Fiber optic sensors have gained traction in the scientific community over the past few decades thanks to their many desirable properties， including low power consumption， low weight， quick response time， high sensitivity， and immunity to electromagnetic interference. They have been widely used in various sensing applications for physical^［1-5］， chemical^［6-8］， and biological^［9-11］ measurements. Temperature and lateral load measurement are crucial in fiber optic sensing research since these are essential physical quantities in experimental study and production life.

In 2021， YI Guo et al.^［12］ proposed a tip Thin-wall Hybrid-structure Fabry-Perot Interferometer（THFPI）based on zero cross-sensitive， compact， and high robustness. The tip THFPI was fabricated by stretching and discharging simultaneously when the Hollow-core Fiber（HCF）and Single-mode Fiber（SMF）are spliced. In 2021， XU Ben et al.^［13］ proposed a Mach Zehnder interferometer based on MMF-PCF-MMF for measuring strain， pressure， and other physical quantities.

In 2020， ZHOU Ning et al.^［14］ proposed a reflective intensity-modulated fiber-optic sensor based on Micro Electro Mechanical Systems（MEMS）for pressure measurements. The sensor consisted of two multimode optical fibers with a spherical end， a quartz tube with dual holes， a silicon-sensitive diaphragm， and a High Borosilicate Glass Substrate（HBGS）. In 2021， ZHENG Jiewen et al.^［15］ proposed a fiber sensor based on SMF to simultaneously measure lateral load， refractive index， and high temperature. The cap-shaped MI sensor's lateral load， Refractive Index（RI）， and high-temperature wavelength sensitivity were -1.412 nm/N， 200.07 nm/RIU， and 8.4 pm/℃.

This article investigates an MZI/FPI sensor comprising two cascaded conical SMFs and a HCF gas cavity. Temperature can be measured using the M-Z sensing principle， and lateral load can be measured using the F-P sensing principle. Compared to other sensors， this sensor has a simple structure preparation process， cheap raw material prices， and good sensing performance. Although cone and cavity structures are widely used， this article provides a way to combine them， enabling simultaneous measurement of two parameters with low interference between them. And this article adopts a double cone structure， which has better excitation effect and better temperature measurement sensitivity compared to a single cone structure. At the same time， through experimental verification， the sensor has high sensitivity for temperature and lateral load.

Figure 1 shows the structural diagram of the proposed Mach-Zehnder/Fabry-Pérot Interferometer（MZI/FPI）sensor， consisting of two cascaded fiber tapers of SMF-28 and an air cavity of HCF（75/150 μm）. The distance between the waist of two cascaded fiber optic tapers is L₁， and the length of the air cavity is L₂. In addition， the transmission spectrum of a double-cone is more pronounced than that of a single-cone， as shown in Fig. 2.

The left end is a double taper structure， and the right is an air cavity structure， forming MZ/FP interference. As shown in Fig. 1， the optical signal is emitted from the right SMF， and the first reflection and transmission occur at the interface between the SMF and the air cavity. The transmitted light undergoes a second reflection and transmission at the interface between the air cavity and the SMF. F-P interference reflection spectrum is formed. The transmitted light continues propagating， and the first excitation occurs at the junction of the SMF and the first tapered structure. Part of the light is excited onto the cladding fiber， while the remaining light propagates along the fiber core. Then， the cladding mode and core mode light are coupled at the second conical structure， forming the MZ interference transmission spectrum. We can obtain the MZ transmission spectrum and F-P reflection spectrum. Theoretically， temperature can be measured through transmission spectroscopy， while lateral load can be measured through reflection spectroscopy.

The core mode and higher-order cladding mode mainly form the transmission spectrum. The interference equation between the core mode and higher-order cladding mode can be expressed as

where I₁ and I₂are the light intensities of the core mode and the higher-order cladding mode， respectively. By the same distance L₁， the phase difference φ between the two modes can be expressed as

Among them Δneff is the difference in effective refractive index between the core and higher-order cladding modes， and λ is the input light wavelength. When the phase difference meets the conditionφ=(2m+1)π， m=0，1，2， the interference light intensity reaches the minimum value， and the spectral valley wavelength can be given as

where λm is the central wavelength of the m^th order interference wave valley. From Eq.（3）， it can be seen that when Δneff remains constant， as fiber optic expands when heated， L₁ increases， λm will correspondingly increase， exhibiting a red shift phenomenon in the spectrum. The Free Spectra Range（FSR）of the interference fringe of the double-cone MZI can be given by

When conducting temperature measurements， the Mach Zehnder interferometric sensing part is affected by temperature， causing changes in mode parameters and fiber length， resulting in a shift in the spectral valley. It can be expressed as

In the above equation，ε=dL/L represents the applied temperature change. According to Eq.（5）， we can calculate the change in environmental temperature by tracking the offset of the valley wavelength in the interference spectrum， thereby measuring temperature.

In addition， the sensor can measure lateral loads by applying weights to the air cavity section. The equation for reflection spectrum F-P interference is as follows

where I is the intensity of the interference light， I₁ is the intensity of the first reflected light， I₂ is the intensity of the second reflected light， and ϕair the air cavity's phase shift. The specific calculation formula is as follows：

In the above equation， n₁ is the refractive index of the air cavity under lateral load， and L₂is the length of the air cavity， and λ is the input light wavelength. When the phase difference meets the condition ϕair=(2f+1)π， f=0，1，2， the interference light intensity reaches the minimum value， and the spectral valley wavelength can be given as

From Eq.（8）， it can be seen that when the lateral load on the HCF part increases， the air inside the cavity is compressed， n₁increases， and λf also increases， exhibiting a red shift phenomenon in the spectrum. The FSR of the interference fringe of the air cavity FPI can be given by

In an optical fiber， the taper structure can effectively excite light from the core into the cladding. As shown in Fig. 3， the manufacturing process of this structure is as follows： first， fix a section of SMF with the coating removed in the fusion machine（Fujikura 80 s）. The second step is to ensure that the middle end of the SMF melts to form the expected taper， using an 80 bits arc power and 2 000 ms arc discharge time for multiple discharges to create the first cone， as shown in Fig. 3（a）. During the third step， the same discharge process was performed at a distance of about 17 mm to form a second cone， as shown in Fig. 3（b）. The fourth step is to cut a single-mode fiber approximately 2.5 cm away from the waist of the second conical structure and use a fiber fusion machine to fuse SMF and HCF. The discharge time is 300 ms， and the discharge power is -25 bits， as shown in Fig. 3（c）. The fifth step is to cut a section of HCF with a length of approximately 50 μm and use a fiber optic fusion machine to fuse it with the SMF. The same discharge time and power as the previous step are used， as shown in Fig. 3（d）.

The sensor parameters in this experiment are as follows： the length of the two taper regions is 393.8 μm and 413.2 μm， respectively， while the waist diameter is 60.7 μm and 64.3 μm. The distance between the two tapers is 16.5 mm. The length of the air cavity is 58.6 μm. The distance between the air cavity and the waist of the second taper is 27.2 mm. The actual sensor under the microscope is shown in Fig. 4. During the preparation process， by observing the spectrometer， the transmission spectrum performance generated by a larger waist radius is poor， and a lower waist radius can easily lead to low structural stability. The waist radius of the two cone-shaped structures is around 50~75 μm， which is prone to producing good transmission spectra. At the same time， precise cutting of HCF requires high requirements for the instrument. The HCF in the figure has slight deformation during fusion， which has no special impact on the measurement of reflection spectrum. In theory， the shorter the HCF section， the better the reflection spectrum performance. However， in specific experiments， the cutting difficulty of HCF is relatively high. When the length of HCF is controlled at（90 ± 40）μm， the performance of the reflection spectrum is better and the success rate of preparation is also high. When the length of HCF exceeds 150 μm， the reflection spectrum performance is very low. The sensing measurement of the temperature part is completed by the biconical structure part， and the sensing measurement of the lateral load part is completed by the HCF part. The sensing length of the entire sensor depends on the distance between the leftmost and rightmost structures.

For temperature measurement， a Broadband Source（BBS）with an output wavelength range of 1 440 and 1 640 nm and an optical spectral analyzer with a resolution of 0.1 nm（OSA， YOKOGAWA， AQ6370D）， which is centered around 1 540 nm are used. The sensor is placed in a muffle furnace， and the experimental setup is shown in Fig. 5（a）. Light departs from BBS， passes through sensors in the muffle furnace， and reaches OSA.

We measured and recorded transmission spectra at intervals of 10 ℃， ranging from 30 to 80 ℃ Celsius. Ensure each temperature is maintained for 10 minutes before measurement to enhance accuracy. As shown in Fig. 5（b）， illustrates the Mach-Zehnder Interferometer（MZI）sensor's transmission spectrum variation with increasing temperature， demonstrating a red shift in all spectral peaks and troughs.

Track the wave dips near 1 515 nm and 1 550 nm， as shown in Fig. 5（c）. When the temperature ranges from 30 ℃ to 80 ℃， for valleys near 1 515 nm， the valley wavelength shifts from 1 515.5 nm to 1 518.3 nm， and the sensitivity of the corresponding heating wavelength is 56.29 pm/℃， the linear fitting R² is 0.982， and the signal-to-noise ratio of the valley to the peak is 16.51 dB. For valleys near 1 550 nm， the valley wavelength shifts from 1 552.5 nm to 1 555.3 nm， and the sensitivity of the corresponding heating wavelength is 57.14 pm/℃， the linear fitting R² is 0.983， and the signal-to-noise ratio of the valley to the peak is 16.31 dB.

We repeated the production of multiple sensor structures and conducted temperature experiments， and the experimental results are shown in Fig. 5（d）. 1-Dip A to 3-Dip B are all used to verify the temperature sensing characteristics of the sensor structure. The structural parameters of these sensors have slight errors， but they all have sensitivity to temperature sensing. 4-1-Dip and 4-2-Dip are experimental results of temperature rise and fall for the same group of sensors. From the graph， it can be seen that the sensor's sensitivity performance remains almost unchanged during temperature rise and fall， with an error rate of only 2.45%. The main source of error is that there may be some error between the displayed temperature on the thermometer and the actual temperature received by the sensor during experimental recording. It can be concluded that the sensor has repeatability and stability.

BBS and Optical Spectral Analysis（OSA）are used for lateral load measurement， as described above. Place the sensor between two glass plates； the experimental setup is shown in Fig. 6（a）. Light starts from BBS， passes through 3 dB coupler， reaches the HCF part of the sensor， reflects back to 3 dB coupler， and finally reaches OSA. Control the room temperature at 25 ℃. When the lateral load rises from 0 N to 5 N， take a reading every 1 N. Maintain stability for 1 minute at each load， and measure and record the reflectance spectrum to ensure accuracy. Fig. 6（b）depicts the reflection spectrum of the FPI sensor as the lateral load increases. As the load increases， all peaks and valleys will undergo a red shift.

Track the wave troughs near 1 510 nm and 1 550 nm， as shown in Fig. 6（c）. When the lateral load ranges from 0 N to 5 N， for valleys near 1 510 nm， the valley wavelength shifts from 1 509.3 nm to 1 514.9 nm， the lateral load sensitivity is 1.123 nm/N， the linear fitting R² is 0.997， and the valley to peak signal-to-noise ratio is 11.77 dB. For valleys near 1 550 nm， the valley wavelength shifts from 1 549.6 nm to 1 555.2 nm， the lateral load sensitivity is 1.140 nm/N， the linear fitting R² is 0.995， and the valley to peak signal-to-noise ratio is 12.42 dB.

We repeated the production of multiple sensor structures and conducted load experiments， and the experimental results are shown in Fig. 6（d）. Due to the difficulty of HCF cutting， the length of HCF in each group is not consistent. However， it can be seen from the graph that the sensor structure has the same sensing characteristics for the load， and the sensing performance is determined by the length of the HCF. The shorter the HCF， the better the sensing performance. 4-1-Dip and 4-2-Dip are the experimental results of the same group of sensors for load increase and decrease. From the graph， it can be seen that the sensing performance of the sensor remains almost unchanged with an error of 4.61% when the load increases and decreases. The main source of error may be slight deformation of the optical fiber caused by manual operation. In short， sensors have repeatability and stability for load sensing.

The experiment shows that the MZI/FPI sensor structure proposed in this article has good temperature and lateral load sensitivity. This article lists in Table 1 some fiber optic sensors that also measure physical quantities of temperature and lateral load. It can be seen that comparison with the related sensors are shown in Table 1， the MZI/FPI fiber optic sensor proposed has a simple structure， an easy preparation process， and lower raw material and instrument costs. Its sensitivity performance is also very good.

In summary， we propose a new type of MZI/FPI sensor formed by splicing a section of HCF with a double cone structure made of SMF， which can simultaneously measure temperature and lateral load. This article discusses the working principle of the sensor and conducts experimental research on it. In the temperature experiment， the sensitivity of the sensor to temperature was 56.29 pm/℃ and 57.14 pm/℃ for the valleys near 1 515 nm and 1 550 nm， respectively. In the lateral load experiment， the sensitivity to the lateral load was 1.123 nm/N and 1.140 nm/N for the valleys near 1 510 nm and 1 550 nm， respectively. In the experiment， it was found that shorter gas cavity structures produce better F-P interference reflection spectra. Although cone structures are widely used， this article uses a double-cone structure to achieve MZ interference. Compared to a single-cone structure， the excited interference spectrum has better sensitivity. And the size of the tapered waist has a significant impact on the MZ interference transmission spectrum. The MZI/FPI fiber optic sensor proposed in this article has high sensitivity to temperature and lateral load parameters. It also has the advantages of convenient manufacturing， low cost， and high reliability， which is conducive to its application in scientific research and industrial production.