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Abstract
We propose a simple technique based on optical time domain reflectometry (OTDR) for measuring the cutoff wavelength and core radius distributions in a pure silica core fiber for the first time. The proposed technique can simultaneously measure several important fiber parameters such as the mode field diameter, relative-index difference, effective area, and chromatic dispersion, including the cutoff wavelength and core radius. We experimentally demonstrate that our proposed technique can successfully evaluate these fiber parameter distributions and can be applied for the measurements of few-mode and multi-core fibers with pure silica cores using multi-channel OTDR and mode couplers.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Network traffic in fiber-optic communication systems has continued to increase owing to their growing number of applications and high demand. To support the growth of network traffic, the spectral efficiency (SE) of the transmission system has been improved by using multilevel modulation formats and wavelength division multiplexing [1]. To further increase the SE, improvements to the system optical signal-to-noise ratio (OSNR) are necessary [2]. To improve the system OSNR, we require an increase in the signal power limited by the nonlinear effects and fiber fuse phenomenon [3], or a reduction in the loss of the system. The use of a pure silica core fiber (PSCF) having low loss [4], low nonlinearity [4], and higher fiber fuse propagation threshold [5] than conventional GeO2-doped core fibers is one of the most powerful means of improving OSNR. PSCFs have been introduced into the optical fiber submarine cable systems, and to date, PSCFs having a loss of 0.142 dB/km have been achieved [6]. In recent years, transmission capacity has approached its fundamental limit for single-mode fibers (SMFs) [7]. To expand the transmission capacity of SMFs, space-division multiplexing (SDM) using few-mode fibers (FMFs) or multi-core fibers (MCFs) has been intensively researched [8]. Since improving the system OSNR is indispensable for expanding the transmission capacity even in the SDM transmission, FMFs or MCFs with pure silica core are attractive. Moreover, PSCFs with low loss, low nonlinear coefficient, and high fiber fuse propagation threshold enable us to reduce the number of optical amplifiers installed in the transmission system, which means that we can reduce the system cost. Therefore, PSCFs are attractive and promising transmission media.
Fiber parameters such as the mode field diameter (MFD), cutoff wavelength, and chromatic dispersion are particularly important for fiber system design. Nondestructive techniques for measuring the longitudinal characteristics of GeO2-doped core fibers have been proposed using optical time domain reflectometry (OTDR) [9–11], which can also be applied to FMFs and MCFs with GeO2-doped cores using multi-channel OTDR and mode couplers [12–15]. In particular, Refs. [12–15] report the techniques for measuring the MFD, relative-index difference, effective area, and chromatic dispersion in FMFs or uncoupled MCFs with GeO2-doped cores. In principle, this technique can also measure the MFD, effective area, and chromatic dispersion of PSCFs provided that two different kinds of PSCFs are used as reference fibers. This is because the principle of the technique for measuring the above parameters is independent of whether the core of the fiber to be measured is GeO2-doped silica or pure silica. However, we have to consider how to measure the relative-index difference of PSCFs, since the measurement principle depends on the fiber material to be measured. Moreover, a technique for measuring the core radius and cutoff wavelength, which are also important parameters, has not yet been proposed.
In this article, we propose a technique for measuring several fiber parameters including the relative-index difference, core radius, and cutoff wavelength of PSCFs using a bidirectional OTDR technique. The proposed technique enables us to measure the core radius and cutoff wavelength of PSCFs by utilizing the fact that the refractive index of the core is constant along the fiber link. To the best of our knowledge, this is the first proposed technique for measuring the core radius and cutoff wavelength using the bidirectional OTDR technique. A new formula for estimating the relative-index difference is also proposed. The MFD, effective area, cutoff wavelength, core radius, and relative-index difference are successfully evaluated for a fiber link composed of PSCFs using the proposed technique. Moreover, the measured chromatic dispersion is in good agreement with that obtained using the phase-shift technique. Our proposed technique will be applied to the measurements of FMFs and MCFs with pure silica cores using multi-channel OTDR and mode couplers.
2. Theoretical background
2.1 Longitudinal fiber parameter estimation
Here, we provide a theoretical background of our proposed technique for simultaneously measuring fiber parameters such as the MFD, 2w, effective area, Aeff, core radius, a, relative-index difference, Δ, and cutoff wavelength, λc, based on the bi-directional OTDR technique.
Figure 1 presents a diagram of the bidirectional OTDR technique used to measure the longitudinal fiber parameters of the optical fiber link comprising test fibers and two reference fibers. The fiber parameters of the two reference fibers should be different from each other and have to be known in advance to determine the fiber parameters of test fibers. The optical fiber link comprises PSCFs. Note that when applying this technique to FMFs, we have to connect the cores of the reference and test fibers accurately to avoid the crosstalk between different modes.
The backscattered powers from position z can be expressed as
For backscattered powers, S1(λ, z) = 10logP1(λ, z) and S2(λ, L−z) = 10logP2(λ, L−z), (in dB), launched from opposite ends of the fiber link with an entire length of L, the imperfection loss contribution, I (λ, z), can be expressed as [17]
Substituting Eq. (3) into Eq. (4), the following equation is obtained:
The longitudinal variation in the local scattering coefficient, αs(z), is negligible compared with that of the MFD [18]. In other words, the local scattering coefficient, αs(z), can be regarded as a constant independent of the distance, z. Therefore, the imperfection loss contribution, In (λ, z), normalized by that at a reference point, z0, in reference fiber #1 can be derived from Eq. (5) as
The MFD at an arbitrary position, z, can be derived using Eqs. (6) and (7) as follows [11]:
The effective area, Aeff, defined in [19] can be expressed in terms of the MFR, w (λ, z), as [20]:
where ke (λ, z) is the correction factor, which depends on the wavelength. It is noted that the correction factor, ke (λ, z), is 1 when the electric-field distribution is Gaussian.Here, we assume that the factor ke (λ, z) is approximately the same along the fiber. Thus, substituting Eq. (9) into Eq. (8) obtains the effective area, Aeff (λ, z), at an arbitrary position, z, as
Next, we consider the estimation of the core radius, a(z), of the PSCF using a step-index profile. The MFR, w, can be given by the following empirical equation [21]:
where ka (v, z) denotes a coefficient that depends on the normalized frequency, v. The coefficient, ka (v, z), depends on the index profile.We assume that the coefficient, ka (v, z), is approximately the same along the fiber. Thus, substituting Eq. (11) into Eq. (8) yields an approximate expression for estimating the core radius, a(z), at position z as follows:
Next, we consider how to estimate the relative-index difference of the PSCF. By using Eq. (5), the normalized imperfection contribution, In (λ, z), is given by
As with the MFD, the local scattering coefficient, αs (z), at position z can be derived as
It is well-known that the Rayleigh scattering coefficient for fluorine-doped glasses is almost directly proportional to the dopant content [22]. Therefore, the local scattering coefficient αs(z) is approximately expressed as
where K is a proportionality constant.Combining Eqs. (14) and (15), we can obtain the relation in terms of the relative-index difference, Δ(z), at position z as
The normalized imperfection loss contribution, In (λ, z), can be rewritten using Eqs. (3) and (5) as follows:
The normalized imperfection loss contribution, In (λ, z1), at the second reference point, z1, is given as
Taking Eqs. (8), (12), (16), (17), and (18) into account, we can derive the cutoff wavelength, λc (z), at position z as
2.2 Chromatic dispersion estimation
Chromatic dispersion D is approximately expressed as the sum of the material dispersion, Dm, and the waveguide dispersion, Dw [23]:
The material dispersion, Dm, is defined as [24]
For PSCFs, the material dispersion, Dm, can be estimated using the Sellmeier dispersion formula, in which the coefficients correspond to pure silica glass whereas the waveguide dispersion, Dw, for the LP01 mode can be expressed as [25]
The wavelength dependence of the MFR for the fiber with a step-index profile is given by the following equation [26]:
where g0 and g1 can be determined from the MFRs at the two wavelengths, estimated using Eq. (8).Therefore, by substituting Eq. (23) into Eq. (22), we obtain the waveguide dispersion, Dw, as [25]
The waveguide dispersion can be estimated using the MFRs from Eqs. (8), (23), and (24).
3. Experiments
3.1 Fibers under test
Three types of PSCFs were prepared for the reference and test fibers. The fiber link comprised two reference fibers and a test fiber. Two types of reference pure silica core fibers were used to determine the absolute value of the MFD of the test fiber. Note that we applied bends to the positions before and after splices between the fibers to exclude the LP11 mode from the fiber link. Table 1 lists the fiber parameters of the reference and test fibers measured with the reference techniques described as follows. The MFD and effective area were measured using the variable-aperture technique [27,28]. The chromatic dispersion and cutoff wavelength were measured using the phase-shift and transmitted-power techniques, respectively [27]. The relative-index difference and the core radius were measured using the refracted near-field technique [29]. Using these measured results as benchmarks, we confirmed the effectiveness of the proposed technique as presented in the following subsections.
Table 1. Fiber parameters of reference and test fibers
3.2 Fiber parameter measurement
Figure 2 shows the measured bi-directional backscattered powers of the fiber link at a wavelength of 1.55 µm. We used the commercially available OTDR (Anritsu MT9062C) for the measurements. The pulse width of the OTDR was 100 ns (corresponding to a spatial resolution of 10 m), and the average time was 180 s. The red and blue lines represent the backscattered powers of the LP01 mode measured from both ends of the fiber link, which correspond to S1(z) and S2(L−z), respectively. We can see from Fig. 2 that Fresnel reflection obscures the backscattered power at the input ends of the optical pulse. We cannot obtain the fiber parameters correctly in the section where the reflection obscures the backscattered power, and the length of this section depends on the pulse width.
Fig. 2. Bi-directional OTDR waveforms at a wavelength of 1.55 µm. The red and blue lines represent the backscattered powers of the LP01 mode measured from both ends, respectively.
Figure 3 shows the imperfection loss contribution, I (λ, z), of the fiber link, which corresponds to Eq. (4). The blue and red lines show the imperfection loss contribution, I (λ, z), at the wavelengths of 1.31 and 1.55 µm, respectively.
Figure 4 shows the MFD distributions of the fiber link at wavelengths of 1.31 and 1.55 µm. The measured MFD distributions of the fiber link were in good agreement with the values measured by the variable aperture technique [27,28], as shown in Table 1.
Figure 5 shows the effective area, Aeff, at a wavelength of 1.55 µm plotted as a function of fiber length. The estimated effective areas at the wavelengths of 1.31 and 1.55 µm were in good agreement with those obtained by variable aperture technique [27,28], as shown in Table 1.
Figure 6 shows the core radius distribution. The core radius was obtained using Eq. (12). The core radius obtained with the proposed technique agreed well with that measured using the refracted near-field technique [29] as shown in Table 1.
Next, to confirm the utility of Eq. (16), we measured the relative-index difference, Δ, of the fiber link comprising PSCFs.
Figure 7 shows the relative-index difference, Δ, distribution of the fiber link, which was estimated using Eq. (16). The estimated relative-index difference obtained with the proposed technique was in good agreement with the values measured using the refracted near-field technique [29], as shown in Table 1.
The cutoff wavelength distribution shown in Fig. 8 was estimated using Eq. (19). The cutoff wavelength distribution estimated by the present technique was in good agreement with that measured using the transmitted-power technique [27] as shown in Table 1.
Figure 9 shows the chromatic dispersion distributions of the fiber link at 1.31 and 1.55 µm. The waveguide dispersion distribution along the fiber link for the LP01 mode was estimated using Eq. (24) and MFRs at wavelengths of 1.31 and 1.55 µm. The material dispersion was obtained by substituting Sellmeire’s coefficients of pure silica glass [30] into the Sellmeire dispersion formula. The material dispersions of pure silica glass were estimated to be 3.51 and 21.76 ps/km/nm at 1.31 and 1.55 µm, respectively. The experimental results for the chromatic dispersion of the test fiber were in good agreement with the values measured by the phase-shift technique, as shown in Table 1.
Next, we estimated the chromatic dispersion as a function of wavelength from Eqs. (16), (21), and (24). In the calculations, the experimental values at a position of 4 km in the fiber link were used.
Figure 10 shows the chromatic dispersion plotted as a function of wavelength at a position of 4 km along the fiber link.
Fig. 10. Chromatic dispersion D at a position of 4 km along the fiber link as a function of wavelength. The solid and broken lines represent the results obtained with the proposed and phase-shift techniques, respectively.
The solid and broken lines show the chromatic dispersions estimated using the proposed and phase-shift techniques [27], respectively. The experimental results estimated using our technique were in good agreement with those measured by the phase-shift technique. As a result, we experimentally confirmed that the proposed technique can evaluate the chromatic dispersion of a fiber link composed of PSCFs.
Table 2 summarizes fiber parameters of the test fiber measured with reference techniques and those at position of 4 km in the fiber link measured with our proposed technique. The experimental results of the test fiber obtained with the proposed technique approximately agreed with those obtained from the reference techniques. From these results, we confirmed that the proposed technique can estimate the MFD, 2w, the effective area, Aeff, the cutoff wavelength, λc, the core radius, a, the relative-index difference, Δ, and the chromatic dispersion along the fiber link comprising PSCFs.
Table 2. Experimental Results of Test Fiber at Position of 4 km
4. Conclusion
We proposed a simple technique based on bidirectional OTDR for simultaneously measuring the MFD, effective area, cutoff wavelength, core radius, relative-index difference, and chromatic dispersion along PSCFs. A new formula for estimating the relative-index difference, core radius, and cutoff wavelength was derived from the imperfection loss contribution. The fiber parameter distributions were successfully evaluated for a fiber link composed of PSCFs using the proposed technique. Moreover, it was found that the chromatic dispersion estimated with the proposed technique was in good agreement with that obtained using the phase-shift technique. From these results, we conclude that our proposed technique is effective for estimating the characteristics of PSCFs and is useful for applications in the measurements of FMFs and MCFs with pure silica cores using multichannel OTDR and mode couplers.
Acknowledgements
The authors would like to express their sincere thanks to Dr. N. Honda for her fruitful comments and continuous encouragement.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. A. Sano, H. Masuda, T. Kobayashi, M. Fujiwara, K. Horikoshi, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguchi, H. Yamazaki, Y. Sakamaki, and H. Ishii, “Ultra-high capacity WDM transmission using spectrally-efficient PDM 16-QAM modulation and C- and extended L-band wideband optical amplification,” J. Lightwave Technol. 29(4), 578–586 (2011). [CrossRef]
2. R. J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010). [CrossRef]
3. R. Kashyap and K. J. Blow, “Observation of catastrophic self-propelled self-focusing in optical fibers,” Electron. Lett. 24(1), 47–49 (1988). [CrossRef]
4. Y. Yamamoto, Y. Kawaguchi, and M. Hirano, “Low-loss and low-nonlinearity pure-silica-core fiber for C- and L-band broadband transmission,” J. Lightwave Technol. 34(2), 321–326 (2016). [CrossRef]
5. K. Hamatani, K. Kurokawa, S. Nozoe, T. Matsui, K. Tsujikawa, and K. Nakajima, “Dopant dependence of fiber fuse propagation threshold,” in 24th Microoptics Conference (MOC) (2019), Paper P-30.
6. Y. Tamura, H. Sakuma, K. Morita, M. Suzuki, Y. Yamamoto, K. Shimada, Y. Honma, K. Sohma, T. Fujii, and T. Hasegawa, “Lowest-ever 0.1419-dB/km loss optical fiber,” in Optical Fiber Communication Conference (OFC) (2017), Paper Th5D.1.
7. J. Sakaguchi, W. Klaus, J.-M. D. Mendinueta, B.J. Puttnam, R.S. Luis, Y. Awaji, N. Wada, T. Hayashi, T. Nakanishi, T. Watanabe, Y. Kokubun, T. Takahata, and T. Kobayashi, “Realizing a 36-core, 3-mode Giber with 108 spatial channels,” in Optical Fiber Communication Conference (OFC) (2015), Paper Th5C.2.
8. D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013). [CrossRef]
9. K. Nakajima, M. Ohashi, and M. Tateda, “Chromatic dispersion distribution measurement along a single-mode optical fiber,” J. Lightwave Technol. 15(7), 1095–1101 (1997). [CrossRef]
10. M. Ohashi, “Novel OTDR technique for measuring the relative-index differences of fiber links,” IEEE Photonics Technol. Lett. 18(24), 2584–2586 (2006). [CrossRef]
11. A. Rossaro, M. Schiano, T. Tambosso, and D. D’Alessandro, “Spatially resolved chromatic dispersion measurement by a bidirectional OTDR technique,” IEEE J. Select. Topics Quantum Electron. 7(3), 475–483 (2001). [CrossRef]
12. M. Ohashi, H. Kubota, Y. Miyoshi, and R. Maruyama, “Longitudinal fiber parameter measurements of two-mode fiber links by using OTDR,” in 14th European Conference and Exhibition and Optical Communication (ECOC) (2014), Paper Th.1.4.5.
13. A. Nakamura, K. Okamoto, Y. Koshikiya, and T. Manabe, “Effective mode field diameter for LP11 mode and its measurement technique,” IEEE Photon. Technol. Lett. 28(22), 2553–2556 (2016). [CrossRef]
14. M. Ohashi, Y. Miyoshi, H. Kubota, R. Maruyama, and N. Kuwaki, “Longitudinal fiber parameter measurements of multi-core fiber using OTDR,” Opt. Express 22(24), 30137–30147 (2014). [CrossRef]
15. M. Ohashi, S. Asuka, Y. Miyoshi, and H. Kubota, “Effective area Measurement of two-mode fiber using bidirectional OTDR technique,” in 21st OptoElectronics and Communications Conference (OECC) (2016), Paper WC1-3.
16. E. Brinkmeyer, “Backscattering in single-mode fiber,” Electron. Lett. 16(9), 329–330 (1980). [CrossRef]
17. P. Divita and V. Rossi, “Backscattering measurements in optical fibers: separation of power decay from imperfection contribution,” Electron. Lett. 15(15), 467–469 (1979). [CrossRef]
18. M. S. O’Sullivan and J. Ferner, “Interpretation of SM fiber OTDR signature,” Proc. SPIE 0661, 171–176 (1986). [CrossRef]
19. G. Agrawal, Nonlinear Fiber Optics, Academic Press (San Diego, CA), 2nd Edition (1995).
20. . “Definition and test methods for statistical, and nonlinear related attributes of single-mode fibre and cable,” ITU-T Recommendation G. 650.2:2015 (E).
21. D. Marcuse, “Gaussian approximation of the fundamental modes of graded-index fibers,” J. Opt. Soc. Am. 68(1), 103–109 (1978). [CrossRef]
22. K. Tsujikawa, M. Ohashi, K. Shiraki, and M. Tateda, “Scattering property of F and GeO2 codoped silica glasses,” Electron. Lett. 30(4), 351–352 (1994). [CrossRef]
23. K. Okamoto, Fundamentals of Optical Waveguides, Academic Press, 2nd Edition (2005).
24. D. Marcuse, “Interdependence of waveguide and material dispersion,” Appl. Opt. 18(17), 2930–2932 (1979). [CrossRef]
25. M. Ohashi, T. Kawasaki, H. Kubota, Y. Miyoshi, A. Nakamura, and D. Iida, “Expression to predict the chromatic dispersion of a high-order mode in few-mode fibers,” IEICE ComEX 10(2), 67–72 (2021). [CrossRef]
26. M. Ohashi and M. Tateda, “Novel technique for measuring longitudinal chromatic dispersion distribution in singlemode fibres,” Electron. Lett. 29(5), 426–427 (1993). [CrossRef]
27. “Definition and test methods for linear, deterministic attributes of single-mode fibre and cable,” ITU-T Recommendation G. 650.1:2020 (E).
28. “Measurement methods and test procedures – mode field diameter,” IEC 60793-1-45:2017(E).
29. K. I. White, “Practical application of the refracted near-field technique for the measurement of optical fiber refractive index profiles,” Opt. Quantum Electron. 11(2), 185–196 (1979). [CrossRef]
30. K. Kobayashi, S. Shibata, N. Shibata, and T. Izawa, “Refractive-index dispersion of doped fused silica,” in Integrated optics and optical fiber communication international conference (IOOC) (1977), Paper B8-3.
