1. Introduction

Stimulated Brillouin scattering (SBS), as a third-order nonlinear phenomenon involving the interaction between photon and phonon, can realize the energy conversion from incident optical waves to scattered waves [1,2]. SBS interaction in optical fibers can excite different types of elastic waves, such as longitudinal, radial, torsional, bending, and mixed elastic waves, defending two kinds of SBS process including forward Stimulated Brillouin scattering (FSBS) and backward Stimulated Brillouin scattering (BSBS). Since the whole SBS process follows the momentum and energy conservation law, the intrinsic frequency of the acoustic wave generated is the shift deviation between the incident and scattered light, i.e., the Brillouin frequency shift (BFS). One of the simple criteria to distinguish the FSBS from the BSBS is whether the scattering wave and the incident wave propagate in the same direction. Secondly, the acoustic field involved in FSBS is composed of radial modes R_{0, m} (m = 1, 2, 3, 4, …), and the torsional radial modes R_{2, n} (n = 1, 2, 3, 4, …), which propagates throughout the entire cross-section of the fiber including the fiber core and cladding, while the acoustic field of BSBS is composed of longitudinal traveling acoustic waves propagating longitudinally and confined within the fiber core. Unlike the BSBS with typical spectrum of one dominant peak profile with MHz linewidth, the multi-peak FSBS spectrum originates from the transverse participation of diverse acoustic modes inside the fiber, diversifying the options for multi-parameter sensing involving from inside the fiber such as temperature [3] and strain [4], to the ambient environment outside the fiber such as humidity [5,6], glucose solution concentration [7] and ethanol solution concentration [8–10]. Furthermore, the FSBS offers an appealing solution for non-contact determination of the fiber material and structure in a distributed manner, such as sound velocity [11] and Poisson’s ratio [12] as well as fiber diameter [13].

In recent years, relying on FSBS-based optomechanics, the sensitivity of temperature sensors with single-mode fibers [14], large-area fibers [15] and photonic crystal fibers [16] are characterized as 8.5 kHz/°C, 27.6 kHz/°C and 100.0 kHz/°C, respectively. FSBS-based resonance peaks in optical fibers typically present a 3-dB spectral linewidth of about several MHz which is narrower than that of BSBS (i.e., 30 MHz), determining an enhanced spectral resolution for sensing demodulation with one-order of magnitude improvement. It has been demonstrated that the optimal measurement error of the FSBS optomechanical temperature sensor can be upgraded to less than 0.5 °C which is lower than that of BSBS [17]. More importantly, the multi-peak FSBS spectrum provides diverse opportunities for simultaneous discriminative measurement offering both the temperature and other critical sensing parameters, such as strain, salt solution concentration and humidity. However, due to the weak strength of the FSBS interaction in standard communication fibers, an FSBS-based temperature sensor with a high signal-to-noise ratio (SNR) and high sensitivity remains challenging.

Thin-diameter fibers (TDFs) are one special type of commercially available fibers with the diameters of both the fiber core and cladding smaller than that of the conventional standard single-mode fiber (SSMF) by almost the same proportion [18]. Their cladding diameter can be even declined down to a dozen of micrometers. TDFs exhibit advantages such as small sizes, low bending loss, good flexibilities, excellent opto-mechanical properties and high nonlinear optical coefficients [19], which can be widely applied for integrated sensors [20–22], atom capture [23] and light velocity manipulation [24]. Especially, regarding the TDF-based fiber-optic sensor exposure to ambient environment change, the evanescent light field in TDFs is prone to realize the self-coupling of the optical field for its sensitivity improvement. For instance, the sensitivity of the Mach-Zehnder interferometer-based curvature sensor with the utilization of TDFs can be enhanced by over one order of magnitude [25]. Recently, the FSBS in single-mode fibers with 80-µm fiber diameter was characterized, revealing the fiber geometry dependence of the FSBS spectrum [19]. To date, a thoughtful investigation of FSBS-involved optomechanics as well as underlying fundamentals as per the fiber geometry dependence, especially for sensing-orientated optimization remains ambiguous.

In this paper, we theoretically investigated the characteristics of FSBS in TDFs for sensing performance optimization of optomechanical temperature sensors. The theoretical framework of the FSBS-based temperature sensing in TDFs in terms of the sensitivity and measurement error was derived. Thanks to the good confinement of both optical and acoustic fields, the FSBS-involved electrostrictive force exhibits a decreasing trend toward the fiber diameter increment. Then, an FSBS-based temperature sensor with a diameter of fiber ranging from 10 µm to 125 µm is simulated, showing that the sensitivity of the sensor exhibits negative correlations with the fiber diameter. Meanwhile, the measurement error of the FSBS-based temperature sensor decreases as the fiber diameter reduces from 125 µm to 50 µm. In experimental validation, the FSBS temperature sensor with 60-µm TDFs verified that temperature sensitivities by employing the acoustic modes from R_0,4 to R_0,15 subsequently increased from 35.23 kHz/°C to 130.38 kHz/°C separated by a gap of 8.74 kHz/°C whilst the corresponding minimum measurement error (i.e., 0.15 °C at the resonant frequency of 958 MHz) is 2.5 times lower than that of the 125 µm-SSMF (i.e., 0.39 °C at the resonant frequency of 558 MHz), which agrees well with theoretical predictions. It provides valuable insights into the sensitivity and accuracy optimization of FSBS-based temperature sensors, paving the way for applications in environmental monitoring and biomedical fields.

2. Principle

FSBS involves two major classes of acoustic modes, including R_{0, m} and R_{2, n} which describe the radial and torsional-radial propagating acoustic modes, respectively. The axisymmetric radial transverse acoustic mode properties are determined by the Pochhammer-Chree equation [26], considering the axial wave vector that is close to zero, which is given by

V_L, a is the radius of the fiber cladding. J₀, J₂ are the zero-order and the second-order Bessel functions, respectively. According to Eq. (1), the discrete solution (${y_m}$) of the Bessel function can be solved. Hence, the intrinsic frequency ${f_m}$ of the R_0,m is given by [27],

Regarding the TDF, the reduced diameter (2a) of the fiber facilitates increased resonant frequency ${f_m}$. As the fiber diameter decreases, there is accordingly a larger frequency interval within the FSBS resonance frequency domain and the highest resonance frequency can be distributed above GHz. The longitudinal velocity of sound V_L which is expressed as V_L = $\sqrt {{C_{11}}(T )/\rho } $, where $\; {C_{11}}$ represents the material elastic coefficient and $\rho $ is the material density. In particular, the elastic coefficient ${C_{11}}$ plays a critical role in the temperature dependency of V_L, which essentially attributes to the temperature sensing based on the FSBS.

The general formula of the relationship between ${C_{11}}$ and temperature T can be expressed as ${C_{11}}(T )= {C_{11}}(0 )+ \frac{s}{{exp \left( {\frac{{{\theta_E}}}{T}} \right) - 1}}$, where s is a constant (i.e., 6.45 × 10⁹ in silica fibers), ${C_{11}}(0 )$ represents the material elastic coefficient at 0 $\textrm{K}$ while ${\theta _E}$ is the Einstein temperature, which equal 77.992 GPa and 420 K in silica fibers, respectively. As T increases, ${V_L}$ in optical fibers as well as the BFS will be changed [28,29].

By investigating the relationship between the elastic coefficient C₁₁ and temperature dependence of SiO₂ [30], it is an approximate linear relationship between V_L with the temperature ranging from 20 °C to 870 °C. Furthermore, the enhanced temperature sensitivity linearly dependent on the order of activated radial modes,

The accuracy (i.e., the measurement error) of the FSBS-based temperature sensor. The relative BFS of R_0,m under the variation of temperature ΔT can be expressed as $\Delta {f_m}/{f_m} = \; C_T^R \cdot \Delta T$, where $\Delta {f_R}$ and ${f_R}$ represent the variation of BFS and frequency of R_0,m, respectively, and $C_T^R$ is the relative temperature coefficient for R_0,m (∼8.8 × 10⁻⁵ /$^\circ $C for SMF). The relative standard deviation (RSD) [31] represents the standard deviation of the relative frequency shifts of R_0,m. Therefore, the measurement error of the FSBS-based temperature sensor in terms of R_0,m is expressed as

According to Eq. (4), the reduced fiber diameter in TDFs basically enhances ${Q_m}$ as well as the FSBS gain whilst the intrinsic frequency ${f_m}$ of each order acoustic mode will be shifted towards a higher value, which is hence beneficial to the SNR enhancement. It worths noting that, with respect to the backward SBS with a linewidth of tens of MHz, the linewidth of the resonant peak of FSBS is typically about 1 MHz, which generally contributed to a ten-fold higher resolution of the temperature sensing demodulation.

On the other hand, regarding the fact that the SNR of the detected Stokes does not increase monotonically with the higher order of acoustic mode, the resonant peak order with the highest gain will shift and locate to a certain order of acoustic mode as the fiber diameter decreases. In this scenario, the optimization of a high-accuracy FSBS-based temperature sensor relies on the proper fiber diameter, which balances the trade-off between the high-frequency value of the resonant peak and its high SNR.

3. Numerical simulations

According to Eq. (4), the SNR associated with the resonant peak of the FSBS plays a key role on the performance of the FSBS-based temperature sensor. The resonant peak gain of the FSBS is subject to the phonon-photon coupling factor ${Q_m}$, which is determined by the integral of the optical force and the displacement vector of the acoustic field. Considering that the amplitude of the displacement field of the acoustic field exhibits slight dependence on the fiber diameter [33], the resonant peak gain of the FSBS in TDFs would be thus dominant by the optical force which mainly corresponds to the electrostrictive force in optical fibers.

The electrostrictive force variation of the fiber diameters from 10 µm-125 µm is simulated and the fiber core is reduced proportionally to the diameter of the fiber cladding, as shown in Fig. 1. Generally, the electrostrictive force increases with the decrease of the fiber diameter. Regarding the good confinement of the optical field in SSMFs, the FSBS process is mainly confined within the fiber core while the optical energy distributed in the fiber cladding can be ignored. However, different from that in SSMF, the TDF yields part of the light field propagating along the whole fiber cross-section, owing to the tiny size of both fiber cladding and core diameter in TDFs. Thus, an enhanced electrostrictive force at the boundary of the fiber cladding could be highly activated. The growth rate of electrostriction force swells lightly by reducing the fiber diameter from 125 µm to 20 µm, because only a small portion of the light energy originally confined within the fiber core leaks into the fiber cladding while most of the light energy still exists in the fiber core, as shown in the insets of Fig. 1. Note that, as the fiber diameter is less than 20 µm, the core diameter is too small to well confine the light field while a large amount of light energy would be distributed in the fiber cladding and electrostrictive force at the boundary of the fiber cladding could be highly motivated, resulting in the sharply increased electrostrictive force under the fiber diameter down to 10 µm.

 

Fig. 1. Calculated average electrostrictive force versus the fiber diameter (the insets: the electrostrictive force distribution over the fiber cross-section at different diameters).

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3.1 Sensitivity of FSBS-based temperature sensor

Typically, the highest order Stokes of FSBS in SMFs can reach the 17^th, corresponding to the resonant peak frequency of ∼800 MHz [7]. Hence, three typical high-order radial acoustic modes of R_0,8, R_0,12 and R_0,17 are simulated. Accordingly, the relationship between the sensitivities of the FSBS-based temperature sensor and the fiber diameter is numerically calculated, according to Eq. (3). As shown in Fig. 2, the sensor based on the higher order of R_0,m with the smaller fiber diameter exhibits an enhanced temperature sensitivity. The sensitivity of FSBS-based temperature sensors of R_0,8 and R_0,12 with a fiber diameter of 10 µm are 408.14 kHz/°C and 618.44 kHz/°C, respectively. Furthermore, the temperature sensor of R_0,17 sensitivity with the 10 µm fiber diameter is 881.32 kHz/°C which is 12.5 times higher than that of 125 µm-SSMF (i.e., 70.51 kHz/°C). Consequently, it could be concluded that the temperature sensitivities significantly increase versus the decreasing diameter of the fiber. Since the same order of the resonant peak frequency based on the reduced fiber diameter is located at a higher frequency, the identical temperature change is supposed to impose a higher BFS corresponding to the same order of resonant peak frequency.

 

Fig. 2. Calculated temperature sensitivity sensor of R_0,8, R_0,12, R_0,17 as a function of the fiber diameter.

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3.2 Accuracy of FSBS-based temperature sensor

Considering that the refractive index of the fiber cladding and fiber core remains unchanged. According to Eq. (4), the SNR and frequency of the resonant peak play a crucial role in the temperature sensor accuracy. The resonant peaks of FSBS spectra in the frequency domain and the sensor measurement errors of R_0,m under different fiber diameters are simulated, as shown in Fig. 3.

 

Fig. 3. (a) FSBS spectra with different fiber diameters ranging from 50 µm to 125 µm. (b) Relationship between the measurement error of the temperature sensor and resonant peak frequency.

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Figure 3 (a) illustrates that the maximum resonant gains in FSBS spectra elevate via the descent of the fiber diameter. Apparently, the maximum resonant peak gain shows an increasing enhancement as the fiber diameter is reduced from 125 to 50 µm, which corresponds to the increased electrostrictive force with the same situation (as shown in Fig. 1). In TDFs, an electrostrictive force at the boundary of the fiber cladding can be highly activated, which hence determines an enlarged phonon-photon coupling factor ${Q_m}$. Consequently, the FSBS interactions turn out to be significantly intensified for the Stokes gain enhancement. Furthermore, in the case of the declined fiber diameter in TDFs, the resonant peak order with the maximum gain in the FSBS spectrum will gradually shift towards the lower order of the Stokes component. In this case, since the miniature diameter of the fiber would not support the good confinement of the light field within the fiber core while optical energy would leakage to the fiber cladding to a large extent, the acoustic mode with the largest gain moves from the 7^th order with 125 µm towards the lower order, which eventually occurs at the 4^th order with the fiber diameter of 50 µm. Figure 3 (b) shows the trend of the temperature sensor measurement error as a function of the fiber diameter ranging from 125 µm to 50 µm. The measurement error of the temperature sensor declines as the fiber diameter is reduced. In terms of a trade-off between the SNR and the frequency of resonant peak for higher accuracy of FSBS-based temperature sensor, the optimization of the fiber diameter is found as 50 µm, exhibiting the minimum temperature error of 0.15 °C, which is 2.5 times lower than that of 125 µm-SSMF (i.e., 0.39 °C).

4. Experimental setup and method

The schematic of the FSBS-based temperature sensor with TDFs is shown in Fig. 4, in which two kinds of TDFs with the diameter of 7/80 and 4/60 microns were utilized as the proof-of-concept. The output from a laser source (Laser 1, λ_p = 1550.056 nm) is used as the pump light to produce a series of optical pulses with a pulse width of 1 ns and a period of 20 µs by an electro-optic modulator (EOM). Amplified by an erbium-doped fiber amplifier (EDFA), the pump light was then passed through an optical filter for the removal of the amplified spontaneous emission. The pump pulses with a peak power of 6 W were injected into the TDF with stripped outer coatings by a glue remover.

 

Fig. 4. Experimental setup for FSBS observation time domain signal. EOM: electro-optic modulator; EDFA: erbium-doped fiber amplifier; PC: polarization controller; ISO: isolator; OC: coupler; BPF: bandpass filter; PD: photodetector.

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A second laser source (Laser 2) with a central wavelength of 1555.013 nm was launched into the TDF through a 50/50 optical coupler (OC) as the probe light and a polarization controller (PC) was used to adjust its polarization. The probe laser power was set as 10 mW. With the FSBS interaction, the phase delay of the forward propagating probe light was modified by the radial acoustic modes excited by pump pulses. It should be mentioned that, the probe laser power would have an impact on the SNR. Here, the probe laser power was properly set (i.e., 10 mW in our case) so that the received optical power at the PD is high enough for a maximum detected SNR without severe saturation. For temperature sensing, the TDF was placed in a water bath, where the TDF was isolated and proofed from the water by plastic wrap. In experiments, the temperature gradually changed from 20 °C to 50 °C with 5 °C intervals. The measurements were collected after waiting for the stable temperature every 20 minutes. By using a bandpass filter (BPF) to remove the pump light, the probe signals were detected by a photodetector (PD) (Bandwidth: 20 GHz), and sampled by an oscilloscope (Sampling rate: 20 G; Bandwidth: 4 G) for data acquisition.

Figure 5(a) shows the detected signal traces of a 1000 ns time domain window with 80 µm-TDF exposed in the air, which is distributed equally and symmetric. Where the interval (tr = 13.3 ns) is determined by the period of one acoustic wave vibrating inside the fiber. With the Fourier transform, the signals in the time domain can be turned into a frequency domain power spectrum density signal, as shown in Fig. 5(b). The power spectrum density contains multiple resonance peaks which subsequently correspond to the acoustic modes from R_0,2 to R_0,13. Meanwhile, the corresponding displacement vector distributions of their acoustic modes are also illustrated in Fig. 5(b). Here, the subscript order m of R_0,m (m = 2, 3, 4…) essentially reflects the numbers of round-trip oscillations of the acoustic wave across the transverse profile of the fiber. Different acoustic modes R_0,m with different strengths essentially attributes to various overlapping factor ${Q_m}$ in the FSBS spectrum, which is well confirmed with the above mentioned theoretical predictions.

 

Fig. 5. (a) Measured power of the signal wave as a function of time at the output. (b) Power spectral density of the measured output signal trace.

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4.1 Sensitivity of FSBS-based temperature sensor

Figure 6 shows the normalized Lorentzian-fit temperature dependence of the 80 µm-TDF FSBS spectrum of R_0,9 and its corresponding central frequency shift. It is found that, within the temperature range from 20 °C to 50 °C, the frequency shift of R_0,9 removes linearly from 646.4 to 648.1 MHz. The linear relationship with the frequency shift-temperature coefficient of R_0,9 is 56.2 kHz/°C, which is 1.6 times higher than the temperature sensitivity of SSMF in terms of the same 9^th order resonant peak.

 

Fig. 6. (a) Measured normalized Lorentzian-fit 80 µm-TDF FBS spectra of R_0,9 mode under different temperatures. (b) Frequency shift-temperature coefficient of R_0,9 mode within the range from 20 $^\circ $C to 50 $^\circ $C.

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The temperature variation will change Young’s modulus, Poisson’s ratio, density and refractive index of the fiber, which ultimately alters the BFS in its FSBS spectrum. Figure 7 represents theoretical, numerical and experimental sensitivities of acoustic mode R_0,m with the 60 µm-TDF. Temperature sensitivities of 60 µm-TDF from R_0,4-R_0,15 vary within the range of 35.2-130.3 kHz/°C, corresponding to a linear increasing step of 8.7 kHz/°C per acoustic mode order. Note that, temperature sensitivities of 80 µm-TDF have been also experimentally verified, exhibiting a similar increasing tendency with a step of 6.0 kHz/°C as per the increased acoustic mode order. The experimental results are consistent well with the theoretical and numerical data.

 

Fig. 7. Measured temperature sensor sensitivities versus resonance peak orders of 60 µm-TDF.

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In terms of the sensitivity of the FSBS-based temperature sensor, further improvement can be achieved. For instance, by utilizing a smaller Einstein temperature ${\theta _E}$ of fiber material [28] instead of conventional silica fibers, which can increase the slope of V_L with temperature variation and give rise to an increased coefficient of FSBS temperature sensitivity. It is worthy noting that, optical fibers with much smaller diameters (e.g., nanofibers) might be beneficial to further improvement of the sensitivity, providing maintaining good confinement of the light field within the fiber core. Otherwise, optical energy in the fiber core would leakage to the fiber cladding to a large extent, resulting in sharp declined gains of high order resonant peaks as well as the limited temperature sensitivity. Note that, simulations have revealed that silica fibers with reduced fiber cladding sizes but the same core size could also provide the increasing gains of FSBS resonant peak as the cladding diameter of the fiber decreases [19]. Therefore, in terms of the sensing performance, the utilization of such fibers is expected to yield the sensitivity enhancement, which deserves further investigation and experimental validation by fabricating and implementing such kinds of fibers for FSBS-based optomechanical temperature sensors.

4.2 Accuracy of FSBS-based temperature sensor

As a proof-of-concept, the accuracies of FSBS-based temperature sensors with diameters of 80 µm-TDF and 60 µm-TDF were evaluated. Figure 8 shows the experimental FSBS gain spectra of single-mode fibers with diameters of 125 µm-SSMF, 80 µm-TDF and 60 µm-TDF, respectively. Here, the TDFs with diameters of both 60 and 80 µm are single mode silica fibers, which have the same material composition with respect to the SSMF, i.e., the fiber core and cladding are composed of pure silica and 0.36% GeO₂-doped silica, respectively. The FSBS with TDF possesses a BFS spectrum over an extended frequency range because the smaller fiber diameter determines a larger frequency interval between each resonant peak in the FSBS spectrum. In comparison, the normalized FSBS spectra are calculated by the measured gain divided by the used fiber length. The highest gains of resonant peaks in measured FSBS spectra with 80 µm- and 60 µm-TDF are 0.0023 and 0.0032, which is 1.4 and 3.2 times higher than that of 125 µm-SSMF, respectively. As the size of both fiber cladding and core gradually decreases, the optical field will leak from the fiber core into the cladding, which will correspondingly increase the gain of the FSBS resonant peak.

 

Fig. 8. Measured FSBS Gain spectra with fiber diameters of 125 µm-SSMF and 80/60 µm-TDFs

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The measurement error of the temperature sensor with 125 µm-SSMF and 80/60 µm-TDFs is experimentally quantified. According to Eq. (4), the increase of the resonant peak frequency and SNR will effectively improve the accuracy of the FSBS-based temperature sensor. In Fig. 9, all measurement errors of the FSBS-based temperature sensors with three different fiber diameters show a descending trend with the reduced fiber diameter. In the measurement of FSBS spectra, the highest-order resonant peak at a cutoff frequency occurs as its corresponding gain is slightly beyond the average noise floor. In experiments, the cutoff frequency of the highest order FSBS resonant peak with 125 µm SSMF is around 800 MHz while its minimum measurement error of 0.33 °C appears at the 558 MHz with the 12^th order resonant peak. Alternatively, the cutoff frequencies of 80 µm and 60 µm-TDF can reach as high as 1000 MHz and 1450 MHz. The corresponding minimum measurement error is 0.21 °C at the frequency of 721 MHz for 80 µm TDFs and 0.15 °C at the frequency of 958 MHz for 60 µm, respectively. Thus, the minimum measurement error of the 60 µm-TDF turns out to be 2.5 times lower than that of 125 µm-SSMF, which is well consistent with the simulated prediction. Consequently, the appropriate reduction of fiber diameter plays a crucial role in optimizing the accuracy of the FSBS-based temperature sensor.

 

Fig. 9. Measurement error of FSBS-based temperature sensor in 125 µm-SSMF, 80/60 µm-TDFs versus the resonant frequency.

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In addition, the refractive index difference between the fiber core and fiber cladding could be considered for further improvement of the accuracy of the proposed FSBS-based sensors with TDFs. For example, the fiber core doped with high-concentration germanium ions will elevate its refractive index, which would be beneficial to TDF fabrication with reduced fiber core diameter while maintaining a moderated cladding diameter. In this scenario, the enlarged refractive index difference between the fiber core and cladding would effectively enhance the electrostrictive force within the FSBS process [19], hence allowing the increased all resonant peak SNRs for the accuracy improvement of the proposed temperature sensor.

Table 1 briefly summarizes several typical silica fiber-based temperature sensors for comparison, including fiber Bragg gratings, Fabry Perot/Mach-Zehnder fiber interferometer, Raman/Rayleigh scattering and backward/forward Brillouin scattering fiber sensors. Compared to the Mach-Zehnder or Fabry-Perot interferometers, the fiber Bragg grating-based temperature sensor typically provides a moderate sensitivity with a higher accuracy of 0.2 °C. With respect to Raman scattering, Rayleigh/backward Brillouin scattering-based distributed fiber temperature sensors usually allow almost one order of magnitude improvement of the measurement accuracy. By utilizing the TDF instead of the SSMF, forward Brillouin scattering-based temperature sensors can achieve three-fold sensitivity enhancement with a minimized accuracy of 0.15 °C, which highlights its potential for high-precision sensing applications. Particularly, the distributed sensing ability of the FSBS optomechanical sensor is highly expected regarding the utilization and combination of the optical time domain reflectometry technique.

Table 1. Fiber-optic temperature sensor comparison

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5. Conclusion

In summary, FSBS-based temperature sensors with sensitivity improvement as well as optimized accuracy by utilizing TDFs have been theoretically and experimentally demonstrated. Both theoretical and experimental investigations reveal that the smaller diameter of fiber core and cladding would essentially elevate the sensitivity of the FSBS-based temperature sensor. Furthermore, in terms of the trade-off between the increased frequency and the enhanced SNR of the resonant peak in FSBS, as the fiber diameter declines, the optimization of its measurement accuracy can be realized by using TDFs with proper reduced diameter. In experimental validations, the temperature sensitivities of the temperature sensor in 60 µm-TDF linearly increase from 35.23 kHz/°C at the 4^th to 130.38 kHz/°C at the 15^th with a step of about 8.74 kHz/°C per order. The temperature measurement error reaches a minimum of 0.15 °C at the resonant peak frequency of 958 MHz. It is believed that the proposed TDF-based FSBS temperature sensor with reduced fiber diameters could provide a promising solution for developing more sensitive and precise temperature sensor probes with a miniaturized size comparable to the blood capillary in human beings, which would be potentially desirable in fields of biomedical and wearable intelligent monitoring technology, e.g., cancer detection [43] and human body temperature monitoring [44].