160 km SSMF, and (c) 150 km DSF. The vertical axis is normalized by the DC level.

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Fig. 9.
Fig. 9. Measurement results for temporal intensity noise caused by GAWBS depolarization noise as a function of transmission distance. (a) 80 km, (b) 160 km, (c) 240 km, (d) 320 km, and (e) 400 km SSMF. The vertical axis is normalized by the DC level.

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Fig. 10.
Fig. 10. Measurement optical spectra obtained for θA = 0 and 90 degrees as a function of transmission distance. (a) 80 km, (b) 160 km, (c) 240 km, (d) 320 km, and (e) 400 km SSMF.

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Fig. 11.
Fig. 11. Numerical estimation of XT tolerance for 256, 1024, and 4096 QAM signals. a) Diagram of numerical analysis model. (b) Numerical results of BER as a function of the XT applied to the QAM signal.

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Fig. 12.
Fig. 12. Measured XT values in Figs. 8 and 9 as a function of transmission distance. The orange, blue, and green plots correspond to ULAF, SSMF, and DSF, respectively.

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Tables (1)

Tables Icon

Table 1. Estimated transmission distance tolerant of GAWBS depolarization noise for 256, 1024, 4096 QAM signals in three fibers with 7% overhead FEC. ( ) indicates corresponding transmission distances with GAWBS phase noise.

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Equations (13)

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Δ n x ( r , θ ) = n 0 3 2 { ( P 11 cos 2 θ + P 12 sin 2 θ ) S r r ( r , θ ) + ( P 11 sin 2 θ + P 12 cos 2 θ ) S θ θ ( r , θ ) − ( P 11 − P 12 ) cos ⁡ θ sin ⁡ θ S r θ ( r , θ ) }   ,
Δ n y ( r , θ ) = n 0 3 2 { ( P 12 cos 2 θ + P 11 sin 2 θ ) S r r ( r , θ ) + ( P 12 sin 2 θ + P 11 cos 2 θ ) S θ θ ( r , θ ) + ( P 11 − P 12 ) cos ⁡ θ sin ⁡ θ S r θ ( r , θ ) }   .
S r r ( r , θ ) = C m a { A 2 [ − 2 ( r / a ) 2 J 2 ( α y m r a ) + 5 α y m ( r / a ) J 3 ( α y m r a ) − ( α y m ) 2 J 4 ( α y m r a ) ] + A 1 [ 2 ( r / a ) 2 J 2 ( y m r a ) − 2 y m ( r / a ) J 3 ( y m r a ) ] } cos ⁡ 2 θ = S r r ′ ( r ) cos ⁡ 2 θ ,
S θ θ ( r , θ ) = C m a { A 2 [ 2 ( r / a ) 2 J 2 ( α y m r a ) + α y m ( r / a ) J 3 ( α y m r a ) ]   + A 1 [ − 2 ( r / a ) 2 J 2 ( y m r a ) + 2 y m ( r / a ) J 3 ( y m r a ) ] } cos ⁡ 2 θ = S θ θ ′ ( r ) cos ⁡ 2 θ ,
S r θ ( r , θ ) = C m a { A 2 [ 4 ( r / a ) 2 J 2 ( α y m r a ) − 4 α y m ( r / a ) J 3 ( α y m r a ) ]   + A 1 [ − 4 ( r / a ) 2 J 2 ( y m r a ) + 4 y m ( r / a ) J 3 ( y m r a ) − y m 2 J 4 ( y m r a ) ] } sin ⁡ 2 θ = S r θ ′ ( r ) sin ⁡ 2 θ ,
A 1 = ( 6 − y m 2 ) J 2 ( α y m ) ,   A 2 = ( 6 − y m 2 2 ) J 2 ( y m ) − 3 y m J 3 ( y m )   .
Δ n x ( r ) ¯ = 1 2 π ∫ 0 2 π Δ n x ( r , θ ) d θ = n 0 3 8 ( P 11 − P 12 ) [ S ′ r r ( r ) − S ′ θ θ ( r ) − S ′ r θ ( r ) ]   ,
Δ n y ( r ) ¯ = 1 2 π ∫ 0 2 π Δ n y ( r , θ ) d θ = n 0 3 8 ( P 12 − P 11 ) [ S ′ r r ( r ) − S ′ θ θ ( r ) − S ′ r θ ( r ) ] = − Δ n x ( r ) ¯   .
δ φ x = k l ∫ 0 2 π ∫ 0 a Δ n x ( r ) ¯ ⋅ E ( r ) r d r d θ = − δ φ y ,
E ( r ) = 1 π w 2 exp ⁡ [ − ( r w ) 2 ] , w = A eff π ,
d = sin 2 ( δ φ x − δ φ y 2 ) = sin 2 ( δ φ x ) ≈ δ φ x 2
I = cos 2 θ A = 1 2 ( 1 + cos ⁡ 2 θ A )   .
I ( t ) = sin 2 δ θ ( t ) ≈ δ θ 2 ( t ) .
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