Characterization of stimulated Brillouin scattering in a circular-core two-mode fiber using optical time-domain analysis An Li,* Qian Hu, and William Shieh Department of Electrical and Electronic Engineering, The University of Melbourne, Melbourne, VIC 3010, Australia * [email protected]
Abstract: We show characterization of stimulated Brillouin scattering (SBS) in a circular-core two-mode fiber (c-TMF) using Brillouin optical time-domain analysis (BOTDA) with a pulsed pump and a counterpropagating continuous wave probe. By using two free-space mode combiners (FSMCs), we can launch any combination of spatial modes into both ends of the c-TMF. Combined with coherent detection, measurement of distributed Brillouin gain spectra (BGS) is achieved for all possible counter-propagating spatial mode pairs with high spectral resolution and stability. Both intra- and inter-modal SBS are investigated for the c-TMF. The inter-modal SBS between two degenerate LP11 modes (LP11a/LP11b) is demonstrated for the first time. From the Brillouin frequency shift (BFS) measured in each intra-modal SBS, the distributed modal birefringence between non-degenerate modes (LP01/LP11) and degenerate LP11 modes is obtained. The proposed setup can potentially be used as a c-TMF based distributed Brillouin sensor. ©2013 Optical Society of America OCIS codes: (060.1810) Buffers, couplers, routers, switches, and multiplexers; (060.2270) Fiber characterization; (060.2370) Fiber optics sensors; (290.5900) Scattering, stimulated Brillouin.
References and links 1.
Y. Han and G. Li, “Coherent optical communication using polarization multiple-input-multiple-output,” Opt. Express 13(19), 7527–7534 (2005). 2. W. Shieh, Q. Yang, and Y. Ma, “107 Gb/s coherent optical OFDM transmission over 1000-km SSMF fiber using orthogonal band multiplexing,” Opt. Express 16(9), 6378–6386 (2008). 3. T. Omiya, M. Yoshida, and M. Nakazawa, “400 Gbit/s 256 QAM-OFDM Transmission over 720 km with a 14 bit/s/Hz Spectral Efficiency Using an Improved FDE Technique,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference (OFC/NFOEC) 2013, paper OTh4E.1. 4. P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001). 5. R. 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). 6. 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, “305 Tb/s Space Division Multiplexed Transmission Using Homogeneous 19-Core Fiber,” J. Lightwave Technol. 31(4), 554–562 (2013). 7. S. Chandrasekhar, A. H. Gnauck, X. Liu, P. J. Winzer, Y. Pan, E. C. Burrows, T. F. Taunay, B. Zhu, M. Fishteyn, M. F. Yan, J. M. Fini, E. M. Monberg, and F. V. Dimarcello, “WDM/SDM transmission of 10 x 128Gb/s PDM-QPSK over 2688-km 7-core fiber with a per-fiber net aggregate spectral-efficiency distance product of 40,320 km·b/s/Hz,” Opt. Express 20(2), 706–711 (2012). 8. A. Li, A. Al Amin, X. Chen, and W. Shieh, “Transmission of 107-Gb/s mode and polarization multiplexed COOFDM signal over a two-mode fiber,” Opt. Express 19(9), 8808–8814 (2011). 9. A. Li, A. A. Amin, X. Chen, S. Chen, G. Gao, and W. Shieh, “Reception of Dual-Spatial-Mode CO-OFDM Signal Over a Two-Mode Fiber,” J. Lightwave Technol. 30(4), 634–640 (2012). 10. C. Koebele, M. Salsi, D. Sperti, P. Tran, P. Brindel, H. Mardoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Astruc, L. Provost, F. Cerou, and G. Charlet, “Two mode transmission at 2×100 Gb/s, over 40 km-long prototype few-mode fiber, using LCOS-based programmable mode multiplexer and demultiplexer,” Opt. Express 19(17), 16593–16600 (2011).
#196707 - $15.00 USD Received 29 Aug 2013; revised 17 Oct 2013; accepted 18 Oct 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031894 | OPTICS EXPRESS 31894
11. S. Randel, R. Ryf, A. Sierra, P. J. Winzer, A. H. Gnauck, C. A. Bolle, R.-J. Essiambre, D. W. Peckham, A. McCurdy, and R. Lingle, Jr., “6×56-Gb/s mode-division multiplexed transmission over 33-km few-mode fiber enabled by 6×6 MIMO equalization,” Opt. Express 19(17), 16697–16707 (2011). 12. A. Li, J. Ye, X. Chen, and W. Shieh, “low loss fused mode coupler for few-mode transmission,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference (OFC/NFOEC) 2013, paper OTu3G. 13. Y. Jung, S. Alam, Z. Li, A. Dhar, D. Giles, I. P. Giles, J. K. Sahu, F. Poletti, L. Grüner-Nielsen, and D. J. Richardson, “First demonstration and detailed characterization of a multimode amplifier for space division multiplexed transmission systems,” Opt. Express 19(26), B952–B957 (2011). 14. N. Bai, E. Ip, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. Man Chung, A. P. T. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, G. Li, and T. Wang, “Mode-division multiplexed transmission with inline few-mode fiber amplifier,” Opt. Express 20(3), 2668–2680 (2012). 15. A. Li, X. Chen, A. Al Amin, J. Ye, and W. Shieh, “Space-Division Multiplexed High-Speed Superchannel Transmission Over Few-Mode Fiber,” J. Lightwave Technol. 30(24), 3953–3964 (2012). 16. L. Gruner-Nielsen, S. Yi, J. W. Nicholson, D. Jakobsen, K. G. Jespersen, R. Lingle, and B. Palsdottir, “Few Mode Transmission Fiber With Low DGD, Low Mode Coupling, and Low Loss,” J. Lightwave Technol. 30(23), 3693–3698 (2012). 17. P. Sillard, M. Astruc, D. Boivin, H. Maerten, and L. Provost, “Few-Mode Fiber for Uncoupled Mode-Division Multiplexing Transmissions,” in 37th European Conference and Exposition on Optical Communications (ECOC), paper Tu.5.LeCervin.7. 18. T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada, “Brillouin Optical-Fiber Time Domain Reflectometry,” IEICE Trans. Commun. E76-B(4), 382–390 (1993). 19. T. Horiguchi and M. Tateda, “BOTDA-nondestructive measurement of single-mode optical fiber attenuation characteristics using Brillouin interaction: theory,” J. Lightwave Technol. 7(8), 1170–1176 (1989). 20. P. St. J. Russell, D. Culverhouse, and F. Farahi, “Experimental observation of forward stimulated Brillouin scattering in dual-mode single-core fibre,” Electron. Lett. 26(15), 1195–1196 (1990). 21. K. Y. Song, Y. H. Kim, and B. Y. Kim, “Intermodal stimulated Brillouin scattering in two-mode fibers,” Opt. Lett. 38(11), 1805–1807 (2013). 22. S. Li, M.-J. Li, and R. S. Vodhanel, “All-optical Brillouin dynamic grating generation in few-mode optical fiber,” Opt. Lett. 37(22), 4660–4662 (2012). 23. I. Bongrand, C. Montes, E. Picholle, J. Botineau, A. Picozzi, G. Cheval, and D. Bahloul, “Soliton compression in Brillouin fiber lasers,” Opt. Lett. 26(19), 1475–1477 (2001). 24. L. Ursini, M. Santagiustina, and L. Palmieri, “Polarization-Dependent Brillouin Gain in Randomly Birefringent Fibers,” IEEE Photon. Technol. Lett. 22(10), 712–714 (2010). 25. B. Y. Kim, J. N. Blake, H. E. Engan, and H. J. Shaw, “All-fiber acousto-optic frequency shifter,” Opt. Lett. 11(6), 389–391 (1986). 26. H. S. Park, K. Y. Song, S. H. Yun, and B. Y. Kim, “All fiber wavelength-tunable acousto-optic switches based on intermodal coupling in fibers,” J. Lightwave Technol. 20(10), 1864–1868 (2002).
1. Introduction The exponential growth of Internet traffic has led to a huge bandwidth demand on the highspeed optical transport, from core to access networks. Much research has been focused on standard single-mode fiber (SSMF) to improve the spectral efficiency (SE) by various multiplexing techniques, e.g., polarization-division multiplexing [1], orthogonal-frequency division multiplexing (OFDM) [2], and multilevel modulation [3]. However, SSMF is fast approaching its so-called nonlinear Shannon limit [4,5]. To solve the capacity crunch problem, recently space-division multiplexing (SDM) based on either multi-core fiber (MCF) [6,7] or multi-mode fiber (MMF) [8–12] has been proposed. By utilizing another dimension – the spatial mode, the spectral efficiency (SE) can be increased several times than that of SSMF. Few-mode fiber (FMF) has recently attracted much interest due to many advantages such as high SE per core, cost and energy efficient amplification [13,14], ease of splicing and low-cost [15]. Compared with conventional MMF, FMF supports only a limit number of spatial modes (normally 3-6 modes), which greatly simplifies the system design. By utilizing the techniques of coherent detection and multi-input-multi-output (MIMO) digital signal processing (DSP), linear impairments of a FMF such as chromatic dispersion (CD), polarization-mode dispersion (PMD), differential-modal-delay (DMD) and mode coupling, can be completely rewound by the MIMO algorithm at the receiver, enabling high-speed mode-division multiplexed (MDM) transmission. To realize the full potential of MDM, the FMF needs be fully characterized. Previous experiments on MDM transmission [8–11] and
#196707 - $15.00 USD Received 29 Aug 2013; revised 17 Oct 2013; accepted 18 Oct 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031894 | OPTICS EXPRESS 31895
fiber design [16,17] have explored a number of global parameters of a FMF including the loss, CD and DMD. However, distributed effects in a FMF are not well understood, such as the mode coupling and modal birefringence, because measurement of these effects is not straightforward. Stimulated Brillouin scattering (SBS) is one of the major nonlinear effects in a silica fiber which can be utilized for many applications, such as fiber characterization, optical amplification, and fiber sensor. Measurement of the Brillouin gain spectrum (BGS) could provide important information along the fiber, such as the effective refractive index of the guided mode, which is very sensitive to the temperature and strain. Distributed measurement or sensing can also be achieved using techniques such as Brillouin optical time-domain reflectometer (BOTDR) [18] or Brillouin optical time-domain analysis (BOTDA) [19]. The SBS effects have been intensively studied on single-mode fibers (SMFs) including the standard single-mode fiber and polarization-maintaining fiber (PMF). For the SBS effects in FMF, however, only a few reports can be found. For example, an early work in [20] has demonstrated the forward SBS between co-propagating LP01 and LP11 modes on a dual-mode fiber. Very recently, Song, et al. [21] reported the inter-modal SBS between the counterpropagated LP01 and LP11 modes in an elliptical-core two-mode fiber (e-TMF). Compared with the most used circular-core fibers, these specially designed elliptical-core fibers are not suitable for use as a transmission fiber due to the reduced capacity and high cost compared with circular-core TMF fibers. Li, et al. [22] demonstrated all-optical generation of Brillouin dynamic grating (BDG) in a FMF. All these measurements touch the interesting topic of generating SBS effect in a FMF. However, the SBS in a circular-core FMF has not been fully characterized. The complication is that FMF supports not only the non-degenerate mode (such as LP01) but also degenerate mode (such as LP11a and LP11b). In this work, we demonstrate detailed measurement of the SBS in a circular-core two-mode fiber (c-TMF). Unlike the specially designed e-TMF in [21], a c-TMF can support three spatial modes: LP01 mode and two degenerate LP11 modes - LP11a and LP11b. The intra- and inter-modal SBS between the three supported spatial modes has been fully explored. To the best of our knowledge, the intermodal SBS between the two-degenerate LP11 modes are demonstrated and characterized for the first time. Measurement of the distributed SBS over the c-TMF has been achieved by the BOTDA technique using high power pulsed pump and a weak continuous wave (cw) probe. From the distributed Brillouin gain spectra (BGS), the mode birefringence between LP01/LP11 mode and between degenerate LP11 modes (LP11a/LP11b) is also obtained. The proposed setup can potentially be used as a c-TMF based distributed Brillouin sensor through characterization of the Brillouin dynamic grating (BDG) [22] generated by the intra- or inter-modal SBS effect. It is worth noting that the electrostrictively excited low-frequency cladding Brillouin scattering (CBS) may perturb the SBS dynamics in sufficiently long fibers [23]. For a stable measurement of SBS the CBS effect must be suppressed, which can be achieved by various methods such as removing the fiber coating, using short FMF or reducing the pump power. 2. Fundamentals of SBS and BOTDA When light propagates through a fiber, acoustic waves (phonons) will be excited and a fraction of the light will be backscattered due to the interaction between photon and acoustic phonon, known as the spontaneous Brillouin scattering. The backscattered light will undergo a frequency downshift (stokes) or upshift (anti-stokes), and the frequency shift depends on the acoustic velocity and is given by
υB =
2nVa
λ
(1)
#196707 - $15.00 USD Received 29 Aug 2013; revised 17 Oct 2013; accepted 18 Oct 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031894 | OPTICS EXPRESS 31896
where υ B is the Brillouin frequency shift (BFS), n is the effective refractive index (ERI), Va is the effective velocity of the acoustic wave, and λ is the wavelength of light. If a weak probe light is also counter-propagating along the fiber and has the same frequency downshift, stimulated Brillouin scattering will happen and the probe wave will experience gain. Through time-domain analysis using a pulsed pump and a counter-propagating cw probe, distributed measurement or sensing along the fiber can be achieved. This technique is also known as the Brillouin optical time-domain analysis (BOTDA) [19]. For FMFs the SBS becomes more complicated as many spatial modes can be involved [21]. 3. Experimental setup 3.1 Fiber under test The fiber under test (FUT) is a 4-km custom-designed circular-core TMF. The TMF is a Gedoped circular-core step-index fiber that supports three spatial modes, LP01, LP11a and LP11b, the same as we used in [8]. The fiber parameters are summarized in Table 1. Table 1. Parameters for Custom-designed Step-index Two-mode Fiber [8,9] Parameter Spool Length* Core Diameter* Cladding Diameter* Refractive Index (Core) Refractive Index (Cladding) Effective Refractive Index (LP01) Effective Refractive Index (LP11) Chromatic Dispersion (LP01) Chromatic Dispersion (LP11) Effective Area (LP01) Effective Area (LP11) Differential Modal Delay(LP01/LP11) * LP11 Cut-off Wavelength Fiber Loss(LP01,LP11)* * Measured value.
Unit m µm µm
ps/(nm*km) ps/(nm*km) µm2 µm2
Value 4,000 11.9 109 1.4519 1.4440 1.4498 1.4468 22.1 17 94.7 99.9
ps/m
3.0
nm dB/km
2323 0.26
3.2 Mode stripper and mode converter A mode stripper (MS) is a device that can strip out higher order modes. The MS can be realized by tightly winding the bare TMF over an 8-mm post of about 20 turns. In so doing, the modal rejection ratio to the LP11 mode is above 30 dB, with very low loss (< 0.2 dB) for the LP01 mode and negligible polarization dependence. A mode converter (MC) can convert the fundamental mode in a FMF to the specific higher order mode, e.g., LP11 mode, or the other way round. Various known methods can realize mode conversion, such as long-period fiber grating (LFPG) [9], spatial light modulator (SLM) [10], free-space phase plate [11], and fused spatial mode coupler (SMC) [12]. In this experiment, we use LPFG based MC to realize mode conversion between LP01 and LP11 modes in a TMF. The advantage of LPFG based MC is that it is very compact and the conversion ratio is tunable. The LPFG is generated by pressing a metal grating to the TMF. The metal grating is fabricated with 20 evenly-spaced grooves on one polished surface. The groove pitch is 510 ± 5 μm, which equals to the beating length between LP01 and LP11 modes. The center wavelength and conversion ratio (or extinction ratio, ER) is controlled by the applied force and angle to the fiber [9]. The measured performance can be found in Fig. 4 of [9]. It is confirmed that the losses of the fabricated MCs are about 1.5 dB with polarization dependent loss (PDL) of 0.4 - 1.2 dB. The modal ER is maintained beyond 20 dB for a 13-nm wavelength range from 1545 to 1558 nm.
#196707 - $15.00 USD Received 29 Aug 2013; revised 17 Oct 2013; accepted 18 Oct 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031894 | OPTICS EXPRESS 31897
3.3 Free-space mode combiner (FSMC) To analyze the SBS between different spatial modes, mode multiplexer/de-multiplexer (MUX/DeMUX) is needed to combine or split the spatial mode. We use free-space mode combiner (FSMC) as the mode MUX/DeMUX. Configuration of the FSMC is shown in Fig. 1. The FSMC consists of three XY translation stages, two 50:50 non-polarizing beamsplitters (BS), and four collimating lenses with focal length f = 11.0 mm. For LP01 mode, the signal is directly launched into the free-space SMC from a single-mode fiber (SMF). For LP11 mode, the signal is mode converted from fundamental mode to LP11 mode by a LPFG based MC before being launched into the FSMC from a TMF. The two input TMFs and one input SMF that carry LP11a, LP11b or LP01 mode are mounted on the XY stages so that the fiber position can be manually aligned to maximum the coupling ratio to the output TMF. The collimated beams are subsequently combined together by the two BS’s through either transmission or reflection path, and finally focused and coupled to the output TMF by a packaged fiber collimator. The BS is polarization insensitive with less than 5% difference in transmission for s- and p-polarization at 1550 nm. The TMFs mounted on the XY stage are connectorized with specially designed FC-type connectors whose ferrule can be axially rotated. By adjusting the key thus the TMF, the orientation of the two LP11 modes can be manipulated to be orthogonal (90°) to each other. An infrared CCD camera can be placed in the unused path of either the first or second BS, so that the position, pattern and orientation of the individual or combined modes can be monitored in real time. The output TMF is connected with the 4-km FUT. The theoretical minimum loss is 3 dB for LP01 mode and 6 dB for the two LP11 modes, respectively. The FSMC is reciprocal and therefore it can also be used as a mode DeMUX. LP11b
LP01
TMFin
SMFin
TMFin LP11a
XY stage
Collimating lens f = 11.0 mm
TMFout BS
BS
Collimator
LP11a + LP11b + LP01
Camera
Fig. 1. Schematic diagram of a 3 × 1 FSMC. The translation stages have two free axes, X and Y (Z is the light propagation direction). BS: 50:50 non-polarizing beamsplitter. The second BS can be removed in case only two modes need to be multiplexed so that it becomes a 2 × 1 FSMC.
3.4 Experimental setup The experimental configuration for characterization of SBS in a c-TMF is shown in Fig. 2. We build a mode-multiplexed pump-probe setup to analyze the intra- and inter-modal SBS. By utilizing two FSMCs, the pump and probe wave can be launched in one or a combination of the three supported spatial modes, LP01, LP11a and/or LP11b. A tunable external-cavity laser (ECL) with nominal 100-kHz linewidth is used as a light source. The laser wavelength is set at 1550 nm in our experiment. The 1550-nm cw light from ECL is first divided with a 50:50 single-mode coupler. The upper path is further divided with a 50:50 single-mode coupler to
#196707 - $15.00 USD Received 29 Aug 2013; revised 17 Oct 2013; accepted 18 Oct 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031894 | OPTICS EXPRESS 31898
provide the pump and probe wave. The lower path is first amplified by an erbium doped fiber amplifier (EDFA), and then divided again by a 1 × 3 coupler to generate 3 carriers as the local oscillators (LOs) for heterodyne coherent detection. The pump wave is modulated by an electro-optical modulator (EOM) driven by an arbitrary function generator (AFG). The EOM can generate 30 ns Gaussian pulse at 5-kHz repetition frequency in order to achieve high pump power. The pump pulse is then split to three paths by a 1 × 3 coupler and amplified by three EDFAs. For the upper two paths, MS and MC are used to generate LP11a and LP11b mode, and for the lower path the pump pulse simply passes through to provide LP01 mode. Finally, the three spatial modes are mode multiplexed by a FSMC and launched into the FUT. The probe wave is cw and modulated by a Mach-Zehnder modulator (MZM) driven by a RF synthesizer. The synthesizer can generate cosine wave up to 40 GHz. By biasing the MZM at null point with the main carrier much suppressed, a double-sideband (DSB) probe signal can be obtained. The DSB signal then passes through a tunable 10-GHz optical band-pass filter (OBPF) with center frequency set at the lower sideband (longer wavelength) signal. The upper sideband (shorter wavelength) is thus attenuated by > 20 dB, and the probe signal becomes single-sideband (SSB) with its frequency downshifted from the carrier. The spectrum of the probe wave before and after OBPF is shown in the insets (i) and (ii) of Fig. 2. The probe signal is then split into three paths by another 1 × 3 coupler to generate three spatial modes, and mode multiplexed with another FSMC. The mode combined probe wave is then fed into the FUT in opposite direction.
Fig. 2. Experimental setup for the BOTDA measurement of BGS of a 4-km c-TMF. ECL: external-cavity laser; MZM: Mach-Zehnder modulator; EOM: electro-optic modulator; AFG: arbitrary function generator; EDFA: Erbium-doped fiber amplifier; OBPF: optical band-pass filter; PC: polarization controller; OC: optical circulator; MS: mode stripper; MC: mode converter; BR: balanced receiver; TDS: time-domain (sampling) scope; FUT: fiber under test. Insets in the bottom: spectrum of probe signal (i) before OBPF, and (ii) after OBPF.
#196707 - $15.00 USD Received 29 Aug 2013; revised 17 Oct 2013; accepted 18 Oct 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031894 | OPTICS EXPRESS 31899
To detect the probe signal, three optical circulators (OCs) are inserted before the FSMC in the pump path. The counter-propagating probe is first mode de-multiplexed to three spatial modes by the same FSMC in the pump path. The optical signal in each mode is then directed to the coherent receiver which is coupled with a 1550 nm local oscillator (LO) from the same ECL through a 90° optical hybrid for coherent detection. The outputs of the hybrids are subsequently detected by 6 balanced receivers (BRs). The photo detectors (PDs) in each BR have a 3-dB bandwidth of 15 GHz. Finally, the electrical signals comprising the in-phase (I) and quadrature (Q) components of all 3 modes are sampled by a 25-GSa/s time-domain sampling scope (TDS). The TDS is synchronized and triggered by the AFG with the same frequency of the pump pulse, so that distributed measurement of BGS is enabled. The state of polarization (SOP) of LOs is aligned with the pump and probe wave at the input end of pump (point A in Fig. 2), so that the electrical signal power after coherent detection is maximized. Since a circular-core FMF is used as the FUT which is normally a randomly birefringent fiber, the state of polarization (SOP) of pump/probe wave is not maintained and will scramble over distance. Therefore, even though the SOP of pump and probe is well aligned at the input end of pump, it will deviate during propagation because the pump-probe wave is counterpropagating. In extreme cases the SOP can be orthogonal, which will lead to zero SBS gain. This problem can be solved by various means such as using a polarization maintained fiber, fast scrambling the pump or probe polarization, and nonlinear polarization pulling (NLPP) [24]. Nevertheless, in our case the fiber is tightly spooled and placed on an vibration isolated optical table to avoid perturbation, and also a short distance of FMF (
Abstract: We show characterization of stimulated Brillouin scattering (SBS) in a circular-core two-mode fiber (c-TMF) using Brillouin optical time-domain analysis (BOTDA) with a pulsed pump and a counterpropagating continuous wave probe. By using two free-space mode combiners (FSMCs), we can launch any combination of spatial modes into both ends of the c-TMF. Combined with coherent detection, measurement of distributed Brillouin gain spectra (BGS) is achieved for all possible counter-propagating spatial mode pairs with high spectral resolution and stability. Both intra- and inter-modal SBS are investigated for the c-TMF. The inter-modal SBS between two degenerate LP11 modes (LP11a/LP11b) is demonstrated for the first time. From the Brillouin frequency shift (BFS) measured in each intra-modal SBS, the distributed modal birefringence between non-degenerate modes (LP01/LP11) and degenerate LP11 modes is obtained. The proposed setup can potentially be used as a c-TMF based distributed Brillouin sensor. ©2013 Optical Society of America OCIS codes: (060.1810) Buffers, couplers, routers, switches, and multiplexers; (060.2270) Fiber characterization; (060.2370) Fiber optics sensors; (290.5900) Scattering, stimulated Brillouin.
References and links 1.
Y. Han and G. Li, “Coherent optical communication using polarization multiple-input-multiple-output,” Opt. Express 13(19), 7527–7534 (2005). 2. W. Shieh, Q. Yang, and Y. Ma, “107 Gb/s coherent optical OFDM transmission over 1000-km SSMF fiber using orthogonal band multiplexing,” Opt. Express 16(9), 6378–6386 (2008). 3. T. Omiya, M. Yoshida, and M. Nakazawa, “400 Gbit/s 256 QAM-OFDM Transmission over 720 km with a 14 bit/s/Hz Spectral Efficiency Using an Improved FDE Technique,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference (OFC/NFOEC) 2013, paper OTh4E.1. 4. P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001). 5. R. 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). 6. 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, “305 Tb/s Space Division Multiplexed Transmission Using Homogeneous 19-Core Fiber,” J. Lightwave Technol. 31(4), 554–562 (2013). 7. S. Chandrasekhar, A. H. Gnauck, X. Liu, P. J. Winzer, Y. Pan, E. C. Burrows, T. F. Taunay, B. Zhu, M. Fishteyn, M. F. Yan, J. M. Fini, E. M. Monberg, and F. V. Dimarcello, “WDM/SDM transmission of 10 x 128Gb/s PDM-QPSK over 2688-km 7-core fiber with a per-fiber net aggregate spectral-efficiency distance product of 40,320 km·b/s/Hz,” Opt. Express 20(2), 706–711 (2012). 8. A. Li, A. Al Amin, X. Chen, and W. Shieh, “Transmission of 107-Gb/s mode and polarization multiplexed COOFDM signal over a two-mode fiber,” Opt. Express 19(9), 8808–8814 (2011). 9. A. Li, A. A. Amin, X. Chen, S. Chen, G. Gao, and W. Shieh, “Reception of Dual-Spatial-Mode CO-OFDM Signal Over a Two-Mode Fiber,” J. Lightwave Technol. 30(4), 634–640 (2012). 10. C. Koebele, M. Salsi, D. Sperti, P. Tran, P. Brindel, H. Mardoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Astruc, L. Provost, F. Cerou, and G. Charlet, “Two mode transmission at 2×100 Gb/s, over 40 km-long prototype few-mode fiber, using LCOS-based programmable mode multiplexer and demultiplexer,” Opt. Express 19(17), 16593–16600 (2011).
#196707 - $15.00 USD Received 29 Aug 2013; revised 17 Oct 2013; accepted 18 Oct 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031894 | OPTICS EXPRESS 31894
11. S. Randel, R. Ryf, A. Sierra, P. J. Winzer, A. H. Gnauck, C. A. Bolle, R.-J. Essiambre, D. W. Peckham, A. McCurdy, and R. Lingle, Jr., “6×56-Gb/s mode-division multiplexed transmission over 33-km few-mode fiber enabled by 6×6 MIMO equalization,” Opt. Express 19(17), 16697–16707 (2011). 12. A. Li, J. Ye, X. Chen, and W. Shieh, “low loss fused mode coupler for few-mode transmission,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference (OFC/NFOEC) 2013, paper OTu3G. 13. Y. Jung, S. Alam, Z. Li, A. Dhar, D. Giles, I. P. Giles, J. K. Sahu, F. Poletti, L. Grüner-Nielsen, and D. J. Richardson, “First demonstration and detailed characterization of a multimode amplifier for space division multiplexed transmission systems,” Opt. Express 19(26), B952–B957 (2011). 14. N. Bai, E. Ip, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. Man Chung, A. P. T. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, G. Li, and T. Wang, “Mode-division multiplexed transmission with inline few-mode fiber amplifier,” Opt. Express 20(3), 2668–2680 (2012). 15. A. Li, X. Chen, A. Al Amin, J. Ye, and W. Shieh, “Space-Division Multiplexed High-Speed Superchannel Transmission Over Few-Mode Fiber,” J. Lightwave Technol. 30(24), 3953–3964 (2012). 16. L. Gruner-Nielsen, S. Yi, J. W. Nicholson, D. Jakobsen, K. G. Jespersen, R. Lingle, and B. Palsdottir, “Few Mode Transmission Fiber With Low DGD, Low Mode Coupling, and Low Loss,” J. Lightwave Technol. 30(23), 3693–3698 (2012). 17. P. Sillard, M. Astruc, D. Boivin, H. Maerten, and L. Provost, “Few-Mode Fiber for Uncoupled Mode-Division Multiplexing Transmissions,” in 37th European Conference and Exposition on Optical Communications (ECOC), paper Tu.5.LeCervin.7. 18. T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada, “Brillouin Optical-Fiber Time Domain Reflectometry,” IEICE Trans. Commun. E76-B(4), 382–390 (1993). 19. T. Horiguchi and M. Tateda, “BOTDA-nondestructive measurement of single-mode optical fiber attenuation characteristics using Brillouin interaction: theory,” J. Lightwave Technol. 7(8), 1170–1176 (1989). 20. P. St. J. Russell, D. Culverhouse, and F. Farahi, “Experimental observation of forward stimulated Brillouin scattering in dual-mode single-core fibre,” Electron. Lett. 26(15), 1195–1196 (1990). 21. K. Y. Song, Y. H. Kim, and B. Y. Kim, “Intermodal stimulated Brillouin scattering in two-mode fibers,” Opt. Lett. 38(11), 1805–1807 (2013). 22. S. Li, M.-J. Li, and R. S. Vodhanel, “All-optical Brillouin dynamic grating generation in few-mode optical fiber,” Opt. Lett. 37(22), 4660–4662 (2012). 23. I. Bongrand, C. Montes, E. Picholle, J. Botineau, A. Picozzi, G. Cheval, and D. Bahloul, “Soliton compression in Brillouin fiber lasers,” Opt. Lett. 26(19), 1475–1477 (2001). 24. L. Ursini, M. Santagiustina, and L. Palmieri, “Polarization-Dependent Brillouin Gain in Randomly Birefringent Fibers,” IEEE Photon. Technol. Lett. 22(10), 712–714 (2010). 25. B. Y. Kim, J. N. Blake, H. E. Engan, and H. J. Shaw, “All-fiber acousto-optic frequency shifter,” Opt. Lett. 11(6), 389–391 (1986). 26. H. S. Park, K. Y. Song, S. H. Yun, and B. Y. Kim, “All fiber wavelength-tunable acousto-optic switches based on intermodal coupling in fibers,” J. Lightwave Technol. 20(10), 1864–1868 (2002).
1. Introduction The exponential growth of Internet traffic has led to a huge bandwidth demand on the highspeed optical transport, from core to access networks. Much research has been focused on standard single-mode fiber (SSMF) to improve the spectral efficiency (SE) by various multiplexing techniques, e.g., polarization-division multiplexing [1], orthogonal-frequency division multiplexing (OFDM) [2], and multilevel modulation [3]. However, SSMF is fast approaching its so-called nonlinear Shannon limit [4,5]. To solve the capacity crunch problem, recently space-division multiplexing (SDM) based on either multi-core fiber (MCF) [6,7] or multi-mode fiber (MMF) [8–12] has been proposed. By utilizing another dimension – the spatial mode, the spectral efficiency (SE) can be increased several times than that of SSMF. Few-mode fiber (FMF) has recently attracted much interest due to many advantages such as high SE per core, cost and energy efficient amplification [13,14], ease of splicing and low-cost [15]. Compared with conventional MMF, FMF supports only a limit number of spatial modes (normally 3-6 modes), which greatly simplifies the system design. By utilizing the techniques of coherent detection and multi-input-multi-output (MIMO) digital signal processing (DSP), linear impairments of a FMF such as chromatic dispersion (CD), polarization-mode dispersion (PMD), differential-modal-delay (DMD) and mode coupling, can be completely rewound by the MIMO algorithm at the receiver, enabling high-speed mode-division multiplexed (MDM) transmission. To realize the full potential of MDM, the FMF needs be fully characterized. Previous experiments on MDM transmission [8–11] and
#196707 - $15.00 USD Received 29 Aug 2013; revised 17 Oct 2013; accepted 18 Oct 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031894 | OPTICS EXPRESS 31895
fiber design [16,17] have explored a number of global parameters of a FMF including the loss, CD and DMD. However, distributed effects in a FMF are not well understood, such as the mode coupling and modal birefringence, because measurement of these effects is not straightforward. Stimulated Brillouin scattering (SBS) is one of the major nonlinear effects in a silica fiber which can be utilized for many applications, such as fiber characterization, optical amplification, and fiber sensor. Measurement of the Brillouin gain spectrum (BGS) could provide important information along the fiber, such as the effective refractive index of the guided mode, which is very sensitive to the temperature and strain. Distributed measurement or sensing can also be achieved using techniques such as Brillouin optical time-domain reflectometer (BOTDR) [18] or Brillouin optical time-domain analysis (BOTDA) [19]. The SBS effects have been intensively studied on single-mode fibers (SMFs) including the standard single-mode fiber and polarization-maintaining fiber (PMF). For the SBS effects in FMF, however, only a few reports can be found. For example, an early work in [20] has demonstrated the forward SBS between co-propagating LP01 and LP11 modes on a dual-mode fiber. Very recently, Song, et al. [21] reported the inter-modal SBS between the counterpropagated LP01 and LP11 modes in an elliptical-core two-mode fiber (e-TMF). Compared with the most used circular-core fibers, these specially designed elliptical-core fibers are not suitable for use as a transmission fiber due to the reduced capacity and high cost compared with circular-core TMF fibers. Li, et al. [22] demonstrated all-optical generation of Brillouin dynamic grating (BDG) in a FMF. All these measurements touch the interesting topic of generating SBS effect in a FMF. However, the SBS in a circular-core FMF has not been fully characterized. The complication is that FMF supports not only the non-degenerate mode (such as LP01) but also degenerate mode (such as LP11a and LP11b). In this work, we demonstrate detailed measurement of the SBS in a circular-core two-mode fiber (c-TMF). Unlike the specially designed e-TMF in [21], a c-TMF can support three spatial modes: LP01 mode and two degenerate LP11 modes - LP11a and LP11b. The intra- and inter-modal SBS between the three supported spatial modes has been fully explored. To the best of our knowledge, the intermodal SBS between the two-degenerate LP11 modes are demonstrated and characterized for the first time. Measurement of the distributed SBS over the c-TMF has been achieved by the BOTDA technique using high power pulsed pump and a weak continuous wave (cw) probe. From the distributed Brillouin gain spectra (BGS), the mode birefringence between LP01/LP11 mode and between degenerate LP11 modes (LP11a/LP11b) is also obtained. The proposed setup can potentially be used as a c-TMF based distributed Brillouin sensor through characterization of the Brillouin dynamic grating (BDG) [22] generated by the intra- or inter-modal SBS effect. It is worth noting that the electrostrictively excited low-frequency cladding Brillouin scattering (CBS) may perturb the SBS dynamics in sufficiently long fibers [23]. For a stable measurement of SBS the CBS effect must be suppressed, which can be achieved by various methods such as removing the fiber coating, using short FMF or reducing the pump power. 2. Fundamentals of SBS and BOTDA When light propagates through a fiber, acoustic waves (phonons) will be excited and a fraction of the light will be backscattered due to the interaction between photon and acoustic phonon, known as the spontaneous Brillouin scattering. The backscattered light will undergo a frequency downshift (stokes) or upshift (anti-stokes), and the frequency shift depends on the acoustic velocity and is given by
υB =
2nVa
λ
(1)
#196707 - $15.00 USD Received 29 Aug 2013; revised 17 Oct 2013; accepted 18 Oct 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031894 | OPTICS EXPRESS 31896
where υ B is the Brillouin frequency shift (BFS), n is the effective refractive index (ERI), Va is the effective velocity of the acoustic wave, and λ is the wavelength of light. If a weak probe light is also counter-propagating along the fiber and has the same frequency downshift, stimulated Brillouin scattering will happen and the probe wave will experience gain. Through time-domain analysis using a pulsed pump and a counter-propagating cw probe, distributed measurement or sensing along the fiber can be achieved. This technique is also known as the Brillouin optical time-domain analysis (BOTDA) [19]. For FMFs the SBS becomes more complicated as many spatial modes can be involved [21]. 3. Experimental setup 3.1 Fiber under test The fiber under test (FUT) is a 4-km custom-designed circular-core TMF. The TMF is a Gedoped circular-core step-index fiber that supports three spatial modes, LP01, LP11a and LP11b, the same as we used in [8]. The fiber parameters are summarized in Table 1. Table 1. Parameters for Custom-designed Step-index Two-mode Fiber [8,9] Parameter Spool Length* Core Diameter* Cladding Diameter* Refractive Index (Core) Refractive Index (Cladding) Effective Refractive Index (LP01) Effective Refractive Index (LP11) Chromatic Dispersion (LP01) Chromatic Dispersion (LP11) Effective Area (LP01) Effective Area (LP11) Differential Modal Delay(LP01/LP11) * LP11 Cut-off Wavelength Fiber Loss(LP01,LP11)* * Measured value.
Unit m µm µm
ps/(nm*km) ps/(nm*km) µm2 µm2
Value 4,000 11.9 109 1.4519 1.4440 1.4498 1.4468 22.1 17 94.7 99.9
ps/m
3.0
nm dB/km
2323 0.26
3.2 Mode stripper and mode converter A mode stripper (MS) is a device that can strip out higher order modes. The MS can be realized by tightly winding the bare TMF over an 8-mm post of about 20 turns. In so doing, the modal rejection ratio to the LP11 mode is above 30 dB, with very low loss (< 0.2 dB) for the LP01 mode and negligible polarization dependence. A mode converter (MC) can convert the fundamental mode in a FMF to the specific higher order mode, e.g., LP11 mode, or the other way round. Various known methods can realize mode conversion, such as long-period fiber grating (LFPG) [9], spatial light modulator (SLM) [10], free-space phase plate [11], and fused spatial mode coupler (SMC) [12]. In this experiment, we use LPFG based MC to realize mode conversion between LP01 and LP11 modes in a TMF. The advantage of LPFG based MC is that it is very compact and the conversion ratio is tunable. The LPFG is generated by pressing a metal grating to the TMF. The metal grating is fabricated with 20 evenly-spaced grooves on one polished surface. The groove pitch is 510 ± 5 μm, which equals to the beating length between LP01 and LP11 modes. The center wavelength and conversion ratio (or extinction ratio, ER) is controlled by the applied force and angle to the fiber [9]. The measured performance can be found in Fig. 4 of [9]. It is confirmed that the losses of the fabricated MCs are about 1.5 dB with polarization dependent loss (PDL) of 0.4 - 1.2 dB. The modal ER is maintained beyond 20 dB for a 13-nm wavelength range from 1545 to 1558 nm.
#196707 - $15.00 USD Received 29 Aug 2013; revised 17 Oct 2013; accepted 18 Oct 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031894 | OPTICS EXPRESS 31897
3.3 Free-space mode combiner (FSMC) To analyze the SBS between different spatial modes, mode multiplexer/de-multiplexer (MUX/DeMUX) is needed to combine or split the spatial mode. We use free-space mode combiner (FSMC) as the mode MUX/DeMUX. Configuration of the FSMC is shown in Fig. 1. The FSMC consists of three XY translation stages, two 50:50 non-polarizing beamsplitters (BS), and four collimating lenses with focal length f = 11.0 mm. For LP01 mode, the signal is directly launched into the free-space SMC from a single-mode fiber (SMF). For LP11 mode, the signal is mode converted from fundamental mode to LP11 mode by a LPFG based MC before being launched into the FSMC from a TMF. The two input TMFs and one input SMF that carry LP11a, LP11b or LP01 mode are mounted on the XY stages so that the fiber position can be manually aligned to maximum the coupling ratio to the output TMF. The collimated beams are subsequently combined together by the two BS’s through either transmission or reflection path, and finally focused and coupled to the output TMF by a packaged fiber collimator. The BS is polarization insensitive with less than 5% difference in transmission for s- and p-polarization at 1550 nm. The TMFs mounted on the XY stage are connectorized with specially designed FC-type connectors whose ferrule can be axially rotated. By adjusting the key thus the TMF, the orientation of the two LP11 modes can be manipulated to be orthogonal (90°) to each other. An infrared CCD camera can be placed in the unused path of either the first or second BS, so that the position, pattern and orientation of the individual or combined modes can be monitored in real time. The output TMF is connected with the 4-km FUT. The theoretical minimum loss is 3 dB for LP01 mode and 6 dB for the two LP11 modes, respectively. The FSMC is reciprocal and therefore it can also be used as a mode DeMUX. LP11b
LP01
TMFin
SMFin
TMFin LP11a
XY stage
Collimating lens f = 11.0 mm
TMFout BS
BS
Collimator
LP11a + LP11b + LP01
Camera
Fig. 1. Schematic diagram of a 3 × 1 FSMC. The translation stages have two free axes, X and Y (Z is the light propagation direction). BS: 50:50 non-polarizing beamsplitter. The second BS can be removed in case only two modes need to be multiplexed so that it becomes a 2 × 1 FSMC.
3.4 Experimental setup The experimental configuration for characterization of SBS in a c-TMF is shown in Fig. 2. We build a mode-multiplexed pump-probe setup to analyze the intra- and inter-modal SBS. By utilizing two FSMCs, the pump and probe wave can be launched in one or a combination of the three supported spatial modes, LP01, LP11a and/or LP11b. A tunable external-cavity laser (ECL) with nominal 100-kHz linewidth is used as a light source. The laser wavelength is set at 1550 nm in our experiment. The 1550-nm cw light from ECL is first divided with a 50:50 single-mode coupler. The upper path is further divided with a 50:50 single-mode coupler to
#196707 - $15.00 USD Received 29 Aug 2013; revised 17 Oct 2013; accepted 18 Oct 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031894 | OPTICS EXPRESS 31898
provide the pump and probe wave. The lower path is first amplified by an erbium doped fiber amplifier (EDFA), and then divided again by a 1 × 3 coupler to generate 3 carriers as the local oscillators (LOs) for heterodyne coherent detection. The pump wave is modulated by an electro-optical modulator (EOM) driven by an arbitrary function generator (AFG). The EOM can generate 30 ns Gaussian pulse at 5-kHz repetition frequency in order to achieve high pump power. The pump pulse is then split to three paths by a 1 × 3 coupler and amplified by three EDFAs. For the upper two paths, MS and MC are used to generate LP11a and LP11b mode, and for the lower path the pump pulse simply passes through to provide LP01 mode. Finally, the three spatial modes are mode multiplexed by a FSMC and launched into the FUT. The probe wave is cw and modulated by a Mach-Zehnder modulator (MZM) driven by a RF synthesizer. The synthesizer can generate cosine wave up to 40 GHz. By biasing the MZM at null point with the main carrier much suppressed, a double-sideband (DSB) probe signal can be obtained. The DSB signal then passes through a tunable 10-GHz optical band-pass filter (OBPF) with center frequency set at the lower sideband (longer wavelength) signal. The upper sideband (shorter wavelength) is thus attenuated by > 20 dB, and the probe signal becomes single-sideband (SSB) with its frequency downshifted from the carrier. The spectrum of the probe wave before and after OBPF is shown in the insets (i) and (ii) of Fig. 2. The probe signal is then split into three paths by another 1 × 3 coupler to generate three spatial modes, and mode multiplexed with another FSMC. The mode combined probe wave is then fed into the FUT in opposite direction.
Fig. 2. Experimental setup for the BOTDA measurement of BGS of a 4-km c-TMF. ECL: external-cavity laser; MZM: Mach-Zehnder modulator; EOM: electro-optic modulator; AFG: arbitrary function generator; EDFA: Erbium-doped fiber amplifier; OBPF: optical band-pass filter; PC: polarization controller; OC: optical circulator; MS: mode stripper; MC: mode converter; BR: balanced receiver; TDS: time-domain (sampling) scope; FUT: fiber under test. Insets in the bottom: spectrum of probe signal (i) before OBPF, and (ii) after OBPF.
#196707 - $15.00 USD Received 29 Aug 2013; revised 17 Oct 2013; accepted 18 Oct 2013; published 16 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.031894 | OPTICS EXPRESS 31899
To detect the probe signal, three optical circulators (OCs) are inserted before the FSMC in the pump path. The counter-propagating probe is first mode de-multiplexed to three spatial modes by the same FSMC in the pump path. The optical signal in each mode is then directed to the coherent receiver which is coupled with a 1550 nm local oscillator (LO) from the same ECL through a 90° optical hybrid for coherent detection. The outputs of the hybrids are subsequently detected by 6 balanced receivers (BRs). The photo detectors (PDs) in each BR have a 3-dB bandwidth of 15 GHz. Finally, the electrical signals comprising the in-phase (I) and quadrature (Q) components of all 3 modes are sampled by a 25-GSa/s time-domain sampling scope (TDS). The TDS is synchronized and triggered by the AFG with the same frequency of the pump pulse, so that distributed measurement of BGS is enabled. The state of polarization (SOP) of LOs is aligned with the pump and probe wave at the input end of pump (point A in Fig. 2), so that the electrical signal power after coherent detection is maximized. Since a circular-core FMF is used as the FUT which is normally a randomly birefringent fiber, the state of polarization (SOP) of pump/probe wave is not maintained and will scramble over distance. Therefore, even though the SOP of pump and probe is well aligned at the input end of pump, it will deviate during propagation because the pump-probe wave is counterpropagating. In extreme cases the SOP can be orthogonal, which will lead to zero SBS gain. This problem can be solved by various means such as using a polarization maintained fiber, fast scrambling the pump or probe polarization, and nonlinear polarization pulling (NLPP) [24]. Nevertheless, in our case the fiber is tightly spooled and placed on an vibration isolated optical table to avoid perturbation, and also a short distance of FMF (
