Abstract

A novel fiber-optic refractometer is proposed and demonstrated to achieve temperature- and axial strain-compensated refractive index measurement using highly sensitive outer-cladding modes in a tapered bend-insensitive fiber based Mach-Zehnder interferometer. Peak wavelength shifts associated with different spatial frequency peaks are calibrated to obtain a wavelength-related character matrix λMRI,T,ε for simultaneous measurement of multiple environmental variables. A phase-related character matrix ΦMRI,T,ε is also acquired by direct determination of refractive index, temperature, and axial strain induced phase shifts of the corresponding sensing modes.

© 2013 OSA

1. Introduction

Refractive index is an important sensing parameter in many applications [1]. Precise refractive index measurement is crucial in various areas such as process control in manufacturing industries, quality control in food industries, protection of ecosystems, biomedical and biochemical applications, etc. Fiber-optic refractometers have received a great deal of attention in recent years for their ability to detect small changes in the refractive index of an analyte, offering unique advantages such as immunity to electromagnetic interference, compact size, potential low cost and quasi-distributed remote operation [211]. Given that the refractive index of a material itself exhibits a dependence on temperature, refractive index sensing cannot be carried out reliably without simultaneous temperature measurement [12]. Optical fiber refractive index sensors generally also exhibit a high degree of cross-sensitivity to strain [13,14]. Therefore an ideal sensing device should be capable of measuring multiple parameters simultaneously. Earlier work on fiber-optic refractive index sensors with temperature compensation reported a tapered single-mode fiber based Mach-Zehnder interferometer [15], a cascaded optical fiber device of long-period grating and photonic crystal fiber modal interferometer [16], a surface long-period grating inscribed in a D-shaped photonic crystal fiber [17], a tapered bend-resistant fiber interferometer [18], and a hybrid configuration of a fiber Bragg grating and a long period grating [19]. Simultaneous three-parameter sensing has recently appeared in the literature, allowing simultaneous strain, temperature and vibration measurement [20,21], multiple parameter vector bending and temperature sensing [22,23], triaxial strain measurement [24], and temperature- and strain-independent torsion measurement [25] to be demonstrated. In particular, simultaneous measurement of refractive index and other parameters has also been reported by the use of polymer-coated fiber Bragg gratings [26], an etched-core fiber Bragg grating [27], and a tilted fiber Bragg grating [28], and a cascaded fiber long period and Bragg gratings [29].

In this paper, a novel fiber-optic refractometer is proposed using a tapered bend-insensitive fiber based Mach-Zehnder interferometer (BIF-MZI) configuration and a new temperature and axial strain compensation scheme is investigated. Refractive index, temperature, and axial strain calibrations are carried out for each outer-cladding mode and different sensitivities of various sensing modes are discussed. Wavelength-related and phase-related character matrices of the BIF-MZI are determined to demonstrate an effective method to measure multiple environmental parameters simultaneously.

2. Operation principle

The bend-insensitive fiber (ClearCurve, Corning) consists of a germanium-doped silica core and pure-silica cladding, having a structure similar to a standard single-mode fiber, except that numerous nano-scale gas filled voids are embedded in the cladding [30]. Figure 1(a) shows a Scanning Electron Microscopy (SEM) picture of the BIF cross-section where a narrow layer of randomly distributed air holes divides the cladding region into the inner-cladding and outer-cladding sub-regions. The proposed in-fiber interferometric sensor consists of a length of the BIF onto which a pair of abrupt tapers is fabricated, with the plastic coating between tapers removed to create a multi-parameter sensing zone, as shown in Fig. 1(b). The pristine BIF is designed to confine the energy in the fiber core region via reflection at the low-index trench and thus reduce its bending loss. Fiber tapering can drive the concentrated energy to propagate in the outer-cladding region of the modified BIF. Input light travels in the fundamental mode of the BIF until it reaches the first taper, where its energy is partially coupled to a number of cladding modes, while a large portion of the energy remains in the fundamental mode, which continues to propagate with negligible optical loss along the middle coating stripped section. Upon reaching the second taper, much of the cladding mode energy is coupled back to the fundamental mode, so that the device constitutes a tapered bend-insensitive fiber based Mach-Zehnder interferometer. The excited cladding modes may be classified into two categories, namely the inner-cladding modes (IC) and outer-cladding modes (OC), according to their respective mode field patterns. The former are characterized by mode-field distribution within the inner-cladding region due to total internal reflection made possible by the presence of the depressed-index trench, and the latter by mode-field sandwiched in the outer-cladding region between the depressed-index trench and the environmental air media.

 

Fig. 1 (a) A SEM cross-sectional image of the bend-insensitive fiber etched with 5% hydrofluoric acid solution for 2 minutes; (b) A schematic illustration of the tapered bend-insensitive fiber based Mach-Zehnder interferometer under various external disturbances with an inset of the abrupt taper picture.

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The optical path length (OPL) difference between the fundamental mode of LP01 and a given cladding mode of LPij propagating through an interferometer of length L at operation wavelength λ leads to a phase difference given by

ΔΦij=Φ01Φij=2πLλ(neff01neffij)=2πΔneffijLλ,
where ∆nijeff represents the difference between the effective refractive indices of the two modes. When the phase difference between the core mode of LP01 and a cladding mode of LPij is equal to 2, an interference maximum is observed in the transmission spectrum, for which the m-order peak wavelength is located at

λmij=ΔneffijLm.

The intensity of the core and cladding modes interference spectrum is thus expressed by

I=I01+ijIij+2ijI01Iijcos(2πΔneffijLλ).

Since O(∆nijeff) ≈10−3, L = 10−1 m, and O(λ) ≈10−6 m, then O(∆nijeffL/λ) ≈102. Thus the optical path length difference ∆OPL = ∆nijeffL between the core and cladding modes is large enough that ∆nijeffL >> λ and m >> 1, the separation between successive maxima in the interference spectrum may be approximated to

Δλij=λm1ijλmijλ02ΔneffijL,
where λ0 is the center wavelength in the wavelength span. The interference between the fundamental mode and a particular outer-cladding mode of LPij will therefore result in an oscillating interference pattern with a period of ∆λij corresponding to intensity peak at a spatial frequency ξij which can be expressed as

ξij=1ΔλijΔneffijLλ02.

The demodulation method of the multiplexed signal of a tapered bend-insensitive fiber based Mach-Zehnder interferometer is depicted in Fig. 2. The Fast Fourier Transform (FFT) of the interference spectrum is first performed, showing multiple peaks in the spatial frequency domain of the received signal that correspond to different groups of cladding modes. The application of a narrow band-pass filter with a rectangle window function to the original interference spectrum allowed individual spatial frequency components to be isolated and transformed back to the wavelength domain, where their phase information is extracted in the form of filtered interference spectra accordingly. Since the measured spectrum is only for a limited wavelength range, the FFT makes an implicit assumption that the spectrum is repetitive outside the measured interval. Thus in the filtered interference spectra, a low-frequency sinusoidal envelope due to the presumed repeating spectral properties is always superimposed on a high-frequency sinusoidal signal corresponding to a specific cladding mode. In this way, each peak in the FFT spectrum could be calibrated separately for its filtered spectral shift response to different environmental parameters such as refractive index, temperature, and axial strain. A second calibration is achieved by directly considering phase responses of multiple peaks in the FFT spectrum to provide another means of carrying out temperature- and axial strain-compensated refractive index measurement. As changes occur in environmental parameters, the difference in the effective refractive indices between the core mode and one specific cladding mode, ∆neff, will change correspondingly to (∆neff + δ(∆neff)), and lead to a peak wavelength shift δλ in the position of the m-order peak of each spatial frequency component originally at λ to a new position λ' in the interference spectrum. The peak wavelength shift δλ and an associated phase shift δΦ can be expressed using Eqs. (6.1)-(6.2). It is obvious that the peak wavelength and phase will shift in opposite directions with changing environmental parameters.

 

Fig. 2 Flow chart of the demodulation algorithm for an interference spectrum between the fundamental mode and multiple cladding modes.

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δλ=δ(ΔneffLm)=(δ(Δneff)Δneff)λ,
δΦ=δ(2πλ02ξλ)=2πξδλ.

The spectral shifts accompanying changes in concentrations of external solutions may be explained by considering that an increase in external refractive index causes a corresponding increase δ(∆neff,RI) in the effective refractive index of the cladding modes, while leaving the core mode essentially unaffected. Thus the interference peak wavelength blueshift and the corresponding phase redshift due to an increase in the external refractive index is

δλ=(δ(Δneff,RI)Δneff)λ,
δΦ=2πLδ(Δneff,RI)λ.

Temperature changes also produce peak wavelength shifts in the spectral interference between the fundamental mode and the cladding modes, since the thermo-optic coefficient of the germanium-doped silica core is greater than that of the pure silica cladding. As a result, the effective refractive index of the core will increase more rapidly than cladding modes by an amount δ(∆neff,T). Therefore the interference peak wavelength redshift and the corresponding phase blueshift with increasing surrounding temperature are given by

δλ=(δ(Δneff,T)Δneff)λ,
δΦ=2πLδ(Δneff,T)λ.

An axial strain ε applied on the fiber will cause an increase δL in the interferometer length, along with a change δ(∆neff,ε) in the refractive index difference between the core and cladding modes induced by the photo-elastic effect and waveguide geometry effect. This also results in relocation of a given interference maximum from λ to λ' with

δλ=(δLL+δ(Δneff,ε)Δneff,ε)λ,
The peak wavelength shift is induced by changes in both the fiber interferometer length (first term) and the effective refractive index difference (second term). The second term is contributed by the longitudinal stress induced photoelastic effect and the fiber geometry modification due to a change in the fiber diameter. Provided that the fiber is elastic and mechanically homogeneous, the increasing fiber length will decrease the fiber diameter, and the difference in the effective refractive index between the fundamental mode and cladding modes will be altered due to the change in the fiber transverse index profile. Therefore interference peak wavelength blueshifts and redshifts are both possible, depending upon the sign of δ(∆neff,ε) and the relative magnitudes of δL/L and δ(∆neff,ε)/∆neff,ε. The corresponding phase shift can be expressed by

δΦ=2π(Δneff,εδL+Lδ(Δneff,ε))λ.

3. Experimental methods

The abrupt tapers were created on the bend-insensitive fiber using a fusion splicer (Ericsson, FA995) with a custom taper fabrication program. An optical micrograph of the taper with a waist diameter of 50 µm and a length of 700 µm is shown in the inset of Fig. 1(b). The in-fiber Mach-Zehnder interferometer was constructed by fabricating two identical tapers separated by a distance L = 10.0 cm along the BIF. A 50:50 fiber coupler was used to combine outputs from L- and C-band erbium-doped fiber amplifiers. The resultant signal was sent to the input end of the BIF interferometer, which was in turn connected to an optical spectrum analyzer (Agilent, 86142A) with a wavelength resolution of 0.06 nm, from which a transmission spectrum comprising 10,000 data points over a spectral range of 1520 nm to 1610 nm could be observed and recorded. During the refractive index calibration procedure, the peak wavelength and phase shifts associated with the spatial frequencies under consideration were determined by submerging the tapered bend-insensitive fiber in a series of solutions consisting of varying concentrations of glycerol solution at a constant 20.0 °C. The percent by weight of glycerol in these solutions could be used to determine the solution refractive index. Temperature calibration was achieved by mounting the fiber interferometer in an oven with temperature resolution of 0.1 °C. Strain measurements were carried out by suspending the fiber interferometer horizontally between a motorized translational platform and a stationary platform, each end of the fiber being fixed to their respective positions with super glue. The motorized platform was driven to move along the axis of the BIF-MZI so as to stretch the fiber longitudinally by sequential strain increases of 200 microstrain, while the relative zero-strain was determined as the fiber was stretched to a particular pre-strain state.

Figure 3(a) shows a typical interference spectrum for the case of the BIF-MZI suspended in air at 24.6 °C with zero-strain. Figure 3(b) shows a corresponding FFT spectrum where distinct peaks at spatial frequencies of 0, 0.0444 nm−1, 0.0888 nm−1, 0.1333 nm−1, 0.1555 nm−1 and 0.1777 nm−1 are visible. The differences between the effective refractive indices of the core mode and specific cladding-modes are calculated using the spatial frequencies of the respective FFT peaks in Fig. 3(b) according to Eq. (5). Then a finite element analysis using COMSOL Multiphysics is carried out to simulate the effective mode indices and mode field patterns of both the fundamental mode and different cladding modes. When the simulated effective index difference between the fundamental mode and one cladding mode matches the calculated result of one particular FFT peak, its mode field pattern is obtained with the result presented in the inset of Fig. 3(b). The simulation results clearly show that the indicated peaks correspond to the fundamental mode LP01 (0 nm−1), inner cladding mode IC (0.0444 nm−1), and groups of outer-cladding modes, hereafter referred to as the OC-1 (0.0888 nm−1), OC-2 (0.1333 nm−1), OC-3 (0.1777 nm−1) and OC-4 (0.1555 nm−1) modes, respectively. It is noted that the spatial frequency peak with highest intensity corresponding to the OC-4 mode is located between the OC-2 mode and the OC-3 mode, which may tend to cause crosstalk problem and exhibit poor linearity under changes in external refractive index, temperature, and axial strain. It is clear that the optical fields of all these outer-cladding modes are effectively confined to the outer-cladding region due to the presence of the depressed-index trench which is treated as a pure air layer in a simplified structural model with custom mesh parameters over the geometry. However the higher-order outer-cladding mode (OC-3) has a greater number of intensity nodes along the radial direction than the lower-order outer-cladding mode (OC-1). Furthermore, the optical field intensity of the higher-order outer-cladding mode is pushed radially toward the depressed-index trench. Therefore the OC-3 mode has a smaller effective index and larger effective index difference from the fundamental mode and consequently higher spatial frequency than those of the OC-1 mode with an optical field concentrated closer to the cladding-environment boundary, as indicated by Eq. (5).

 

Fig. 3 (a) Transmission spectrum of the BIF-MZI suspended in air at 24.6 °C with zero-strain; (b) FFT spectrum of the BIF-MZI with an inset of the simulated mode field patterns of the fundamental mode, IC mode, OC-1 mode, the OC-2 mode, the OC-3 mode, and OC-4 mode respectively.

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Figure 4(a) presents the filtered interference spectra corresponding to extracted 0.0888 nm−1, 0.1333 nm−1, and 0.1777 nm−1 spatial frequency components obtained from Fig. 3. According to Eq. (4) and (5), the peak wavelength separation is the reciprocal of the spatial frequency. Thus the higher-order outer-cladding mode (OC-3) with a larger spatial frequency has shorter wavelength spacing than the lower-order outer-cladding mode (OC-1). A plot of the phase spectrum in the spatial frequency domain is shown in Fig. 4(b), where the normalized phase in the range of 0 to 2π was computed using the Fourier transform method at each spatial frequency.

 

Fig. 4 (a) Filtered transmission spectra of the BIF-MZI corresponding to isolated spatial frequency components; (b) Spatial frequency dependent phase spectrum of the BIF-MZI.

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4. Experimental results and discussion

The OC1-, OC2-, and OC3-modes indicated in Fig. 3(b), corresponding to the FFT peaks at 0.0888 nm−1, 0.1333 nm−1 and 0.1777 nm−1, were selected for simultaneous refractive index, temperature, and axial strain sensing based on the consistency of their responses to each of the environmental parameters investigated in the experiment. Both the peak wavelength and the phase responses associated with individual outer-cladding modes were studied. Figure 5 shows the transmission spectra of the BIF-MZI submerged in solutions of 10% and 25% glycerol at 20.0 °C with zero-strain.

 

Fig. 5 Transmission spectra of the BIF-MZI submerged in solutions of 10% and 25% glycerol at 20.0 °C with zero-strain.

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Figure 6 presents overlays of filtered frequency components obtained by submerging the BIF-MZI in 10% and 25% glycerol with the OC-1, OC-2, and OC-3 modes shown in Fig. 6(a)-6(c), respectively. The expected spectral blueshifts are clearly visible for different outer-cladding modes, and the magnitude of the peak wavelength shifts are seen to differ from one mode to the next. Figure 7 shows the spatial frequency dependent phase spectra of the BIF-MZI in solutions of 10% and 25% glycerol, along with the isolated 0.0888 nm−1, 0.1333 nm−1 and 0.1777 nm−1 spatial frequency components. All three spatial frequency components were found to experience the expected phase redshifts, and associated peak wavelength shifts, in opposing directions.

 

Fig. 6 Filtered transmission spectra of the BIF-MZI in solutions of 10% and 25% glycerol corresponding to different groups of outer-cladding modes of (a) the OC-1 mode, (b) the OC-2 mode, and (c) the OC-3 mode.

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Fig. 7 Spatial frequency dependent phase spectra of the BIF-MZI in solutions of 10% and 25% glycerol.

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A refractive index calibration plot showing peak wavelength shifts over a 0.04533 RIU range, corresponding to solutions of 5% to 40% glycerol, is presented in Fig. 8(a). Peak wavelength positions for the OC-1, OC-2, and OC-3 modes were found to shift by a total of 7.371 nm, 3.402 nm, and 1.647 nm over this range, exhibiting peak wavelength-related refractive index coefficients of −164.9 nm/RIU, −73.3 nm/RIU, and −36.7 nm/RIU, respectively. Figure 8(b) presents a calibration plot showing relative peak wavelength positions as a function of temperature from 24.6 °C to 46.4 °C. Over this range, the peak wavelength positions associated with the OC-1, OC-2, and OC-3 modes were found to shift by 1.062 nm, 1.368 nm, and 1.107 nm, respectively, with peak wavelength-related temperature coefficients of 0.0487 nm/°C, 0.0640 nm/°C, and 0.0511 nm/°C. Finally, axial strain calibration was carried out by stretching the fiber interferometer with strains up to 800 microstrain, resulting in peak wavelength shifts of 0.423 nm, 0.135 nm, and 0.162 nm corresponding to the OC-1, OC-2, and OC-3 modes, and associated peak wavelength-related axial strain coefficients of −529 nm/ε, −169 nm/ε, and −216 nm/ε, respectively, as shown in Fig. 8(c).

 

Fig. 8 Peak wavelength shift calibration curves for (a) refractive index, (b) temperature, and (c) axial strain, for the OC-1, OC-2, and OC-3 modes.

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Figure 9 shows phase shift based calibration plots for each of the three sensing parameters. Refractive index calibration yielded phase-related refractive index coefficients of 90.8 rad/RIU, 62.8 rad/RIU, and 40.6 rad/RIU for the OC-1, OC-2, and OC-3 modes, respectively and are plotted in Fig. 9(a). In turn, phase-related temperature coefficients for the OC-1, OC-2, and OC-3 modes are −0.027 rad/°C, −0.053 rad/°C, and −0.057 rad/°C, respectively, as shown in Fig. 9(b). The phase-related axial strain coefficients for the OC-1, OC-2, and OC-3 modes were respectively calculated to be 295 rad/ε, 141 rad/ε, and 241 rad/ε, and their corresponding calibration curves are plotted in Fig. 9(c). Reduction in the taper diameter of the BIF-MZI is shown to result in excitation of a significant number of additional outer-cladding modes which exhibit particularly high sensitivity to changes in environmental refractive index since their mode fields are tightly concentrated near the periphery of the fiber, as shown in the inset of Fig. 3(b). This confers a significant advantage to the BIF-MZI over the standard SMF-MZI in terms of its refractive index sensitivity. Furthermore, the layer consisting of numerous nano-scale gas filled voids in the cladding could significantly modify the optical field distribution of different modes and enhance the capability of differentiate the refractive index sensitivity from other crosstalk parameters distinctively.

 

Fig. 9 Phase shift calibration curves for (a) refractive index, (b) temperature, and (c) axial strain, for the OC-1, OC-2, and OC-3 modes.

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According to Eq. (6.2), the external perturbation induced phase shift associated with a particular spatial frequency peak is directly correlated to the induced peak wavelength shift with a multiplication factor of the corresponding spatial frequency. Since the fixed spatial frequency is determined in both the peak wavelength shift and the phase shift monitoring methods, the information retrieved from the induced phase shift should be mathematically and physically identical to that from the induce peak wavelength shift. As indicated in Eqs. (7)-(9), the phase-related sensing coefficient in Fig. 9 is only related to δ(∆neff) while the peak wavelength-related sensing coefficient in Fig. 8 is a function of δ(∆neff)/∆neff which is influenced not only by the change of the difference in the effective refractive indices between the core mode and the outer-cladding modes but also by the selection of the FFT peak spatial frequencies or the outer-cladding mode orders. Thus the phase shift monitoring method is preferred in the following discussion on the sensing performances of the proposed in-fiber interferometer due to its computational simplicity and straightforward sensitivity analysis.

The variation in refractive index sensitivities among the three outer-cladding modes shown in Fig. 9(a) can be understood by referring to the simulated mode field patterns presented in Fig. 3(b). The higher-order outer-cladding mode (OC-3) whose optical field exhibits high intensity near the internal low-index ring will generally be characterized by a lower effective refractive index, and a lower sensitivity to changes in external refractive index relative to the lower-order outer-cladding mode (OC-1), which exhibits higher intensity near the cladding-environment surface. According to Eq. (7.2), the phase-related refractive index coefficient is determined by changes in the effective index difference between the outer-cladding modes and the fundamental mode confined in the fiber core region. As such, the lower-order outer-cladding mode of OC-1 in the BIF-MZI is expected to demonstrate higher refractive index sensitivity than the higher-order outer-cladding mode of OC-3, as observed. The enhanced temperature sensitivity of the higher-order outer-cladding mode OC-3 displayed in Fig. 9(b) can also be explained by referring to mode field cross-sectional intensity distributions. The intensity pattern associated with the lower-order outer-cladding mode OC-1 is essentially distributed in the pure silica region, for which the thermo-optic coefficient is smaller than that of the germanium-doped silica. Thus the effective index of the OC-1 mode changes less rapidly than that of the OC-3 mode, and consequently the OC-3 mode exhibits higher phase-related temperature sensitivity than the OC-1 mode according to Eq. (8.2). The waveguide geometry effect may be considered to influence the relative strain sensitivities of the three outer-cladding modes. Stretching of the fiber interferometer will lead to a slight decrease in the fiber diameter between tapers. This reduction in diameter would be accompanied by a decrease in effective indices of outer-cladding modes, due to a greater depth of penetration of their associated evanescent fields into the low-index external medium. Mode fields most concentrated near the cladding-environment boundary are therefore expected to exhibit particularly high sensitivity to axial strain, since the increase in the penetration depths of their evanescent optical fields would be proportionally greater than would be the case for modes concentrated further from this boundary. This accounts for the greatest observed sensitivity of the OC-1 mode in Fig. 9(c). The comparative strain sensitivities of the OC-2 and OC-3 modes, for which the field patterns are more concentrated near the depressed-index ring, may be explained by considering the asymmetries introduced by the presence of the air voids. The optical properties of the fiber should be more significantly distorted near the depressed index ring upon axial strain than other parts of the fiber. Thus, heightened sensitivity should be expected from the high-order outer-cladding mode OC-3, for which the intensity is more greatly focused near the low-index ring relative to mode fields of the OC-2 mode with maximum intensity further from this region.

In Fig. 9, phase-related refractive index measurement uncertainties are 9 rad/RIU, 4 rad/RIU, and 4 rad/RIU, and temperature measurement uncertainties are 0.001 rad/°C, 0.0004 rad/°C, and 0.001 rad/°C, and axial strain measurement uncertainties are 6 rad/ε, 19 rad/ε, and 13 rad/ε, for the OC-1, OC-2, and OC-3 modes respectively. The experimental results show that the phase shifts of the outer-cladding modes of OC-1, OC-2, and OC-3 exhibit good linearity under changes in temperature and axial strain, but not in external refractive index. Furthermore, it is noticed that the phase response of the same outer-cladding mode is nonlinear which has enhanced refractive index sensitivity with an increasing external refractive index since the evanescent field associated with the outer-cladding mode is utilized to detect the external refractive index change. If a nearly linear refractive index sensing range around a low refractive index region is selected from 1.339 to 1.364, the refractive index coefficients for the OC-1, OC-2, and OC-3 modes are 67 ± 7 rad/RIU, 51 ± 3 rad/RIU, and 30 ± 2 rad/RIU, respectively. When a larger sensing range extending to a high refractive index region up to 1.384 is selected, the approximately linear refractive index coefficients for the OC-1, OC-2, and OC-3 modes are 91 ± 9 rad/RIU, 63 ± 4 rad/RIU, and 41 ± 4 rad/RIU, respectively. Thus increasing the refractive index sensing range will lead to much higher refractive index sensitivity while suffer from relative high measurement uncertainty which arises from the fact that the linear approximation breaks down in the high refractive index region. In order to measure the external refractive index more accurately, the nonlinear response of the proposed in-fiber interferometric refractometer within the whole refractive index range should be expressed using a nonlinear refractive index coefficient of a quadratic polynomial or even higher degree polynomials depending on the actual refractive index measurement range.

The refractive index, temperature, and axial strain coefficients calibrated above provide an opportunity to construct a character matrix of the proposed fiber interferometer sensor, which can facilitate discrimination between the refractive index and the temperature as well as the axial strain effects, achieving refractive index measurement with temperature and axial strain compensation of high sensitivity and high accuracy. Defining the peak wavelength-related refractive index, temperature, and axial strain coefficients of the ith FFT spatial frequency peak respectively as λCiRI, λCiT, and λCiε, the wavelength-related character matrix λMRI,T,ε may be generated to obtain refractive index, temperature, and axial strain information from the wavelength shift data measured from any set of three FFT peaks as follows:

(Δλ1Δλ2Δλ3)=MλRI,T,ε(ΔRIΔTΔε)=(CλRI1CλT1Cλε1CλRI2CλT2Cλε2CλRI3CλT3Cλε3)(ΔRIΔTΔε),
(ΔRIΔTΔε)=MλRI,T,ε1(Δλ1Δλ2Δλ3),
where ∆λi are the peak wavelength shifts associated with the ith FFT spatial frequency peaks, and ∆RI, ∆T, and ∆ε are the refractive index, temperature, and axial strain changes with respect to a reference state.

A second character matrix ΦMRI,T,ε may also be defined to allow accurate refractive index sensing with temperature and axial strain compensation based on phase shift data. Using ΦCiRI, ΦCiT, and ΦCiε respectively to represent the phase-related refractive index, temperature, and axial strain coefficients for the ith FFT frequency peak,

(ΔΦ1ΔΦ2ΔΦ3)=MΦRI,T,ε(ΔRIΔTΔε)=(CΦRI1CΦT1CΦε1CΦRI2CΦT2CΦε2CΦRI3CΦT3CΦε3)(ΔRIΔTΔε),
(ΔRIΔTΔε)=MΦRI,T,ε1(ΔΦ1ΔΦ2ΔΦ3),
where ∆Φi are the phase shifts associated with the ith FFT frequency peaks. Following the error analysis for the simultaneous measurements of multiple parameters [31]:
(δRIδTδε)=MΦ'RI,T,εΔ(δΦ1δΦ2δΦ3),
where δRI, δT, and δε, represent the errors of refractive index, temperature, and axial strain, respectively, ∆ is the determinant of ΦMRI,T,ε, ΦM'RI,T,ε is the adjugate matrix, and δΦi are the errors in phase associated with the ith FFT spatial frequency peaks. The errors of refractive index, temperature, and axial strain are calculated to be 0.003 RIU, 1 °C, and 74 µε, respectively.

4. Conclusion

In conclusion, a novel approach to realize temperature- and axial strain-compensated refractive index sensing using a tapered bend-insensitive fiber based Mach-Zehnder interferometer has been presented in this work. Application of the fast Fourier transform to a complex interference pattern obtained from the BIF-MZI shows multiple peaks in the spatial frequency domain from which numerous sensing modes could be isolated and selected for sensing applications. A peak wavelength shift method and a phase shift monitoring method have been experimentally demonstrated to measure multiple environmental parameters simultaneously, allowing the wavelength- and phase-related character matrices λMRI,T,ε and ΦMRI,T,ε to be calibrated. The proposed approach shows great potential for applications in which resolving a high degree of cross-sensitivity between refractive index and more than two other parameters is required since only the number of distinct peaks in the Fourier-transformed spectrum limits the number of simultaneously detectable parameters in principle.

Acknowledgments

The research is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grants and Canada Research Chairs (CRC) Program. Ping Lu would like to acknowledge the Province of Ontario Ministry of Research and Innovation and the University of Ottawa for the financial support of the Vision 2020 Postdoctoral Fellowship.

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9. Q. Wu, Y. Semenova, P. Wang, and G. Farrell, “High sensitivity SMS fiber structure based refractometer--analysis and experiment,” Opt. Express 19(9), 7937–7944 (2011). [CrossRef]   [PubMed]  

10. K. Zhou, Z. Yan, L. Zhang, and I. Bennion, “Refractometer based on fiber Bragg grating Fabry-Pérot cavity embedded with a narrow microchannel,” Opt. Express 19(12), 11769–11779 (2011). [CrossRef]   [PubMed]  

11. J. Wo, G. Wang, Y. Cui, Q. Sun, R. Liang, P. P. Shum, and D. Liu, “Refractive index sensor using microfiber-based Mach-Zehnder interferometer,” Opt. Lett. 37(1), 67–69 (2012). [CrossRef]   [PubMed]  

12. O. Frazão, L. A. Ferreira, and F. M. Araújo, “Applications of fiber optic grating technology to multi-parameter measurement,” Fiber Integr. Opt. 24(3–4), 227–244 (2005).

13. Y.-J. Rao, Y.-P. Wang, Z.-L. Ran, and T. Zhu, “Novel fiber-optic sensors based on long-period fiber gratings written by high-frequency CO2 laser pulses,” J. Lightwave Technol. 21(5), 1320–1327 (2003). [CrossRef]  

14. R. Yang, Y.-S. Yu, C. Chen, Y. Xue, X.-L. Zhang, J.-C. Guo, C. Wang, F. Zhu, B.-L. Zhang, Q.-D. Chen, and H.-B. Sun, “S-tapered fiber sensors for highly sensitive measurement of refractive index and axial strain,” J. Lightwave Technol. 30(19), 3126–3132 (2012). [CrossRef]  

15. P. Lu, L. Men, K. Sooley, and Q. Chen, “Tapered fiber Mach-Zehnder interferometer for simultaneous measurement of refractive index and temperature,” Appl. Phys. Lett. 94(13), 131110 (2009). [CrossRef]  

16. D. J. J. Hu, J. L. Lim, M. Jiang, Y. Wang, F. Luan, P. P. Shum, H. Wei, and W. Tong, “Long period grating cascaded to photonic crystal fiber modal interferometer for simultaneous measurement of temperature and refractive index,” Opt. Lett. 37(12), 2283–2285 (2012). [CrossRef]   [PubMed]  

17. H.-J. Kim, O.-J. Kwon, S. B. Lee, and Y.-G. Han, “Polarization-dependent refractometer for discrimination of temperature and ambient refractive index,” Opt. Lett. 37(11), 1802–1804 (2012). [CrossRef]   [PubMed]  

18. P. Lu, J. Harris, Y. Xu, Y. Lu, L. Chen, and X. Bao, “Simultaneous refractive index and temperature measurements using a tapered bend-resistant fiber interferometer,” Opt. Lett. 37(22), 4567–4569 (2012). [CrossRef]   [PubMed]  

19. D. A. C. Enríquez, A. R. da Cruz, and M. T. M. R. Giraldi, “Hybrid FBG-LPG sensor for surrounding refractive index and temperature simultaneous discrimination,” Opt. Laser Technol. 44(4), 981–986 (2012). [CrossRef]  

20. Y. J. Rao, P. J. Henderson, D. A. Jackson, L. Zhang, and I. Bennion, “Simultaneous strain, temperature and vibration measurement using a multiplexed in-fibre-Bragg-grating/fibre-Fabry-Perot sensor system,” Electron. Lett. 33(24), 2063–2064 (1997). [CrossRef]  

21. H.-K. Kang, H.-J. Bang, C.-S. Hong, and C.-G. Kim, “Simultaneous measurement of strain, temperature and vibration frequency using a fiber-optic sensor,” Meas. Sci. Technol. 13(8), 1191–1196 (2002). [CrossRef]  

22. Z. Yong, C. Zhan, J. Lee, S. Yin, and P. Ruffin, “Multiple parameter vector bending and high-temperature sensors based on asymmetric multimode fiber Bragg gratings inscribed by an infrared femtosecond laser,” Opt. Lett. 31(12), 1794–1796 (2006). [CrossRef]   [PubMed]  

23. C. Zhan, Y. Zhu, S. Yin, and P. Ruffin, “Multi-parameter harsh environment sensing using asymmetric Bragg gratings inscribed by IR femtosecond irradiation,” Opt. Fiber Technol. 13(2), 98–107 (2007). [CrossRef]  

24. T. Mawatari and D. Nelson, “A multi-parameter Bragg grating fiber optic sensor and triaxial strain measurement,” Smart Mater. Struct. 17(3), 035033 (2008). [CrossRef]  

25. O. Frazão, R. M. Silva, J. Kobelke, and K. Schuster, “Temperature- and strain-independent torsion sensor using a fiber loop mirror based on suspended twin-core fiber,” Opt. Lett. 35(16), 2777–2779 (2010). [CrossRef]   [PubMed]  

26. L. Men, P. Lu, and Q. Chen, “Intelligent multiparameter sensing with fiber Bragg gratings,” Appl. Phys. Lett. 93(7), 071110 (2008). [CrossRef]  

27. S.-M. Lee, S. S. Saini, and M.-Y. Jeong, “Simultaneous Measurement of refractive index, temperature, and strain using etched-core fiber Bragg grating sensors,” IEEE Photon. Technol. Lett. 22(19), 1431–1433 (2010). [CrossRef]  

28. N. J. Alberto, C. A. Marques, J. L. Pinto, and R. N. Nogueira, “Three-parameter optical fiber sensor based on a tilted fiber Bragg grating,” Appl. Opt. 49(31), 6085–6091 (2010). [CrossRef]  

29. C. Trono, F. Baldini, M. Brenci, F. Chiavaioli, and M. Mugnaini, “Flow cell for strain- and temperature-compensated refractive index measurements by means of cascaded optical fibre long period and Bragg gratings,” Meas. Sci. Technol. 22(7), 075204 (2011). [CrossRef]  

30. M.-J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, M. A. McDermott, R. B. Desorcie, D. A. Nolan, J. J. Johnson, K. A. Lewis, and J. J. Englebert, “Ultra-low bending loss single-mode fiber for FTTH,” J. Lightwave Technol. 27(3), 376–382 (2009). [CrossRef]  

31. W. Jin, W. C. Michie, G. Thursby, M. Konstantaki, and B. Culshaw, “Simultaneous measurement of strain and temperature: error analysis,” Opt. Eng. 36(2), 598–609 (1997). [CrossRef]  

References

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  1. S. Singh, “Refractive index measurement and its applications,” Phys. Scr. 65(2), 167–180 (2002).
    [CrossRef]
  2. P. Polynkin, A. Polynkin, N. Peyghambarian, and M. Mansuripur, “Evanescent field-based optical fiber sensing device for measuring the refractive index of liquids in microfluidic channels,” Opt. Lett. 30(11), 1273–1275 (2005).
    [CrossRef] [PubMed]
  3. Q. Wang and G. Farrell, “All-fiber multimode-interference-based refractometer sensor: proposal and design,” Opt. Lett. 31(3), 317–319 (2006).
    [CrossRef] [PubMed]
  4. M. C. Phan Huy, G. Laffont, V. Dewynter, P. Ferdinand, P. Roy, J.-L. Auguste, D. Pagnoux, W. Blanc, and B. Dussardier, “Three-hole microstructured optical fiber for efficient fiber Bragg grating refractometer,” Opt. Lett. 32(16), 2390–2392 (2007).
    [CrossRef] [PubMed]
  5. C. Caucheteur, M. Wuilpart, C. Chen, P. Mégret, and J. Albert, “Quasi-distributed refractometer using tilted Bragg gratings and time domain reflectometry,” Opt. Express 16(22), 17882–17890 (2008).
    [CrossRef] [PubMed]
  6. T. Guo, H.-Y. Tam, P. A. Krug, and J. Albert, “Reflective tilted fiber Bragg grating refractometer based on strong cladding to core recoupling,” Opt. Express 17(7), 5736–5742 (2009).
    [CrossRef] [PubMed]
  7. O. Frazão, T. Martynkien, J. M. Baptista, J. L. Santos, W. Urbanczyk, and J. Wojcik, “Optical refractometer based on a birefringent Bragg grating written in an H-shaped fiber,” Opt. Lett. 34(1), 76–78 (2009).
    [CrossRef] [PubMed]
  8. M. Han, F. W. Guo, and Y. F. Lu, “Optical fiber refractometer based on cladding-mode Bragg grating,” Opt. Lett. 35(3), 399–401 (2010).
    [CrossRef] [PubMed]
  9. Q. Wu, Y. Semenova, P. Wang, and G. Farrell, “High sensitivity SMS fiber structure based refractometer--analysis and experiment,” Opt. Express 19(9), 7937–7944 (2011).
    [CrossRef] [PubMed]
  10. K. Zhou, Z. Yan, L. Zhang, and I. Bennion, “Refractometer based on fiber Bragg grating Fabry-Pérot cavity embedded with a narrow microchannel,” Opt. Express 19(12), 11769–11779 (2011).
    [CrossRef] [PubMed]
  11. J. Wo, G. Wang, Y. Cui, Q. Sun, R. Liang, P. P. Shum, and D. Liu, “Refractive index sensor using microfiber-based Mach-Zehnder interferometer,” Opt. Lett. 37(1), 67–69 (2012).
    [CrossRef] [PubMed]
  12. O. Frazão, L. A. Ferreira, and F. M. Araújo, “Applications of fiber optic grating technology to multi-parameter measurement,” Fiber Integr. Opt. 24(3–4), 227–244 (2005).
  13. Y.-J. Rao, Y.-P. Wang, Z.-L. Ran, and T. Zhu, “Novel fiber-optic sensors based on long-period fiber gratings written by high-frequency CO2 laser pulses,” J. Lightwave Technol. 21(5), 1320–1327 (2003).
    [CrossRef]
  14. R. Yang, Y.-S. Yu, C. Chen, Y. Xue, X.-L. Zhang, J.-C. Guo, C. Wang, F. Zhu, B.-L. Zhang, Q.-D. Chen, and H.-B. Sun, “S-tapered fiber sensors for highly sensitive measurement of refractive index and axial strain,” J. Lightwave Technol. 30(19), 3126–3132 (2012).
    [CrossRef]
  15. P. Lu, L. Men, K. Sooley, and Q. Chen, “Tapered fiber Mach-Zehnder interferometer for simultaneous measurement of refractive index and temperature,” Appl. Phys. Lett. 94(13), 131110 (2009).
    [CrossRef]
  16. D. J. J. Hu, J. L. Lim, M. Jiang, Y. Wang, F. Luan, P. P. Shum, H. Wei, and W. Tong, “Long period grating cascaded to photonic crystal fiber modal interferometer for simultaneous measurement of temperature and refractive index,” Opt. Lett. 37(12), 2283–2285 (2012).
    [CrossRef] [PubMed]
  17. H.-J. Kim, O.-J. Kwon, S. B. Lee, and Y.-G. Han, “Polarization-dependent refractometer for discrimination of temperature and ambient refractive index,” Opt. Lett. 37(11), 1802–1804 (2012).
    [CrossRef] [PubMed]
  18. P. Lu, J. Harris, Y. Xu, Y. Lu, L. Chen, and X. Bao, “Simultaneous refractive index and temperature measurements using a tapered bend-resistant fiber interferometer,” Opt. Lett. 37(22), 4567–4569 (2012).
    [CrossRef] [PubMed]
  19. D. A. C. Enríquez, A. R. da Cruz, and M. T. M. R. Giraldi, “Hybrid FBG-LPG sensor for surrounding refractive index and temperature simultaneous discrimination,” Opt. Laser Technol. 44(4), 981–986 (2012).
    [CrossRef]
  20. Y. J. Rao, P. J. Henderson, D. A. Jackson, L. Zhang, and I. Bennion, “Simultaneous strain, temperature and vibration measurement using a multiplexed in-fibre-Bragg-grating/fibre-Fabry-Perot sensor system,” Electron. Lett. 33(24), 2063–2064 (1997).
    [CrossRef]
  21. H.-K. Kang, H.-J. Bang, C.-S. Hong, and C.-G. Kim, “Simultaneous measurement of strain, temperature and vibration frequency using a fiber-optic sensor,” Meas. Sci. Technol. 13(8), 1191–1196 (2002).
    [CrossRef]
  22. Z. Yong, C. Zhan, J. Lee, S. Yin, and P. Ruffin, “Multiple parameter vector bending and high-temperature sensors based on asymmetric multimode fiber Bragg gratings inscribed by an infrared femtosecond laser,” Opt. Lett. 31(12), 1794–1796 (2006).
    [CrossRef] [PubMed]
  23. C. Zhan, Y. Zhu, S. Yin, and P. Ruffin, “Multi-parameter harsh environment sensing using asymmetric Bragg gratings inscribed by IR femtosecond irradiation,” Opt. Fiber Technol. 13(2), 98–107 (2007).
    [CrossRef]
  24. T. Mawatari and D. Nelson, “A multi-parameter Bragg grating fiber optic sensor and triaxial strain measurement,” Smart Mater. Struct. 17(3), 035033 (2008).
    [CrossRef]
  25. O. Frazão, R. M. Silva, J. Kobelke, and K. Schuster, “Temperature- and strain-independent torsion sensor using a fiber loop mirror based on suspended twin-core fiber,” Opt. Lett. 35(16), 2777–2779 (2010).
    [CrossRef] [PubMed]
  26. L. Men, P. Lu, and Q. Chen, “Intelligent multiparameter sensing with fiber Bragg gratings,” Appl. Phys. Lett. 93(7), 071110 (2008).
    [CrossRef]
  27. S.-M. Lee, S. S. Saini, and M.-Y. Jeong, “Simultaneous Measurement of refractive index, temperature, and strain using etched-core fiber Bragg grating sensors,” IEEE Photon. Technol. Lett. 22(19), 1431–1433 (2010).
    [CrossRef]
  28. N. J. Alberto, C. A. Marques, J. L. Pinto, and R. N. Nogueira, “Three-parameter optical fiber sensor based on a tilted fiber Bragg grating,” Appl. Opt. 49(31), 6085–6091 (2010).
    [CrossRef]
  29. C. Trono, F. Baldini, M. Brenci, F. Chiavaioli, and M. Mugnaini, “Flow cell for strain- and temperature-compensated refractive index measurements by means of cascaded optical fibre long period and Bragg gratings,” Meas. Sci. Technol. 22(7), 075204 (2011).
    [CrossRef]
  30. M.-J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, M. A. McDermott, R. B. Desorcie, D. A. Nolan, J. J. Johnson, K. A. Lewis, and J. J. Englebert, “Ultra-low bending loss single-mode fiber for FTTH,” J. Lightwave Technol. 27(3), 376–382 (2009).
    [CrossRef]
  31. W. Jin, W. C. Michie, G. Thursby, M. Konstantaki, and B. Culshaw, “Simultaneous measurement of strain and temperature: error analysis,” Opt. Eng. 36(2), 598–609 (1997).
    [CrossRef]

2012 (6)

2011 (3)

2010 (4)

2009 (4)

2008 (3)

C. Caucheteur, M. Wuilpart, C. Chen, P. Mégret, and J. Albert, “Quasi-distributed refractometer using tilted Bragg gratings and time domain reflectometry,” Opt. Express 16(22), 17882–17890 (2008).
[CrossRef] [PubMed]

L. Men, P. Lu, and Q. Chen, “Intelligent multiparameter sensing with fiber Bragg gratings,” Appl. Phys. Lett. 93(7), 071110 (2008).
[CrossRef]

T. Mawatari and D. Nelson, “A multi-parameter Bragg grating fiber optic sensor and triaxial strain measurement,” Smart Mater. Struct. 17(3), 035033 (2008).
[CrossRef]

2007 (2)

C. Zhan, Y. Zhu, S. Yin, and P. Ruffin, “Multi-parameter harsh environment sensing using asymmetric Bragg gratings inscribed by IR femtosecond irradiation,” Opt. Fiber Technol. 13(2), 98–107 (2007).
[CrossRef]

M. C. Phan Huy, G. Laffont, V. Dewynter, P. Ferdinand, P. Roy, J.-L. Auguste, D. Pagnoux, W. Blanc, and B. Dussardier, “Three-hole microstructured optical fiber for efficient fiber Bragg grating refractometer,” Opt. Lett. 32(16), 2390–2392 (2007).
[CrossRef] [PubMed]

2006 (2)

2005 (2)

P. Polynkin, A. Polynkin, N. Peyghambarian, and M. Mansuripur, “Evanescent field-based optical fiber sensing device for measuring the refractive index of liquids in microfluidic channels,” Opt. Lett. 30(11), 1273–1275 (2005).
[CrossRef] [PubMed]

O. Frazão, L. A. Ferreira, and F. M. Araújo, “Applications of fiber optic grating technology to multi-parameter measurement,” Fiber Integr. Opt. 24(3–4), 227–244 (2005).

2003 (1)

2002 (2)

S. Singh, “Refractive index measurement and its applications,” Phys. Scr. 65(2), 167–180 (2002).
[CrossRef]

H.-K. Kang, H.-J. Bang, C.-S. Hong, and C.-G. Kim, “Simultaneous measurement of strain, temperature and vibration frequency using a fiber-optic sensor,” Meas. Sci. Technol. 13(8), 1191–1196 (2002).
[CrossRef]

1997 (2)

W. Jin, W. C. Michie, G. Thursby, M. Konstantaki, and B. Culshaw, “Simultaneous measurement of strain and temperature: error analysis,” Opt. Eng. 36(2), 598–609 (1997).
[CrossRef]

Y. J. Rao, P. J. Henderson, D. A. Jackson, L. Zhang, and I. Bennion, “Simultaneous strain, temperature and vibration measurement using a multiplexed in-fibre-Bragg-grating/fibre-Fabry-Perot sensor system,” Electron. Lett. 33(24), 2063–2064 (1997).
[CrossRef]

Albert, J.

Alberto, N. J.

Araújo, F. M.

O. Frazão, L. A. Ferreira, and F. M. Araújo, “Applications of fiber optic grating technology to multi-parameter measurement,” Fiber Integr. Opt. 24(3–4), 227–244 (2005).

Auguste, J.-L.

Baldini, F.

C. Trono, F. Baldini, M. Brenci, F. Chiavaioli, and M. Mugnaini, “Flow cell for strain- and temperature-compensated refractive index measurements by means of cascaded optical fibre long period and Bragg gratings,” Meas. Sci. Technol. 22(7), 075204 (2011).
[CrossRef]

Bang, H.-J.

H.-K. Kang, H.-J. Bang, C.-S. Hong, and C.-G. Kim, “Simultaneous measurement of strain, temperature and vibration frequency using a fiber-optic sensor,” Meas. Sci. Technol. 13(8), 1191–1196 (2002).
[CrossRef]

Bao, X.

Baptista, J. M.

Bennion, I.

K. Zhou, Z. Yan, L. Zhang, and I. Bennion, “Refractometer based on fiber Bragg grating Fabry-Pérot cavity embedded with a narrow microchannel,” Opt. Express 19(12), 11769–11779 (2011).
[CrossRef] [PubMed]

Y. J. Rao, P. J. Henderson, D. A. Jackson, L. Zhang, and I. Bennion, “Simultaneous strain, temperature and vibration measurement using a multiplexed in-fibre-Bragg-grating/fibre-Fabry-Perot sensor system,” Electron. Lett. 33(24), 2063–2064 (1997).
[CrossRef]

Bickham, S. R.

Blanc, W.

Bookbinder, D. C.

Brenci, M.

C. Trono, F. Baldini, M. Brenci, F. Chiavaioli, and M. Mugnaini, “Flow cell for strain- and temperature-compensated refractive index measurements by means of cascaded optical fibre long period and Bragg gratings,” Meas. Sci. Technol. 22(7), 075204 (2011).
[CrossRef]

Caucheteur, C.

Chen, C.

Chen, L.

Chen, Q.

P. Lu, L. Men, K. Sooley, and Q. Chen, “Tapered fiber Mach-Zehnder interferometer for simultaneous measurement of refractive index and temperature,” Appl. Phys. Lett. 94(13), 131110 (2009).
[CrossRef]

L. Men, P. Lu, and Q. Chen, “Intelligent multiparameter sensing with fiber Bragg gratings,” Appl. Phys. Lett. 93(7), 071110 (2008).
[CrossRef]

Chen, Q.-D.

Chiavaioli, F.

C. Trono, F. Baldini, M. Brenci, F. Chiavaioli, and M. Mugnaini, “Flow cell for strain- and temperature-compensated refractive index measurements by means of cascaded optical fibre long period and Bragg gratings,” Meas. Sci. Technol. 22(7), 075204 (2011).
[CrossRef]

Cui, Y.

Culshaw, B.

W. Jin, W. C. Michie, G. Thursby, M. Konstantaki, and B. Culshaw, “Simultaneous measurement of strain and temperature: error analysis,” Opt. Eng. 36(2), 598–609 (1997).
[CrossRef]

da Cruz, A. R.

D. A. C. Enríquez, A. R. da Cruz, and M. T. M. R. Giraldi, “Hybrid FBG-LPG sensor for surrounding refractive index and temperature simultaneous discrimination,” Opt. Laser Technol. 44(4), 981–986 (2012).
[CrossRef]

Desorcie, R. B.

Dewynter, V.

Dussardier, B.

Englebert, J. J.

Enríquez, D. A. C.

D. A. C. Enríquez, A. R. da Cruz, and M. T. M. R. Giraldi, “Hybrid FBG-LPG sensor for surrounding refractive index and temperature simultaneous discrimination,” Opt. Laser Technol. 44(4), 981–986 (2012).
[CrossRef]

Farrell, G.

Ferdinand, P.

Ferreira, L. A.

O. Frazão, L. A. Ferreira, and F. M. Araújo, “Applications of fiber optic grating technology to multi-parameter measurement,” Fiber Integr. Opt. 24(3–4), 227–244 (2005).

Frazão, O.

Giraldi, M. T. M. R.

D. A. C. Enríquez, A. R. da Cruz, and M. T. M. R. Giraldi, “Hybrid FBG-LPG sensor for surrounding refractive index and temperature simultaneous discrimination,” Opt. Laser Technol. 44(4), 981–986 (2012).
[CrossRef]

Guo, F. W.

Guo, J.-C.

Guo, T.

Han, M.

Han, Y.-G.

Harris, J.

Henderson, P. J.

Y. J. Rao, P. J. Henderson, D. A. Jackson, L. Zhang, and I. Bennion, “Simultaneous strain, temperature and vibration measurement using a multiplexed in-fibre-Bragg-grating/fibre-Fabry-Perot sensor system,” Electron. Lett. 33(24), 2063–2064 (1997).
[CrossRef]

Hong, C.-S.

H.-K. Kang, H.-J. Bang, C.-S. Hong, and C.-G. Kim, “Simultaneous measurement of strain, temperature and vibration frequency using a fiber-optic sensor,” Meas. Sci. Technol. 13(8), 1191–1196 (2002).
[CrossRef]

Hu, D. J. J.

Jackson, D. A.

Y. J. Rao, P. J. Henderson, D. A. Jackson, L. Zhang, and I. Bennion, “Simultaneous strain, temperature and vibration measurement using a multiplexed in-fibre-Bragg-grating/fibre-Fabry-Perot sensor system,” Electron. Lett. 33(24), 2063–2064 (1997).
[CrossRef]

Jeong, M.-Y.

S.-M. Lee, S. S. Saini, and M.-Y. Jeong, “Simultaneous Measurement of refractive index, temperature, and strain using etched-core fiber Bragg grating sensors,” IEEE Photon. Technol. Lett. 22(19), 1431–1433 (2010).
[CrossRef]

Jiang, M.

Jin, W.

W. Jin, W. C. Michie, G. Thursby, M. Konstantaki, and B. Culshaw, “Simultaneous measurement of strain and temperature: error analysis,” Opt. Eng. 36(2), 598–609 (1997).
[CrossRef]

Johnson, J. J.

Kang, H.-K.

H.-K. Kang, H.-J. Bang, C.-S. Hong, and C.-G. Kim, “Simultaneous measurement of strain, temperature and vibration frequency using a fiber-optic sensor,” Meas. Sci. Technol. 13(8), 1191–1196 (2002).
[CrossRef]

Kim, C.-G.

H.-K. Kang, H.-J. Bang, C.-S. Hong, and C.-G. Kim, “Simultaneous measurement of strain, temperature and vibration frequency using a fiber-optic sensor,” Meas. Sci. Technol. 13(8), 1191–1196 (2002).
[CrossRef]

Kim, H.-J.

Kobelke, J.

Konstantaki, M.

W. Jin, W. C. Michie, G. Thursby, M. Konstantaki, and B. Culshaw, “Simultaneous measurement of strain and temperature: error analysis,” Opt. Eng. 36(2), 598–609 (1997).
[CrossRef]

Krug, P. A.

Kwon, O.-J.

Laffont, G.

Lee, J.

Lee, S. B.

Lee, S.-M.

S.-M. Lee, S. S. Saini, and M.-Y. Jeong, “Simultaneous Measurement of refractive index, temperature, and strain using etched-core fiber Bragg grating sensors,” IEEE Photon. Technol. Lett. 22(19), 1431–1433 (2010).
[CrossRef]

Lewis, K. A.

Li, M.-J.

Liang, R.

Lim, J. L.

Liu, D.

Lu, P.

P. Lu, J. Harris, Y. Xu, Y. Lu, L. Chen, and X. Bao, “Simultaneous refractive index and temperature measurements using a tapered bend-resistant fiber interferometer,” Opt. Lett. 37(22), 4567–4569 (2012).
[CrossRef] [PubMed]

P. Lu, L. Men, K. Sooley, and Q. Chen, “Tapered fiber Mach-Zehnder interferometer for simultaneous measurement of refractive index and temperature,” Appl. Phys. Lett. 94(13), 131110 (2009).
[CrossRef]

L. Men, P. Lu, and Q. Chen, “Intelligent multiparameter sensing with fiber Bragg gratings,” Appl. Phys. Lett. 93(7), 071110 (2008).
[CrossRef]

Lu, Y.

Lu, Y. F.

Luan, F.

Mansuripur, M.

Marques, C. A.

Martynkien, T.

Mawatari, T.

T. Mawatari and D. Nelson, “A multi-parameter Bragg grating fiber optic sensor and triaxial strain measurement,” Smart Mater. Struct. 17(3), 035033 (2008).
[CrossRef]

McDermott, M. A.

Mégret, P.

Men, L.

P. Lu, L. Men, K. Sooley, and Q. Chen, “Tapered fiber Mach-Zehnder interferometer for simultaneous measurement of refractive index and temperature,” Appl. Phys. Lett. 94(13), 131110 (2009).
[CrossRef]

L. Men, P. Lu, and Q. Chen, “Intelligent multiparameter sensing with fiber Bragg gratings,” Appl. Phys. Lett. 93(7), 071110 (2008).
[CrossRef]

Michie, W. C.

W. Jin, W. C. Michie, G. Thursby, M. Konstantaki, and B. Culshaw, “Simultaneous measurement of strain and temperature: error analysis,” Opt. Eng. 36(2), 598–609 (1997).
[CrossRef]

Mugnaini, M.

C. Trono, F. Baldini, M. Brenci, F. Chiavaioli, and M. Mugnaini, “Flow cell for strain- and temperature-compensated refractive index measurements by means of cascaded optical fibre long period and Bragg gratings,” Meas. Sci. Technol. 22(7), 075204 (2011).
[CrossRef]

Nelson, D.

T. Mawatari and D. Nelson, “A multi-parameter Bragg grating fiber optic sensor and triaxial strain measurement,” Smart Mater. Struct. 17(3), 035033 (2008).
[CrossRef]

Nogueira, R. N.

Nolan, D. A.

Pagnoux, D.

Peyghambarian, N.

Phan Huy, M. C.

Pinto, J. L.

Polynkin, A.

Polynkin, P.

Ran, Z.-L.

Rao, Y. J.

Y. J. Rao, P. J. Henderson, D. A. Jackson, L. Zhang, and I. Bennion, “Simultaneous strain, temperature and vibration measurement using a multiplexed in-fibre-Bragg-grating/fibre-Fabry-Perot sensor system,” Electron. Lett. 33(24), 2063–2064 (1997).
[CrossRef]

Rao, Y.-J.

Roy, P.

Ruffin, P.

C. Zhan, Y. Zhu, S. Yin, and P. Ruffin, “Multi-parameter harsh environment sensing using asymmetric Bragg gratings inscribed by IR femtosecond irradiation,” Opt. Fiber Technol. 13(2), 98–107 (2007).
[CrossRef]

Z. Yong, C. Zhan, J. Lee, S. Yin, and P. Ruffin, “Multiple parameter vector bending and high-temperature sensors based on asymmetric multimode fiber Bragg gratings inscribed by an infrared femtosecond laser,” Opt. Lett. 31(12), 1794–1796 (2006).
[CrossRef] [PubMed]

Saini, S. S.

S.-M. Lee, S. S. Saini, and M.-Y. Jeong, “Simultaneous Measurement of refractive index, temperature, and strain using etched-core fiber Bragg grating sensors,” IEEE Photon. Technol. Lett. 22(19), 1431–1433 (2010).
[CrossRef]

Santos, J. L.

Schuster, K.

Semenova, Y.

Shum, P. P.

Silva, R. M.

Singh, S.

S. Singh, “Refractive index measurement and its applications,” Phys. Scr. 65(2), 167–180 (2002).
[CrossRef]

Sooley, K.

P. Lu, L. Men, K. Sooley, and Q. Chen, “Tapered fiber Mach-Zehnder interferometer for simultaneous measurement of refractive index and temperature,” Appl. Phys. Lett. 94(13), 131110 (2009).
[CrossRef]

Sun, H.-B.

Sun, Q.

Tam, H.-Y.

Tandon, P.

Thursby, G.

W. Jin, W. C. Michie, G. Thursby, M. Konstantaki, and B. Culshaw, “Simultaneous measurement of strain and temperature: error analysis,” Opt. Eng. 36(2), 598–609 (1997).
[CrossRef]

Tong, W.

Trono, C.

C. Trono, F. Baldini, M. Brenci, F. Chiavaioli, and M. Mugnaini, “Flow cell for strain- and temperature-compensated refractive index measurements by means of cascaded optical fibre long period and Bragg gratings,” Meas. Sci. Technol. 22(7), 075204 (2011).
[CrossRef]

Urbanczyk, W.

Wang, C.

Wang, G.

Wang, P.

Wang, Q.

Wang, Y.

Wang, Y.-P.

Wei, H.

Wo, J.

Wojcik, J.

Wu, Q.

Wuilpart, M.

Xu, Y.

Xue, Y.

Yan, Z.

Yang, R.

Yin, S.

C. Zhan, Y. Zhu, S. Yin, and P. Ruffin, “Multi-parameter harsh environment sensing using asymmetric Bragg gratings inscribed by IR femtosecond irradiation,” Opt. Fiber Technol. 13(2), 98–107 (2007).
[CrossRef]

Z. Yong, C. Zhan, J. Lee, S. Yin, and P. Ruffin, “Multiple parameter vector bending and high-temperature sensors based on asymmetric multimode fiber Bragg gratings inscribed by an infrared femtosecond laser,” Opt. Lett. 31(12), 1794–1796 (2006).
[CrossRef] [PubMed]

Yong, Z.

Yu, Y.-S.

Zhan, C.

C. Zhan, Y. Zhu, S. Yin, and P. Ruffin, “Multi-parameter harsh environment sensing using asymmetric Bragg gratings inscribed by IR femtosecond irradiation,” Opt. Fiber Technol. 13(2), 98–107 (2007).
[CrossRef]

Z. Yong, C. Zhan, J. Lee, S. Yin, and P. Ruffin, “Multiple parameter vector bending and high-temperature sensors based on asymmetric multimode fiber Bragg gratings inscribed by an infrared femtosecond laser,” Opt. Lett. 31(12), 1794–1796 (2006).
[CrossRef] [PubMed]

Zhang, B.-L.

Zhang, L.

K. Zhou, Z. Yan, L. Zhang, and I. Bennion, “Refractometer based on fiber Bragg grating Fabry-Pérot cavity embedded with a narrow microchannel,” Opt. Express 19(12), 11769–11779 (2011).
[CrossRef] [PubMed]

Y. J. Rao, P. J. Henderson, D. A. Jackson, L. Zhang, and I. Bennion, “Simultaneous strain, temperature and vibration measurement using a multiplexed in-fibre-Bragg-grating/fibre-Fabry-Perot sensor system,” Electron. Lett. 33(24), 2063–2064 (1997).
[CrossRef]

Zhang, X.-L.

Zhou, K.

Zhu, F.

Zhu, T.

Zhu, Y.

C. Zhan, Y. Zhu, S. Yin, and P. Ruffin, “Multi-parameter harsh environment sensing using asymmetric Bragg gratings inscribed by IR femtosecond irradiation,” Opt. Fiber Technol. 13(2), 98–107 (2007).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

L. Men, P. Lu, and Q. Chen, “Intelligent multiparameter sensing with fiber Bragg gratings,” Appl. Phys. Lett. 93(7), 071110 (2008).
[CrossRef]

P. Lu, L. Men, K. Sooley, and Q. Chen, “Tapered fiber Mach-Zehnder interferometer for simultaneous measurement of refractive index and temperature,” Appl. Phys. Lett. 94(13), 131110 (2009).
[CrossRef]

Electron. Lett. (1)

Y. J. Rao, P. J. Henderson, D. A. Jackson, L. Zhang, and I. Bennion, “Simultaneous strain, temperature and vibration measurement using a multiplexed in-fibre-Bragg-grating/fibre-Fabry-Perot sensor system,” Electron. Lett. 33(24), 2063–2064 (1997).
[CrossRef]

Fiber Integr. Opt. (1)

O. Frazão, L. A. Ferreira, and F. M. Araújo, “Applications of fiber optic grating technology to multi-parameter measurement,” Fiber Integr. Opt. 24(3–4), 227–244 (2005).

IEEE Photon. Technol. Lett. (1)

S.-M. Lee, S. S. Saini, and M.-Y. Jeong, “Simultaneous Measurement of refractive index, temperature, and strain using etched-core fiber Bragg grating sensors,” IEEE Photon. Technol. Lett. 22(19), 1431–1433 (2010).
[CrossRef]

J. Lightwave Technol. (3)

Meas. Sci. Technol. (2)

C. Trono, F. Baldini, M. Brenci, F. Chiavaioli, and M. Mugnaini, “Flow cell for strain- and temperature-compensated refractive index measurements by means of cascaded optical fibre long period and Bragg gratings,” Meas. Sci. Technol. 22(7), 075204 (2011).
[CrossRef]

H.-K. Kang, H.-J. Bang, C.-S. Hong, and C.-G. Kim, “Simultaneous measurement of strain, temperature and vibration frequency using a fiber-optic sensor,” Meas. Sci. Technol. 13(8), 1191–1196 (2002).
[CrossRef]

Opt. Eng. (1)

W. Jin, W. C. Michie, G. Thursby, M. Konstantaki, and B. Culshaw, “Simultaneous measurement of strain and temperature: error analysis,” Opt. Eng. 36(2), 598–609 (1997).
[CrossRef]

Opt. Express (4)

Opt. Fiber Technol. (1)

C. Zhan, Y. Zhu, S. Yin, and P. Ruffin, “Multi-parameter harsh environment sensing using asymmetric Bragg gratings inscribed by IR femtosecond irradiation,” Opt. Fiber Technol. 13(2), 98–107 (2007).
[CrossRef]

Opt. Laser Technol. (1)

D. A. C. Enríquez, A. R. da Cruz, and M. T. M. R. Giraldi, “Hybrid FBG-LPG sensor for surrounding refractive index and temperature simultaneous discrimination,” Opt. Laser Technol. 44(4), 981–986 (2012).
[CrossRef]

Opt. Lett. (11)

D. J. J. Hu, J. L. Lim, M. Jiang, Y. Wang, F. Luan, P. P. Shum, H. Wei, and W. Tong, “Long period grating cascaded to photonic crystal fiber modal interferometer for simultaneous measurement of temperature and refractive index,” Opt. Lett. 37(12), 2283–2285 (2012).
[CrossRef] [PubMed]

H.-J. Kim, O.-J. Kwon, S. B. Lee, and Y.-G. Han, “Polarization-dependent refractometer for discrimination of temperature and ambient refractive index,” Opt. Lett. 37(11), 1802–1804 (2012).
[CrossRef] [PubMed]

P. Lu, J. Harris, Y. Xu, Y. Lu, L. Chen, and X. Bao, “Simultaneous refractive index and temperature measurements using a tapered bend-resistant fiber interferometer,” Opt. Lett. 37(22), 4567–4569 (2012).
[CrossRef] [PubMed]

J. Wo, G. Wang, Y. Cui, Q. Sun, R. Liang, P. P. Shum, and D. Liu, “Refractive index sensor using microfiber-based Mach-Zehnder interferometer,” Opt. Lett. 37(1), 67–69 (2012).
[CrossRef] [PubMed]

P. Polynkin, A. Polynkin, N. Peyghambarian, and M. Mansuripur, “Evanescent field-based optical fiber sensing device for measuring the refractive index of liquids in microfluidic channels,” Opt. Lett. 30(11), 1273–1275 (2005).
[CrossRef] [PubMed]

Q. Wang and G. Farrell, “All-fiber multimode-interference-based refractometer sensor: proposal and design,” Opt. Lett. 31(3), 317–319 (2006).
[CrossRef] [PubMed]

M. C. Phan Huy, G. Laffont, V. Dewynter, P. Ferdinand, P. Roy, J.-L. Auguste, D. Pagnoux, W. Blanc, and B. Dussardier, “Three-hole microstructured optical fiber for efficient fiber Bragg grating refractometer,” Opt. Lett. 32(16), 2390–2392 (2007).
[CrossRef] [PubMed]

O. Frazão, T. Martynkien, J. M. Baptista, J. L. Santos, W. Urbanczyk, and J. Wojcik, “Optical refractometer based on a birefringent Bragg grating written in an H-shaped fiber,” Opt. Lett. 34(1), 76–78 (2009).
[CrossRef] [PubMed]

M. Han, F. W. Guo, and Y. F. Lu, “Optical fiber refractometer based on cladding-mode Bragg grating,” Opt. Lett. 35(3), 399–401 (2010).
[CrossRef] [PubMed]

Z. Yong, C. Zhan, J. Lee, S. Yin, and P. Ruffin, “Multiple parameter vector bending and high-temperature sensors based on asymmetric multimode fiber Bragg gratings inscribed by an infrared femtosecond laser,” Opt. Lett. 31(12), 1794–1796 (2006).
[CrossRef] [PubMed]

O. Frazão, R. M. Silva, J. Kobelke, and K. Schuster, “Temperature- and strain-independent torsion sensor using a fiber loop mirror based on suspended twin-core fiber,” Opt. Lett. 35(16), 2777–2779 (2010).
[CrossRef] [PubMed]

Phys. Scr. (1)

S. Singh, “Refractive index measurement and its applications,” Phys. Scr. 65(2), 167–180 (2002).
[CrossRef]

Smart Mater. Struct. (1)

T. Mawatari and D. Nelson, “A multi-parameter Bragg grating fiber optic sensor and triaxial strain measurement,” Smart Mater. Struct. 17(3), 035033 (2008).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

(a) A SEM cross-sectional image of the bend-insensitive fiber etched with 5% hydrofluoric acid solution for 2 minutes; (b) A schematic illustration of the tapered bend-insensitive fiber based Mach-Zehnder interferometer under various external disturbances with an inset of the abrupt taper picture.

Fig. 2
Fig. 2

Flow chart of the demodulation algorithm for an interference spectrum between the fundamental mode and multiple cladding modes.

Fig. 3
Fig. 3

(a) Transmission spectrum of the BIF-MZI suspended in air at 24.6 °C with zero-strain; (b) FFT spectrum of the BIF-MZI with an inset of the simulated mode field patterns of the fundamental mode, IC mode, OC-1 mode, the OC-2 mode, the OC-3 mode, and OC-4 mode respectively.

Fig. 4
Fig. 4

(a) Filtered transmission spectra of the BIF-MZI corresponding to isolated spatial frequency components; (b) Spatial frequency dependent phase spectrum of the BIF-MZI.

Fig. 5
Fig. 5

Transmission spectra of the BIF-MZI submerged in solutions of 10% and 25% glycerol at 20.0 °C with zero-strain.

Fig. 6
Fig. 6

Filtered transmission spectra of the BIF-MZI in solutions of 10% and 25% glycerol corresponding to different groups of outer-cladding modes of (a) the OC-1 mode, (b) the OC-2 mode, and (c) the OC-3 mode.

Fig. 7
Fig. 7

Spatial frequency dependent phase spectra of the BIF-MZI in solutions of 10% and 25% glycerol.

Fig. 8
Fig. 8

Peak wavelength shift calibration curves for (a) refractive index, (b) temperature, and (c) axial strain, for the OC-1, OC-2, and OC-3 modes.

Fig. 9
Fig. 9

Phase shift calibration curves for (a) refractive index, (b) temperature, and (c) axial strain, for the OC-1, OC-2, and OC-3 modes.

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

Δ Φ ij = Φ 01 Φ ij = 2πL λ ( n eff 01 n eff ij )= 2πΔ n eff ij L λ ,
λ m ij = Δ n eff ij L m .
I= I 01 + ij I ij +2 ij I 01 I ij cos( 2πΔ n eff ij L λ ) .
Δ λ ij = λ m1 ij λ m ij λ 0 2 Δ n eff ij L ,
ξ ij = 1 Δ λ ij Δ n eff ij L λ 0 2 .
δλ=δ( Δ n eff L m )=( δ( Δ n eff ) Δ n eff )λ,
δΦ=δ( 2π λ 0 2 ξ λ )=2πξδλ.
δλ=( δ( Δ n eff,RI ) Δ n eff )λ,
δΦ= 2πLδ( Δ n eff,RI ) λ .
δλ=( δ( Δ n eff,T ) Δ n eff )λ,
δΦ= 2πLδ( Δ n eff,T ) λ .
δλ=( δL L + δ( Δ n eff,ε ) Δ n eff,ε )λ,
δΦ= 2π( Δ n eff,ε δL+Lδ( Δ n eff,ε ) ) λ .
( Δ λ 1 Δ λ 2 Δ λ 3 )= M λ RI,T,ε ( ΔRI ΔT Δε )=( C λ RI 1 C λ T 1 C λ ε 1 C λ RI 2 C λ T 2 C λ ε 2 C λ RI 3 C λ T 3 C λ ε 3 )( ΔRI ΔT Δε ),
( ΔRI ΔT Δε )= M λ RI,T,ε 1 ( Δ λ 1 Δ λ 2 Δ λ 3 ),
( Δ Φ 1 Δ Φ 2 Δ Φ 3 )= M Φ RI,T,ε ( ΔRI ΔT Δε )=( C Φ RI 1 C Φ T 1 C Φ ε 1 C Φ RI 2 C Φ T 2 C Φ ε 2 C Φ RI 3 C Φ T 3 C Φ ε 3 )( ΔRI ΔT Δε ),
( ΔRI ΔT Δε )= M Φ RI,T,ε 1 ( Δ Φ 1 Δ Φ 2 Δ Φ 3 ),
( δRI δT δε )= M Φ ' RI,T,ε Δ ( δ Φ 1 δ Φ 2 δ Φ 3 ),

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