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Abstract
We describe a method for measuring spatial mode dispersion (SMD) distribution along a strongly coupled multicore fiber (SC-MCF). The SMD has been defined for characterizing an SC-MCF, and it changes with respect to local fiber bending and twisting. However, conventional measurement methods characterize only the overall SMD, and cannot identify fiber portions where the environmental conditions affect the SMD. This paper demonstrates distributed SMD measurement along an SC-MCF by auto-correlating Rayleigh backscattering amplitudes obtained with coherent optical reflectometry. We confirm our method experimentally, and distinguish the difference between the SMD growth along twisted and non-twisted fiber sections in concatenated SC-MCFs.
© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Space division multiplexing (SDM) using multicore fiber (MCF) or few-mode fiber has been attracting considerable attention as a technique for realizing a large transmission capacity exceeding that of current single-mode fiber (SMF) based transmission line [1–6]. Recently, Pb/s/fiber SDM transmissions have been demonstrated by using MCF [1,2]. The MCF can be divided into two types: non-coupled and coupled MCF. Non-coupled MCF is a simple and well-known medium for realizing SDM where each core acts as an independent transmission path. However, it is difficult to increase the number of cores of non-coupled MCF while suppressing inter-core crosstalk because there is a tradeoff between core pitch and inter-core crosstalk. In contrast, coupled MCF designed with a lower core pitch can realize a higher core density than non-coupled MCF, and inter-core crosstalk can be compensated for by employing multiple-input multiple-output (MIMO) processing at the receiver. One interesting property of coupled MCF is its Gaussian-like impulse response whose width increases in proportion to the square root of the propagation distance L as a result of the strong random mode coupling along the fiber, when the core pitch is adequately designed. This property is helpful for reducing the complexity of MIMO processing especially in long-haul transmissions, and a transmission distance exceeding a thousand kilometers has been achieved by using such strongly coupled MCF (SC-MCF) with 6 spatial channels [3].
For the purpose of characterizing SC-MCF, spatial mode dispersion (SMD) has been defined and measured in a similar manner to polarization mode dispersion (PMD) [4,5]. It has been reported that SMD is sensitively affected by fiber bending and twisting [4,6] and so can be expected to change locally in a transmission line due to the external stress caused by cabling, cable installation and environmental changes after installation. However, the distribution of SMD along an SC-MCF has only been measured by cutting the fiber at arbitrary positions. If we can measure the SMD distribution non-destructively, it would help us to characterize SC-MCFs in many scenarios such as when identifying portions of transmission lines that affect the end-to-end characteristic, which is essential for system design.
In this paper, we propose a non-destructive method for measuring the SMD distribution along an SC-MCF. The SMD distribution can be measured with the proposed method using the random interference pattern of the Rayleigh backscattering amplitudes obtained with coherent optical frequency domain reflectometry (C-OFDR). We experimentally confirm the feasibility of the proposed method with two kinds of SC-MCFs by observing their SMDs, which increase in proportion to √L.
This paper is organized as follows. Section II describes the principle of SMD distribution measurement using our proposed method. Section III reports the experimental setup we used. Section IV contains our experimental results and discussion, and Section V provides the conclusion.
2. Measurement principle
Figure 1 shows a schematic diagram of SMD measurement with our proposed method. We utilize the Rayleigh backscattering amplitudes obtained with a coherent optical reflectometry technique to measure the SMD in arbitrary portions. With coherent optical reflectometry, the backscattering amplitudes have a randomly jagged appearance, which results from interference between multiple backscattered lights which meet in a spatially resolved portion of a fiber [7–9]. When we perform reflectometry with an SC-MCF, the backscattered lights propagate from an arbitrary portion of the fiber to the launched fiber end with super-modes, which randomly couple with each other. Since the super-modes in the SC-MCF are associated with multiple paths with different delays and randomly coupling, the backscattering amplitude observed with the reflectometry can be considered superposed results of the delayed replicas of the backscattering interference pattern. Consequently, the accumulated SMD can be characterized with the auto-correlation of the observed backscattering amplitudes of an arbitrary portion of the fiber. Assuming that the backscattering replicas have a Gaussian distribution with a standard deviation of σε, the measured backscattering amplitude at the position of delay τ can be described as
where and are the complex backscattering amplitudes with/without mode coupling, and τm and θ(τm) are the relative delay and random phase component of the mth backscattering replica generated by mode coupling, respectively. Since the SMD Δτ is defined as twice the standard deviation of the impulse response (optical intensity) [4,5], Eq. (1) can be rewritten asAs implied in Eq. (2), the probability distribution of the backscattering replica is determined by Δτ. An auto-correlation of , R(τ’), is performed to analyze the probability distribution aswithwhere δτ’,0 is the Kronecker delta, and * denotes the complex conjugate. Since ε(τ) randomly fluctuates along the delay time due to the interference between backscattered lights, we assume the correlation of ε(τ) with itself in Eq. (3) asThe first term of Eq. (3) represents a correlation of with itself, and the second term accounts for the correlation between backscattering replicas whose delay times differ. An example of |R(τ’)| is shown on the right in Fig. 1. In addition to the central peak, small peaks are distributed around the center, where the square root of the second moment of |R(τ’)| except for the central peak reflects the SMD. Therefore, the SMD distribution can be measured by performing an auto-correlation analysis of the backscattering amplitude in arbitrary sections [11]. It should be noted that the number of data points for the correlated backscattering section is related to the correlation noise, which comes from the imperfect randomness of the waveform used for the correlation. Many data points are required for the correlation to suppress measurement error. However, that leads to spatial accuracy degradation in the SMD distribution.
According to previous reports, the SMD of an SC-MCF is of sub-μs order even with a distance of tens of kilometers [3–6]. C-OFDR is an attractive way of realizing the proposed method because it enables us to obtain the backscattering amplitude with ps-order resolution [8–10].
The principle of our SMD measurement is similar to that of a low coherence interferometric method standardized as an alternative test method for PMD measurement [12], and our algorithm for characterizing SMD with an auto-correlation fringe is also based on Ref [12]. With the interferometric method, the overall dispersion is characterized from the auto-correlation fringe of low coherence signals from a broadband light source using a Michelson or Mach-Zehnder interferometer [12,13]. In contrast, our proposed method uses randomly fluctuating Rayleigh backscattering amplitudes and their digitally processed auto-correlation fringes, thus allowing us to obtain the distributed SMD along fibers.
3. Experimental setup
Figure 2 shows the C-OFDR setup that we used in our experiment. The laser source was a continuously tunable laser diode whose wavelength sweep rate was 100 nm/s. We swept 8 nm centered at 1550 nm, which corresponds to a delay time resolution of 1 ps, and a spatial resolution of 100 μm. The probe light was launched into an arbitrary core of the fiber under test (FUT) with a fan-in/fan-out (FI/FO) device. The backscattered light was coherently detected with a polarization diversity receiver, and acquired by an A/D converter with a sampling rate of 1.25 GS/s and sampling points of 100 MSa. In this setup, the measurable distance range was about 4 km, which was limited by the sampling rate. The measured delay resolution was almost the theoretical value over the measurement range achieved by compensating for the sweep nonlinearity of the laser with the concatenative reference method [14,15] based on the reference signal obtained with the Mach-Zehnder interferometer shown on the left in Fig. 2. The backscattering amplitudes in the delay time domain were obtained by Fourier-transforming the beat signals. In the auto-correlation analysis, the inner product of the Jones vectors was calculated with two different polarization signals.
Fig. 2 Setup for C-OFDR measurement. TLS: tunable laser source, SMF: single-mode fiber, BPD: balanced photodetector, BPF: band-pass filter.
We prepared three kinds of two-core fibers, FUT-1, 2 and 3 as shown in Tab. 1 and Fig. 3. To introduce strong mode coupling, the core alignments of FUT-3 were twisted along the fiber with a twisting rate of 4π rad./m, which was achieved by rotating the preform during the drawing process [6]. We estimated the overall SMD and SMD coefficient of each FUT by using a fixed analyzer method [4,6,12]. Figure 4 shows the setup we used for the fixed analyzer method. In this setup, SMFs were spliced under a cladding alignment condition on both the input and output sides of the FUT. The overall SMD was characterized by Fourier-transforming the output spectrum pattern and calculating the second moment of the transformed data. Figure 5 shows the Fourier-transformed results measured for 1550 ± 8 nm. The SMD coefficients of FUT-1, 2 and 3 were estimated to be 35, 38 and 15 ps/√km, respectively.
Table 1. Characteristics of FUTs. D: core pitch, Δ: refractive index difference, <τ>: SMD coefficient, R: bending radius, L: fiber length.
4. Experimental results and discussion
Figure 6 shows auto-correlation fringes measured at arbitrary positions for each FUT. The auto-correlation of each position was calculated with 400000 data points of backscattering amplitude, which corresponds to a 40-m fiber section. We observed a Gaussian-like correlation distribution with each FUT, and their widths broadened with distance. Figure 7 shows the SMDs along each FUT characterized by calculating with the square root of the second moment of the auto-correlation fringes shown in Fig. 6. The calculations were performed with an algorithm based on that in the appendix of Ref [12], where the central peak with a width of several times the delay resolution was eliminated. We observed the SMD growth, which was proportional to √L for each FUT, as expected. By applying least square fittings to the measured SMDs, the SMD coefficients of FUT-1, 2 and 3 were estimated to be 40, 35 and 21 ps/√km, respectively, and these values were in good agreement with the results characterized with the fixed analyzer method. The variation in the measured SMDs along each FUT was considered to be the result of measurement error caused by the correlation noise mentioned in Section 2, or the randomly fluctuating appearance of the correlation fringe caused by the phase difference among backscattering replicas as implied in Eq. (4).
Next, we connected FUT-2 to the end of FUT-3, and investigated the SMD growth along the concatenated fibers, with a view to distinguishing the SMD difference caused by fiber twisting. Figure 8 shows the SMDs along the concatenated fibers plotted with respect to the square root of distance. We could observe a clear difference between the SMD coefficients of FUT-3 and 2. According to the fittings, the SMD coefficients of the fiber sections of FUT-3 and 2 were estimated to be 21 and 38 ps/√km respectively, which agreed with the single-fiber characteristics shown in Fig. 7. With our method, the measurable distance range is in a trade-off relationship with the SMD resolution due to the sampling rate limit of the A/D converter. A higher sampling rate would help us to observe the SMD growth and distinguish the SMD difference more clearly over a long range.
5. Conclusion
We proposed a technique for measuring the SMD distribution along an SC-MCF by auto-correlating the Rayleigh backscattering amplitudes obtained with C-OFDR. We used our proposed method to demonstrate SMD distribution measurement with three kinds of SC-MCFs, and the results agreed well with those obtained with the conventional method. Our method also enabled us to distinguish the difference between the SMDs in twisted and non-twisted fiber sections in concatenated SC-MCFs. We believe that our method will prove a powerful tool for investigating structural uniformity after fiber manufacture or cabling, or maintaining transmission lines after installation.
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