## Abstract

We propose and demonstrate a new technique for measuring mode couplings along a multi-core fiber (MCF) that employs a multi-channel optical time domain reflectometer (OTDR). The mode couplings along seven core fibers are successfully obtained using a synchronous seven-channel OTDR.

© 2012 OSA

## 1. Introduction

Recently, space division multiplexed (SDM) transmission using multi-core fiber (MCF) has been receiving a lot of attention with a view to increasing the achievable total spectral efficiency (SE) and transmission capacity of a single fiber [1–6]. By combining SDM with a seven-core fiber and dense wavelength division multiplexing (DWDM), 109 Tb/s [1] and 112 Tb/s [3] QPSK transmissions have been demonstrated. An SDM transmission with an SE of 60 b/s/Hz per fiber has been achieved by using a 32 QAM-OFDM format [5] and a 305 Tb/s transmission has also been reported with a 19-core MCF [6]. In an MCF transmission, the mode coupling between adjacent cores, which are closely placed in a 30 ~50 μm distance, causes crosstalk, resulting in degradation of the transmission performance [7]. Therefore, it is very important to diagnose the mode coupling along a MCF in detail. However, there is no technique for measuring the way the mode coupling occurs in the MCF.

In this paper, we describe a novel technique for measuring the mode coupling along an MCF by using a synchronous multi-channel optical time domain reflectometer (OTDR). The multi-channel OTDR has a measurement dynamic range of more than 50 dB, and mode coupling is successfully obtained between all the adjacent cores in the MCFs. This paper elaborates on the preliminary report found in [8] by providing detailed information about this technique. Specifically, we provide clarification with reference to the relationship between the mode coupling of the MCF and polarization mode coupling in a polarization-maintaining fiber, the mode coupling equality between two cores, and a 180-degree symmetric variation of the mode coupling caused by the difference in the excitation end of an MCF. Furthermore, by using another MCF, we show that it is possible to measure the mode coupling between cores separated for over two core pitches for the first time.

## 2. Principle and experimental setup for MCF mode coupling measurement

The coupled power equations between two adjacent waveguides can be expressed as [9]

*P*and

_{m}*P*are the transmitted powers in each waveguide along the

_{n}*z*-axis,

*α*and

_{m}*α*are the losses in the waveguides, and

_{n}*h*is the mode coupling coefficient from core

_{m,n}*n*to core

*m*. More generally, the transmitted power along a core

*m*in a seven-core MCF,

*P*, is given by

_{m}*α*is the fiber loss in the core

_{m}*m*,

*h*is the power increase caused by mode coupling from core

_{m,n}P_{n}*n*to core

*m*, and –

*h*is the power decrease caused by mode coupling from core

_{n,m}P_{m}*m*to core

*n*.

*h*is equal to

_{m,n}*h*. If the mode coupling coefficient

_{n,m}*h*can be measured as a function of position, we can analyze the optical power distribution along each core, which will provide useful knowledge about SDM transmission using MCF.

_{m,n}In 1983, Nakazawa reported a novel method for measuring polarization mode coupling along a polarization-maintaining (PM) fiber based on an OTDR technique [10, 11]. With this technique, an optical pulse is coupled into a PM fiber so that the polarization direction of the pulse coincides with one of the principal axes of the fiber. Then, the polarization mode coupling along the fiber, which appears on the orthogonal axis (another principal axis), can be measured from the power ratio between the backscattered signals passing through each principal axis.

Based on this idea, we propose a new technique for measuring the mode coupling between the cores of an MCF. Instead of a single-channel OTDR, we introduce a synchronous multi-channel OTDR, which enables us to measure all the mode couplings simultaneously. A schematic view of the measurement system is shown in Fig. 1 . Here, the multi-channel OTDR consists of seven OTDR units that are synchronously operated by using an external clock signal. The detected data of the backscattered signals are transferred to a PC via Ethernet.

By changing the input optical pulse width from 5 ns to 20 μs, the spatial resolution of the OTDR measurement can be varied from 0.5 m to 2 km.

An optical pulse from the ch.1 OTDR unit passes through an optical combiner and is coupled into core 1 of the MCF. The backscattered lights passing through each unexcited core of the MCF are detected simultaneously by the seven-channel synchronous OTDR. The backscattered power in core *n*, *P _{bsn}*, that results from mode coupling with core 1 can be obtained by solving Eq. (1) by employing

*m*= 1 as shown below [10, 11]. First, the transmitted power after propagation over a fiber length

*L*is given as the solution of Eq. (1) with the conditions

*P*

_{1}(0) =

*P*

_{0}and

*P*(0) = 0:

_{n}*α*. Then, the backscattered powers

*P*

_{bs}_{1}and

*P*that arrive at the fiber input end from a position

_{bsn}*z*=

*L*to position

*L*+

*V*/2 (

_{g}W*V*: group velocity,

_{g}*W*: pulse width) due to the backward Rayleigh scattering can be expressed as

*S*is the recapture factor of the Rayleigh scattering component into a backward direction [12],

*α*is the Rayleigh scattering coefficient, and

_{R}*K*is a constant that is determined by the Fourier transformation of the autocorrelation function of the mode-coupling fluctuation as described below. It is important to note that the backscattered power from the excited core is almost unchanged since all the mode couplings are much less than 20 dB. Thus, from Eq. (4) we can obtain the mode coupling ratio

*η*

_{n}_{,1}(

*L*) by dividing the backscattered signal

*P*with

_{bsn}*P*

_{bs}_{1}as follows:where we assumed that

*h*

_{n}_{,1}

*L*<< 1.

According to the coupled mode theory for an optical waveguide, the mode coupling power coefficient *h _{n,m}* from core

*m*to

*n*can be expressed as [9]

*K*is a mode coupling coefficient in the field expression and is integrated over the propagation direction

_{n,m}*z*to obtain

*h*. ${\tilde{K}}_{n,m}$ is independent of

_{n,m}*z*.

*f*(

*z*) is the waveguide fluctuation caused by random irregularities, which introduces the mode coupling of the electric field between cores

*n*and

*m*.

*P*is the transmission optical power and <

*f*(

*z*)

*f*(

*z*-

*z′*)> is the autocorrelation function of

*f*(

*z*).

With polarization mode coupling in a birefringent fiber, we can replace *E _{n}* with

*E*and

_{x}*E*with

_{m}*E*and it is very important to note that the electric field distributions of

_{y}*E*and

_{x}*E*are almost the same. Hence,

_{y}*K*can be simplified as

_{x,y}*h*between

_{x,y}*x*and

*y*axes can be expressed as

*E*is different from that of

_{n}*E*, and the autocorrelation function and the propagation constant are different from those for polarization mode coupling,

_{m}*h*in MCFs would become a different value from

_{n,m}*h*.

_{x,y}From Refs [10, 11], the value *K* is expressed as

*g*(

*r*)

*g*(

*r*-

*r′*)> is the autocorrelation function of the diagonal element of the dielectric tensor

*g*(

*r*), that is, the refractive index of the original waveguide.

*w*is the spot size. Assuming <

*g*(

*r*)

*g*(

*r*-

*r′*)> ≈<

*g*(

*z*)

*g*(

*z*-

*z′*)> in the waveguide, we can simplify

*K*as

*K*indicates the ratio of the Fourier transformation of the autocorrelation function of the coupled mode fluctuation

*f*(

*z*) to the Fourier transformation of the autocorrelation of the refractive index fluctuation

*g*(

*z*) for the diagonal component of the dielectric tensor.

Equation (5) shows an important result, namely that the slope of *η _{n}*

_{,1}(

*L*) represents twice the mode coupling coefficient

*h*

_{n}_{,1}. This results from the roundtrip measurement of the backward Rayleigh scattering. In addition, a mode coupling coefficient

*h*

_{n}_{,1}at a position

*z*

_{0}can be obtained from

The mode coupling coefficients *h _{n}*

_{,1}(

*n*= 2~7) are simultaneously evaluated from only one OTDR measurement, in which an optical pulse from the OTDR is coupled into core 1 as shown in Fig. 2(a) . The mode coupling between other adjacent cores can be obtained by coupling the input optical pulses into other cores as shown in Fig. 2(b)-2(d). The mode coupling coefficients (15 coefficients) between all adjacent cores are nondestructively obtained using just four OTDR measurements. Even when the number of MCF cores is increased, it remains possible to measure the mode coupling coefficients between all adjacent cores by increasing the number of measurements. For example, with the 19-core MCF described in Ref [6], the required number of OTDR measurements is 12.

When we take account of all the mode coupling along the MCF including non-adjacent core couplings, Eq. (2) can be expressed in a matrix form as:

*h*(

_{m,n}*z*) into Eq. (15), we obtain a 7 x 7 matrix. This matrix can be diagonalized by calculating the eigen values with the corresponding eigen vectors. Then, we can obtain the coupled optical power

*P*(

_{n}*z*) including the effect of all core mode couplings.

Figure 3 shows the configuration (a) and a photograph (b) of our optical beam combiner for connecting the multi-channel OTDR to a test MCF. The center of the side-polished fiber, whose tip consists of six triangular pyramids, is adjusted to the center core of the MCF to couple the light beam. Backscattered beams from the outer cores are reflected at the surfaces of the side-polished fiber tip to which HR coatings are applied. Then, each reflected beam is coupled into a fiber with a GRIN lens for optical power detection. Table 1 shows the coupling loss and crosstalk of the combiner. The coupling loss between each core of the MCF and an SMF ranges from 1.4 to 2.4 dB, and the crosstalk between cores is less than −50 dB. The backscattered light power from each core of the MCF is calibrated before the measurements by taking account of the coupling loss and the sensitivity difference between OTDR channels.

## 3. Experimental results

We used two kinds of MCF fabricated using the stack-and-draw method. The fiber parameters are shown in Table 2 . The crosstalk values of Fibers A and B measured with a conventional transmission method were approximately −41 and −24 dB, respectively.

#### 3.1 Mode coupling measurement of Fiber A

Figure 4(a)
and 4(b), respectively, show the backscattered signals from the seven cores of Fiber A when 0.5 and 1 μs optical pulses were coupled into core 1. The *P _{bs}*

_{1}peaks observed at

*z*= 0 and 2.9 km were caused by the Fresnel reflections at the input and output MCF facets, respectively. Here, a Fresnel reflection at the input MCF facet was coupled into other channels of the optical combiner because of the crosstalk at the combiner. As a result, the

*P*

_{bs}_{2}to

*P*

_{bs}_{7}peaks were also observed at

*z*= 0 km. A single core fiber was butt-jointed to the output MCF facet to measure the MCF crosstalk by using a conventional transmission method, resulting in a large Fresnel reflection at the single core fiber facet. This reflection was coupled into cores 2 to 7 of the MCF and caused the large

*P*

_{bs}_{2}to

*P*

_{bs}_{7}peaks at

*z*= 2.9 km. Since thepulse power is small in Fig. 4(a), we can see that the power levels of the backscattered signals from the unexcited cores were low. The dynamic ranges for mode coupling measurement were 46 and 55 dB, respectively. A maximum dynamic range of 78 dB was achieved for a 20 μs pulse width. Here, it is possible to increase the dynamic range of the OTDR measurement without reducing the spatial resolution by amplifying the optical pulse launched into the test fiber using a low-noise optical amplifier.

The mode coupling ratio from core 1 to core *n* is calculated from the measurement results shown in Fig. 4(b). The results are plotted in Fig. 5(a)
. To reduce the Fresnel reflection part at the input end, the initial part of *P _{bs}*

_{1}is linearly corrected as shown by the broken line in Fig. 4(b), and the mode coupling ratio

*η*

_{n}_{,1}is calculated by dividing

*P*with

_{bsn}*P*

_{bs}_{1}. Since

*K*in Eq. (5) is a small quantity, we neglect it here. Measurement results for the mode coupling ratio when a 1 μs optical pulse was coupled into cores 2, 4, and 6, are shown in Fig. 5(b), 5(c) and 5(d), respectively. From Fig. 5(a)-5(d), we can see for the first time that the slopes of the mode coupling ratio were not uniform and were different from each other, which indicates that the present method is a powerful tool with which to measure the mode coupling coefficient along an MCF.To confirm the mode coupling ratio equality between two cores, we measured the mode coupling change by oppositely exciting core

*n*of Fiber A. Then, we could compare η

_{1,n}and η

_{n,1}(n = 2, 4, 6) shown in Fig. 6(a) -6(c). These figures clearly indicate that the mode coupling ratios were independent of the coupling direction.

In the next step, to confirm the position-dependency of the mode coupling between adjacent cores, we measured the mode coupling ratio by coupling a 1 μs optical pulse (resolution: 100 m) into core 1 from the other end of Fiber A. The measured results are plotted in Fig. 7
. For example, η_{6,1} obtained in Fig. 5(a) can be compared with the 180 degree rotated data of η_{6,1} obtained from Fig. 7, and the result is shown in Fig. 8
. From Fig. 8, the mode coupling from both ends exhibits exactly the same variation, which shows that the mode coupling can be measured from one end of a test MCF. This is a great advantage of the present technique.

Table 3 compares crosstalk values measured with the multi-channel OTDR and a conventional transmission method. The difference between the two values was less than 0.53 dB, which was due to measurement accuracies of the transmission method and OTDR method. This indicates that the measured values obtained by the multi-channel OTDR technique are in good agreement with those obtained with the conventional method. Therefore, the present technique is a very useful method for measuring both local and total mode coupling.

In Fig. 9(a)
, by substituting *η*_{2,1} (*z*) of Fig. 5(a) into Eq. (14), we show how a local mode coupling coefficient between cores 1 and 2 changes. Here, *Δz* is set at 100 m. The mode coupling ratio measurement data, which are separated by intervals of 100 m, are substituted into Eq. (14). The local mode coupling coefficient between cores 4 and 5 is also shown in Fig. 9(b). The results show that the mode coupling coefficient changes as a function of position, thus revealing a structural irregularity. The ripples that occur every 100 m may be caused by the differentiation, however, the change in the mode coupling coefficient over a longer span can be seen as a low frequency spatial component, which may be attributed to the fiber drawing process. To improve the measurement accuracy for local mode coupling coefficients, it is important to increase the signal to noise ratio of the received backscattered signal and the distance resolution by reducing the input pulse width.

#### 3.2 Mode coupling measurement of Fiber B

Figure 10(a) and 10(b) show backscattered signals from the seven cores of Fiber B when 0.5 and 2 μs optical pulses were coupled into cores 1 and 2, respectively. In this case, the mode coupling between cores separated over two core pitches was successfully observed as shown in Fig. 10(b). Since the core pitch in Fiber B is 40 μm, while that in Fiber A is 46 μm, Fiber B causes the larger mode coupling.

The mode coupling ratios between all adjacent cores are plotted in Fig. 11(a) -11(d). The coupling ratios were approximately 100 times larger than those of Fiber A in Fig. 5. In Fig. 12(a) and 12(b), we show the local mode coupling coefficients between cores 1 and 2 and cores 2 and 3, respectively. Note here that the vertical axis is much larger than that in Fig. 9. These figures show that the mode coupling coefficient depends strongly on both the local fiber position and each core number.

Table 4 compares the crosstalk values of Fiber B measured with the multi-channel OTDR and a conventional transmission method. The difference between the two values was less than 0.49 dB, which is almost the same as that of Fiber A shown in Table 3.

## 4. Conclusion

We have successfully demonstrated a new technique for measuring mode coupling along an MCF that utilizes a multi-channel OTDR. A measurement dynamic range of more than 50 dB was obtained and the mode couplings between all adjacent cores in two kinds of MCFs were successfully measured. We found that the mode coupling coefficient was not uniform along each fiber because of its structural irregularity. The present technique is expected to constitute a powerful tool for analyzing local mode coupling along an MCF.

## Acknowledgment

We would like to express our sincere thanks to Furukawa Electric Company for supplying MCFs for our OTDR measurements. This research was supported by the National Institute of Information and Communications Technology (NICT), Japan under “Research on Innovative Optical Fiber Technology”.

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