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Highly sensitive temperature sensing probes based on liquid cladding elliptical micro/nanofibers

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Abstract

A highly sensitive temperature probe based on a liquid cladding elliptical micro/nanofiber is proposed, which exploits a fiber loop mirror with an output port probe for remote and highly-sensitive measurements based on evanescent field coupling. The thermo-optical effective liquid cladding avoids the influence of other environmental parameters (except for temperature), while protecting the micro/nanofibers from external disturbance and contamination. This renders the sensing probe only sensitive to temperature changes, making it suitable for real-world temperature measurements. An isopropanol cladding elliptical microfiber with a diameter of 3.4 µm demonstrated a sensitivity of −16.38 nm/°C for a remote temperature measurement.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Optical fiber temperature sensors have attracted extensive attention and shown potential for applications due to their advantages of immunity to electromagnetic interference, small size, and durability against corrosive and harsh environments. Various configurations have been proposed for fiber temperature sensors, such as fiber gratings [1,2], optical fiber interferometers [37], microstructure fiber-based sensors [811], photonic crystal fiber-based sensors [1215], and other interesting structures [1619]. However, fabrication of fiber gratings commonly requires expensive equipment and precise fabrication technology, optical fiber interferometers have low sensitivity, and microstructure fiber-based sensors require complicated fabrication processes, such as femtosecond laser micromachining. Most of these temperature sensors are challenged with cross-interference with other environmental parameters, such as refractive index and strain, and they cannot then be applied to remote sensing.

As a special kind of fiber, micro/nanofibers (MNFs) have demonstrated great potential in micro- and nano-scale photonic systems for highly sensitive applications. MNFs can interact with the external environment significantly due to relatively strong evanescent fields [20], which are more sensitive to the external environments and can provide higher sensitivity. Hence, MNF sensors based on the evanescent field effect are widely used in the measurement of refractive index [21], humidity [22], and other fields [23]. Typical structures of optical MNF sensors either employ intensity-dependent scheme or depend on optical phase or path. However, the intensity-dependent optical sensors have low sensitivity and the measurement results are easily influenced by the microfiber surrounding environment, and the optical sensors depending on the optical phase such as microfiber loop/knot/coil resonator need to be assembled by micromanipulation, which are mostly complicated. Moreover, MNFs can be fragile and demonstrate optical performance degeneration due to light scattering from dust particles [8,9], and most of the microfiber based optical sensors cannot avoid the cross-influence of the surrounded environmental parameter and achieve remote measurements.

In this paper, a remote, highly sensitive temperature configuration is proposed that contains a loop of optical fiber formed between the output ports of two directional couplers. Then, an end mirrored liquid cladding highly birefringent (Hi-Bi) microfiber is spliced to one output port of the second directional coupler to form a detection probe, so that this configuration can be used for remote sensing using only one fiber in the sensing zone. The detection probe based on a liquid cladding Hi-Bi microfiber utilizes the different perceptions between two polarization modes from the change of a liquid cladding to measure the temperature. The thermo-optical effective cladding avoids the influence of other environmental parameters except for temperature, protecting the MNFs from external disturbances and contamination. The alterable liquid cladding allows the availability of high sensitivity or an extensive measurement range. An isopropanol cladding elliptical microfibers with an ellipticity of 0.3 and a major axis length of 3.4 µm demonstrates a temperature sensitivity of −16.38 nm/°C.

2. Sensing principle

Figure 1 illustrates a schematic diagram of the experimental setup that includes an optical fiber loop formed between the ports of two-directional 3 dB couplers. A polarization controller (PC) is located between these two couplers. A liquid cladding elliptical microfiber includes two single-mode fiber (SMF) pigtails, with one pigtail spliced at one output port of the second coupler and the end of the other pigtail coated with a gold film as a reflection mirror. The light from a broadband light source (BLS) splits into two beams at the first coupler, which re-couples at the second coupler, and the end mirror in the output port of the second coupler reflects and rejects the light into the second coupler. The two-polarization mode light interferes when returning to the first coupler, which is monitored by an optical spectrum analyzer (OSA).

 figure: Fig. 1.

Fig. 1. The schematic diagram for the sensing measurement.

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The sensing probe model is theoretically analyzed using the Jones Matrix method where the relationship between the input and output is described as

$$\begin{array}{c} \left( {\begin{array}{c} {E_{2x}^{\prime}}\\ {E_{2y}^{\prime}} \end{array}} \right) = ({{T_{cc}}T_{SMF1}^{\prime}{R^{\prime}}(\theta ){T_{cd}} + {T_{cd}}T_{SMF2}^{\prime}{T_{cc}}} )R_3^{\prime}(\theta ){T_{HBF}}M{T_{HBF}}{R_3}(\theta )\\ \times ({{T_{cd}}{T_{SMF1}}R(\theta ){T_{cc}} + {T_{cc}}{T_{SMF2}}{T_{cd}}} )\left( {\begin{array}{c} {{E_{1x}}}\\ {{E_{1y}}} \end{array}} \right), \end{array}$$
where $\left( {\begin{array}{c} {{E_{1x}}}\\ {{E_{1y}}} \end{array}} \right)$ denotes the input light vector of port 1, ${T_{cc}}$ and ${T_{cd}}$ represent the Jones Matrix of the straight-arm and cross-arm of the fiber coupler, respectively, which is expressed as
$${T_{cd}} = \left( {\begin{array}{cc} {\sqrt {0.5} }&0\\ 0&{\sqrt {0.5} } \end{array}} \right),$$
$${T_{cc}} = \left( {\begin{array}{cc} 0&{j\sqrt {0.5} }\\ {j\sqrt {0.5} }&0 \end{array}} \right),$$
${T_{SMF}}$ is the phase retardation matrix when the fiber induces some phase delay, written as
$${T_{SMF}} = \left( {\begin{array}{cc} {{e^{ - j\Gamma }}}&0\\ 0&{{e^{j\Gamma }}} \end{array}} \right),$$
$R(\theta )$ is a rotation matrix introduced by a polarization controller (PC), defined as
$$R(\theta )= \left( {\begin{array}{cc} {\cos \theta }&{\sin \theta }\\ { - \sin \theta }&{\cos \theta } \end{array}} \right),$$
${R_3}(\theta )$ is a rotation matrix representing the rotation of birefringence axes induced by splicing point between the SMF and the birefringent fiber
$${R_3}(\theta )= \left( {\begin{array}{cc} {\cos {\theta_3}}&{\sin {\theta_3}}\\ { - \sin {\theta_3}}&{\cos {\theta_3}} \end{array}} \right)$$
${T_{HBF}}$ represents the phase retardation matrix introduced by MNFs, given by
$${T_{HBF}} = \left( {\begin{array}{cc} {{e^{ - j\frac{{\pi BL}}{\lambda }}}}&0\\ 0&{{e^{j\frac{{\pi BL}}{\lambda }}}} \end{array}} \right),$$
where B is the birefringence of the MNF, and L is the length of the highly birefringent fiber. M is the reflection matrix expressed as
$$M = \left( {\begin{array}{cc} 1&0\\ 0&{ - 1} \end{array}} \right),$$
The transmission spectrum is expressed as
$$T = \frac{{{I_{out}}}}{{{I_{in}}}} = \frac{{{{|{{E_{2x}}} |}^2} + {{|{{E_{2y}}} |}^2}}}{{{{|{{E_{1x}}} |}^2} + {{|{{E_{1y}}} |}^2}}}$$
that depends on the phase retardation induced by the birefringence of the SMF and Hi-Bi microfiber, independent of the polarization of the incident light [24]. The birefringence B of the elliptical microfiber is of the order of 10−3, which is at least eight orders of magnitude higher than that of a single-mode fiber. The single-mode fiber is fixed during the experiments so that the phase retardation matrix induced by the tension of the SMF is ignored in the theoretical calculation. The transmission T depends on the phase difference $\phi$ between the two polarization modes propagating through the Hi-Bi microfiber as
$$T \propto {\cos ^2}({{\phi / 2}} ),$$
where
$$\phi = \frac{{4\pi BL}}{\lambda }.$$
The wavelength interval $\Delta \lambda $ is obtained by
$$\Delta \lambda = \frac{{{\lambda ^2}}}{{B \cdot 2L}},$$
with the resonant wavelength as
$${\lambda _R} = \frac{{B \cdot 2L}}{k}.$$

The wavelength interval and resonant wavelength are functions of the birefringence of the fiber. So, if the birefringence changes, then both the wavelength interval and the resonant wavelength change. The wavelength shift caused by the external environment is calculated as

$$\Delta {\lambda _R} = \Delta B \cdot 2L + B \cdot 2\Delta L$$
where $\Delta {\lambda _R}$ is the wavelength shift of the interference fringe, $\Delta B$ is the variation of birefringence caused by the external environment, $\Delta L$ is the change in the fiber length induced by the external environment, and the wavelength shift in the spectrum is determined by $\Delta L$ and $\Delta B$. In our experiment, there is little or no change in the fiber length. Hence, the $\Delta L$ induced wavelength shift is ignored, and the sensing principle formula can be rewritten as
$$\Delta {\lambda _R} = \Delta B \cdot 2L.$$

The birefringence of the liquid cladding elliptical fiber is analyzed with the three-layer model, shown in Fig. 2, that contains a 62.5 µm diameter liquid cladding, a silica elliptical core with a major axis “2a” and minor axis “2b,” and a small, circular Ge-doped center region with a diameter of d ≈ (8.3 /125) * 2a. The ellipticity of the microfiber is defined as (a-b)/a.

 figure: Fig. 2.

Fig. 2. The three-layer model of a liquid cladding elliptical MNF.

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The mode property of the water cladding elliptical microfiber with an ellipticity of 0.3 is demonstrated in Fig. 3, which shows the effective index of the lower order modes as a function of the normalized diameter D (${{\sqrt {2a \times 2b} } / \lambda }$). When the normalized diameter D is reduced to a specific value (approximately 1.2 for the water cladding elliptical microfiber with an ellipticity of (a-b)/a = 0.3), only the non-degenerated HE11 mode exists that corresponds to the single-mode condition of a circular fiber. The elliptical cross-section of the microfiber generates the non-degeneracy of the two polarization modes of HE11 (HE11x and eHE11y), known as birefringence (or phase birefringence) of the optical fiber.

 figure: Fig. 3.

Fig. 3. The effective refractive index as a function of the normalized diameter.

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The birefringence of the liquid cladding elliptical microfiber is dependent on the refractive index of the cladding and the parameter of the elliptical microfiber. Figures 4(a)–4(b) demonstrate the birefringence of the elliptical microfibers as a function of the normalized diameter for the different cladding (air cladding with refractive index of about 1 and liquid cladding with refractive index of about 1.3) corresponding to an ellipticity of ${{( a\textrm{ - }b) } / a} = 0.5$, ${{( a\textrm{ - }b) } / a} = 0.3$, and ${{( a\textrm{ - }b) } / a} = 0.1$, respectively. The birefringence increases with increasing ellipticity for the same liquid cladding microfiber, and decreases with the increase of the refractive index of cladding for the elliptical microfiber with the same normalized diameter, as shown in Figs. 4(c)–4(d). The decrease of the refractive index for the liquid cladding induces an increase of the birefringence, resulting in the resonant wavelength shift. Because the refractive index of the liquid decreases with temperature increases, this principle can then be used for temperature sensing.

 figure: Fig. 4.

Fig. 4. The birefringence as a function of the normalized diameter for elliptical microfiber with different cladding, (a) refractive index of cladding is 1, (b) refractive index of cladding is 1.3 (liquid cladding), and the birefringence as a function of the refractive index of the cladding for different size elliptical microfibers with normalized diameter of 0.67 (figure (c)) and 1.2 (figure (d)), respectively.

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3. Liquid cladding elliptical microfiber sensing probe fabrication

The liquid cladding elliptical microfiber is fabricated by following a three-step process. First, a pre-processed SMF with a rectangular-like cross-section is fabricated by the following method [25]. A femtosecond IR laser cuts away parts of the silica cladding on opposite sides of the SMF-28 fiber under an irradiation intensity of ∼20 J/cm2. The femtosecond laser is produced by a Ti:sapphire laser with a central wavelength of 800 nm, a duration of 120 fs, and a repetition rate of 1 kHz. The laser pulse is focused onto the cladding surface of the SMF with a 3 µm focal spot size by a microscope objective (×10), and the location of the laser is adjusted accurately through a computer-controlled translation stage monitored by an liquid crystal display (LCD). The laser moves along the cladding of the SMF longitudinally on a pre-programmed snake track at 10 µm/s, which results in an approximate rectangular-like cross-section, as shown in Fig. 5(a).

 figure: Fig. 5.

Fig. 5. (a) The retangular-like cross-section of pre-processed SMF, and (b) the elliptical cross-section of the elliptical microfiber.

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Second, the “processed” SMF is taper-drawn to the wavelength or sub-wavelength scale by using computer-controlled fiber taper fabrication equipment under a hydrogen flame. The diameter of the flame is approximately ∼1 cm, which is larger compared to the length of a pre-processed fiber section. The flame scans back-and-forth along the fiber with a scan length of 1 cm and a velocity of 15 mm/s, while the two translation stages move in the opposite direction with the same velocity of 2.3 mm/s. The rectangular-like cross-section turns into an elliptical cross-section when the diameter of microfiber is in the order of a wavelength or sub-wavelength, as shown in Fig. 5(b), and then the elliptical Hi-Bi microfiber is obtained. This computer-controlled process guarantees the reproducibility of the elliptical Hi-Bi microfibers.

Finally, the obtained Hi-Bi microfiber is encapsulated in a capillary tube with AB glue at both ends (AB glue is a type of colloid that can fix the fiber at the end of the tube with a good ability to seal). The length and inner diameter of the tube are approximately 5 cm and 300 µm, respectively. The Hi-Bi microfiber is straight and suspended in the central portion of the tube. Two 300 µm diameter air holes are drilled at each end of the capillary tube using a femtosecond laser. One hole is immersed in the liquid sample while the other remains open to the air. The liquid sample fills the glass tube to act as the microfiber cladding within a few seconds, thus completing the fabrication of the liquid cladding microfiber.

4. Experimental results and discussion

In this experiment, the light source is an amplified spontaneous emission (ASE) broadband source (ASE-FL7006 with a wavelength range from 1530 nm to 1610 nm). Two couplers are both 3 dB couplers with a central wavelength of 1550 nm, and the polarization controller has a central wavelength of 1550 nm. An AQ6370 optical spectrum analyzer monitors the transmission spectrum. The parameters of the elliptical MNFs are (a-b)/a = 0.3 and 2a = 3.4 µm. The transmission spectrums of the sensing system based on the air cladding elliptical microfiber are shown in Fig. 6, and the difference in the extinction ratio of the black, red and blue spectrums is induced by adjusting the PC. The left inset of the Fig. 6 is a real picture of an encapsulated elliptical microfiber with an SMF pigtail, and a gold film with 99% purity and thickness of 90 nm is deposited at the end of the SMF pigtail by magnetron sputtering within 5 min at 3 A/s, which demonstrates a reflectivity of 93%. The SEM picture of the gold film is shown in the right inset of Fig. 6.

 figure: Fig. 6.

Fig. 6. The transmission spectrums under different polarization angles. Left inset is a real picture of an encapsulated elliptical microfiber with an SMF pigtail, and the right inset is the SEM picture of the gold film coated the end of the SMF pigtail.

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Because the extinction ratio of the transmission spectra is influenced by adjusting the polarization controller, when the spectrum with the best peak-to-notch ratio (the black spectrum) is achieved, the polarization controller will not be adjusted and stay stable, and the experiment setup is used to conduct the following experiments. The air cladding elliptical microfiber is placed into a digital temperature oven to measure its temperature response. When the environmental temperature increases from 25 to 100 ℃, the sensing probe demonstrates a temperature sensitivity of 6.4 pm/℃, as shown in Fig. 7, the inset of which is a magnification of the peak around the wavelength of 1559.6 nm. This low sensitivity is due to the sufficiently small Ge-doped core region, estimated as, which induces little birefringence change due to the internal stress caused by the temperature change.

 figure: Fig. 7.

Fig. 7. The transmission spectrum evolution for the air cladding elliptical fiber with temperature increases from 25 to 100 °C. Inset is the magnification of a peak around the wavelength of 1559.6 nm.

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When the capillary tube is filled with water, refractive index oil, and isopropanol liquid, the birefringence of the elliptical microfiber decreases, and the transmission spectrum broadens. The blue, red, and purple curves in Fig. 8 represent the transmission spectrums of the sensing system based on the water, refractive index oil, and isopropanol cladding elliptical MNFs, respectively. The wavelength intervals become larger with increasing refractive index of the liquid.

 figure: Fig. 8.

Fig. 8. The transmission spectrums based on the sensing probe with different liquid claddings.

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The refractive index of water changes by varying its temperature and the thermo-optical coefficient of water is on the order of ∼ −1×10−4 RIU/°C. Figure 9(a) shows the spectrum evolution when the water temperature varies from 25 to 45 °C and the transmission spectrum shifts to short wavelengths with a sensitivity of −2.57 nm/°C. Figure 9(b) demonstrates the theoretical transmission spectrum evolution with the birefringence obtained from Fig. 4(b) when temperature increases from 25 to 45 °C, and the transmission spectrum also shifts to short wavelengths with a sensitivity of −2.91 nm/°C. The slight difference between the theoretical analysis and experimental results may be a result of the measurement of the size of the elliptical microfiber or additional birefringence induced by the taper region.

 figure: Fig. 9.

Fig. 9. (a) The experimental transmission spectrums and (b) theoretical transmission spectrums of the water cladding elliptical MNFs at different temperatures, and (c) the resonant wavelength as a function of temperature for the experimental measurements and theoretical analysis, respectively.

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The temperature sensitivity is improved by changing the water cladding to the refractive index oil and an isopropanol solution cladding with the same elliptical microfiber, respectively. Emptying the glass tube to change the cladding liquid is straightforward, by placing a tissue across one air hole to absorb the liquid. Before re-filling the other liquid sample, the glass tube is cleaned by repeating the filling and removal with 99.5% propyl alcohol. Then, another liquid sample may be re-filled into the tube to perform as a different liquid cladding.

The transmission spectrums at different temperatures for a refractive index oil cladding elliptical microfiber with an index of 1.3 is shown in Fig. 10. The wavelength interval becomes smaller due to its higher birefringence compared to that of the water cladding elliptical microfiber. The wavelength dip still shifts to shorter wavelengths with a sensitivity of −4.95 nm/°C when the temperature increases from 25 to 45 °C. This high sensitivity is induced by the higher thermo-optical coefficient of approximately −3×10−4 RIU/°C of the oil refractive index.

 figure: Fig. 10.

Fig. 10. (a) The transmission spectrum of elliptical MNFs with a refractive index oil cladding with an index of 1.3 at different temperatures. (b) The resonant wavelength as a function of temperature.

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The thermo-optical coefficient of the isopropanol solution is approximately −4×10−4 RIU/°C, which is predicted to induce higher temperature sensitivity. The transmission spectrums of elliptical MNFs with the isopropanol cladding at different temperatures are shown in Fig. 11(a). The higher refractive index of the cladding induces smaller birefringence, resulting in the wider wavelength intervals. The resonant wavelength dip does not appear in the wavelength span from 1530 to 1610 nm at a room temperature of 25 °C when the water cladding is changed over to the isopropanol cladding. When the temperature is increased to 28 °C, the resonant wavelength dip appears to be 1604.2 nm, which is used to measure the temperature as the starting point. The peak wavelength still shifts to the shorter wavelength with the temperature increase, as shown in Fig. 11(b), demonstrating a temperature sensitivity of −16.38 nm/°C, which is much higher than that of conventional temperature sensors, as listed in Table 1.

 figure: Fig. 11.

Fig. 11. (a) The transmission spectrum of the isopropanol cladding elliptical MNFs at different temperatures. (b) The resonant wavelength as a function of temperature.

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Tables Icon

Table 1. Comparison of temperature sensitivities for a variety of structures of sensors.

The sensitivity of this configuration can be improved to be higher by selecting a liquid cladding with a higher thermo-optical coefficient or an optimal design of the parameters of the elliptical microfiber by analyzing the temperature sensitivity. The sensitivity (S) of the dip wavelength to the temperature surrounding the Hi-Bi microfiber is expressed as

$$S = \frac{{d\lambda }}{{dT}} = \frac{{d\lambda }}{{dn}} \cdot \frac{{dn}}{{dT}} = \frac{{\lambda {{\partial B} / {\partial n}}}}{{B - \lambda {{\partial B} / {\partial \lambda }}}} \cdot \frac{{dn}}{{dT}} = \frac{{\lambda {{\partial B} / {\partial n}}}}{G} \cdot \frac{{dn}}{{dT}}$$

Equation (15) shows that the sensitivity S is determined by the RI-induced birefringence variation ${{\partial B} / {\partial n}}$, the wavelength-dependent dispersion of the birefringence ${{\partial B} / {\partial \lambda }}$, and the thermo-optical coefficient of the liquid cladding ${{dT} / {dn}}$. G is group birefringence, and with Eq. (15) and the results from Fig. 4, the sensitivity S is numerically calculated and shown in Fig. 12.

 figure: Fig. 12.

Fig. 12. The sensitivity as a function of (a) the normalized diameter and (b) the cladding refractive index.

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Figure 12(a) demonstrates the sensitivity as a function of the normalized diameter for different ellipticities at a wavelength of 1.58 µm when the cladding of the elliptical microfiber is water (with a refractive index of 1.333 and thermo-optical coefficient of −1×10−4 RIU/°C). This sensitivity does not change monotonically with the normalized diameter and is enhanced significantly when the group birefringence G approaches zero. However, the sensitivity in Eq. (15) is calculated for a specific wavelength. Considering the spectral width in an interferometric dip, an infinite sensitivity cannot be achieved [26]. The sensitivity for the elliptical microfiber in our experiments is marked in the figure, which is in good agreement.

Figure 12(b) demonstrates the sensitivity as a function of the cladding refractive index for different ellipticities (assuming ${{dn} / {dT}} = \textrm{ - }1 \times {10^{ - 4}}$ RIU/°C). The absolute value of the sensitivity increases with the cladding refractive index and enhances significantly when the cladding refractive index approaches the refractive index of the microfiber. However, the light cannot propagate within the liquid cladding microfiber when the refractive index of the liquid is higher than that of the microfiber. The sensitivity of the interferometer based on water, refractive index oil, and isopropanol liquid cladding elliptical microfiber sensing probes are denoted as points in Fig. 12(b), which are also in good agreement.

5. Conclusion

A remote temperature sensing probe based on a liquid cladding elliptical microfiber was designed and fabricated. The sensing principle was analyzed, and the fabrication of different liquid cladding elliptical MNFs was realized by combining a femtosecond laser micromachining method with fused biconical taper technology. A temperature sensing experiment based on different liquid cladding elliptical MNF sensing probes was performed, showing that the wavelength dip of the transmission spectrum shifts to short wavelengths with increasing temperature, and the measured sensitivity can reach −16.38 nm/°C for an isopropanol cladding elliptical microfiber probe. The temperature sensing probe features a simple structure and high sensitivity, which can achieve remote measurement and is not influenced by other environmental parameters, making it a promising fiber sensor in sea monitor, biological sensing field and some other harsh environment remote monitoring fields.

Funding

Natural Science Foundation of Hebei Province (QN2016078, F2016203392); National Natural Science Foundation of China (61605168); Science and Technology Project of Qin Huangdao City (201601B050).

Disclosures

The authors declare no conflicts of interest.

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Figures (12)

Fig. 1.
Fig. 1. The schematic diagram for the sensing measurement.
Fig. 2.
Fig. 2. The three-layer model of a liquid cladding elliptical MNF.
Fig. 3.
Fig. 3. The effective refractive index as a function of the normalized diameter.
Fig. 4.
Fig. 4. The birefringence as a function of the normalized diameter for elliptical microfiber with different cladding, (a) refractive index of cladding is 1, (b) refractive index of cladding is 1.3 (liquid cladding), and the birefringence as a function of the refractive index of the cladding for different size elliptical microfibers with normalized diameter of 0.67 (figure (c)) and 1.2 (figure (d)), respectively.
Fig. 5.
Fig. 5. (a) The retangular-like cross-section of pre-processed SMF, and (b) the elliptical cross-section of the elliptical microfiber.
Fig. 6.
Fig. 6. The transmission spectrums under different polarization angles. Left inset is a real picture of an encapsulated elliptical microfiber with an SMF pigtail, and the right inset is the SEM picture of the gold film coated the end of the SMF pigtail.
Fig. 7.
Fig. 7. The transmission spectrum evolution for the air cladding elliptical fiber with temperature increases from 25 to 100 °C. Inset is the magnification of a peak around the wavelength of 1559.6 nm.
Fig. 8.
Fig. 8. The transmission spectrums based on the sensing probe with different liquid claddings.
Fig. 9.
Fig. 9. (a) The experimental transmission spectrums and (b) theoretical transmission spectrums of the water cladding elliptical MNFs at different temperatures, and (c) the resonant wavelength as a function of temperature for the experimental measurements and theoretical analysis, respectively.
Fig. 10.
Fig. 10. (a) The transmission spectrum of elliptical MNFs with a refractive index oil cladding with an index of 1.3 at different temperatures. (b) The resonant wavelength as a function of temperature.
Fig. 11.
Fig. 11. (a) The transmission spectrum of the isopropanol cladding elliptical MNFs at different temperatures. (b) The resonant wavelength as a function of temperature.
Fig. 12.
Fig. 12. The sensitivity as a function of (a) the normalized diameter and (b) the cladding refractive index.

Tables (1)

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Table 1. Comparison of temperature sensitivities for a variety of structures of sensors.

Equations (16)

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( E 2 x E 2 y ) = ( T c c T S M F 1 R ( θ ) T c d + T c d T S M F 2 T c c ) R 3 ( θ ) T H B F M T H B F R 3 ( θ ) × ( T c d T S M F 1 R ( θ ) T c c + T c c T S M F 2 T c d ) ( E 1 x E 1 y ) ,
T c d = ( 0.5 0 0 0.5 ) ,
T c c = ( 0 j 0.5 j 0.5 0 ) ,
T S M F = ( e j Γ 0 0 e j Γ ) ,
R ( θ ) = ( cos θ sin θ sin θ cos θ ) ,
R 3 ( θ ) = ( cos θ 3 sin θ 3 sin θ 3 cos θ 3 )
T H B F = ( e j π B L λ 0 0 e j π B L λ ) ,
M = ( 1 0 0 1 ) ,
T = I o u t I i n = | E 2 x | 2 + | E 2 y | 2 | E 1 x | 2 + | E 1 y | 2
T cos 2 ( ϕ / 2 ) ,
ϕ = 4 π B L λ .
Δ λ = λ 2 B 2 L ,
λ R = B 2 L k .
Δ λ R = Δ B 2 L + B 2 Δ L
Δ λ R = Δ B 2 L .
S = d λ d T = d λ d n d n d T = λ B / n B λ B / λ d n d T = λ B / n G d n d T
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