We describe the nondestructive measurement of mode coupling along a few-mode fiber using a synchronous multi-channel optical time-domain reflectometer (OTDR). By installing a few-mode fiber (FMF) coupler made with a phase mask method, we excite the LP01 mode in an FMF under the test as an input mode, and then we detect backward Rayleigh scattered LP11a or LP11b modes, which were generated as a result of the mode coupling through the coupler. The mode coupling distribution between the LP01 and LP11a,b modes along the test FMF was successfully measured with a 10-m spatial resolution by obtaining the ratio between the backscattered LP01 mode and LP11a or LP11b. The value of the mode coupling obtained with the present method agreed well with that obtained with the conventional transmission method.
© 2014 Optical Society of America
Space division multiplexing (SDM) and mode division multiplexing (MDM) are receiving a lot of attention with a view to increasing the total capacity achievable in a single fiber using multi-core fiber (MCF) and few-mode fiber (FMF) [1–6]. In particular, a 1.01 Pbit/s transmission over 52 km has been demonstrated by the SDM of 222 WDM channels of 456 Gbit/s PDM-32QAM signals with a low-crosstalk 12-core MCF . As regards MDM, MIMO-based three-mode transmission over FMF has been realized with 6x6 MIMO and six modes has been realized with 12x12 MIMO, which made it possible to achieve 73.7 Tbit/s-119 km  and 30.7 Tbit/s-177 km  transmissions, respectively.
One of the most critical issues in relation to MCF and FMF transmission is the inter-core and inter-modal crosstalk. It has been found that stochastic mode coupling along a fiber as a result of longitudinal perturbations is the dominant factor causing the crosstalk. If we can measure the distribution of the mode-coupling coefficient along the propagation direction, it will give us useful knowledge with which to identify the source of transmission performance degradation in SDM and MDM transmissions.
In 1984, we proposed a technique for measuring polarization mode coupling along a polarization-maintaining (PM) fiber using an optical time-domain reflectometer (OTDR) [7, 8]. With this technique, one of the polarization axes is excited with an optical pulse and we measure the backward Rayleigh scattering from the same direction and orthogonal direction. By obtaining the ratio between them, we could measure the way in which polarization mode coupling occurred along the PM fiber.
Recently, we extended this idea to the measurement of mode coupling between two cores along an MCF . In this scheme, we extended the OTDR method in such a way that one of the cores is excited with an optical pulse to measure the ratio of the backward Rayleigh scattering between the excited and unexcited cores. This synchronous OTDR scheme is depicted in Fig. 1, and shows that we excite the center core and receive the OTDR signals from all cores. This technique can diagnose the nonuniformity of the mode-coupling coefficient along the fiber caused by the fiber’s structural irregularity, such as a strong correlation between the change in the mode coupling ratio and the cladding diameter fluctuation along the MCF .
In this paper, we describe nondestructive mode coupling measurement along an FMF using a multi-channel OTDR. The principle of the technique was presented at OFC 2014  and here we describe it in detail by measuring the mode coupling in two FMFs. The multi-channel OTDR has a measurement dynamic range of more than 40 dB, and the mode coupling distribution was successfully measured between the LP01 and LP11a, b modes with a spatial resolution of 10 m. We prepared two FMFs, fiber A and fiber B, and studied their detailed mode coupling (crosstalk) behavior including bending losses.
2. Experimental setup for FMF mode coupling measurement
Figure 2 shows the measurement setup for mode coupling along an FMF. Here, we did not install a polarizer in the experimental setup, and we do not consider polarization dependence in the mode coupling measurement. The optical masking apparatus shown in Fig. 2(b) is installed to remove the Fresnel reflection at the fiber end, which may otherwise distort the backward Rayleigh scattering waveforms . Two optical switches are installed between two optical circulators in each channel of the optical masking apparatus. Here, a 0.5 km SMF is also installed in front of the switches to adjust the timing between the electrical control signal and the backscattered optical signal. A 100 ns optical pulse (which yields a spatial resolution of 10 m) was emitted from ch. 1 of a synchronous multi-channel OTDR operated at 1550 nm and coupled to the LP01 mode of an FMF through the LP01 port of a phase-plate-based mode coupler  as shown in Fig. 2(c). The crosstalk between the LP01 and LP11 modes in the mode coupler was –30 dB, and the coupling losses for the LP01 and LP11 modes were –4 and –8.6 dB, respectively. The backscattered lights from unexcited higher-order modes of the FMF were then detected simultaneously by the three-channel synchronous OTDR. For example, the backscattered power in the LP11a mode, Pbs_11a, which resulted from mode coupling with the LP01 mode, was detected through the LP11a port of the mode coupler (demultiplexer) by ch. 2 of the multi-channel OTDR. In order to take account of the mode-dependent loss at the mode coupler, we calibrated the powers, Pbs, measured at each output port to compensate for their losses. The mode dependences in the coupling losses in the optical masking apparatus and multi-channel OTDR were also taken into account in the same way. Then the mode-coupling ratio between the LP01 and LP11 modes along the fiber can be obtained from the power ratio between Pbs_01 and Pbs_11:7, 8] and the crosstalk caused by the mode coupler. Since the crosstalk between the LP01 and LP11 modes in the mode coupler was as small as –30 dB, the effect on K in Eq. (1) is negligible. Note that Eq. (1) is valid when the mode-coupling coefficient h is small.
3. Experimental results for fiber A
The structural and fiber parameters of the test FMFs, namely fiber A and fiber B, are summarized in Table 1 and the calculated near field intensity distribution of the LP01 and LP11 modes are shown in Fig. 3. We first measured the mode coupling distribution along a 5.9 km GI-FMF (fiber A) supporting the LP01 and LP11a,b modes with core and cladding diameters of 32.6 and 116.5 μm, respectively, and cutoff wavelengths of 2315 nm (LP11) and 1529 nm (LP21). The chromatic dispersion was 20 ps/nm/km for all modes, and Aeff was 149 μm2 for the LP01 mode and 204 μm2 for the LP11 mode.
Figure 4(a) shows the backscattered signals from an FMF (fiber A) measured through the LP01, LP11a, and LP11b ports when a 100 ns input optical pulse was coupled into the LP01 mode. It can be seen that the backscattered power profile in the LP11a and LP11b modes is not uniform especially after ~3 km as shown by the blue and red curves. This deviation is caused by the longitudinal variation in the loss difference between the LP01 and LP11 modes, exp[(α11 – α01)L], as plotted in Fig. 4(b), which was measured with a conventional OTDR for each mode. Here, the loss difference between LP01 and LP11a was the same as that between LP01 and LP11b, one of which is plotted in Fig. 4(b). This indicates that the mode attenuation is not uniform along the FMF, and this results in non-uniformity in the backscattered power profile. This is not the case for mode coupling between single-mode cores in MCF. When evaluating the mode-coupling ratio η11,01, we take account of the non-uniformity in the attenuation coefficient difference (calibration factor), α11 – α01, by multiplying the mode attenuation difference given by Fig. 4(b), i.e.,Figs. 4(c) and 4(d), and correspond to the coupling with the LP11a and LP11b modes. Small spikes appeared in the slope, which partly consist of fluctuations with a resolution of less than 10 m, are due to noise that occurs when evaluating the mode coupling ratio. The clearly large offset K is likely to be caused by the crosstalk at the mode coupler, but this does not matter when evaluating the crosstalk along an FMF as the mode coupling effect is given by the slope of η, which can be obtained in the same manner as the MCFs mode coupling measurement. From these mode coupling profiles, the calculated crosstalk values between the two modes over a 5.9 km FMF transmission are –21.1 dB (LP01 and LP11a) and –22.4 dB (LP01 and LP11b). In a dB/km unit, they are –28.8 and –30.1 dB/km, respectively. These values are more than 20 dB larger than the crosstalks between two cores in a typical 10 km MCF .
We also undertook the experiment from the other end of the FMF (fiber A). The results are shown in Fig. 5, where Figs. 5(a) and 5(b) are taken from Fig. 4 (we define this as the forward direction) and Figs. 5(c) and 5(d) are the results from the other end of the FMF (we define this as the backward direction). When trace (c) is rotated 180 degrees, it completely overlaps trace (a) and the measured mode coupling slopes shown in traces (b) and (d) agree well. In addition, traces (b) and (d) indicate that the slope of the mode-coupling ratio is mostly uniform, which means that the mode coupling occurs uniformly along FMF.
We compared our OTDR results with those obtained using a conventional transmission method. To execute the transmission method, another phase mask coupler was prepared, where the coupling loss of the coupler was first measured. Here, since it is difficult to distinguish the LP11a and LP11b modes as they are strongly coupled in the presence of a slight stress on the FMF, we evaluated the magnitude of the crosstalk by taking the average of the LP01 to LP11a modes and the LP01 to LP11b modes. Then, the result was compared with that measured using the OTDR method. The mode coupling values thus obtained are summarized in Table 2. We found that the present OTDR results agree well with the crosstalk measured with a conventional transmission method.
We also carried out the mode coupling measurement when launching the pulse in the LP11a or LP11b mode into fiber A. The results are shown in Fig. 6. The mode couplings from the LP11a to LP01 mode [Figs. 6(a) and 6(b)] and from the LP11b to LP01 mode [Figs. 6(c) and 6(d)] induced crosstalk of –20.4 and –21.5 dB as shown in Figs. 6(b) and 6(d), respectively. These values agree well with the crosstalk values of –21.1 and –22.4 dB from the LP01 mode to the LP11a and LP11b modes, respectively, as obtained from Figs. 4(c) and 4(d), which indicates symmetry in the mode coupling.
In the next step, we tried to measure the mode coupling between LP11a and LP11b. We know that there is strong mode coupling between them, and that is hL is not smaller than unity. Therefore, our mode coupling measurement was not accurate, but we can roughly evaluate the way in which the strong mode coupling occurs. The results are shown in Fig. 7. Here, we show the backscattered waveform when we excited the LP11a mode and detected the LP11a and LP11b backward Rayleigh scattering. Approximately 3 dB down LP11b backward Rayleigh scattering was observed as seen in Fig. 7(a-1). The details of the OTDR signals are enlarged in Fig. 7(a-2), where we plotted the fine structure of the backscattered power after subtracting the slope from the measured data to so that the detailed change in Pbs_11a,b can be clearly seen. It is interesting to see the way in which the power of the backscattered signal changes during propagation. Here we see a completely out-of-phase change with a mode coupling period of approximately 50 m. This indicates that strong power coupling occurs during propagation. When we take the ratio between them as shown in Fig. 7(b-1) it becomes almost constant around a mode coupling ratio of 0.62. The initial value of 0.62 comes from the coupling crosstalk at the phase mask mode coupler and FMF itself. The crosstalk between LP11a and LP11b at the mode coupler is large because they have the same polarization as the mode field pattern rotated by 90 degrees in relation to each other. In addition the propagation constant is also the same. Therefore, a slight stress added to the LP11 mode gave rise to a large crosstalk between them. Hence, we observed a large initial value. However, it is important to note that there is no slope and an almost constant value is maintained throughout the fiber. Figure 7(b-1) is enlarged in Fig. 7(b-2), in which we observe a similar change to that seen in Fig. 7(a-2). Since Pbs_11b was divided with Pbs_11a, the ripples at around 50 m have been enhanced. This is due to the strong mode coupling between them. Modal birefringence  may cause a fluctuation in the mode-coupling between the LP11a and LP11b pseudo-modes, but we cannot distinguish it with the present technique which can measure the mode-coupling caused by non-uniform stress in the drawing and winding process.
4. Experimental results for fiber B
In the next step, we measured the mode coupling in fiber B, which is a 4-km long GI-FMF with core and cladding diameters of 23.5 and 126 μm, respectively, and cutoff wavelengths of 2140 nm (LP11) and 1447 nm (LP21). The chromatic dispersions for the LP01 and LP11 modes were 20.4 and 18.8 ps/km/nm, respectively, and Aeff was 151 μm2 for the LP01 mode and 195 μm2 for the LP11 mode.
Figure 8(a) shows the backscattered signals from fiber B measured through the LP01, LP11a, and LP11b ports when a 100 ns input optical pulse was coupled into the LP01 mode. It can be seen that the backscattered power profile in the LP11a and LP11b modes is not uniform and a step-like change is observed as shown by the blue and red curves, which resulted from the bending of fiber B, which may be attributed to the partial stress difference that was caused during the process of winding the fiber onto a bobbin. The calibration factor in this fiber is shown in Fig. 8(b), in which we observe a rapid increase during propagation. A comparison of Fig. 8(b) with Fig. 4(b) shows that the uniformity of the mode dependent loss is much lower in fiber B. The mode-coupling ratios thus obtained are shown in Figs. 8(c) and 8(d), corresponding to the couplings with the LP11a and LP11b modes. Clearly, compared with fiber A, the fluctuation in the crosstalk along fiber B is larger and the crosstalk values between the two modes over a 4 km transmission are –18.9 dB (LP01 and LP11a) and –18.1 dB (LP01 and LP11b). In a dB/km unit, they are –24.9 and –24.1 dB/km, respectively.
OTDR results for fiber B were also compared with those obtained with a conventional transmission method. The mode coupling values thus obtained are summarized in Table 3. We found that the present OTDR results also agree well with the crosstalk measured with a conventional transmission method.
We also carried out a mode coupling measurement for fiber B by launching a pulse in the LP11a or LP11b mode and detecting the LP01 mode. The results are shown in Fig. 9. The mode couplings from the LP11a to LP01 mode [Figs. 9(a) and 9(b)] and from the LP11b to LP01 mode [Figs. 9(c) and 9(d)) induced crosstalk values of –18.5 and –17.7 dB as shown in Figs. 9(b) and 9(d), respectively. These values are in good agreement with the crosstalk values of –18.9 and –18.1 dB from the LP01 mode to the LP11a and LP11b modes, respectively, as obtained from Figs. 8(c) and 8(d), which indicates symmetry in the mode coupling. It is interesting to see that even the detailed local structures shown in Figs. 9 (b) and 9(d) almost coincide with those shown in Figs. 8(c) and 8(d), respectively.
As we described in relation to fiber A, we also measured the mode coupling between LP11a and LP11b in fiber B. The results are shown in Fig. 10. Here, we show the backscattered waveform that we obtained when we excited the LP11a mode and detected the LP11a and LP11b backward Rayleigh scattering. Approximately 3 dB down LP11b backward Rayleigh scattering was observed as seen in Fig. 10(a-1). The details of the OTDR signals are enlarged in Fig. 10(a-2). It is interesting to see again how the power of the backscattered signal changes during the propagation. We again observed an out-of-phase power change between LP11a and LP11b with two periodic fluctuations; one with a period of 10 m and the other with a period of roughly 100 m. These may be attributable to fiber drawing and winding processes. When we measured the ratio between them as shown in Fig. 10(b-1), it became almost constant around a mode coupling ratio of 0.58. However, the mode coupling fluctuation is bigger than in Fig. 7(b-1). Figure 10(b-1) is enlarged in Fig. 10(b-2). Since Pbs_11b was divided with Pbs_11a, the fluctuations are enhanced. These results indicate that the present technique can measure the way in which the mode coupling (crosstalk) occurs during the propagation in the FMFs.
We have successfully demonstrated mode coupling measurement along the propagation direction in FMFs by using a synchronous multi-channel OTDR. The present method allows the nondestructive and simultaneous measurement of mode coupling and its longitudinal distribution, and is expected to provide a powerful tool for analyzing local mode coupling along an FMF.
This work was supported by the National Institute of Information and Communications Technology (NICT), Japan under “Research and Development toward Practical Use of Innovative Optical Fibers”. We express our thanks to R. Maruyama and S. Matsuo of Fujikura Ltd. for supplying the FMFs.
References and links
1. M. Nakazawa, “Giant leaps in optical communication technologies towards 2030 and beyond,” ECOC 2010, Plenary Talk.
2. J. Sakaguchi, B. J. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “19-core fiber transmission of 19 x 100 x 172-Gb/s SDM-WDM-PDM-QPSK signals at 305 Tb/s,” OFC 2012, PDP5C.1.
3. H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency,” ECOC2012, Th3.C.1. [CrossRef]
4. D. Qian, E. Ip, M.F. Huang, M. Li, A. Dogariu, S. Zhang, Y. Shao, Y.K. Huang, Y. Zhang, X. Cheng, Y. Tian, P. Ji, A. Collier, Y. Geng, J. Linares, C. Montero, V. Moreno, X. Prieto, and T. Wang, “1.05 Pb/s transmission with 109 b/s/Hz spectral efficiency using hybrid single- and few-mode cores,” FiO2012, FW6C.3.
5. V. A. J. M. Sleiffer, Y. Jung, V. Veljanovski, R. G. H. van Uden, M. Kuschnerov, Q. Kang, L. Grüner-Nielsen, Y. Sun, D. J. Richardson, S. Alam, F. Poletti, J. K. Sahu, A. Dhar, H. Chen, B. Inan, A. M. J. Koonen, B. Corbett, R. Winfield, A. D. Ellis, and H. de Waardt, “73.7 Tb/s (96x3x256-Gb/s) mode-division-multiplexed DP-16QAM transmission with inline MM-EDFA,” ECOC 2012, Th.3.C.4. [CrossRef]
6. R. Ryf, S. Randel, N. K. Fontaine, M. Montoliu, E. Burrows, S. Chandrasekhar, A. H. Gnauck, C. Xie, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Gruner-Nielsen, R. V. Jensen, and R. Lingle, “32-bit/s/Hz spectral efficiency WDM transmission over 177-km few-mode fiber,” OFC 2013, PDP5A.1. [CrossRef]
7. M. Nakazawa, M. Tokuda, and Y. Negishi, “Measurement of polarization mode coupling along a polarization-maintaining optical fiber using a backscattering technique,” Opt. Lett. 8(10), 546–548 (1983). [CrossRef] [PubMed]
8. M. Nakazawa, N. Shibata, M. Tokuda, and Y. Negishi, “Measurements of polarization mode couplings along polarization-maintaining single-mode optical fibers,” J. Opt. Soc. Am. A 1(3), 285–292 (1984). [CrossRef]
9. M. Nakazawa, M. Yoshida, and T. Hirooka, “Nondestructive measurement of mode couplings along a multi-core fiber using a synchronous multi-channel OTDR,” Opt. Express 20(11), 12530–12540 (2012). [CrossRef] [PubMed]
10. M. Yoshida, T. Hirooka, M. Nakazawa, K. Imamura, R. Sugizaki, and T. Yagi, “Measurement of structural irregularity dependence on mode coupling along multi-core fiber using multi-channel OTDR system,” IEEE Summer Topicals 2013, MC3.3. [CrossRef]
11. M. Nakazawa, M. Yoshida, and T. Hirooka, “Measurement of mode coupling distribution along a few-mode fiber using a synchronous multi-channel OTDR,” OFC 2014, W3D.7. [CrossRef]
12. W. Q. Thornburg, B. J. Corrado, and X. D. Zhu, “Selective launching of higher-order modes into an optical fiber with an optical phase shifter,” Opt. Lett. 19(7), 454–456 (1994). [CrossRef] [PubMed]
13. H. Kogelnik and P. Winzer, “Modal birefringence in weakly guiding fibers,” J. Lightwave Technol. 30(14), 2240–2245 (2012). [CrossRef]