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Abstract
In-situ monitoring of refractive index changes during a liquid-solid phase transition is achieved by measurement of the transmission spectrum from a single tilted fiber Bragg grating immersed in water. Differential wavelength shifts of multiple mode resonances are used to eliminate cross-talk from temperature, throughout the phase transition, and from strains occurring after solidification. The measured sudden shift of refractive index at the phase transition is shown to be consistent with the expected difference from water to ice, in spite of the observed onset of compressive strain on the fiber by the frozen water. Beyond the obvious application to research on the dynamics of liquid-solid phase transitions, this work demonstrates the multiparameter measurement capabilities of multiresonant gratings.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Conventional wisdom states that liquid water played an indispensable role in the origin of life on our planet [1], where research fields of water material (including water vapor and water ice) have covered astronomy [2], chemistry [3], life science [4], and so on. On the earth’s surface, water mainly exists as liquid water and solid ice, which can be reversibly changed to each other during a freezing or melting process under particular conditions of temperature and atmospheric pressure [5]. To better understand and manipulate such a liquid-solid phase transition, various monitoring methods have been developed to trace physical or/and chemical changes (e.g., refractive index change) occurred in the phase transition, which involves thermoanalytical [6], acoustic [7], and spectroscopy [8] technologies. However, the reported thermoanalysis and spectroscopy-based methods are with bulk components and not suitable for in-situ monitoring; though the acoustic method can monitor submillimeter water/ice samples, the delicate sensing probe may limit some practical applications.
Fiber-optic sensors, benefiting from compact size, robustness, and remote sensing capability, are ideal for in-situ monitoring of the water-ice phase transition. For example, fiber Bragg grating (FBG) sensors have been used for monitoring temperature and strain/pressure changes during different types of phase transition of water [9,10]. However, such FBG sensors only monitor wavelength shift of Bragg resonance that is insensitive to surrounding refractive index (SRI) changes. Yet, to monitor SRI changes during various kinds of liquid-solid phase transitions, three different approaches of fiber-optic refractive index sensors have been reported. The simplest form used the dependence of the Fresnel reflection coefficient at the end-face of a cleaved fiber on the refractive index of the medium in which the fiber is inserted [11–13]. Provided that the refractive index and thermo-optic coefficient of the fiber is well known, this results in a refractive index measurement of the sample, and thus of the phase transition, but requires a separate temperature measurement as well as some ways to compensate for source and channel power fluctuations. Another fiber-optic configuration relied on evanescent field sensing of SRI by a singlemode-multimode-singlemode fiber interferometer [14,15]. These do not require power stability or reference but they can only “measure” refractive index variations, not absolute ones and they also need a separate temperature measurement. Finally, the latter approach was made into an all-fiber system to measure both the refractive index and temperature but required two co-located fiber sensors: a standard temperature-sensing FBG and a fiber interferometer to measure changes in SRI [16,17]. In these earlier works, the additional cross-sensitivity to strain once the medium becomes solid and its evolution as the temperature continues to lower has not been quantified.
To overcome the issues of temperature and strain contaminations in the fiber-optic refractive index sensing of liquid-solid phase transition and to provide absolute refractive index measurements, we propose and demonstrate a tilted fiber Bragg grating (TFBG) sensor for in-situ monitoring of refractive index change during a water-ice phase transition. TFBG couples light from a single mode core (i.e., core mode) to the highly multimode cladding (i.e., cladding modes) [18,19], which forms multiple transmission resonances distributed unevenly in the spectrum. Since the resonances are associated with different modes, their relative sensitivities to temperature, strain, and SRI are also different during water-ice phase transitions, and these sensitivities can be determined empirically by controlled experiments to calibrate the response of the TFBG to be used. With regards to the thermal sensitivities of TFBG resonances, we introduce a constant temperature gauge factor for their wavelength shifts (KT = 1/λ ·∂λ/∂T) of 6.25 × 10−6 °C-1 [18,19]. For the strain contribution to the wavelength shifts, a recalibration similar to that use in Ref. [19] for temperature is carried out to determine a strain gauge factor (Kε) that will be used to measure the contribution of strain to the wavelength shifts. Next, from simultaneously measured TFBG spectrum and environmental temperature, we quantify the temperature- and strain-induced wavelength shifts of core and cladding modes, and remove their effects on the monitoring of SRI change during the phase transition. Finally, we validate the experimentally measured SRI-induced wavelength shifts, based on simulations of refractive index of solid ice on TFBG around the freezing point.
2. Methods
2.1 Theoretical consideration
TFBG is a tilted periodic structure inscribed in the core of an optical fiber, where the cross-sectional pattern of the core index modulation introduces a self-backward coupling of the core mode and multiple backward couplings between core mode and cladding modes [Fig. 1(a)]. Based on the phase matching condition [20], the multiresonant wavelengths of guided TFBG modes can be expressed as
where λB and λcl are the resonant wavelengths of the core mode and a given cladding mode, respectively, $N_{eff}^{co}$ and $N_{eff}^{cl}$ are the effective core and cladding mode indices at the corresponding resonant wavelengths, respectively, ΛZ is the projection of the grating period along the core axis (i.e., axial grating periodicity).
Fig. 1. Optical monitoring of water-ice phase transition with a multiresonant TFBG. (a) Schematic of backward mode coupling in TFBG. A backward-propagating cladding mode, with evanescent field around fiber surface, is coupled from a forward-propagating incident core mode. (b) Experimental setup of in-situ monitoring of TFBG spectrum and temperature for water-ice phase transition. The arrows indicate propagation directions of optical (black) and electrical (dark blue) signals. PC: computer. (c) Transmission spectrum of a 7° TFBG used in experiments, where the spectrum was measured under water surroundings at ∼20 °C. Four resonances of three cladding modes and one core mode, with wavelengths of λ1, λ2, λ3 and λB (indicated by dashed lines), respectively, are selected for monitoring the phase transition process (see Sec. 3.2). Insets show intensity patterns of typical modes within the selected TFBG resonances (see Fig. S1 of the Supplementary information for full size images and more details).
Next, we consider a straight TFBG surrounded by water, where a decreasing temperature across the freezing point of water can induce a water-ice phase transition. The TFBG is subjected to the three effects of temperature (T), axial strain (ε), and surrounding refractive index (nSRI). Based on the resonant wavelength dependence of the TFBG modes on the three effects [20], the total wavelength shifts of a cladding mode resonance during the water-ice phase transition, can be described as:
It is noted that the term of ΔλSRI in Eq. (3) does not contribute to the phase transition-induced wavelength shift of the core mode [i.e., $\varDelta {\lambda _{Tot,B}} = ({{K_T}\mathrm{\Delta }T + {K_\varepsilon }\mathrm{\Delta }\varepsilon } ){\lambda _B}$], since it is insensitive to the surrounding refractive index change (ΔnSRI).
Finally, it is found that KT can be regarded as a constant around 6.25 × 10−6 °C-1 over the full TFBG spectrum [19], while Kε will be determined by further investigations for different TFBG resonances (see Sec. 3.1) [18]. Assuming that KT and Kε are known, the effect of Δε on the TFBG sensor could be quantified by a synchronized monitoring of ΔλTot,B and ΔT (that can be easily measured by a thermometer). Therefore, based on the known ΔT and Δε, ΔλT and Δλε can be estimated and removed from ΔλTot of the cladding modes in Eq. (3), which will allow to determine the ΔnSRI-induced ΔλSRI in situ during the water-ice phase transition.
2.2 TFBG fabrication
TFBG sensors used in this work, were written in hydrogen-loaded CORNING SMF-28 fibers, with a pulsed KrF excimer laser at 248 nm (PM-848, Light Machinery), by using the phase-mask method [20]. Hydrogenation process of the SMF-28 fibers was performed under a pressure of 15.2 MPa, a temperature of 20 °C, and a duration of 14 days. All fabricated TFBGs were annealed under 120 °C for 12 hours to release the hydrogen remaining inside optical fiber prior to sensing experiments. Considering a limited spectral range (1520-1570 nm) of an optical sensor interrogator used for in-situ TFBG monitoring (see Sec. 2.3), a tilt angle of 7° and a Bragg wavelength close to 1570 nm were chosen, so that the core mode and cladding mode resonances can be fully covered within the 50 nm spectral region. Since the sensitivity does not depend on tilt angle, but rather on mode effective index, there is nothing specific about the choice of 7° apart from the fact that it resulted in major resonances with amplitudes of >5 dB [Fig. 1(c)] and more across our measurement range. To avoid Bragg wavelength shift with the tilt angle, both of the phase mask and the optical fiber were rotated along the direction of laser illumination in the TFBG inscription setup. Finally, to avoid broadening and/or splitting of mode resonances caused by possible non-uniformity of the freezing transition along the TFBG, relatively short 1-cm long TFBGs were fabricated.
2.3 Experimental setups
Two experimental setups were involved in this work: a) a conventional setup [20] was used for measuring TFBG transmission spectra in the calibration experiments of strain gauge factor, where the setup includes a broadband amplified spontaneous emission (ASE) source (ASE-CL-17-N-B, HOYATEK) and an optical spectrum analyzer (OSA) (AQ6317B, ANDO); b) a swept laser interrogator (SLI) (si720, Micron Optics) was used for continuous acquisition of TFBG spectra during the in-situ monitoring of water-ice phase transition [Fig. 1(b)], where the SLI consists of build-in light source and detector. The calibration of strain gauge factor only requires discrete TFBG spectra under static strain values, so that the AQ6317B OSA with a resolution of 0.02 nm is sufficient and provides more accurate wavelength shift values. However, to monitor a fully dynamic process of water-ice phase transition, a rapid TFBG spectral measurement is necessary, where we used the si720 SLI with a spectral range from 1520 to 1570 nm, a resonance wavelength measurement accuracy of 2.5 pm, and a sampling rate of full spectrum of 0.5 Hz.
During the in-situ monitoring of water-ice phase transition (e.g., water freezing), the TFBG sensor was firstly taped on a frame that was submerged in a water container, then placed inside a commercial freezer with an internal temperature below −10 °C. The K-type thermocouple of a thermometer (TMD-56, Amprobe) with a temperature resolution of 0.1 °C, was fixed parallel to the TFBG sensor under same surroundings, to monitor the temperature change during the phase-transition process. Finally, it is noted that we started the simultaneous acquisitions of TFBG spectra and temperature immediately after the introduction of the devices in the freezer and closing its door, and stopped when the thermometer indicated a temperature below −10 °C.
2.4 Data preprocessing
Due to the spectral sampling rate of 0.5 Hz and a monitoring duration longer than one hour, a relatively large data volume of more than 2000 TFBG spectra was acquired in single phase transition experiment. To extract resonant wavelengths of core mode and multiple cladding modes [Fig. 1(c)], we made a MATLAB code with following procedure: a) find the Bragg wavelength from each TFBG spectrum by locating the intensity minimum in the wavelength region from 1567 to 1570 nm; b) locate a narrow spectral window of ∼300 pm around a relatively stable distance from the Bragg resonance for each selected cladding mode; c) determine resonant wavelengths of the cladding modes, by locating minima within the designated spectral windows. Thus, raw wavelengths of selected mode resonances can be automatically extracted from thousands of TFBG spectra in MATLAB. It is noted that fitting individual resonances with advanced functions (e.g., Gaussian) can provide more accurate wavelength measurement, though the data preprocessing is time-consuming for such large spectral data volume. Moreover, benefiting from the rapid spectral sampling, other methods such as temporal sliding averaging or low-pass filtering can be applied on the time evolution of extracted wavelengths to further enhance the measurement accuracy.
2.5 Simulation
We simulate the effective mode indices of the selected cladding modes, under specific wavelengths, temperature, and SRIs, for the validation of corresponding experimental results [21–24]. All simulations were performed with a commercial general fiber solver (FIMMWAVE, Photon Design) [23–25], which provides a rigorous mode solution to vectorial wave equation in cylindrical co-ordinates. The simulation model includes three layers: the fiber core, fiber cladding, and surroundings, where the core and cladding diameters are 8.2, and 125 µm, respectively, and the calculation boundary is located at a diameter of 160 µm. For material refractive indices, we simply assumed a pure silica cladding layer with a temperature-dependent refractive index dispersion of nSiO2(λ,T) [26], a doped silica core layer with an empirically determined core refractive index of nSiO2(λ,T) + 8.2e-3 [24], and a surrounding layer with an adjustable refractive index (water or ice). Finally, it is noted that the two sets of polarized modes within the selected cladding resonances are largely overlapped under conditions of water/ice surroundings [Fig. 1(c)], so that only TE-polarized HE1,m and HE2,m modes are considered in the simulations [24].
3. Results
3.1 Calibration of strain gauge factor
Similar with the calibration of the temperature gauge factor for TFBGs [19], a strain gauge factor of a given TFBG mode can be estimated from dividing the strain sensitivity of the mode by the corresponding resonant wavelength. First, we measured a group of transmission spectra from a 7° TFBG [Fig. 2(a)] under various axial strains, which were quantified by a strain gage. To investigate the distribution of strain gauge factors of different TFBG modes, resonant wavelengths of 21 modes (20 cladding modes and one core mode) are extracted from the TFBG spectrum under each axial strain, by using a Gaussian fitting method [18]. Second, the strain sensitivity of each selected TFBG resonance is estimated from a linear fitting slope of extracted resonant wavelength versus applied strain [for instance, a strain sensitivity of the core mode resonance is estimated at 1.2 pm/µε in Fig. 2(b)]. Third, based on the estimated strain sensitivities [Fig. 2(c)] and corresponding gauge factors [Fig. 2(d)] across the TFBG spectrum, a positive wavelength dependence is observed for both parameters. It is worthy to note that the reduced strain sensitivity with an increased wavelength distance to the Bragg resonance (i.e. decreased effective mode index), agrees well with the previously reported results [20,27], while the range of values obtained are consistent with other results on the photo-elastic properties of fiber gratings [18,28–30]. Finally, with a linear fitting of the wavelength-dependent strain gauge factors, a calibrated function of Kε(λ) = −1.28e-6 + 1.3e-9×λ is obtained [Fig. 2(d)], which can be further used for estimating the contributions of strain to the wavelength shifts of different resonances of the TFBGs in this work.
Fig. 2. Calibration of wavelength-dependent strain gauge factor for TFBG inscribed in SMF-28 fiber. (a) Transmission spectrum of a 7° TFBG, used in the calibration experiment, measured under zero-axial strain (ε = 0). (b) Extracted Bragg wavelengths versus various axial strains, applied on the TFBG. The red line indicates a linear fitting function. (c) Fitted strain sensitivities of different TFBG mode resonances. Note that five resonances are randomly selected within every 10 nm spectral region from 1520 to 1560 nm. Error bars are estimated from 95% confidence intervals of the linear fitting slopes. (d) Corresponding strain gauge factors at different resonant wavelengths. Linear and quadratic functions (red lines) are applied for fitting the wavelength-dependent strain sensitivities (c) and gauge factors (d), respectively.
3.2 In-situ monitoring of water-ice phase transition
To experimentally demonstrate the in-situ monitoring capability of ΔnSRI, induced by the water-ice phase transition, for a TFBG sensor, we performed a freezing experiment of phase transition from liquid water to solid ice, with a temperature range from ∼20 down to −10 °C. Based on the above-mentioned experimental setup (see Sec. 2.3), we continuously acquired ∼2100 TFBG spectra and ∼4200 temperature points, during a ∼70 mins in-situ monitoring of the water freezing process. Due to the various nSRI sensitivities of cladding modes [20,31], three cladding resonances with wavelengths of 1523.81, 1532.95, and 1541.94 nm [i.e., λ1, λ2, and λ3 in Fig. 1(c)] are selected for monitoring ΔnSRI-induced ΔλSRI. More specifically, λ1 is possibly the best measurable resonance with highest SRI sensitivity for monitoring of ΔnSRI, while λ2 and λ3 with lower SRI sensitivities are mainly selected for validating the compensation method of ΔT and Δε contaminations (see Sec. 2.1). By using the data preprocessing method (see Sec. 2.4), we extracted resonant wavelengths of the selected cladding modes (λ1, λ2, and λ3) and core mode (λB) from all acquired TFBG spectra, where a 0.05 Hz low-pass filter was applied to smooth temporal fluctuations of the extracted wavelengths.
From the time-dependence of the measured wavelength shifts [Fig. 3(a-d)], the whole process of water freezing can be divided into three phases, consisting of liquid water cooling (>0 °C), constant temperature of the water-ice mixture (∼0 °C), and cooling solid ice (<0 °C). While the time evolution of the extracted resonant wavelength shifts (i.e., ΔλTot) show somewhat complex variations with general blue shifts of ∼0.9 nm [Fig. 3(a)], small but clear deviations between the resonances are observed after ∼35th minute in the process. Based on the constant KT of 6.25 × 10−6 °C-1, the contributions of the temperature ΔT to the wavelength shifts (ΔλT) corresponds to total blue shifts of ∼0.3 nm over the full freezing process [Fig. 3(b)]. Next, by subtracting ΔλT from ΔλTot for the core mode (λB), Δε and corresponding Δλε of the cladding modes are calculated with the calibrated Kε(λ) [Fig. 2(d)], where remaining blue shifts of ∼0.6 nm with increased deviations are observed [Fig. 3(c)]. Finally, by subtracting ΔλT and Δλε from ΔλTot for the cladding mode resonances, the remaining wavelength shifts of ΔλSRI due to ΔnSRI are obtained [Fig. 3(d)]. The measured time evolution of ΔλSRI consist of four different phases [Fig. 3(d)]: a) small and slow red-shifts of <0.01 nm from 0 to ∼35 mins; b) large and rapid blue-shifts of ∼0.04, ∼0.06, and ∼0.08 nm for λ1, λ2, and λ3, respectively, from ∼35 to ∼40 mins; c) small and slow blue-shifts of ∼0.01 nm from ∼40 to 65 mins; d) small and relatively fast red-shifts of <0.01 nm from ∼65 to 70 mins.
Fig. 3. Wavelength shifts of four selected TFBG resonances, during phase transition from liquid water to solid ice (i.e., water freezing). (a-d) Time evolution of wavelength shifts of four mode resonances, induced by general (a) and individual effects of temperature (b), strain (c), and surrounding refractive index (d), in water-ice phase transition. Corresponding time evolution of environmental temperature, measured from a thermocouple, is included in (a-d). Dashed lines indicate the start and end of the water-ice mixture phase where the temperature remains fixed at 0 °C. (e-h) Corresponding results of wavelength shifts in (a-d), shown along temperature dimension from ∼20 down to −10 °C. The changes of temperature (ΔT), strain (Δε), and SRI (ΔnSRI) are shown with the corresponding wavelength shifts in (f-h).
To better understand the time evolutions of ΔλTot, ΔλT, Δλε, and ΔλSRI of the TFBG resonances during the water freezing process [Fig. 3(a-d)], the wavelength shifts are replotted against temperature (using the thermocouple readings at each time point) [Fig. 3(e-h)]. While the temperature-induced wavelength shifts ΔλT are linear [Fig. 3(f)], the other wavelength shifts [Fig. 3(e, g, h)] seem more complex and indicate three distinguishable phases of liquid water (>0 °C), water-ice mixture (∼0 °C), and solid ice (<0 °C) for the TFBG surroundings. Based on the comparisons between ΔλTot, ΔλT, and Δλε [Fig. 3(e-g)], it is found that ΔλT is dominant in ΔλTot with nearly zero strain on the TFBG (i.e., Δλε ≈ 0@T > 0 °C) during the water phase [Fig. 3(g)]. On the other hand, when the temperature reaches 0 °C, Δλε jumps suddenly by around −0.3 nm as the ice “clamps” down on the TFBG and then continues to decrease as it contracts (with the TFBG) by ∼0.25 nm with further cooling [Fig. 3(g)]. Moreover, ΔλSRI of the cladding modes show positive increases of <0.01 nm for decreasing temperature towards 0 °C [Fig. 3(h)], indicating an increased nSRI in accordance with the thermo-optic properties of liquid water [32]. The much larger variations of ΔλSRI at the mixture phase (T ∼0 °C), around 0.05, 0.07, and 0.1 nm for λ1, λ2, and λ3 [Fig. 3(h)], respectively, indicate a large reduction of nSRI caused by the water-ice phase transition at 0 °C. Further temperature decrease leads again to an increase in ΔλSRI associated with contraction and densification of the solid ice. Finally, for illustrating the origins of ΔλT, Δλε, and ΔλSRI of TFBG resonances, the corresponding ΔT, Δε, and ΔnSRI estimated from T, Δλε@λB (i.e., Δλε measured at λB), and ΔλSRI@λ1, respectively, are also included by the right-hand side vertical axes in Fig. 3(f-h). It is noted that a constant SRI sensitivity of 2.86 nm/RIU is assumed (based on simulation results of Fig. 4) to extract ΔnSRI from ΔλSRI@λ1.
Fig. 4. Validation of SRI-induced wavelength shifts during water-ice phase transition. (a) Schematic of rearrangement of water (H2O) molecules surrounding optical fiber surface, caused by water freezing. (b) Changes of ΔλSRI of three selected cladding mode resonances from water (0 °C) to ice (−7 °C) surroundings, extracted from Fig. 3(h). (c) Corresponding changes of effective cladding mode indices (ΔNeff), estimated from ΔλSRI in (b). The error bars in (b) and (c), are estimated from the wavelength measurement accuracy of ∼3.9 pm. (d) Simulated refractive indices of surrounding ice layer at −7 °C, at selected cladding mode wavelengths. A reported refractive index dispersion of water ice at −7 °C [34], is indicated by the dashed black curve. The error bars are determined by the wavelength accuracy of ∼3.9 pm and corresponding SRI sensitivities of the three cladding modes.
3.3 Validation of experimental ΔλSRI at the freezing point
The phase transition between liquid water and solid ice, causes a ∼9% density decrease at the freezing point of 0 °C [Fig. 4(a)] [33], resulting in a sudden large change of refractive index (ΔnSRI). To validate the measurements of ΔnSRI-induced ΔλSRI [Fig. 3(h)], the step changes of ΔλSRI@0 °C (i.e., ΔλSRI measured at 0 °C) are ideal for simulating such density-dependent nSRI. However, based on the closest temperature conditions of reported refractive indices of water and ice at TFBG wavelength region, we assume a temperature-dependent refractive index dispersion of the liquid water at 0 °C [32], and simulate wavelength-dependent nSRI of solid ice at −7 °C [34], with the experimental effective index changes of the three cladding modes, where we compare the simulated nSRI with related reference values for validating the experimental results [Fig. 3(h)]. More specifically, based on the three-layer simulation model [Fig. 4(a), see Sec. 2.5], an effective core mode index of 1.44828 is firstly computed at λB and 0 °C, where a corresponding grating period (ΛZ) of 541.99 nm is estimated with Eq. (1). Next, the changes of the experimental ΔλSRI from water@0 °C to ice@−7 °C of −0.094, −0.067, and −0.048 nm [Fig. 4(b)], are converted into the corresponding changes of effective mode index (i.e., ΔNeff) of −1.74e-4, −1.23e-4, and −0.89e-4 [Fig. 4(c)], respectively, with Eq. (2). After, we assume a refractive index baseline of liquid water@0 °C [32], and run the simulation model at the resonant wavelengths (λ1, λ2, and λ3) with trial nSRI values of solid ice@−7 °C [Fig. 4(d)], until the simulated ΔNeff equal to the experimental ones in Fig. 4(c). The uncertainties of the calculated nSRI are estimated from the experimental wavelength accuracy divided by the SRI sensitivities (ΔλSRI/ΔnSRI) of different mode resonances. The wavelength accuracy is defined as a sum of the SLI measurement accuracy of 2.5 pm and a maximum standard deviation of ΔλSRI fluctuations of ∼1.4 pm that is extracted from the time evolutions of ΔλSRI@0 °C under the water surroundings [i.e., from 20 to 35 mins in Fig. 3(d)]. The estimated nSRI uncertainties of 1.4e-3@λ1, 2.0e-3@λ2, and 2.9e-3@λ3 are indicated as error bars in Fig. 4(d), where a cladding mode resonance at shorter wavelength (e.g., λ1) clearly shows a smaller nSRI uncertainty due to its relatively higher SRI sensitivity. Finally, the simulated results of nSRI@−7 °C of solid ice, are compared with the related wavelength-dependent refractive indices at the same temperature [34], where the relative differences are only 0.60%, 0.68%, and 0.85% at λ1, λ2, and λ3, respectively [Fig. 4(d)]. Therefore, considering the temperature-dependence of nSRI of solid ice [34], the in-situ monitoring results of ΔλSRI with the TFBG sensor, likely reflect the real reduction of nSRI during the water-ice phase transition at 0 °C.
4. Discussion
One of the formidable advantages for a multiresonant grating (e.g., TFBG) is the self-compensation capability of cross-sensitivities [18,35], such as temperature and strain effects on refractive index sensing. Usually, such contaminations induced by temperature and strain perturbations can be made significantly smaller (by experiment design to control temperature and strain) than the desired wavelength response to refractive index change for conventional TFBG sensors [20]. However, for monitoring ΔnSRI during the water-ice phase transition, the major contributions to the wavelength shifts of TFBG resonances are inevitably the temperature and strain [(ΔλT+Δλε)/ΔλTot > 90%, Fig. 3(a-c, e-g)]. Moreover, ΔnSRI and Δε are also dependent on ΔT. To solve the issue, we involve the temperature and strain gauge factors to recalculate the mode-dependent temperature and strain sensitivities, so that ΔλT and Δλε of the TFBG resonances are obtained from the thermometer-measured ΔT [Fig. 3(b, f)] and Bragg resonance-estimated Δε [Fig. 3(c, g)], respectively. As a result, the pure ΔλSRI that only contribute <10% of ΔλTot are quantified for the selected cladding mode resonances [Fig. 3(d, h)]. With regards to the strain contribution, the results reported here indicate a relatively small but clear variation of the gauge factor Kε with wavelength that appears to have been overlooked in earlier reports on the strain sensitivity of TFBG cladding modes [30].
For TFBG-based refractive index sensors, the last guided cladding mode (i.e., cutoff mode) with an effective index closest to nSRI provides the highest refractive index sensitivity [23,24]. Unfortunately, limited by the 50 nm wavelength range of the SLI used for the in-situ monitoring (see Sec. 2.3), the effective index of the last cladding mode around 1520 nm is only ∼1.356, which is still much higher than nSRI of 1.316 for water (and even more for ice) [32]. Also, the ΔλSRI results [Fig. 3(d, h)] clearly confirm the increase in sensitivity with decreasing resonance wavelength and better signal-to-noise ratio. The consequence of this is that the lowest cladding mode resonance (i.e., λ1) provides a measurement of nSRI that is closest to the reference value [Fig. 4(d)], but not by much as all the three resonances show relative differences of less than 1% from the expected values in water and ice. A proof of the higher accuracy of the lowest cladding mode resonance (i.e., λ1) is provided however by the clear increasing trend in the solid ice phase [Fig. 3(h)], where such a trend is not so evident from the other two resonances. As the sensitivity of resonances increases almost exponentially towards cutoff, a larger angle TFBG with longer Bragg wavelength should improve the accuracy of this approach. As an example, a TFBG with a Bragg wavelength at 1610 nm has a cutoff wavelength in water near 1537 nm, i.e., more than 70 nm away from the Bragg, compared to less than 50 nm here, and strong resonances are obtained at such distance from the Bragg by increasing the tilt angle to 10 degrees [24]. Therefore, a sensing interrogator with a wavelength range that can cover both of core mode and cutoff mode of the multiresonant TFBG sensor (i.e., greater than 70 nm), would allow for a significant increase in the accuracy of the in-situ monitoring of small ΔnSRI during the water-ice phase transitions.
5. Conclusion
In summary, we have experimentally demonstrated that a multiresonant TFBG sensor is capable of monitoring fully dynamic refractive index changes of ∼0.03 that are “hidden” into the large wavelength shifts of cladding modes due to temperature and strain effects occurring in a water-ice phase transition over a significant temperature excursion from +20 to −10 °C. In order to achieve the elimination of the temperature and strain contributions from the measurements of the cladding mode wavelength shifts, we used the core mode resonance and a separately measured temperature and applied temperature and strain gauge factors to correct the shifts of the cladding mode resonances. It was further demonstrated that simulations of the cladding mode resonance shifts could be used to determine the actual values of the surrounding refractive index for water and ice, within 1% accuracy. It was noted that this accuracy can be improved with modifications of the TFBG design and a wider spectrum interrogation system to access higher sensitivity modes near cutoff, associated with a careful calibration of the modifications of the core index dispersion of the TFBG due to its fabrication process [18,24]. Finally, it is important to note that the main aim of the in-situ monitoring of ΔλSRI during the water-ice phase transition, is to expand the sensing applications of the multiresonant TFBGs to more challenging environments with highly contaminated strain/temperature effect and rapid refractive index dynamics, but not to accurately measure absolute nSRI values. In particular, the phase transition was measured here with a time resolution of 2 seconds (limited by the instruments used), but there are fast spectral interrogators in the market with more than 30 kHz spectrum acquisition rates, which would open the way for liquid-solid phase transition measurements on sub-millisecond time scales.
Funding
National Natural Science Foundation of China (62105315, 12274386, 62275038, 11874323); National Key Research and Development Program of China (2021YFF0600203); Zhejiang Provincial Key Research and Development Program (2022C04007); Natural Science Foundation of Liaoning Province (2022-YGJC-84); Natural Sciences and Engineering Research Council of Canada (RGPIN-2019-06255).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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