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Abstract
A temperature-insensitive high-sensitivity refractive index sensor is proposed and experimentally demonstrated, which is based on utilization of a thinned helical fiber grating but with an intermediate period (THFGIP). Attributed to the reduced diameter and an intermediate period of the grating, the proposed sensor has a high surrounding refractive-index (SRI) sensitivity and a low temperature sensitivity. The average SRI sensitivity of the proposed sensor is up to 829.9 nm/RIU in the range of 1.3410–1.4480 RIU. Moreover, unlike the traditional sensitivity-enhancement method by increasing the waveguide dispersion factor, here the waveguide dispersion factor at the resonant wavelength was decreased by reducing the diameter of the fiber grating and as a result, the crosstalk effect due to the temperature change can be further suppressed. The proposed temperature-insensitive SRI sensor has the superiorities of simple structure, ease fabrication, and low cost, which could be found more potential applications in the SRI sensing fields.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Surrounding refractive index (SRI) sensing is of great importance in biological detection [1–3], chemical analysis [4], and environment monitoring [5]. Owing to those unique advantages, e.g., anti-electromagnetic interference, light weight, compact size, corrosion resistance, and high sensitivity to the ambient medium, the fiber-based SRI sensors have recently attracted a great interest [6–17]. To date, various of the fiber-based SRI sensors have been proposed and demonstrated, which include the long-period fiber grating (LFG)–based one [6], the cascaded fiber Bragg gratings (FBGs) but with droplet-like structure (CFBGD) one [7], the surface plasmon resonance (SPR)-based fiber one [8], the LFG but using the over-coupled resonant mode one [9], the dispersion turning point (DTP) method-based LFGs [10–12], the LFG with a reduced diameter one [13], the tapered no-core fiber (TNCF) [14], and the spindle-shaped few-mode fiber (SFF) one [15]. Most of the devices mentioned above enable to provide a high SRI sensitivity [7–13], meanwhile they are also very sensitive to the changes in other environment parameters such as temperature, torsion, and strain. As a result, the crosstalk effects among these testing parameters, especially for the crosstalk effect between the SRI and the temperature cannot avoided, which inevitably restrains the practical applications of these devices themselves.
To solve the above issue, the SRI sensors based on structures of the TNCF and SFF have been proposed and demonstrated, where the temperature-crosstalk effect due to the temperature change can be effectively eliminated [14,15], however such two SRI sensors still suffer from the deficiencies of complex structure, high loss, and significant difficulty in practical fabrication. Meanwhile, the FBG-based temperature-insensitive sensors [18–20] and the FBG-based temperature-compensation sensor [21] have also been proposed and demonstrated, however, all of them were not used as SRI sensors. As alternatives, most recently, the fiber gratings with a period less than 100 µm (FGIPs) [16,17] have been proposed and used as the SRI sensors, where the mode coupling happens between the core mode and the high radial-order cladding modes instead of the low radial-order ones in the conventional LFGs. In addition, the fiber gratings written in a thinned fiber (TFGs) [13,22] have been proposed and used as the SRI sensors, where the cladding diameter of the utilized fiber grating is purposely reduced. As a result, the obtained SRI sensitivities in both the FGIPs and the TFGs become much higher than those of conventional LFGs but the temperature cross-sensitivities are not greater than those of the conventional LFGs-based SRI sensors [13,16,17,22]. Although the thinned helical long-period fiber gratings (THLFGs) with low insertion-loss can easily be fabricated by controlling the velocity difference between two translational stages as the optical fiber is heated and rotated [13,22], the helical fiber grating with an intermediate period (HFGIP) written in a thinned single-mode fiber (THFGIP) has not been reported and demonstrated yet, which, however, is believed to have both a higher SRI sensitivity and a less temperature-sensitivity than those previous fiber-based SRI sensors since the parameter of the waveguide dispersion factor [22] can also be adjusted in addition to the condition of the short grating-period.
In this study, we propose and experimentally demonstrate a temperature-insensitive high-sensitivity SRI sensor, which was realized by using an intermediate-period helical fiber grating but written in a single-mode fiber with a reducing diameter. Attributed to the reduced diameter and an intermediate period of the grating, the SRI sensitivity in the proposed sensor is strongly enhanced. Moreover, unlike the traditional sensitivity-enhancement method by increasing the waveguide dispersion factor, here the waveguide dispersion factor at the resonant wavelength was decreased by reducing the diameter of the fiber grating and as a result, the crosstalk effect due to the temperature change can be further suppressed. The proposed temperature-insensitive SRI sensor has the superiorities of simple structure, ease fabrication, and low cost, which could be found more potential applications in the SRI sensing fields.
2. Operation principle
In a single-mode fiber-based LFG/HFGIP, since the mode coupling resonantly occurs between the core mode and the cladding mode at a specific wavelength, the phase matching condition is expressed by,
where Λ represents the period of the grating, λres represents the resonant wavelength, and Δne =nco,e-ncl,e represents the difference in effective index between the core mode (i.e., the fundamental mode LP01) and the specific cladding mode, in which nco,e and ncl,e are the effective indices of the core mode and the coupled cladding mode, respectively. As is reported that the temperature and SRI sensitivities for any one LFG/HFGIP can be expressed by the following two equations, respectively [10,22], where α represents the thermal expansion coefficient for unit length of the fiber. γ is the waveguide dispersion factor defined by, where Δng represents the group index difference, which is given byMoreover, the Гtemp and Гsur in Eqs. (2) and (3) describe the temperature and SRI dependences, respectively, which can be expressed by
To testify the above assumption, we have done some simulations. For all the calculations, the fiber parameters are particularly adopted as following: the original core diameter rco = 8.2 µm, the original cladding diameter rcl = 125.0 µm, the difference in the refractive index (RI) between the core and the cladding is 0.0044 and the initial SRI is 1.0 (i.e., the original surrounding-material is air). In addition, four thinned fibers with cladding diameters of 75.0, 87.5, 100 and 112.5 µm, respectively are particularly adopted in the simulations in which the core and the cladding diameters are assumed to be adiabatically changed during the thinning process of the fiber itself [23].
Based on utilization of the dispersion equation [24] and the Eqs. (4) and (5), the relations between the dispersion factors γ with the diameters of the fiber cladding under the cases of three different operating wavelengths and the cases of five different the coupled cladding modes, respectively, have been calculated, the results are shown in Fig. 1), where Fig. 1(a) shows the case that the resonant mode couplings for LP0,1–LP1,10, LP0,1–LP1,11, LP0,1–LP1,12, LP1,10– LP1,13, and LP1,10–LP1,14, respectively, are assumed and the operating wavelength is fixed at 1520 nm. Whereas the Fig. 1(b) shows the cases that the operating wavelengths are assumed to be 1490 nm, 1520 nm, and 1550 nm, respectively, where such three wavelengths were particularly selected to show the variation trend of the dispersion factor in terms of the different wavelengths, while the resonant mode-coupling is fixed to be the one (LP0,1–LP1,12). From the Fig. 1, it can be seen that the absolute value of the parameter γ decreases with the increment of both the resonant wavelength and the radial order of the coupled cladding mode. More importantly, one can easily find that the parameter γ has a same change-trend with that of the fiber diameter, i.e., the absolute value of the parameter γ decrease with the decrement of the cladding diameter, which implicitly indicates that the temperature sensitivity can be suppressed using a fiber grating with a reduced diameter.
Fig. 1. The waveguide dispersion factors γ vs. diameter of the fiber cladding. (a) Mode couplings between the core mode LP0,1 and the cladding modes LP1,10–LP1,14, respectively, while the operating wavelength is fixed at wavelength of 1520 nm. (b) The operating wavelengths are assumed 1490 nm, 1520 nm, and 1550 nm, respectively, while the mode coupling is assumed to be the one (LP0,1–LP1,12).
For more clarity, two kinds of fibers, i.e., the original fiber (with the cladding and core diameters of 125 µm and 8.2 µm, respectively) and the thinned fiber (with cladding and core diameters of 87.5 µm and the 5.74 µm, respectively) were particularly considered. We further calculated the dispersion spectra of the effective index difference Δne, the group index Δng, the parameter γ, and the grating period Λ, respectively for both of the two fibers, the results are shown in Fig. 2(a) and Fig. 2(b), respectively, where the subscripts “o” and “t” appended to parameters Δne, Δng, and γ (as shown in Fig. 2) mean that the parameters are the ones corresponding to either the original or the thinned fibers, respectively. From Fig. 2(a), once again one can find that the absolute values of Δne and Δng both increase with the decrement of the fiber (cladding) diameter. However, Fig. 2(b) shows that the absolute value of the factor γt (obtained from the thinned fiber grating) is about 1.3, which is nearly 2–3 times less than the same parameter but obtained from the original fiber (i.e., γo = 3.1), implicitly means that temperature sensitivity can be suppressed at least two folds by reducing the diameter of the fiber grating from the 125 µm to 87.5 µm. Meanwhile, from the Fig. 2(b), it can be found that at wavelength of the 1520 nm, the diameters and the required periods for the gratings written in thinned and the original fibers are 87.5 µm and 164 µm, 94 µm and 125 µm, substituting these values into the Eq. (7), it is easy to find that the SRI sensitivity could be enhanced by approximately three times by using the thinned fiber instead of the original one.
Fig. 2. Simulation results for the two cases where the original fiber and the thinned fiber with diameter 87.5 µm are considered, respectively. In two cases, the resonant mode-coupling between LP0,1 and LP1,12 is assumed. (a) Dispersion spectra of the effective index difference Δne and the group index Δng. (b) The waveguide dispersion factors γ and period Λ vs. the wavelengths ranging from 1400 nm to 1700nm.
Theoretically, the temperature crosstalk effect can be further suppressed by using the thinned fiber with a cladding diameter less than 87.5 µm, while to maintain a high SRI sensitivity of the proposed sensor, the condition of a further shorter grating period is essential, which will considerably increase the fabrication difficulty for such ultra-thin fiber grating and meanwhile considerably degrade the mechanical performance of the grating itself. Therefore, as a trade-off, the proposed THFGIP with a cladding diameter and grating period 87.5 µm and 94 µm, respectively, is particularly considered in this study.
3. Fabrication and measurement results
To experimentally testify the simulation results, the THFGIP proposed above was fabricated. The real fabrication parameters for the THFGIP are arranged to be exactly consistent with those used in the simulation. The experimental setup is shown in Fig. 3, which consists of a CO2 laser (Synrad, FSTI60SFH), three motorized translational stages (ThorLab, LTS300/M), a motorized rotator (ThorLab, DDR25/M), and a testing system for measuring the transmission spectrum of the fabricated THFGIP.
During the fabrication, both ends of the selected fiber are fixed at the clamp on stage 3 and the center of the rotator on stage 2, respectively. Unlike most of the CO2 laser direct-writing techniques where the fiber is directly heated by the laser beam through a focused lens, here a sapphire tube is specially utilized in place of the focused lens and as a result the fiber can be homogeneously heated to its fused status [25]. Meanwhile, the whole part of the fiber was moved by driving the translation stages 2 and 3, and rotated by driving the rotator on stage 2 at the same time. The diameter and period of the THFGIP are precisely controlled by adjusting the speeds of both the translational stages and the rotator simultaneously. In concrete, the diameter of the THFGIPs can be precisely controlled by choosing a suitable velocity ratio of the stage 2 and the stage 3 according to the following equation,
where Do and Dt represent the diameters of the original and thinned fiber, respectively. V2 and V3 represent the moving velocities of the stage 2 and the stage 3, respectively (in the unit of mm/s). Meanwhile, the period of the THFGIP can be precisely controlled according to the following relation, where Ω represents the rotation speed of the rotator (in the unit of rpm). To keep the fiber straight all the time during the fabrication process, a stable axial stress was applied on the utilized fiber, which is realized just by making the speed of the stage 2 a little smaller than that of the stage 3. In our experiment, the rotation speed of the rotator was set as 300 rpm, whereas the velocities of stage 2 and stage 3 were set as 0.23 mm/s and 0.47 mm/s, respectively. The really-obtained diameter, period, and total length of the THFGIP are 87.5 µm, 94 µm, and 47 mm (with 500 periods), respectively.Figure 4 shows the measured spectrum for one typical of the fabricated THFGIPs, which can be recorded by using an optical spectrum analyzer (Yokogawa, AQ6370) and a supercontinuum light source (YSL, SC-5). Figure 4 shows that there exists a deep notch centered at wavelength of 1520 nm. Moreover, it can also be seen that the insertion loss of the THFGIP is approximately 2 dB, which is much less than those of the interferometer-based fiber sensors [14,15].
Figure 5 shows the microscopic images of the raw SMF (left figure) and the fiber with the fabricated THFGIP mentioned above (right figure), which obviously shows that the fabricated THFGIP has clear surface and a uniform diameter of 87.5 µm along the whole length of the grating.
Fig. 5. The microscopic images of the original SMF (left figure) and the fabricated THFGIP (right figure).
Next, the sensing characteristics of the fabricated THFGIPs were investigated. In this study, a fabricated THFGIP whose transmission spectrum is given in Fig. 4 was particularly used as the testing object especially for SRI sensing. During SRI measurement, the THFGIP was immersed in a refractive-index matching liquid, whose refractive index (RI) was discretely adjusted as the ones ranging from 1.3410 to 1.4480. For each measurement, RI of the testing liquid was calibrated using the Abbe refractive index measuring instrument (LiChen, WYA-2WAJ). Figure 6 shows the measured transmission spectra of the tested THFGIP upon eleven different SRIs, where specifically, the black line represents the spectrum measured without the testing solvent (i.e., the SRI =1). From the results shown in Fig. 6, it is obviously seen that with the increment of the SRI, the resonance peak (notch peak) shifts towards the longer wavelength. Moreover, it is easy to find that for a change in SRIs ranging from 1.3410 to 1.4480, the wavelength shift is up to 88.8 nm, giving an average SRI sensitivity of approximately 829.9 nm/RIU for a RI in the range of 1.3410–1.4480 RIU, and particularly for the SRI is approximately 1.4480 RIU, the obtained SRI sensitivity is high up to 2939.6 nm/RIU, which is 3–4 times higher than the average one. Noted that the maximum RI which can be tested in this study is limited by the refractive index of the fiber cladding (i.e., 1.4480) [26]. Changes of the notch wavelength vs. the different SRIs concentration and the third-order polynomial fitting are shown in Fig. 7, in which the equation for the fitted curve can be expressed as
where λres and n represent the resonant wavelength and the measured SRIs, respectively, and the fitting degree R2 is 0.98967.Fig. 6. Transmission spectra of the proposed SRI sensor for the surrounding solvent with different RIs.
To further show the accuracy of the proposed SRI sensor, comparisons of the five real SRIs with the measured ones are performed, the results are listed in Table 1, where the first column shows the measured notch wavelength, the second column shows the calibrated refractive index Ir using the Abbe refractive index measuring instrument (LiChen, WYA-2WAJ), the third column shows the corresponding the calculated refractive index Ic, based on the fitting equation shown in Eq. (10), and the fourth column shows the relative error ΔE. From the results shown in the last column of the Table 1, it can be seen that the relative errors for all the measured SRIs are less than 0.47%, and could be even small down to 0.01% when the measured RI is approximately 1.3999, indicating that the proposed sensor has a enough accuracy.
Table 1. The relative-error results obtained in the SRI measurements.
To experimentally validate the temperature-insensitive of the proposed SRI sensor, temperature sensitivity of the utilized THFGIP have been investigated. The fabricated THFGIP mentioned above was used as the testing object again, which was inserted into a temperature controller where the temperature can be changed from 30℃ to 60°C with an interval of 5°C. Figure 8(a) shows the measurement results for transmission spectra of the utilized THFGIP while the ambient temperatures are changed from 30°C to 60°C. Figure 8(b) shows the changes in notch wavelength vs. the applied temperatures, which are directly obtained from the results shown in Fig. 8(a). From the Fig. 8(b), it can be seen that when the temperature is changed from 30°C to 60°C, the notch wavelength almost remains unchanged, the fluctuations of the notch wavelength are less than 0.2 nm, indicating that the proposed sensor is almost temperature-insensitive one.
Fig. 8. Temperature performances of the fabricated THFGIP. (a) Changes of the transmission spectra under the conditions of seven different temperatures. (b) Change of the notch wavelength vs. the applied temperatures.
Finally, for comparison purpose, the SRI and temperature sensitivities obtained so far in different types of the fiber-based SRI sensor are summarized in Table 2. From this table, it can be seen that among all the listed fiber-based SRI sensors, the proposed THFGIP has the second higher SRI sensitivity (only less than that of the SPRFS) and more important it is temperature-insensitive. While for the SPRFS-based SRI sensor, although the presented SRI sensitivity is higher than that of the sensor proposed in this study, it is highly sensitive in temperature also, i.e., the temperature crosstalk-effect is the strongest one which cannot be eliminated by using the device itself. Whereas for the FGIP and HFGIP-based SRI sensors, both of them have a low temperature sensitivity, but the obtained SRI sensitivities are the relative small ones which are about 1/3–1/2 of the one obtained in this study. The comparison results above manifest that the proposed THFGIP is more suitable to a SRI sensor than the other previous ones.
Table 2. Comparisons for SRI and temperature sensitivities obtained in different fiber-based SRI sensors.
4. Conclusion
In this study, a temperature-insensitive high-sensitivity SRI sensor is proposed and demonstrated, which is based on utilization of a thinned helical fiber grating but with an intermediate period (THFGIP). Unlike the traditional sensitivity-enhancement method by increasing the waveguide dispersion factor, here the waveguide dispersion factor at the resonant wavelength was purposely decreased by reducing the diameter of the fiber grating, and as a result, the crosstalk effect due to the temperature change can be further suppressed. While SRI sensitivity of the proposed THFGIP can be strongly enhanced due to utilization of the HLPG but with an intermediate period (less than 100 µm). As typical results, the average SRI sensitivity up to 829.9 nm/RIU in the range of 1.3410–1.4480 RIU, and approximately 2939.6 nm/RIU at 1.4480 RIU have been successfully obtained. The proposed temperature-insensitive SRI sensor has the superiorities of simple structure, ease fabrication, and low cost, which could be found more potential applications in the SRI sensing fields.
Funding
National Key Research and Development Program of China (2023YFB2804900); National Natural Science Foundation of China (62375134); Japan Society for the Promotion of Science (JP 22H01546); Natural Science Research of Jiangsu Higher Education Institutions of China (22KJB510030); Postgraduate Practice and Innovation Program of Jiangsu Province (SJCX23_0575).
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.
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