Open Access
Add to BibSonomyAbstract
We demonstrate an experimental technique to generate and measure arbitrary superpositions of core modes in a multi-core fiber. Two spatial light modulators couple the fundamental mode of a single-mode fiber with multiple-core modes of the MCF to constitute a Mach-Zehnder-type multi-path interferometer. The phase tunability of each path is verified by comparing two-, three-, and four-path interference patterns with the theory. Interference fringes in the wavelength domain estimates the inter-core group index differences with a resolution of 10−5 using a fiber length of 1 m.
© 2015 Optical Society of America
1. Introduction
Multi-core fibers (MCFs) with multiple single-spatial-mode cores are useful for various sensor and laser applications [1–6]. Recent interest has been focused on applying the MCFs to space-division multiplexing optical communication, which can beat the transmission capacity limit of a single-mode optical fiber [7–9]. The fiber design, fabrication, and characterization methods have been developed to suppress the crosstalk between cores while keeping the inter-core spacing reasonably small [10–15].
One of the key parameters to characterize an MCF is the group index differences between different core modes. Previous works have applied the pulse-delay technique [16] to measure the relative group indices in several kilometers of multi-core fiber [17]. In this work, we demonstrate wavelength-domain interferometry, or white-light spectral interferometry [18], in a four-core fiber to measure the group index differences using a relatively short (~1 m) fiber section. To excite and measure a coherent superposition of core modes, we use two spatial light modulators (SLMs) that reflect a beam with spatially varying phase. We show that the SLMs can couple a single-mode fiber (SMF) with an arbitrary coherent superposition of multiple core modes of the MCF, which has not been reported to our knowledge with other MCF coupling devices such as a tapered fiber bundle coupler [12, 19] and a fiber fan-in/out device [20]. This work utilizes the same type of phase patterns used for coherent combination of 49 laser beams from an MCF [3], and extends the previous work to interferometry and fiber characterization.
2. Experimental setup
The experimental setup for the MCF interferometry is schematically shown in Fig. 1. A fiber-coupled light source, a distributed feedback diode laser or a super-luminescent diode with center wavelength of 1550 nm, is collimated (1/e2-diameter of 2.8 mm) before illuminating SLM1, which is a reflection-mode phase modulator (Hamamatsu LCOS-SLM X10468-08) with an 800 × 600 array of 20 μm × 20 μm pixels. A quarter-wave plate (QWP), a half-wave plate (HWP), and a polarizing beam splitter (PBS) set the input to SLM1 as horizontally polarized.
Fig. 1 Schematic of the interferometry through a multi-core fiber. Inset: the fiber cross-section. Q: quarter-wave plate, H: half wave plate, PBS: polarizing beam splitter, M: mirror, SLM: spatial light modulator, L: lens with focal length 15 mm, SMF: single-mode fiber.
An aspheric lens L1 (focal length 15 mm) focuses the reflected beam from SLM1 onto an MCF (Fibercore SM-4C 1550, length 1.00 m), which has four cores (mode field diameter 8 μm, NA 0.14 – 0.17) at the vertices of a 37 μm 37 μm square inside a 125-μm-diameter cladding, as shown in the inset of Fig. 1. SLM1 applies × a linear spatial phase gradient to the incident beam. The reflected beam is tilted by an angle θ = sin−1[λ/(2π) (dφ/dx)], where λ is the wavelength and dφ/dx is the magnitude of spatial gradient of phase. The direction of the phase gradient determines the azimuthal angle α of the tilt. According to the number of cores that should be excited, the SLM surface is divided into sections that apply different reflection directions as shown in Figs. 2(a)–2(d). The gray-scale maps show the phase of each pixel. The period of the grating-like structure is the distance for the phase to change by 2π. The near-field images of the field profiles are shown in Figs. 2(e)–2(h). The average coupling efficiency to each core is 54%, 13%, 4.8%, and 3.6% for one-, two-, three-, and four-core coupling cases, respectively. The upper bound of N-core coupling efficiency is 1/N2 considering 1) N-part division of the input and 2) mode overlap (∝ 1/N) between each section with the SMF mode. The sources of departure from these limits (100%, 25%, 11%, and 6.3%, respectively) include reflection from the MCF surfaces (7%), the imperfect reflectivity of SLM1 (90%), and unidentified spatial mode mismatch. The extinction ratio for the unexcited cores is greater than 27 dB for all the cases. It will be worth exploring the possibility of using a single hologram instead of the divided patterns in Fig. 2. For this purpose, both the amplitude and phase distributions of multi-core interference will have to be patterned on the hologram possibly using two phase-only SLMs and a polarizer [21].
Fig. 2 Phase patterns loaded on the SLM1 surface to couple the input beam into (a) one, (b) two, (c) three, and (d) four cores of the MCF. (e)–(h): Measured near-field intensity profiles at the output face of the MCF with the SLM patterns (a)–(d).
The distance between SLM1 and L2 was minimized to be 8 cm such that the beams from all the sections pass the symmetry axis of L2 as close as possible. Moreover, we align the incident beam to be imaged to the center of the fiber cross-section when SLM1 applies a constant phase throughout the entire surface. Therefore all the cores require the same tilt angle θ for maximum coupling as shown in Figs. 2(a)–2(d). This alignment equalizes the coupling efficiencies within ±10% to all the cores. The procedure to achieve this alignment condition is as follows. First we apply a constant phase to the SLM1 surface (θ = 0) and maximize the coupling of the incident light into one of the cores. We then adjust its period and direction of the SLM1 pattern until the light is coupled to the farthest core from the original position. Let the tilt angle θ and the azimuthal angle α by SLM1 for this case be θ0 and α0, respectively. We reset the reflection angle as (θ,α) = (0,0), and then slowly change the angle to (θ,α) = (θ0/2,α0 + π) while keeping the optimal alignment to the original core by adjusting the position of the MCF. Finally the beam for (θ,α) = (0,0) passes through the center of the lens and points at the center of the MCF cross-section.
The output from the MCF is collimated by an aspheric lens L3 (focal length 15 mm). A QWP and a HWP compensate for the birefringence by the MCF and convert the polarization of the beam to be horizontal. The output polarizations were not significantly different between the cores of the MCF in our experiments. PBS removes the remaining vertical polarization components. By using the same type of patterns and the alignment procedures as SLM1, SLM2 combines the beams from the different cores. Finally, L4 (focal length 15 mm) focuses the light into an SMF (Corning SMF-28e, mode field diameter 10 μm) that leads to an optical power meter.
3. Results and discussion
Figure 3 shows the measured Mach-Zehnder interference fringes using three different pairs of cores. The phase difference Δφ is adjusted by adding a constant phase (plus modulo 2π) to one section of the patterns on SLM2. The interference visibilities V = (Imax − Imin)/(Imax + Imin) are 99.3%, 99.6%, and 99.3% for the horizontally, vertically, and diagonally aligned two cores in Fig. 3, respectively, where Imax(min) is the maximum (minimum) intensity. The imperfect visibility is thought to be mainly due to mismatch between the coupled powers to the interfering paths.
Fig. 3 Output power of the Mach-Zehnder interferometer with three pairs of cores in the MCF. The phase difference Δφ is adjusted by the phase offset of one interfering beam by SLM2.
We extend the interferometer to three- and four-path cases as shown in Fig. 4 and Fig. 5, respectively. We measure general three-path interference by tuning the relative phase of core 2 (Δφ1) and core 3 (Δφ2) with respect to core 1. The measurement results are shown in Fig. 4(a), which are in good agreement with the theoretical calculation in Fig. 4(b) based on the following expression for the output intensity Itotal:
Fig. 4 Results of the three-beam interferometry. (a) Experiment; (b) Theory. Δφ1 and Δφ2 are the relative phases of core 2 and core 3 with respect to core 1, respectively.
Fig. 5 Four-beam interferometry. (a) Schematic of a conventional four-slit diffraction experiment; (b) Results of the four-core interferometry emulating the four-slit experiment in the time domain.
A four-core interference experiment realizes an analogue to a four-slit diffraction experiment shown in Fig. 5(a). We first set the reference phases of all four sections of SLM2 to maximize the output intensity. The four beams from the cores add in phase, corresponding to the diffraction angle θD of zero in Fig. 5(a). The phases of core 2 (Δφ1), core 3 (Δφ2), and core 4 (Δφ3) are tuned with the relation, Δφ2 = 2Δφ1 and Δφ3 = 3Δφ1. The combined electric field Etotal in the output SMF is expressed as:
where A1, A2, A3, and A4 are real constants. The equation corresponds to the output intensity for the diffraction angle θD ≅ λ/(2πd)·Δϕ1 in Fig. 5(a). Figure 5(b) compares the measurement results and the theoretical curve by Eq. (2). The relative magnitudes of A1–4’s were experimentally measured to be 0.96, 1.3, 1.2, and 1.0, respectively. The two results–agree within the experimental uncertainty.To apply the interferometer for measuring the group index differences between the cores, we input a broadband light source (full-width at half-maximum 90 nm) from a super-luminescent diode and measure the output spectra. All the six cases of two-core interferences are measured as shown in Fig. 6. The relative phase between two paths depends on the wavelength and the group index difference as:
where Δϕ, λ, L, Δng, and Δλ2π are the phase difference, the wavelength, the fiber length, the group index difference, and the fringe period in the wavelength domain, respectively. We find the sign of the last term by the direction of fringe shift according to a small change of the relative phase. When we slightly, i.e. by much less than the wavelength, increase the optical path length of the path having a greater (smaller) group index, the fringe in Fig. 6 shifts to the longer (shorter) wavelength. The estimated relative group indices are listed in Table 1. These values correspond to modal beat lengths in a range 5 – 11 mm. The relative measurement uncertainty for L and Δλ2π was 1%.Fig. 6 Six wavelength-domain interference fringes between two of the four cores. The excited cores are shown as yellow circles in the insets.
Table 1. Measured relative group indices of the core modes.
4. Conclusion
In conclusion, we have successfully demonstrated the proposed technique to generate and measure arbitrary superpositions of the core modes of an MCF. The experimentally measured multi-path interference fringes agree with the theory without significant errors. Wavelength-domain two-beam interferometry has estimated the relative group indices of the core modes with a resolution of 10−5. These results may contribute to development of multi-dimensional optical communication systems by providing a versatile method to utilize arbitrary superpositions of multiple waveguide modes.
Acknowledgments
This work has been supported by the KRISS project ‘Convergent Science and Technology for Measurements at the Nanoscale.’
References and links
1. W. N. MacPherson, M. J. Gander, R. McBride, J. D. C. Jones, P. M. Blanchard, J. G. Burnett, A. H. Greenaway, B. Mangan, J. C. Knight, and P. S. J. Russell, “Remotely addressed optical fibre curvature sensor using multicore photonic crystal fibre,” Opt. Commun. 193, 97–104 (2001). [CrossRef]
2. G. M. H. Flockhart, W. N. MacPherson, J. S. Barton, J. D. C. Jones, L. Zhang, and I. Bennion, “Two-axis bend measurement with brgg gratings in multicore optical fiber,” Opt. Lett. 28, 387–389 (2003). [CrossRef] [PubMed]
3. J. Lhermite, E. Suran, V. Kermene, F. Louradour, A. Desfarges-Berthelemot, and A. Barthélémy, “Coherent combining of 49 laser beams from a multiple core optical fiber by a spatial light modulator,” Opt. Express 18, 4783–4789 (2010). [CrossRef] [PubMed]
4. J. E. Antonio-Lopez, Z. S. Eznaveh, P. LiKamWa, A. Schülzgen, and R. Amezcua-Correa, “Multicore fiber sensor for high-temperature applications up to 1000 °C,” Opt. Lett. 39, 4309–4312 (2014). [CrossRef] [PubMed]
5. L. Li, A. Schülzgen, S. Chen, V. L. Temyanko, J. V. Moloney, and N. Peyghambarian, “Phase locking and in-phase supermode selection in monolithic multicore fiber lasers,” Opt. Lett. 31, 2577–2579 (2006). [CrossRef] [PubMed]
6. J. P. Moore and M. D. Rogge, “Shape sensing using multi-core fiber optic cable and parametric curve solutions,” Opt. Express 20, 2967–2973 (2012). [CrossRef] [PubMed]
7. D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nature Photon. 7, 354–362 (2013). [CrossRef]
8. R. G. H. van Uden, R. AmezcuaCorrea, E. Antonio Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nature Photon. 8, 865–870 (2014). [CrossRef]
9. J. Sakaguchi, W. Klaus, J. M. DelgadoMendinueta, 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 fiber with 108 spatial channels,” in Optical Fiber Communication Conference Post Deadline Papers, OSA Technical Digest (online) (Optical Society of America, 2015), paper Th5C.2. [CrossRef]
10. T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Design and fabrication of ultra-low crosstalk and low-loss multi-core fiber,” Opt. Express 19, 16576–16592 (2011). [CrossRef] [PubMed]
11. K. Imamura, Y. Tsuchida, K. Mukasa, R. Sugizaki, K. Saitoh, and M. Koshiba, “Investigation on multi-core fibers with large Aeff and low micro bending loss,” Opt. Express 19, 10595–10603 (2011). [CrossRef] [PubMed]
12. B. Zhu, T. F. Taunay, M. F. Yan, J. M. Fishteyn, E. M. Monberg, and F. V. Dimarcello, “Seven-core multicore fiber transmissions for passive optical network,” Opt. Express 18, 11117–11122 (2010). [CrossRef] [PubMed]
13. K. S. Abedin, T. F. Taunay, M. Fishteyn, M. F. Yan, B. Zhu, J. M. Fini, E. M. Monberg, F. V. Dimarcello, and P. W. Wisk, “Amplification and noise properties of an erbium-doped multicore fiber amplifier,” Opt. Express 19, 16715–16721 (2011). [CrossRef] [PubMed]
14. J. W. Nicholson, A. D. Yablon, S. Ramachandran, and S. Ghalmi, “Spatially and spectrally resolved imaging of modal content in large-mode-area fibers,” Opt. Express 16, 7233–7243 (2008). [CrossRef] [PubMed]
15. H. Otto, F. Jansen, F. Stutzki, C. Jauregui, J. Limpert, and A. Tunnermann, “Improved modal reconstruction for spatially and spectrally resolved imaging (S2),” J. Lightw. Technol. 31, 1295–1299 (2013). [CrossRef]
16. L. G. Cohen and C. Lin, “Pulse delay measurements in the zero material dispersion wavelength region for optical fibers,” Appl. Opt. 16, 3136–3139 (1977). [CrossRef] [PubMed]
17. T. Sakamoto, T. Mori, M. Wada, T. Yamamoto, T. Matsui, K. Nakajima, and F. Yamamoto, “Experimental and numerical evaluation of intercore differential mode delay characteristic of weakly-coupled multi-core fiber,” Opt. Express 22, 31966–31976 (2014). [CrossRef]
18. P. Hlubina, T. Martynkien, and W. Urbańczyk, “Dispersion of group and phase modal birefringence in elliptical-core fiber measured by white-light spectral interferometry,” Opt. Express 11, 2793–2798 (2003). [PubMed]
19. D. J. DiGiovanni and A. J. Stentz, “Tapered fiber bundles for coupling light into and out of cladding-pumped fiber devices,” US Patent 5,864,644 (1999).
20. H. Takara, Y. Ono, H. Abe, H. Masuda, K. Takenaga, S. Matsuo, H. Kubota, K. Shibahara, T. Kobayashi, and Y. Miyamoto, “1000-km 7-core fiber transmisson of 10 × 96 Gb/s PDM-16QAM using Raman amplification with 6.5 W per fiber,” Opt. Express 20, 10100–10105 (2012). [CrossRef] [PubMed]
21. L. Zhu and J. Wang, “Arbitrary manipulation of spatial amplitude and phase using phase-only spatial light modulators,” Sci. Rep. 4, 7441 (2014). [CrossRef] [PubMed]
