Few-mode fibers (FMFs) have found applications in optical communications and sensors with attractive features that standard single mode fiber (SSMF) do not possess. We report our recent progress on FMF based optical sensors, and show the potential of utilizing the spatial dimension for multi-parameter sensing with discrimination capability. We first show a discrete type FMF sensor based on interferometer structure with a short FMF, utilizing the modal interference between either the polarizations (x and y) or the spatial modes (LP01 and LP11). We then show a distributed type FMF sensor by generating the stimulated Brillouin scattering (SBS) in a long FMF. We characterize the Brillouin gain spectrum (BGS) with a pump-probe configuration, and measure the temperature and strain coefficients for LP01 and LP11 modes. The proposed FMF based optical sensor can be applied to sensing a wide range of parameters.
© 2015 Optical Society of America
Optical fiber sensors have been widely studied over the last few decades owing to their advantages of compactness, high reliability, high sensitivity and low fabrication cost . In such sensors, optical fiber is the most critical sensing element. Single-mode fibers (SMFs) are widely used in optical fiber sensors, which can be standard single-mode fiber (SSMF), polarization maintain fiber (PMF) , or photonic crystal fiber (PCF) [3, 4]. The motivation of using different fiber for optical sensing is that the performance of optical fiber sensors (e.g, sensing parameter, sensitivity, reach, etc.) depends not only on the sensing technique but also on the sensing element, i.e., optical fiber. It is necessary to develop a fiber with high performance while keeping the fabrication cost at a low level. Recently, few-mode fiber (FMF) has attracted much research interest because it has the potential to overcome the capacity limit of SSMF [5–8]. By exploring the fifth dimension - the spatial dimension in addition to the other four dimensions of time, wavelength, polarization and phase, FMF can provide more capacities and flexibilities than the SMF counterpart. The advance into spatial dimension has benefited not only the optical communications but also many other fields like optical sensors. FMF based optical fiber sensors emerges as an interesting topic which was studied by B. Y. Kim et al.  in 1980s. Compared with SMF based fiber sensors, FMF based fiber sensors have many unique advantages such as cost effectiveness, high sensitivity, and discrimination capability . Because there is no special structure or core/cladding design for FMF, the fabrication process of FMF is compatible with SSMF, and the cost is much lower than the conventional PMF or specially-designed polarization-maintaining PCF (PM-PCF) , making the FMF very ideal for long range sensing. Furthermore, because multiple effects can jointly affect the performance of the optical fiber sensors (e.g., temperature and strain), discriminative and accurate measurement on each parameter is necessary. It can be realized through characterization of different parameters in a PMF , but the system is rather complicated and costly. Y. H. Kim, et al. recently demonstrated measurement of the temperature and strain coefficients in an elliptical-core two-mode fiber (e-TMF) based on Brillouin dynamic grating (BDG) . The proposed system could potentially achieve discriminative sensing, but the elliptical-core fiber is difficult to fabricate and less popular than circular-core fibers in the telecommunication industry.
In this paper, we explore the spatial dimension by characterizing different spatial modes in circular-core FMFs, in order to achieve a unique FMF-based multi-parameter sensor. We show design and fabrication of two types of FMF sensor: discrete and distributed. The organization of this paper is as follows: In Section 2, we introduce a discrete FMF sensor based on intermodal interference. The system configuration is illustrated, and its sensitivity to the temperature and strain are characterized and compared with a SMF counterpart. In Section 3, we report a distributed FMF sensor based on Brillouin scattering. Different from , we measure the Brillouin frequency shift (BFS) for the stimulated Brillouin scattering (SBS) in different mode pairs by characterizing the Brillouin gain spectrum (BGS) using Brillouin optical time domain analysis (BOTDA) technique . The temperature and strain coefficients for LP01 mode and LP11 mode are obtained. The proposed FMF sensors can be either a temperature-insensitive discrete strain sensor, or a multi-parameter distributed sensor with high discrimination accuracy. They are also more cost effective than the sensors using specialty SMF fibers.
2. Discrete FMF sensor
Discrete sensing in SMFs can be realized by interferometric sensors which have been widely studied for years. The interference pattern can be generated from signals in the same polarization but different paths, or signals in two orthogonal polarizations with birefringence , e.g., using a high birefringence (Hi-Bi) single mode PMF. For FMF, especially a polarization-maintaining FMF (PM-FMF), the interference could happen between both the polarization and spatial modes, known as the polarimetric and intermodal interference . Similar to a PMF, a PM-FMF is sensitive to external perturbations such as the temperature and strain. The responses of polarimetric and intermodal interference to the external perturbations in a PM-FMF are normally very different , which can be utilized for discrimination of multiple parameters.
To compare the performance of FMF based discrete sensor with a SMF based counterpart, we first characterize the temperature response of polarimetric interference in the FMF. It is known that the polarimetric interference can be simply generated by a Sagnac loop interferometer (SLI) using a single-mode PMF, which has attracted a lot of interest recently due to its simple structure and environmental robustness [2, 3]. Similarly, we build a SLI using a PM-FMF, and the experimental setup is shown in Fig. 1. The interfered pattern between the two polarizations of LP01 mode in the PM-FMF is given by 
In this experiment, we use a 10-m PANDA fiber (PM2000, THORLABS) as the sensing fiber which has a core diameter of 7.0 µm and cladding diameter of 125 µm. The second mode cut-off wavelength is at 1720 ± 80 nm. The beating length is 5.2 mm and the attenuation is < 11.5 dB/km @ 1950 nm. When operating at 1550 nm window, it becomes a bi-modal PM-FMF that supports two spatial modes: LP01 and LP11 even mode (LP11e), while the LP11 odd mode (LP11o) is intentionally cut-off. The light source is a broadband amplified spontaneous emission (ASE) source generated from an erbium doped fiber amplifier (EDFA). The broadband light passes through an isolator to remove the influence of back-reflection to the EDFA, and is split into two paths by a conventional 3-dB SMF coupler. The upper and lower paths of the 3-dB SMF coupler are connected with the PM-FMF using center launch technique so as to generate only the fundamental (LP01) mode. The output of the interferometer is connected to a high resolution ( = 0.16 pm) optical spectrum analyzer (OSA). To measure the temperature dependence of the PM-FMF based SLI, the PM-FMF is placed in a water bath with digital proportional-integral-derivative (PID) control and liquid crystal display (LCD) with sensor to monitor the temperature. We record the power spectra of the output of interferometer at different temperatures ranging from 30 °C to 70 °C with a step size of 1 °C. Some of the measured power spectra around 1550 nm are shown in Fig. 2(a). As can be seen, the wavelength spacing between two transmission minima is ~0.667 nm, and the extinction ratio is about 12.1 dB at the transmission minimum located at 1550 nm. We then replace the PM-FMF with a typical single-mode PANDA type PMF (AFW Technologies, DGD = 1.3 ps/m) that has a same fiber length (10 m), and measure again the temperature response for comparison. We calculate the wavelength shift of the minimums as a function of temperature, as shown in Fig. 2(b). The measured temperature coefficient is −1.72 nm/°C for PM-FMF, which is comparable with that of conventional PMF (−1.25 nm/°C). The slightly improved temperature sensitivity of PM-FMF is mostly attributed to the smaller polarimetric birefringence Bxy than that of the conventional PMF.
As was described earlier, intermodal interference could also happen between the spatial modes in a FMF, which makes a FMF based sensor. The intermodal interferometer sensor has the same sensitivity equations (Eqs. (1)-(4)) as the SLI sensor, except that the birefringence factor now becomes the modal birefringence between two spatial modes i and j (e.g., LP01 and LP11 mode), for example, or if the input light is aligned with x- or y-polarization in the PM-FMF. We build an intermodal interferometer sensor to demonstrate the intermodal interference response of the PM-FMF. The experimental setup is shown in Fig. 3. Similar as in Fig. 1, the light source is the same broadband ASE generated from an EDFA. The SMF that carries the ASE light is coupled to one end of the PM-FMF using free-space fiber coupler and offset launch technique so as to generate both the LP01 and LP11 mode. The offset axis is aligned with the fast axis of the PM-FMF so as to generate LP11e mode. The power distribution between LP01 and LP11 mode is determined by the offset distance, and we adjust the offset so that LP01 and LP11 mode has equal power. The other end of the PM-FMF is coupled to another SMF using free-space fiber coupler that is connected to the high resolution OSA. The offset axis is also aligned with the fast axis of the PM-FMF and the offset distance is adjusted where both LP01 and LP11 mode can be received and the optical power reaches maximum. With the same temperature range and step as in Section 2.1 we measure the transmission spectra of the PM-FMF intermodal interferometer under different temperatures, some of which are as shown in Fig. 4(a) and Fig. 4(b). The wavelength shift of the minima as a function of temperature is shown in Fig. 4(c). The input polarization is aligned with the slow- (x-pol) or fast-axis (y-pol) of the PM-FMF at the input port by a film linear polarizer which is placed between the two collimating lenses in the free-space fiber coupler. The measured temperature coefficient is 0.123 nm/°C for LP01x-LP11x mode, and 0.091 nm/°C for LP01y-LP11y mode, respectively. Compared with the polarimetric interferometer based on the same PM-FMF, intermodal interferometer shows much less sensitivity, whose temperature coefficient is only 7% (LP01x-LP11x) and 5% (LP01y-LP11y) of that of the polarimetric interferometer (LP01x-LP01y). This much less sensitivity is potentially attributed to the larger modal birefringence than that the polarimetric birefringence in a PM-FMF(). It implies that our PM-FMF based intermodal interferometer is temperature insensitive. The temperature coefficient also change signs for the polarimetric and intermodal interference.
On the other side of strain sensing, we carried out another experiment by installing the fiber on a fiber stretcher, and pull the fiber in longitudinal direction. The shift of the minimum against applied axial strain is shown in Fig. 5. We find that that the strain coefficient is 1.97 pm/με for intermodal interference between LP01x and LP11x mode, and 0.98 pm/ με for the intermodal interference between LP01y and LP11y mode, sensor. The strain coefficients are comparable with a special-designed PM-PCF based strain sensor (~2.8 pm/με) , showing high strain sensitivity. Due to the fabrication process compatible with single-mode PMF, the PM-FMF based intermodal interferometer may potentially be a cost-effective solution as a temperature-insensitive strain sensor. Compared with the multimode fiber (MMF) based intermodal interferometer which supports hundreds of spatial modes, the proposed FMF intermodal interferometer can selectively launch high extinction ratio LP01 and/or LP11 mode into the sensing fiber without any crosstalk from other spatial modes, leading to high measurement accuracy and stability.
3. Distributed FMF sensor
3.1 Principle of Brillouin distributed sensor
Brillouin scattering, or stimulated Brillouin scattering (SBS) has been well known and studied for single mode fibers (SMFs). For FMFs, because many spatial modes can be involved, the SBS effect can take place not only in a same spatial mode but also between different spatial modes [15, 16], which is denoted as the intra- and inter-modal SBS. As a generalized form, we define the concept Brillouin scattering in a FMF as follows, when a (pump) light in wavelength and mode is propagating through a FMF, due to the interaction between the light photons and acoustic phonons, a fraction of the light will be backscattered. The scattering effect can happen spontaneously (known as the spontaneous Brillouin scattering) in which the acoustic phonons are generated from thermal fluctuations. By contrast, as the optical power gets higher, the acoustic phonons are generated mostly from the optical field of the propagating light, leading to a stimulated effect which is known as the SBS. In both cases, the scattered light will experience a frequency downshift (Stokes) due to the Doppler shift associated with the moving grating by the acoustic wave, which depends on the acoustic velocity and is given by 
Since the forward and backward direction are the only relevant directions in a SMF, the SBS only occurs in the backward direction in SMFs, although spontaneous Brillouin scattering can occur in forward direction due to the guided nature of acoustic waves, which is known as the guided-acoustic-wave Brillouin scattering. Furthermore, when another pump light is counter-propagating along the fiber, which is in the same mode i and is frequency downshifted from the pump light by , the counter-propagated light will be amplified which is called the Brillouin gain, and an acoustic wave (or so-called BDG) is also built up . This effect is commonly known as the intra-modal SBS. If the counter-propagating light with wavelength is sent through another mode , inter-modal SBS may happen. The frequency shift will be related to the ERIs of both spatial modes based on the phase-matching condition, given by 12]. Because the acoustic velocity in a silica fiber is temperature and strain dependent, we can fabricate a Brillouin sensor for temperature and/or strain based on the BOTDA technique. Using temperature as an example, for intra-modal SBS, the temperature dependence of BFS can be derived from Eq. (6) and is given byEq. (7) and is given by
3.2 Experimental setup
In order to characterize SBS in arbitrary spatial modes including both the intra- and inter-modal SBS, we build a reconfigurable few-mode Brillouin optical time domain analyzer (FM-BOTDA). The fiber under test (FUT) is a 3-km custom-designed circular-core five-mode fiber (c-5MF). It has a step-index profile between core and cladding and supports five spatial modes, LP01, LP11a, LP11b, LP21a and LP21b mode at 1550 nm. The fiber parameters are summarized in Table 1. In order to generate SBS in arbitrary spatial modes, the pump or probe wave which is sent through the fundamental mode in the SSMF is converted to one of the supported spatial modes and launched into the 5MF using a free-space mode multiplexer (MMUX), as shown in Fig. 6(a). The MMUX can also be a mode de-multiplexer (MDMUX) if the signal is launched through the opposite direction. To maximize the system flexibility and to make the mode conversion reconfigurable, four liquid crystal on silicon (LCOS) based spatial light modulators (SLMs) are used in the MMUX for mode generation. Unique phase patterns can be programmed onto the SLMs, and the relationship between the SLM phase patterns and the spatial modes as shown in Fig. 6(b).
The setup of our FM-BOTDA is shown in Fig. 7. A 1550 nm external-cavity laser (ECL-1) is used as the light source. Continuous-wave (CW) from ECL-1 is divided into three paths by two 3dB single-mode fiber couplers. The signal flow on each path is as follows:
- 1. CW light in upper path (pump-1) is modulated by an acousto-optic modulator (AOM) driven by a 2-channel arbitrary function generator (AFG), which generates 30 ns Gaussian pulse with 5-kHz repetition rate. After amplification by an erbium-doped fiber amplifier (EDFA), the pulsed pump wave is then selectively converted to a specific spatial mode, and finally fed into the FUT through a mode multiplexer (MMUX-1).
- 2. CW light in middle path (pump-2) is modulated by an intensity modulator (IM) driven by a RF synthesizer. The IM is biased at null point so that a double-sideband (DSB) signal is obtained (frequency @ + νF and – νF). The DSB signal then passes through a tunable optical band-pass filter (OBPF) to remove lower sideband (νF). The single sideband signal is then amplified by an EDFA, selectively converted to a specific spatial mode, and finally fed into the FUT in the opposite direction through another mode multiplexer (MMUX-2).
- 3. CW light in lower path (LO1) is used for providing local oscillator (LO) to the 6 × 6 coherent receiver.
For BGS measurement, the Brillouin amplified signal in pump-2 is de-multiplexed reciprocally by MMUX-1 onto three paths, and converted back to LP01 modes by the subsequent MCs and MSs. The three de-multiplexed optical signals are then directed by three optical circulators (OCs) and fed into a 6 × 6 coherent receiver. The receiver has 6 optical hybrids and 12 balanced PDs with 3-dB bandwidth of 15 GHz. Finally, the 12 tributaries of electrical signal comprising the in-phase and quadrature components of all the modes and polarizations are sampled by three Tektronix digital oscilloscopes with sampling rate of 25-GSa/s. The three oscilloscopes are synchronized and triggered by the AFG so that distributed measurement is enabled. For BDG measurement, we introduce another tunable external-cavity laser (ECL-2) to generate probe wave with wavelength at . The CW from ECL-2 is divided into two branches: the upper branch is modulated with another EOM driven by the same AFG (30 ns Gaussian pulse, 5-kHz repetition rate) to provide pulsed probe wave. The probe wave is then amplified, converted to LP11a mode, and fed into the FUT in the same direction as pump-1 through MMUX-1. The lower branch (LO2) is used for providing LO to the 6 × 6 coherent receiver. The choice of LO depends on which scheme the FM-BOTDA is operating. For BGS scheme LO1 (provided by ECL-1) is used to detect the amplified pump-2 wave, and for BDG scheme LO2 (provided by ECL-2) is used to detect the BDG reflected probe wave. It is also possible to simultaneously detect BGS and BDG providing there are enough coherent receivers. Since the SBS efficiency depends on the state of polarization (SOP) of the two pump waves, we align the SOP of the two pump waves at the input end of pump-1 to maximize the SBS efficiency.
3.3 Results and discussion
We first measure the BGS of the c-5MF under room temperature (25°C) and without axial strain. Pump-1 and pump-2 (serving as probe) in different spatial modes are into the FUT by programming the SLM with different phase patterns. The pump (pump-1) power is 10 mW and the probe (pump-2) power is 1mW. To efficiently generate SBS, we set the center frequency of RF synthesizer νF at 10.5 GHz (≈νB). The BFS is roughly pre-estimated from spontaneous Brillouin scattering.
In each analysis, we scan over a ± 250 MHz frequency range with a step-size of 2 MHz. The signal trace is recorded twice for each frequency and processed offline with MATLAB program. The digital signal processing (DSP) in our program includes the following procedure: (1) IQ imbalance compensation; (2) Fast Fourier Transform (FFT) to get spectrum; (3) Peak search in the vicinity of νF; (4) BGS composition; and (5) Lorentzian curve fitting. The sampling rate of Tektronix oscilloscopes is set at 25GSa/s and the recorded timing length is 40 μs (1 × 106 sample points), which is equivalent to the roundtrip delay of a 4-km fiber. The spectra of received signal are smoothed over 1MHz (10 points) and averaged 2 times to reduce the noise. Figure 8 shows the received probe signal in time and frequency domain. The triangle-like shape is the amplified probe (pump-2) signal due to the Brillouin gain, and the left toggle denotes the time when the pump is coupled into the c-5MF. The trace before toggle shows the probe signal without Brillouin gain or SBS effect (w/o SBS), and trace after toggle shows the probe signal with Brillouin gain or SBS effect (w/ SBS). Consequently, we can accurately measure the distributed BGS by calculating the differential gain spectrum. The proposed method also makes our analysis immune to most system variations. The measured BGS for c-5MF at various distances is shown in Fig. 9. The BGS is then fit to a Lorentzian, so that the center frequency ( = BFS) and full width at half maximum (FWHM) of the Brillouin gain are obtained. The results for pump-probe in different mode pairs at 100-m length of the c-5MF are summarized in Table 2.
We then measure the temperature and strain coefficients of the c-5MF with intra-modal SBS. We choose a 1.18-m fiber segment in the FUT to apply the temperature or strain. We first place the fiber segment into the water bath. We measure the BGS under room temperature (25 °C), and then increasing the temperature from 30 to 90 °C with 10 °C per step while measuring the BGS on each temperature step. After the analysis of temperature sensitivity, we then take the fiber segment out of the water bath, and install it onto a fiber stretcher. The fiber stretcher can apply axial strain by pulling the fiber through linear movement with 1 µm resolution. We measure the BFS on each 0.25 mm step (211.86 µε). The measured BFS as a function of absolute strain or temperature for LP01 mode and LP11 mode are shown in Fig. 10 and Fig. 11. By linear curve fitting, the coefficients are found to be 1.01690 MHz/°C and 0.05924 MHz/µε for LP01 mode, and 0.99099 MHz/°C and 0.04872 MHz/µε for LP11 mode, respectively. We can see that the temperature and strain coefficients are different for the two spatial modes, which means that we can use these coefficients to discriminate temperature and strain following the same equation in . Simultaneous measurement of more parameters is also possible by characterizing more spatial modes. Therefore our proposed FMF can be used as a unique multi-parameter sensor.
We have introduced two novel FMF based optical sensors utilizing the information from spatial dimension. The temperature and strain coefficients of the two FMF sensors are characterized. With the availability of high reliability few-mode devices and advance of fiber-optic technology such as SDM and coherent detection, FMF may have great potential in future fiber sensing systems.
References and links
1. B. Lee, “Review of the present status of optical fiber sensors,” Opt. Fiber Technol. 9(2), 57–79 (2003). [CrossRef]
2. Y. Liu, B. Liu, X. Feng, W. Zhang, G. Zhou, S. Yuan, G. Kai, and X. Dong, “High-birefringence fiber loop mirrors and their applications as sensors,” Appl. Opt. 44(12), 2382–2390 (2005). [CrossRef] [PubMed]
3. X. Dong, H. Y. Tam, and P. Shum, “Temperature-insensitive strain sensor with polarization-maintaining photonic crystal fiber based Sagnac interferometer,” Appl. Phys. Lett. 90(15), 151113 (2007). [CrossRef]
4. J. Villatoro, V. Finazzi, V. P. Minkovich, V. Pruneri, and G. Badenes, “Temperature-insensitive photonic crystal fiber interferometer for absolute strain sensing,” Appl. Phys. Lett. 91(9), 091109 (2007). [CrossRef]
5. A. Li, A. Al Amin, X. Chen, and W. Shieh, “Transmission of 107-Gb/s mode and polarization multiplexed CO-OFDM signal over a two-mode fiber,” Opt. Express 19(9), 8808–8814 (2011). [CrossRef] [PubMed]
6. 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). [CrossRef]
7. 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). [CrossRef] [PubMed]
8. 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). [CrossRef] [PubMed]
10. A. M. Vengsarkar, W. C. Michie, L. Jankovic, B. Culshaw, and R. O. Claus, “Fiber-optic dual-technique sensor for simultaneous measurement of strain and temperature,” J. Lightwave Technol. 12(1), 170–177 (1994).
11. W. Zou, Z. He, and K. Hotate, “Complete discrimination of strain and temperature using Brillouin frequency shift and birefringence in a polarization-maintaining fiber,” Opt. Express 17(3), 1248–1255 (2009). [CrossRef] [PubMed]
12. Y. H. Kim and K. Y. Song, “Mapping of intermodal beat length distribution in an elliptical-core two-mode fiber based on Brillouin dynamic grating,” Opt. Express 22(14), 17292–17302 (2014). [CrossRef] [PubMed]
13. A. Li, Q. Hu, and W. Shieh, “Characterization of stimulated Brillouin scattering in a circular-core two-mode fiber using optical time-domain analysis,” Opt. Express 21(26), 31894–31906 (2013). [CrossRef] [PubMed]
14. W. J. Bock and T. A. Eftimov, “Polarimetric and intermodal interference sensitivity to hydrostatic pressure, temperature, and strain of highly birefringent optical fibers,” Opt. Lett. 18(22), 1979–1981 (1993). [CrossRef] [PubMed]
16. A. Li, Q. Hu, X. Chen, B. Y. Kim, and W. Shieh, “Characterization of distributed modal birefringence in a few-mode fiber based on Brillouin dynamic grating,” Opt. Lett. 39(11), 3153–3156 (2014). [CrossRef] [PubMed]
17. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).