Distributed refractive index sensing based on tapered fibers in optical frequency domain reflectometry

Zhenyang Ding; Keliang Sun; Kun Liu; Junfeng Jiang; Di Yang; Zhe Yu; Jing Li; Tiegen Liu

doi:10.1364/OE.26.013042

1. Introduction

Refractive index (RI) sensors have been widely applied in the fields of chemical and biological applications [1]. Optical fiber RI sensors has been a growing interest in a range of sensing applications due to their well-known advantages such as intrinsic electrical isolation, immunity to electromagnetic interference, compactness, high sensitivity, wide bandwidth and multiplexing capabilities [2]. To date, many different optical fiber RI sensors have been developed based on fiber Bragg grating (FBG) [3], long period fiber grating (LPFG) [4,5], tilted moiré FBG [6], macro-bending optical fiber [1, 7–10], surface plasmon resonance (SPR) [11], photonics crystal fiber [12], Fabry-Perot interferometer [13–16], thin core fiber based sensor [17], in-fiber Mach-Zehnder interferometer [18–21], microsphere resonator [22], optical ring resonator [23], microfiber coil resonator [24] and single-mode–multimode–single-mode (SMS) fiber [25–27], respectively.

Tapered fiber is an ideal sensing medium for RI sensing. Tapered fiber is usually fabricated by heating and stretching an optical fiber to reduce its diameter. Tapered fiber stimulates the cladding mode to enhance the evanescent optical field that modified by the external environment medium. The multimodal interference occurs between the cladding and the fundamental modes, which can be used to detect RI of external environment. Several structures of RI sensor based on tapered fiber have been developed as follow: Villatoro et al. present an optical fiber RI sensor based on the transmission losses caused by the external environment medium in a cladded multimode tapered fiber [28]. Hernández et al. present a cladded multimode tapered fiber with a mirrored end as RI sensor [29]. Ding et al. present a RI sensor based on a long-period grating pair with a fiber-taper section in between [30]. Ji et al. present a RI sensor based on non-adiabatic microfiber with a taper diameter of few micrometers [31]. Lu et al. present a RI sensor based on a tapered plastic optical fiber [32].

The traditional optical fiber RI sensors are single-point sensors [1–32], which is difficult to realize distributed sensing or multiplexing. The distributed RI sensing is imperative for some applications that cannot be achieved by the traditional single-point RI sensors. For example, a distributed RI sensor can detect a diffusion process in a solution. It also can locate the partitioning of different chemical substances in a solution. A distributed RI sensor has potential for realizing for applying to many fields such as monitoring of oil/gas pipelines, safety checking of marine ships and quality inspection in chemical industry. As the optical fiber sensor has the characteristics of corrosion resistance, the chemical reaction process, the diffusion and distribution of fluid or gas can be monitored in real time. In 1998, Froggatt et al. present a distributed strain and temperature measurements method with a millimeter level spatial resolution using the optical frequency shifts of Rayleigh backscattering spectra (RBS) in a single mode fiber (SMF) by optical frequency domain reflectometry (OFDR) [33, 34]. Rayleigh backscattering is caused by random refractive index fluctuations along a SMF, and it can be modeled as a long, weak Fiber Bragg grating (FBG) with random periods. The strain or temperature variation results in a local RBS optical frequency shifts, which can be measured by a cross-correlation between the measurement RBS and reference RBS. Du et al., for the first time, present a distributed RI sensor based on RBS and macro-bending SMF in OFDR [35]. However, there are some drawbacks in this sensor. First, this is not a truly distributed sensor but a quasi-distributed or a multiplexing sensor, because it can only sense where bending structures fabricated on the fiber under test (FUT). The bending structures are discrete on FUT, so FUT is not a continue sensing region. Second, more bending structures can result in much stronger bending loss, which could limit the number of bending structures on FUT due to a finite dynamic range in OFDR. In [35], two bending structures are set on FUT, so there are only two effective sensing points. Third, the RI sensitivity of this sensor is not very high about 20 nm/RIU [35]. Whereas, in a RI sensing based on tapered fiber, the length of a tapered section on FUT can be pulled to several centimeters using a small-scale fiber-tapering device. Some advanced tapering technologies can control the loss of the tapered fiber down to 0.1 to 0.01 dB/mm [36, 37]. The tapered fiber as the sensing medium has a potential to achieve a continuously distributed RI sensing along with a tapered section on FUT. In addition, the back-reflected light carrying with interferogram due to the multimodal interference in the tapered section on FUT will be much stronger than Rayleigh backscattering in a macro-bending SMF, because the back-reflected light contains of Fresnel reflection at the environment medium-cladding interface. If we use OFDR to demodulate the optical frequency shifts of the back-reflection spectra in a tapered fiber, it is hopeful to realize a truly distributed RI sensing with a better performance than the macro-bending fiber based method [35].

In this paper, we present a distributed RI sensor using tapered fibers in OFDR. The tapered fibers can be easily fabricated by pulling it at the softening temperature, and its diameter can be decreased to several micrometers. We do theoretical and numerical analysis of distributed RI sensing based on the tapered fiber in OFDR. We detect RI of an external medium surrounding a tapered fiber by measuring the optical frequency shifts of the local back-reflection spectra using OFDR. By a local back-reflection spectra interpolation, we can increase the measurement resolution of RI without decreasing the spatial resolution. In our experiment, we realize a truly distributed RI sensing with a 4.25 mm spatial resolution in a continuous tapered section with a length of 2.1 cm. We calibrate the relationship between the local optical frequency shifts of the back-reflection spectra and RI. The RI ranges from 1.3574 to 1.3686 and the sensitivity of our presented sensor is about 8565 GHz/RIU (68.52 nm/RIU), which is about three times enhancement compared with the macro-bending fiber based method [35]. To verify the capability of distributed RI sensing using the presented method, we also measure RI variation in a glycerol solution diffusion process. Whereas, the previous single-point or quasi-distributed RI sensors [1–32, 35] cannot locate a RI variation at a millimeter level.

2. Measurement principle and simulation

2.1 Principle of distributed RI sensing

To realize a distributed RI sensing using a tapered fiber, we need to balance the loss of tapered fiber and the RI sensitivity. If it matches the absolutely adiabatic condition, the tapered fiber will has no loss and cannot be used for RI sensing. At the same time, to realize a distributed sensing, we need to avoid that a serious loss occurs in the tapered section. The model of the tapered fiber we used is nonadiabatic. In this model, the transition section is not completely matched the adiabatic condition, some high-order modes can be excited, but the significant high-order mode is HE₁₂. The part of the light guided in the tapered section of FUT will generate the evanescent optical field around the tapered section. The first modes HE₁₁ and HE₁₂ in the tapered section and propagate the environment medium-cladding interface. The intermodal interference between HE₁₁ and HE₁₂ along the tapered section occurs and generates intermodal interference, which are sensitive to environmental RI changes. The phase difference of HE₁₁ and HE₁₂ can be given by [31,38]:

Φ = Δ β L,

where Δβ is the difference between propagation constants of two modes and L is the coupling length. Δβ can be modified by a various RI of environment medium, which can be expressed as:

Δ β = \frac{c (U_{2}^{\infty 2} - U_{1}^{\infty 2})}{4 π n_{c} ρ^{2} ν} \exp (- \frac{2}{V}),

where V is the normalized frequency that can be expressed as:

V = \frac{2 π ρ ν}{c} \sqrt{n_{c}^{2} - n_{e}^{2}},

c is the velocity of light.

ν

is the optical frequency,

ρ

is the radius of the taper waist, n_c is the refractive index of the cladding in the tapered fiber and n_e is the refractive index of environment medium.

U_{1}^{\infty}

and

U_{2}^{\infty}

are the asymptotic values of the U parameters of the HE₁₁ and HE₁₂.

In the previous methods [1–32], the intermodal interference information can be acquired by the transmission light. Whereas, the back-reflected light will also be coupled into the tapered section and carry the intermodal interference information, which also can be used for RI sensing [35]. The back-reflected light contains Rayleigh backscattering and Fresnel reflection at the environment medium-cladding interface. In this model of the tapered fiber, the most part of back-reflected light comes from the fundamental fiber mode HE₁₁. A little part of back-reflected light carries the intermodal interference information, which still can be used for RI sensing. The RI of environment medium variation $δ n_{e}$ can cause the spectral shift of the local back-reflected spectra. The phase of the local back-reflected spectra carrying the intermodal interference information can be expressed as $Φ (ν_{0}, n_{e 0})$ . $ν_{0}$ is the initial optical frequency and $n_{e 0}$ is the initial refractive index of environment medium. The phase due to the variation of $δ n_{e}$ and the optical frequency shift can be expressed as $Φ (ν_{0} + δ ν, n_{e 0} + δ n_{e})$ , where $δ ν$ is the optical frequency shift of the local back-reflected spectra carrying the intermodal interference information. The shift of local back-reflected spectra caused by RI variation can be given by this equation:

Φ (ν_{0}, n_{e 0}) = Φ (ν_{0} + δ ν, n_{e 0} + δ n_{e}) .

Submit Eq. (1), (2) and (3) into (4). The detail derivation is shown in Appendix A. The relationship of

n_{e}

and

δ ν

can be obtained by:

n_{e} = δ n_{e} + n_{e 0} = \sqrt{n_{c}^{2} - {[\frac{c (ν_{0} - δ ν)}{π ρ ν^{2} \ln (\frac{ν_{0} - δ ν}{ν_{0}}) + \frac{c ν_{0}}{\sqrt{n_{c}^{2} - n_{e 0}^{2}}}}]}^{2}} .

Assuming that RES is the ratio of the optical frequency shifts of the local back-reflection spectra and RI variation, namely RI sensitivity. Based on Eq. (5), RES can be obtained from the slope of the linear fitting curve of

n_{e}

and

δ ν

.

2.2 Principle of demodulating the local back-reflection spectra shifts

Here we use OFDR to demodulate the optical frequency shifts of the local back-reflection spectra in the tapered fiber, which is similar to that of the distributed strain and temperature sensing based on the RBS shift in SMF by OFDR [33,34].

The signal processing procedure in our system is as follows:

(1) Operating OFDR system two times to acquire two optical frequency domain signals in various RIs. One is considered as the reference signal and the other is considered as the measurement signal.
(2) Transforming the measurement and reference signals from the optical frequency domain to the spatial domain by a Fast Fourier transform (FFT).
(3) Dividing the total FUT to several sections with a ΔX length that contains N data points as the spatial local back-reflected light signals. ΔX is the effective sensing spatial resolution, which can be given by: $Δ X = N Δ Z,$
where
$Δ Z = c / 2 n Δ ν .$
ΔZ is the spatial resolution of one data point, n is the refractive index of FUT, and Δν is the optical frequency tuning range of the TLS.
(4) Padding M zeros for local back-reflected light section in the spatial domain and length for each section is changed to be M + N.
(5) Transforming each local back-reflected light, by an inverse FFT back to the optical frequency domain, namely the local back-reflection spectra.
(6) Operating the cross-correlation of the local reference and measurement back-reflection spectra. The optical frequency shifts of the local back-reflection spectra can be measured by the shifts of cross-correlation peak, which reflects RI variation. The optical frequency measurement resolution in the system can be given by: $δ n_{\min} = Δ v / M + N,$
The minimal measurable RI variation δn_min can be obtained with:
$δ n_{\min} = δ ν_{\min} / R E S = Δ ν / [R E S (M + N)] .$
Substituting Eq. (6) and (7) into (9), we can obtain a clearer expression of the relationship of δn_min and ΔX:
$δ n_{\min} = \frac{c}{2 n Δ X \cdot R E S \cdot (\frac{M}{N} + 1)} .$
When we pad no zeros for local back-reflected light signals in the spatial domain as M = 0, Eq. (10) can be expressed as:
$δ n_{\min} = \frac{c}{2 n Δ X \cdot R E S} .$
Comparing with Eq. (10) and (11), we need to decrease the value of δn_min by increasing the value of $Δ X$ in the condition that RES is a constant based on Eq. (10). Namely, if we want to improve δn_min, we need to sacrifice $Δ X$ (increase ΔX) as shown in Eq. (11) without any zero padding. When we pad M zeros in the local back-reflected light section at the spatial domain, we can decrease the value of δn_min without changing ΔX and N based on Eq. (10). Namely, we can improve δn_min without sacrificing ΔX.

The local back-reflection spectra for the cross-correlation calculations contain not only the part generated form the intermodal interference, but also the part only generated form the fundamental mode. In this model of the tapered fiber, the most part of back-reflected light comes from the fundamental fiber mode. The local back-reflection spectra contributed by the fundamental mode will not shift when the RI of environment medium occurs variation. As this offset effect in the cross-correlation calculations, the actually RI sensitivity ARES is much lower than RES acquired by Eq. (5).

A R E S \approx η R E S,

where

η

is the ratio of the high-order mode optical power in the tapered fiber. This offset effect in the cross-correlation calculations for local back-reflection spectra also occurs in the distributed RI sensing based on the macro-bending fiber in OFDR. As the fundamental mode also dominate in the local back-reflection spectra of the macro-bending fiber, the RI sensitivity is much lower than the single point RI sensors based on macro-bending fiber [35].

2.3 Simulation of RI sensitivity

Based on Eq. (5), assuming that $ν_{0}$ = 1.9723 × 10⁵ GHz (1520 nm), $n_{e 0}$ = 1.3574, $ρ$ = 2.15 μm and the maximum of $δ ν$ is 9400 GHz, the relationship between n_e and $δ ν$ are simulated as shown in Fig. 1 (a). RES is 8.4 × 10⁵ GHz/RIU acquired from the slope of the linear fitting curve of $n_{e}$ and $δ ν$ . The different values of $η$ as a function of the taper waist diameters have been simulated in Ref [31]. Based on the simulation results in [31], $η \approx 0.01$ , when the diameter of the taper waist is about 4 μm, so the simulated ARES $\approx$ 8400 GHz/RIU based on Eq. (12). We also simulate RI sensitivities in different diameters of the taper waist as shown in Fig. 1(b). A smaller diameter of the taper waist can result in a higher RI sensitivity.

Fig. 1 (a) The simulated results of the relationship between the refractive index of environment medium and the local back-reflection spectra shift when the diameters of the taper waist is about 4.3 μm. RI sensitivities can be obtained from the slope of linear fitting curve. (b) The simulated results of RI sensitivities in different diameters of the taper waist.

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3. Experiments and discussions

3.1 Experimental setup

The experimental setup for distributed RI sensing based on OFDR is shown in Fig. 2. The tuning range, tuning rate, and starting wavelength of the tunable laser source (TLS, Keysight 81607A) are 6 × 10³ GHz (48 nm), 1 × 10⁴ GHz/s (80 nm/s), and 1520nm, respectively. The light from the TLS is separated into the main and auxiliary interferometers by a 1: 99 coupler. The 1% light is led to an auxiliary Michelson interferometer that provides an external clock (f-clock) to trigger the data acquisition to sample the main interference signals at equidistant optical frequency points. The delay fiber of this auxiliary interferometer is 125 m. Two Faraday rotating mirrors can make the auxiliary interferometer polarization insensitive. The 99% light is led to the main Mach-Zehnder interferometer. The measurement path of the main interferometer is composed of FUT with a tapered fiber. The tapered fiber section is immersed in a tank with glycerol solution. The length of FUT is about 4.26 m.

Fig. 2 Experimental setup for distributed RI sensor using tapered fibers in OFDR. TLS is tunable laser source, FRM is Faraday rotating mirror; PC is polarization controller; BPD is balanced photo detector; DAQ is data acquisition card; FUT is fiber under test. The tapered fiber is immersed in a tank with glycerol solution.

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We use a small-scale fiber-tapering device to fabricate the tapered fiber in this study. The raw fiber is a reduced-cladding single mode fiber (RC SMF) (YANGTZE inc., RC1017-F), whose cladding diameter is 80 μm and the coating diameter is 165 μm. The cladding in RC SMF is thinner than the standard SMF, so a RC SMF can be easily stretched to a longer uniform tapered section than a standard SMF. The RC SMF is fixed on the platform with V-shape groove by the magnetic absorption stages and the stages are pulled simultaneously to both sides during the heating process, as shown in Fig. 3. The length of fiber between the two stages is about 40 mm before stretching. The oxyhydrogen flame is used to heat the RC SMF to a softening state. Both ends of the stage stretch the RC SMF at a rate of 200 μm/s. To fabricate a tapered fiber with a uniform taper section, the flame is also driven to move back and forth, at the reciprocating rate of 360 μm/s. The total length of taper fiber is 140 mm after stretching, the elongation amount of the fiber is 100 mm and the diameter of the taper waist of the tapered fiber is 4.3 μm measured by a microscopy shown in Fig. 3. The taper shape in this experiment is a symmetry smooth taper and the schematic diagram of the taper shape is shown in Fig. 2. From the stimulation results in Fig. 1(b), a smaller diameter of the taper waist can result in a higher RI sensitivity. We also try to stretch the tapered fiber with a smaller diameter of the taper waist. As the limitations of our fiber-tapering technologies and devices, these attempts are unsuccessful. A diameter of 4.3 μm in the taper waist is the smallest based on our recent fiber-tapering technologies and devices. Some literatures report that the loss of the tapered fiber can be reduced to 0.1 to 0.01 dB/mm with the diameters of the taper waist of 50 nm [36, 37]. It is expected to achieve a smaller diameter tapered fiber with the improvement of our fiber-tapering technologies and devices.

Fig. 3 Configuration of small-scale fiber-tapering device. The RC SMF was fixed and clamp the fiber on the platform and they are pulled simultaneously to both sides during the heating process. The oxyhydrogen flame is also driven to move back and forth. The diameter of the taper waist section in the tapered fiber is 4.3 μm measured by a microscopy shown in the photography above.

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In this experiment, RI variation can be realized by changing the concentration of glycerol solution. The values of RI with 4 digit accuracy in different concentration of glycerol solution can be obtained from the table in [39]. In this table, the interval of the concentration is 2%. We use a linear interpolation to obtain the values of RI between the intervals. As the glycerol is difficult to diffuse uniformly in a low concentration of glycerol solution, we use an initial concentration of 20% glycerol solution, and add 100% glycerol into this solution to change its concentration. We measure the RIs ranging from 1.3574 to 1.3686 using our proposed senor corresponding to the concentration of glycerol solution ranging from 20% to 29%. In theory, our proposed senor also can measure the RI near water of about 1.3330.

3.2 Experimental results and discussion

Firstly, we show the spatial domain signals of the FUT in Fig. 4(a) and 4(b). This FUT, with the total length of 4.26 m. is fused from two parts. Form the fiber start to 2.8 m is standard SMF, and the rest is RC SMF, which contains the tapered section from 3.51 m to 3.54 m. The intensity of Rayleigh backscattering in the RC SMF is higher than that in the standard SMF. The back-reflected light in the tapered fiber is much higher than that in the RC SMF and standard SMF, because it’s mainly caused by the Fresnel reflection at the environment medium-cladding interface. The high signal-to-noise ratio (SNR) of the back-reflected light in the tapered fiber can achieve a better RI measurement sensitivity and sensing spatial resolution than the macro-bending fiber based method [35]. In addition, as the intensity of Rayleigh backscattering after the tapered fiber (from 3.54 m to the FUT end) is much lower than that before the tapered fiber section shown in Fig. 4(c) and 4(d), the tapered fiber cause a loss of about 20 dB. These two phenomenon verify that this tapered fiber don’t match the absolutely adiabatic condition and it belongs to be nonadiabatic. Comparing with the loss under the RI of the environment medium 1.3574 and 1.3686 shown in Fig. 4(a) and 4(c), the loss is basically unchanged with RI ranging from 1.3574 to 1.3686.

Fig. 4 Measured back-reflected light signals in the spatial domain for a FUT in the different RI of the environment medium. The tapered fiber is from 3.51 m to 3.42 m. (a) RI of the environment medium is 1.3574. (b) is local zoom of (a). (c) RI of the environment medium is 1.3686. (d) is local zoom of (c).

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In the experiment, the RI variation can be realized by changing the concentration of glycerol solution at the temperature of 25°C [39]. Based on the principle above, RI variation can result in the optical frequency shifts of the back-reflection spectra. We measure RI variation by the cross-correlation between the local measurement and reference back-reflection spectra shown in Fig. 5. The shift of the cross-correlation peak reflects the optical frequency shift of local back-reflection spectra. In this experiment, $Δ ν$ = 6 × 10³ GHz, so the ΔZ = 0.017 mm based on Eq. (7). We firstly set the data point number in the local section N = 250, so the sensing spatial resolution ΔX = 4.25 mm based on Eq. (6). When the RI variation δn_min = 0.0009 (RI varies from 1.3595 to 1.3604), the cross-correlation peak doesn’t shift in the condition of N = 250 shown in Fig. 5(a) and 5(c). The reason is that the optical frequency shifts of the back-reflection spectra caused by the RI variation δn_min = 0.0009 cannot be distinguished by the limited optical frequency resolution δν_min = 24 GHz based on Eq. (8) in the system.

Fig. 5 RI measurement based on the optical frequency shifts of the back-reflection spectra in the tapered fiber. Cross-correlation of measurement and reference of the back-reflection spectra with Δn = 0.0009 (RI ranges between 1.3574 and 1.3686). (a) Raw data with the length of N = 250. (b) Padding M = 500 zeros in the local back-reflected light segment in the spatial domain. (c) Local zoom area of (a) and (b). The cross-correlation peak shift one point (8 GHz) after a spectrum interpolation.

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To improve δν_min but not to deteriorate ΔX, we need to pad M zeros in the local back-reflected light signals section at the spatial domain to realize a local back-reflection spectra interpolation. When M = 500 and N = 250, δν_min can be improved to 8 GHz based on Eq. (8). In Fig. 5(b) and 5(c), the cross-correlation peak shifts one point (8 GHz) using the same raw data. As N is 250 as the same as the length of the raw data before the interpolation, we can improve δν_min and δn_min but don’t change ΔX. By the feature of this method, we can achieve a very high δν_min and δn_min without sacrificing ΔX. The extremum δν_min and δn_min will be finally limited to the wavelength repeatability of the TLS.

To obtain RI sensing experimental results of the total tapered section on FUT, we measure the optical frequency shifts of the back-reflection spectra in the tapered fiber as a function of distance at different RIs shown in Fig. 6(a). RI ranges from 1.3574 to 1.3686 by changing the concentration of glycerol solution. We stir the glycerol solution and make the total tapered section remain at the same concentration. In Fig. 6(a), the tapered section ranges from the location of 3.517 m to 3.538 m on FUT with six continuously effective sensing points at the effective sensing length of 2.1 cm. Their optical frequency shifts increase along with RI increasing. Especially, the optical frequency shifts of total six effective sensing points are equal at each RI variation steps, which represents the RI measurement sensitivity of total six effective sensing points are equal. To acquire RI measurement sensitivity of this proposed method in detail, we use the effective sensing points to fit a calibration curve between the back-reflection spectral shift and RI variation in Fig. 6(b). A linear fitting is applied to the calibration data. The optical frequency shifts of the back-reflected light and the RI has a good linear relationship, which R-squared is up to 0.9993. The RI sensitivity is the slope of the fitting line as 8565 GHz/RIU (68.52 nm/RIU) shown in Fig. 6(b). A good agreement is found between the simulated RI sensitivity and experimental RI sensitivity. This RI sensitivity is about three times enhancement compared with the macro-bending fiber based method [35].

Fig. 6 (a) Measured optical frequency shifts of the back-reflection spectra in the tapered fiber as a function of distance at various RIs. The optical frequency shifts of the tapered section increase along with RI increasing. (b) Measured optical frequency shifts of the back-reflection spectra as function of RI. The slope of the fitting line is the RI measurement sensitivity of this method.

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To verify distributed RI sensing capability based on the presented method, we use this method to detect a diffusion process in a glycerol solution. We drop the glycerol solution at one end in the tank and the glycerol will diffuse from one end to the other end of the tank over time. We record RI variation of the tapered fiber in a glycerol solution from the time of 0 s to 40 s. From Fig. 7, we could find that the RI changes from the one end of the tapered fiber to the other due to the glycerol solution diffusion. This capability of locating RI variation at a millimeter level using the presented distributed RI sensing method cannot be achieved by the previous single-point or quasi-distributed RI sensing methods [1–32, 35].

Fig. 7 Distance-time mapping trace of RI variation in a diffusion process of a glycerol solution. The glycerol will diffuse from one end to the other end in the tank over time. The RI variation also occurred from the one end to the other end of the tapered fiber over time.

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For the sensing spatial resolution of the presented sensor, if we want to improve the ΔX, we need to improve ΔZ or decrease the values of N based on Eq. (6). ΔZ is relate to the tuning range of TLS based on Eq. (7). A wider tuning range of TLS can result in a better ΔZ. The choice of the data points in the local section N is related to SNR of the cross-correlation between the measurement and reference of the back-reflection spectra. A smaller N will decrease the SNR of the cross-correlation and results in a greater measurement error of optical frequency shift. If the SNR of the back-reflected light in the tapered fiber increase, we can decrease the values of N further. At the condition of SNR in this system, N = 250 is the best by balancing between the sensing spatial resolution and measurement error. The ΔX = 4.25 mm in this system is better than the sensing spatial resolution of 1 cm in a commercial OFDR product (OBR 4600, LUNA, Blacksburg VA, USA) [40]. The reason is that the back-reflected light in the tapered fiber is much higher than that in the standard SMF shown in Fig. 4, we can still obtain a good SNR of the cross-correlation between the measurement and reference of the back-reflection spectra in a high sensing spatial resolution.

For the measurement distance of the presented sensor, the theoretical maximal measurement distance is a half of the delay fiber of this auxiliary interferometer based on the Nyquist theory. The delay fiber of this auxiliary interferometer in this system is 125 m. The theoretical maximal measurement distance is 62.5 m. We can increase the delay fiber of this auxiliary interferometer to achieve a longer measurement distance, which will be finally limited by the linewidth of TLS. The measurement distance of a commercial OFDR product (OBR 4600, LUNA, Blacksburg VA, USA) can be up to 2 km [40]. However, the measurement distance is only 2.1 cm using our presented sensor. As the limitations of our fiber-tapering technologies and devices, we cannot fabricate a tapered fiber with a longer length. In addition, the glass tapered fiber is fragile. In the future, a large-scale optical fiber drawing machines are used and the polymer optical fiber (POF) with the features of flexibility and elasticity is used as a tapered fiber, it could be pulled to several ten meters or hundred meters.

4. Conclusion

In this paper, we present a distributed RI sensor using tapered optical fibers in OFDR. The tapered fiber, as the sensing medium, is fabricated by heating and stretching the optical fiber to reduce its diameter. RI of the external medium surrounding the tapered fibers are measured by the optical frequency shifts of the back-reflection spectra using OFDR. By a spectrum interpolation, we can increase the measurement resolution of RI without sacrificing the sensing spatial resolution. In our experiment, we realize a truly distributed RI sensing with a 4.25 mm sensing spatial resolution in a 2.1 cm taper waist section. We calibrate the relationship between the back-reflection spectral shifts and RI. The sensitivity of our presented sensor is about 8565 GHz/RIU (68.52 nm/RIU) when RI ranges from 1.3574 to 1.3686. We also measure RI variation during the diffusion of the glycerol solution to verify the capability of distributed RI sensing based on the presented sensor.

As our optical fiber drawing is preliminary, in the future, we will attempt some advanced drawing technologies such as two-step drawing process, two transition process, modified flame-brushing technique, etc. to fabricate a low loss tapered fiber with a smaller diameters of the taper waist [36, 37, 41]. We also need to balance the loss and the RI sensitivity by the different drawing technologies further and obtain a longer RI measurement distance with a higher RI sensitivity. The distributed RI sensing in OFDR based on the tapered fiber has a potential to detect and locate some chemical or biological substances in a large-scale environment.

Appendix A

The detail derivation of Eq. (5) is shown in Appendix A:

Φ (ν_{0}, n_{e 0}) = Δ β (ν_{0}, n_{e 0}) L = \frac{c (U_{2}^{\infty^{2}} - U_{1}^{\infty^{2}})}{4 π n_{c} ρ^{2} ν_{0}} \exp (- \frac{2}{V}) L,

Φ (ν_{0} + δ ν, n_{e 0} + δ n_{e 0}) = Δ β (ν_{0} + δ ν, n_{e 0} + δ n_{e 0}) L = \frac{c (ν_{0} - δ ν) (U_{2}^{\infty^{2}} - U_{1}^{\infty^{2}})}{4 π n_{c} ρ^{2} ν_{0}^{2}} \exp (- \frac{2}{V_{1}}) L,

where

V = \frac{2 π ρ ν_{0}^{}}{c} \sqrt{n_{c}^{2} - n_{e 0}^{2}},

and

V_{1} = \frac{2 π ρ ν_{0}^{2}}{c (ν_{0} - δ ν)} \sqrt{n_{c}^{2} - {(n_{e 0} + δ n_{e})}^{2}} .

Submit Eq. (13), (14) into (4):

\frac{c (U_{2}^{\infty^{2}} - U_{1}^{\infty^{2}})}{4 π n_{c} ρ^{2} ν_{0}} \exp (- \frac{2}{V}) L = \frac{c (ν_{0} - δ ν) (U_{2}^{\infty^{2}} - U_{1}^{\infty^{2}})}{4 π n_{c} ρ^{2} ν_{0}^{2}} \exp (- \frac{2}{V_{1}}) L .

Take the logarithm of both sides of Eq. (17) and obtain Eq. (5).

Funding

National Natural Science Foundation of China (NSFC) (61505138, 61635008, 61475114, 61735011); Tianjin Science and Technology Support Plan Program Funding (16JCQNJC01800); China Postdoctoral Science Foundation (2015M580199, 2016T90205); National Instrumentation Program (Grant No. 2013YQ030915); National Key Research and Development Program (Grant No. 2016YFC0100500).

Acknowledgments

We thank Yonghan Zhou of The University of British Columbia for her technical assistance.

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Distributed refractive index sensing based on tapered fibers in optical frequency domain reflectometry

Abstract

1. Introduction

2. Measurement principle and simulation

2.1 Principle of distributed RI sensing

2.2 Principle of demodulating the local back-reflection spectra shifts

2.3 Simulation of RI sensitivity

3. Experiments and discussions

3.1 Experimental setup

3.2 Experimental results and discussion

4. Conclusion

Appendix A

Funding

Acknowledgments

References and links

Cited By

Figures (7)

Equations (17)

Optics Express