1 Introduction

Fiber optic pressure sensors have advantages such as intrinsic electrical passivity, high-temperature survivability, corrosion resistance, immunity to electromagnetic interference, and compact size [1]. They are very suitable for applications in space-limited harsh environments [2–5]. Various types of pressure sensors have been proposed, including those based on fiber Bragg gratings (FBGs) fabricated in SMFs and highly birefringent photonic crystal fibers (PCFs) [5, 6], Sagnac interferometer, mode interference of a dual-core PCF [7, 8], and a miniature Fabry–Perot cavity [9]. Among them, pressure sensors based on Fabry–Perot interferometer (FPI) have attracted more attention because they have some advantages such as compactness, higher sensitivity, simple fabrication, and lower cost. The FPI cavity can be formed by various methods, for example using an elastic diaphragm at the fiber tip such as undoped fused silica thin layer, polymer, and graphene film [10–13]; creating a sphere cavity in the splice [14]; and splicing a section of solid-core PCF with SMFs [15]. However, the technique based on an elastic diaphragm always involves multiple components and complex alignment. The mechanical strength and thermal stability of the sensors may be degraded due to the different materials of multiple components. The pressure sensors reported in [14, 15] improve the mechanical strength by using all fiber structure. For this type of sensor, cross talk of the temperature is a problem, and it is necessary to compensate for this. Meanwhile, the stability and repeatability should be discussed in the pressure sensing applications. The fiber-tip microcavity pressure sensor [14] demonstrated a pressure sensitivity of 315 pm/MPa and a temperature sensitivity of 1.55 pm/°C, and therefore, the temperature cross talk was calculated to be 5 kPa/°C. The pressure sensor using a solid-core PCF-based FPI [15] showed a low-pressure sensitivity of 5.8 pm/MPa and a temperature sensitivity of 13 pm/°C, which has a high-temperature cross talk of 2.2 MPa/°C. The pressure sensitivity of an F–P cavity with a hollow-core PCF [16] was also as low as 17.3 pm/MPa; however, the temperature cross talk was not discussed. As we know, the repeatability and stability are not yet included in the above reports.

In this paper, we have demonstrated a novel pressure sensor based on FPI using a simplified hollow-core PCF (SHC-PCF). This sensor is simply made by fusing both ends of a section SHC-PCF with SMFs, and a microchannel is drilled by using a femtosecond laser in the PCF to open the FP cavity to the environment and allow air to diffuse in. The pressure sensing mechanism of our pressure sensor is based on the dependence of the air refractive index on pressure. This can significantly improve the pressure response which is 235 times higher than that without a microchannel. In our experiment, a high-pressure sensitivity of 4.071 nm/MPa is obtained, and a low-temperature sensitivity of 1.1 pm/°C at atmospheric pressure is achieved simultaneously. The temperature cross sensitivity of the sensor under different pressures is further investigated in both theory and experiment. The sensor has a compact size and good mechanical strength since it is all fiber structure. We also discuss the stability and repeatability. Hence, it may have potential applications in pressure sensing.

2 Experimental setup

The SHC-PCF in our experiment supported by YOFC Ltd is composed of a hollow core and one layer of airhole cladding, which was proposed by Gérôme et al. [17] and Wu et al. [18], and has similar light guidance as the Kagome-structured PCF which is a new type of hollow-core PCF based on large-pitch Kagome lattice cladding [19]. As reported, the triangular lattice HC-PCF has been thought to be the best trade-off to show a large photonic band gap (PBG) at the wavelength of interest with the fabrication methods now available. But it needs a complicated fabrication process and super-accurate structured design. Compared with it, the fabrication technique of the Kagome-structured PCF is less demanding, and the structure is simpler as well. Only thin, circular capillaries in the stack-and-draw technique and the low drawing temperature are required. And further it is important that the Kagome-structured PCF also exhibits broad transmission regions with relatively low loss in the spectral range of interest [19]. The cross-sectional view of the SHC-PCF is shown in Fig. 1a, and the diameters of air core and air cladding and whole fibers are 32, 70, and 135 μm, respectively. The thickness of the silica struts is estimated to be ∼400 nm. The FPI structure was simply made by splicing both ends of a short-section SHC-PCF with SMFs using conventional fiber cleaving and fusion splicing technique while avoiding any airhole collapse [20, 21]. Figure 1b shows the microscopic image of the SHC-PCF-based FPI. It shows that there is no collapse of the visible airhole in SHC-PCF at either splicing point. The length of SHC-PCF is about 272 μm, which can be controlled accurately by the use of a microscopic CCD camera during the cleaving process. After splicing, a microchannel of 5 × 10 µm is drilled in the middle part of the PCF from the fiber surface to the core using a Ti/sapphire femtosecond laser (SOLSTICE-10 K-230 V). Therefore, outside air can diffuse into the fiber core. The microchannel was machined by the femtosecond laser (3 µJ pulse energy, 1 kHz repetition rate, 800 nm center wavelength, and 100 fs pulse width) focused with a 20× microobjective (NA = 0.50) using a line-scanning method, and there was no additional spectral loss observed in the drilling process, we think the silica struts can prevent the debris matters produced by the laser ablation from polluting the cavity surface of FPI. Figure 1c shows the photograph of the microchannel taken by the optical microscope. The measured reflection spectrum of the FPI structure with different lengths is shown in Fig. 1d. When the length of FP cavity decreases, the interference fringe visibility and the fringe spacing become larger. According to FPI theory, the fringe spacing Δλ can be calculated by \(\Delta \lambda = \lambda^{2} /2nL\) where n is the refractive index of the FPI cavity and L is the length of SHC-PCF. For the FPI cavity shown in Fig. 1b, Δλ can be calculated to be 4.4 nm when n ≈ 1 for air at atmospheric pressure. It agrees well with the value of 4.5 nm measured from Fig. 1d at wavelength of 1550 nm.

Fig. 1
figure 1

a Cross-sectional view of SHC-PCF. b Microscopic image of the FPI based on SHC-PCF with the cavity length of 272 μm. c Optical micrograph of a microchannel with size 5 × 10 μm. d The measured reflection spectrum of the FPI structures with lengths 103, 272, and 330 μm, respectively

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3 Characterization of FPI sensor

The pressure response of the FPI sensor is tested using the experimental setup shown in Fig. 2. A broadband optical source (SLED, 1250–1700 nm, B&A Technology SL3200, China) and an optical spectrum analyzer (OSA, MOI SM-125) with a spectral resolution of 0.01 nm are connected to the FPI sensor. The reflected interference spectrum is recorded using an optical circulator. The FPI sensor probe is inserted into a gas chamber, which is connected to a pressure controller and a high-precision pressure meter (ConST-118). The pressure in the chamber increases from 0 to 1.5 MPa with an interval of 0.1 MPa. For our FPI sensor, the outside air can diffuse into the core of SHC-PCF through the microchannel, so the pressure inside the fiber hollow core is consistent with the gas chamber. Figure 2b shows the pressure response of the FPI sensor with a length of 272 μm. The interference spectrum shifts toward longer wavelength with the applied pressure. Figure 3a shows the shift of the dip wavelength as functions of applied pressure around 1500 and 1580 nm. Figure 3b shows the shift of the dip wavelength as functions of applied pressure for three FPI samples with different cavity lengths (L 1 = 103 μm, L 2 = 272 μm, L 3 = 330 μm). The wavelength shifts linearly with the pressure. The R 2 of linear fitting is higher than 0.9999. The pressure sensitivities obtained are 3.95, 4.071, and 4.107 nm/MPa, respectively, which are weakly dependent on the cavity length.

Fig. 2
figure 2

a Schematic diagram of the experimental setup for pressure measurement of a FPI sensor. b Response of the FPI sensor with a length 272 μm to pressure

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Fig. 3
figure 3

a Wavelength shift versus pressure at 1500 and 1580 nm. b Pressure sensitivity of different FPI cavity lengths. L 1 = 103 μm, L 2 = 272 μm, L 3 = 330 μm. c Wavelength shift as functions of temperature for the FPI sensor

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For FPI, the output intensity can be modeled using the two-beam optical interference equation:

$$I = I_{1} + I_{2} + 2\sqrt {I_{1} I_{2} } { \cos }\left( {\frac{4\pi n \cdot L}{\lambda }} \right),$$

where I 1 and I 2 are the reflective intensities at the two cavity surfaces, L is the cavity length, λ is the operating wavelength, and n is the refractive index in the FPI cavity. For a certain dip λ m in the spectrum under observation, its optical phase difference should be an odd number of π. That is \(\frac{4\pi nL}{{\lambda_{m} }} = (2m + 1)\pi\), here m is an integer. The wavelength of the dip is given by:

$$\lambda_{m} = \frac{4nL}{2m + 1}$$
(1)

In our experiment, the pressure in the cavity is consistent with the applied pressure in the gas chamber due to the existence of a microchannel. The wavelength shift of a given dip as a function of the pressure is induced by the variation in the refractive index of the cavity and cavity length, but the pressure is uniformly applied to all surfaces of the FPI sensor. The effect of pressure on the cavity length is believed to be very small and can be neglected. Generally, the refractive index of air is a complicated function of its temperature (T) and pressure (p). To a good degree of accuracy, the refractive index, n, of the cavity can be described as [22]:

$$n = n_{0} + \gamma \frac{p}{T}$$
(2)

where n 0 is the vacuum refractive index, γ is a constant for air (0.00538 K/psi). From Eqs. (1) and (2), the given dip wavelength can be expressed by

$$\lambda_{m} = \frac{4L}{2m + 1}\left( {n_{0} + \gamma \frac{p}{T}} \right)$$
(3)

Hence, the slope of the wavelength versus pressure can be described by [15, 22]:

$$K = \frac{\partial \lambda }{\partial p} = \frac{{\gamma \lambda_{m} }}{nT}$$
(4)

From Eq. (4), it indicates the wavelength shifts to longer wavelength with the increase in pressure, which shows a same trend with the experimental results shown in Fig. 3. The theoretical pressure sensitivities at room temperature are calculated to be 3.901 and 4.108 nm/MPa at 1500 and 1580 nm, respectively. In Fig. 3a, we can see that the pressure sensitivities in the experiment are obtained to be 3.967 and 4.071 nm/MPa at 1500 and 1580 nm, respectively, which are very close to the theoretical values. The pressure sensitivities are higher than those based on the Sagnac interferometer (3.46 nm/MPa), the dual-core photonic crystal fiber lateral offset splicing (3.47 pm/MPa) and the fiber-tip microcavity (315 pm/MPa). Another thing to be noted is the response of the FPI cavity without a microchannel: The sensitivity is only as low as 17.3 pm/MPa as reported in [16]. The sensitivity based on FPI with a microchannel is enhanced to be 235 times higher than that without a microchannel. So here, we observe that the pressure sensitivity can be significantly and efficiently improved by the microchannel in the SHC-PCF fabricated by a femtosecond laser.

Meanwhile, for a pressure sensor, the cross talk of temperature is a problem and must be considered and compensated for in the applications. To our knowledge, the fiber-tip microcavity pressure sensor [14] demonstrates a temperature cross talk of 5 kPa/°C. The pressure sensor using a solid core PCF-based FPI [15] shows a high-temperature cross talk of 2.2 MPa/°C. In this paper, we also investigate the temperature response of the FPI sensor with a microchannel open to the external environment without additional applied external pressure. The FPI is placed in a heater, and the temperature increased from room temperature to 190°C with a step of 40°C and then cooled down to room temperature. The maximum temperature is limited by the heater we use. The result is shown in Fig. 3c. The dip wavelength is red shift with the temperature rising. We use a linear fit to estimate the temperature sensitivity of 272-μm FPI cavity to be 1.1 pm/°C at 1580 nm. We also find the temperature sensitivity weakly depends on the cavity length of the FPI sensor. For the FPI sensor with a pressure sensitivity of 4.071 nm/MPa at 1580 nm, the temperature cross sensitivity is as low as 0.27 kPa/°C, which is almost 20 times lower than that reported in [14]. The theoretical temperature sensitivity due to the thermal expansion of solid silica (α = 5.5 × 10−7/°C) is calculated to 0.9 pm/°C at 1580 nm. It indicates the expansion of silica plays a major role in determining the temperature sensitivity when the FPI sensor with a microchannel is open to the external environment without additional applied external pressure. In experiment, we also investigate the temperature sensitivity at different pressures. We change the temperature from 30 to 110 °C at step of 20 °C and keep the pressure at 0.5, 1, and 1.5 MPa, respectively. The results are shown in Fig. 4. The dip wavelength is not red shift but blue shift with increasing the pressure and the temperature sensitivities are obtained to be −3.43, −8.62 and −10.1 pm/°C, respectively. The temperature cross sensitivities are corresponding to −0.84, −2.12 and −2.46 kPa/°C, respectively. The temperature sensitivity and the temperature cross sensitivity both increase with the pressure. Meanwhile, they can be theoretically analyzed by using the relationship of air index with temperature and pressure. When the FPI is subjected to temperature variation, n and L will change due to thermo-optic effect of air in cavity and thermal expansion of solid silica to support the FPI sensor, and the slope of the wavelength versus temperature can be described by [15]

$$S_{T} = \frac{\partial \lambda }{\partial T} = \lambda_{m} \left( {\frac{\partial L}{\partial T}\frac{1}{L} + \frac{\partial n}{\partial T}\frac{1}{n}} \right) = \lambda_{m} (\alpha + \xi )$$
(5)

where α is thermal expansion coefficient of silica which is kept as a constant (α = 5.5 × 10−7/°C) and ξ is the thermo-optic coefficient of air. The refractive index of air is proportional to the pressure and inversely proportional to the absolute temperature. From Eq. (3), the thermo-optic coefficient ξ of air in cavity which depends on the pressure and temperature can be given by

$$\xi = - \frac{\gamma p}{{nT^{2} }}$$
(6)

Here, it can be seen that ξ is directly proportional to the pressure. We can get \(\xi = - 28 \times 10^{ - 7} /^\circ {\text{C}}\) at 0.5 MPa and 300 K which is negative and \(\left| \xi \right| > \alpha\). So the thermo-optic effect of air in cavity becomes stronger and stronger with increase in pressure and will lead the dip wavelength to blue shift and dominate the temperature sensitivity rather than thermal expansion of solid silica. From (5) to (6), it can be seen the temperature sensitivity is dependent on the pressure and temperature. At the wavelength of 1550 nm, the temperature sensitivities can be calculated to be −3.5, −7.9, and −12 pm/°C at 0.5, 1, and 1.5 MPa, respectively. These values are well consistent with the experimental ones. Further, the thermo-optic coefficient of air increases with the pressure, followed by the increase in the temperature sensitivity and the accompany temperature cross sensitivity. The temperature cross sensitivity Δ caused by thermo-optic effect of air can be theoretically analyzed using the relationship of air index with temperature and pressure. From formulas (2), (4), and (5), Δ can be given by

$$\Delta = \frac{{S_{T} }}{K} = \frac{P}{T}$$
(7)
Fig. 4
figure 4

Temperature sensitivity at different pressures

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So the temperature cross sensitivity will increase as the pressure increases. Nevertheless, in our experiment, the value is just 2.46 kPa/°C at 1.5 MPa, which is still smaller than that of the fiber-tip microcavity pressure sensor [14].

Because the structure is all-silica fiber, the FPI sensor has great potential to operate stably and reversibly. We record the wavelength shift as functions of time with an interval of 1 min. Figure 5 shows the wavelength shift when the applied pressure is switching between 0.8 and 0.5 MPa; the curve illustrates that the reversibility of the pressure sensor is robust and the stability is well. Meanwhile, we investigate the pressure response of the FPI sensors with drilling one 5 × 10 μm microchannel and three microchannels with same size in SHC-PCF. Figure 6 shows the wavelength shifts as function of time when applied pressure is switching between atmospheric pressure to 1 MPa. The data recording frequency of OSA (MOI SM-125) in our experiment is 2 Hz. It can be seen from Fig. 6 the two curves almost overlap. The rising edges and falling edges are estimated to be about 50, 80, 130, and 60 s, respectively. They are observed to be determined by the speed of the pressure controller in our experiment. We find that the pressure response speed of the sensor has almost nothing to do with the channel size and the number of channels using our data acquisition unit in hand. It is faster than the data recording speed (0.5 s) of OSA on account of the very small FPI cavity and the pressure difference between the cavity and ambient. Moreover, for practical implementation, the microchannel may be getting clogged by debris like a speck of dust, which causes the FPI spectrum decay, as shown in Fig. 7. When the pressure sensor is kept in room natural environment for 1 month, the spectrum evolves from the original (the blue curve) to the black curve accompanied by higher insertion loss and worse fringe visibility, as shown in Fig. 7. But after the sensor is cleaned by immersing and wobbling it in alcohol, the spectrum (the red curve) almost recovers to the original one including the spectral visibility and the insertion loss.

Fig. 5
figure 5

Wavelength fluctuation as functions of time switching between 0.8 and 0.5 MPa

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Fig. 6
figure 6

Pressure response of the FPI sensor with one hole and three holes, respectively

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Fig. 7
figure 7

Measured reflection spectrum of the FPI before and after cleaning in alcohol

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4 Conclusions

An all-silica compact pressure sensor based on micro-FPI is proposed by splicing both ends of a short-section SHC-PCF with SMFs. A femtosecond laser micromachining is used to drill a microchannel in the part of the SHC-PCF, which can make the FPI structure suitable for monitoring the external pressure change due to the dependence of the air refractive index on pressure. The all-silica fiber structure enhances the stability and the mechanical strength of the FPI sensor. It indicates that the micro-FPI sensor may be used potentially as a pressure sensor.