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High Sensitivity Fiber Gas Pressure Sensor with Two Separated Fabry–Pérot Interferometers Based on the Vernier Effect

High Sensitivity Fiber Gas Pressure Sensor with Two Separated Fabry–Pérot... hv photonics Article High Sensitivity Fiber Gas Pressure Sensor with Two Separated Fabry–Pérot Interferometers Based on the Vernier Effect 1 2 1 1 1 2 1 , Xiaokang Song , Liangtao Hou , Xiangyu Wei , Hang Su , Chang Li , Yan Li and Lingling Ran * College of Electronics Engineering, Heilongjiang University, Harbin 150080, China; 2191255@s.hlju.edu.cn (X.S.); 2181194@s.hlju.edu.cn (X.W.); 2191260@s.hlju.edu.cn (H.S.); 2191258@s.hlju.edu.cn (C.L.) Department of Optoelectronics Science, Harbin Institute of Technology at Weihai, Weihai 264209, China; 20b911012@stu.hit.edu.cn (L.H.); liy@hit.edu.cn (Y.L.) * Correspondence: ranlingling@hlju.edu.cn Abstract: A high sensitivity optical fiber gas pressure sensor based on paralleled Fabry–Pérot in- terferometers (FPIs) was demonstrated. One micro-cavity FPI is used as a reference FPI (FPI-1) to generate a Vernier effect and the other FPI (FPI-2) is used as a sensing tip. Both FPIs are connected by a 3-dB coupler to form a paralleled structure. The FPI-1 was fabricated by fusion splicing a piece of hollow core fiber (HCF) between two sections of single-mode fibers (SMF), whereas FPI-2 was formed by fusion splicing a section of HCF between SMF and a piece of HCF with a slightly smaller inner diameter for sensing pressure. The gas pressure sensitivity was amplified from 4 nm/MPa of single FPI to 45.76 nm/MPa of paralleled FPIs with an amplification factor of 11.44 and a linearity of 99.9%. Compared with the traditional fiber gas pressure sensors, the proposed sensor showed great advantages in sensitivity, mechanical strength, cost, and temperature influence resistant, which has potential in adverse-circumstance gas pressure sensing. Keywords: optical fiber sensor; gas pressure; Vernier effect; Fabry–Pérot interferometers; high sensitivity Citation: Song, X.; Hou, L.; Wei, X.; Su, H.; Li, C.; Li, Y.; Ran, L. High 1. Introduction Sensitivity Fiber Gas Pressure Sensor Optical fiber gas pressure sensors have been widely used in automatic production, with Two Separated Fabry–Pérot aerospace, military, and medical diagnosis fields due to their advantages of compactness, Interferometers Based on the Vernier Effect. Photonics 2022, 9, 31. https:// anti-interference, and high-accuracy [1–3]. Various optical fiber sensors, such as long-period doi.org/10.3390/photonics9010031 fiber gratings (LPFGs) [4,5], fiber Bragg gratings (FBGs) [6,7], Mach–Zehnder interferom- eters (MZIs) [8,9], and FPIs [10,11] have been developed to measure gas pressure, and Received: 23 November 2021 among them, FPI is very promising owing to its flexible manufacturing, easy operation, Accepted: 30 December 2021 and convenient combination. Published: 4 January 2022 The mechanism of FPI sensors for measuring gas pressure is to obtain the gas pressure Publisher’s Note: MDPI stays neutral variation tendency by observing the change of the fiber refractive index (RI) or the F–P cavity with regard to jurisdictional claims in length. In the open cavity structure, the F–P cavity is directly in touch with the external published maps and institutional affil- environment, and the gas pressure can be detected by monitoring the shift of the reflection iations. spectrum, which is induced by the change of the RI distribution [12,13]. In 2015, Wang et al. reported an F–P gas pressure sensor based on a side-opened channel structure, which realized the gas pressure sensitivity of 4.24 nm/MPa [14]. In 2016, Hou et al. demonstrated a gas pressure sensor based on an anti-resonant reflecting guidance mechanism with a single HCF, Copyright: © 2022 by the authors. whose gas pressure sensitivity was 3.59 nm/MPa [15]. In fact, the theoretical analysis reported Licensee MDPI, Basel, Switzerland. in [16] showed that the sensitivity of the open structure gas pressure sensor is low, which This article is an open access article is predicted to be less than 5 nm/MPa. However, by using the closed cavity structure, the distributed under the terms and gas pressure difference between inside and outside the cavity can result in the change of conditions of the Creative Commons the F–P cavity length so that the gas pressure can be retrieved by the spectral drifting under Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ this condition [17,18]. In 2019, Cui et al. reported an FPI gas pressure sensor fabricated 4.0/). by an exfoliated ultrathin graphene atomic layer, and a sensitivity of 9620 nm/MPa was Photonics 2022, 9, 31. https://doi.org/10.3390/photonics9010031 https://www.mdpi.com/journal/photonics Photonics 2022, 9, 31 2 of 11 obtained [19]. In 2021, Wang et al. utilized Ecoflex0030 silicone rubber/Polydimethylsiloxane as the end face of the closed F–P cavity, and a sensitivity of 30.2 nm/MPa was realized [20]. However, the mechanical strength and the measuring range of the closed cavity gas pressure sensor are always blamed due to the fact that the thin membrane attached at the fiber end can be easily cracked and further applications will be restricted. Therefore, ensuring a wide measurement range while still maintaining high sensitivity has always been the goal pursued in the field of gas pressure measurement. The Vernier effect has been proven to be an effective method to promote the sensitivity of an optical fiber sensor. The principle of the Vernier effect is to make two interferometers with small free spectral range (FSR) differences generate a superimposed spectrum, which will raise the sensitivity by measuring the response of the envelope. The key point of realizing the Vernier effect is to make FSRs of the two interferometers similar but not completely equal [21]. At present, the cascaded FPIs [22–24], cascaded MZIs [25,26], cascaded Sagnac interferometers (SIs) [27,28], and cascaded ring resonators [29] have successfully realized the Vernier effect. For gas pressure sensing, the Vernier effect based on MZIs [30] and FPIs [31] have been proposed and exhibited an ultra-high sensitivity of 82.131 nm/MPa and 86.64 nm/MPa, but the sensors were fabricated by a femtosecond laser (Fs), which greatly increased the cost and the difficulty of manufacturing, and the temperature crosstalk cannot be ignored. In this paper, a high sensitivity gas pressure sensor using paralleled FPIs based on the Vernier effect is demonstrated. Two separated F–P cavities with slight length difference are connected by a 3-dB coupler for sensing and referencing. The optical paths of these two FPIs are approximately equal, so the Vernier effect can be generated. By using the Vernier effect, the gas pressure sensitivity of the proposed sensor has been greatly improved. Experimental results show that gas pressure sensitivity is enhanced to 45.76 nm/MPa by the Vernier effect with an amplification factor of 11.44 and linearity of 99.9%. In addition, the reference FPI can be isolated from the sensing FPI and detection environment due to the separated structure. Thus, reference FPI cannot be affected by external environmental temperature. Only the temperature response of sensing FPI can be amplified, due to the extremely low thermo-optical coefficient and thermal expansion coefficient of air, leading to a temperature crosstalk of 0.097 KPa/ C. The proposed gas pressure sensor is expected to be used in broader areas for its high sensitivity, low cost, high mechanical strength, and temperature influence resistance. 2. Fabrication and Principle The schematic of the proposed gas pressure sensor is shown in Figure 1. It is con- structed by two paralleled F–P cavities. Figure 1a,c show the schematic of the two FPIs. The first F–P cavity fabricated by fusion splicing a section of HCF (Polymicro Technologies, TSP050125) between two sections of SMF (Corning, SMF28) is used as a reference, as shown in Figure 1a. The second is fabricated by fusion splicing a piece of HCF between SMF and HCF with the slightly smaller inner diameter in order to make the micro-cavity connect to the external environment for sensing the gas pressure, as shown in Figure 1c. Figure 1b,d are the microscope images of the two cavities. The core and the cladding diameters of SMF are 8.3 m and 125 m. The inner diameter and outer diameter of the first section of HCF in sensing FPI are 50 m and 125 m, and those of the second section of HCF in sensing FPI are 5 m and 125 m. Two FPIs are connected by a 3-dB coupler so that the incident light from the broadband light source (BBS, 1400–1600 nm) can be divided into two parts and the reflected light can be coupled into a 3-dB coupler, and then transmitted into an optical spectrum analyzer (OSA, with a resolution of 0.02 nm), as shown in Figure 1e. Photonics 2022, 9, 31 3 of 12 transmitted into an optical spectrum analyzer (OSA, with a resolution of 0.02 nm), as Photonics 2022, 9, 31 3 of 11 shown in Figure 1e. Figure 1. (a,c) Schematic of the two FPIs. (b,d) The microscope images of the two FPIs. (e) Schematic Figure 1. (a,c) Schematic of the two FPIs. (b,d) The microscope images of the two FPIs. (e) Schematic diagram of experimental setup with paralleled FPIs. diagram of experimental setup with paralleled FPIs. The single sensing FPI is shown in Figure 1c. The incident light beams were reflected The single sensing FPI is shown in Figure 1c. The incident light beams were reflected by two splicing surfaces S3 and S4 to form an optical path difference, and the generated by two splicing surfaces S3 and S4 to form an optical path difference, and the generated spectrum could be detected by OSA. The center wavelength of the m order interference dip spectrum could be detected by OSA. The center wavelength of the m order interference can be expressed as: dip can be expressed as: 4L l =  n (1) m s 2m + 1 4L λ=⋅ n (1) ms where L and n represent the length and the RI21 mof + the F–P sensing cavity, respectively. Since s s the gas pressure results in RI changes of the F–P cavity without influence on the cavity where Ls and ns represent the length and the RI of the F–P sensing cavity, respectively. length, the influence of the gas pressure on the cavity length variation can be ignored. The Since the gas pressure results in RI changes of the F–P cavity without influence on the gas pressure sensitivity can be derived as [32,33]: cavity length, the influence of the gas pressure on the cavity length variation can be ig- nored. The gas pressure sensitivity can ¶l be derive 4L d ¶n as [32,433]: n ¶L m s s s s S = =  + Psingle 2m+1 2m+1 ¶P ¶P ¶P (2) ¶n∂∂ λ ¶L44 Ln¶n n ∂L s s s ms s s s = l +  l m m S == ⋅ + ⋅ n ¶P L ¶P n ¶P P −singles s s ∂+ Pm21∂P 2m+1∂P (2)  ∂∂ nL ∂n Combining two FPIs with a 3-dB coupler, the total output light intensity can be ss s =+λλ≈  mm considered as a simple superposition of every single FPI output signal. The output light nP∂∂ L P n∂P ss s  intensity of two paralleled FPIs is given by [34]: Combining two FPIs with a 3-dB coupler, the total output light intensity can be con- sidered as a simple superposition of every single FPI output signal. The output light in- 1 4pL I(l) =  2R 1 cos I (3) å 0 tensity of two paralleled FPIs is given by [34]: 2 l i=1  1  4πL where R represents reflectance of the reflective surface, which can be calculated to be 0.04. IR λ =⋅ 21−cos I () (3)   0 2 λ L represents the length of the F–P reference i =1 cavity; I is the incident light source intensity;   0 i  0 l is the central wavelength. It is well known that the maximum (minimum) value of the where R represents reflectance of the reflective surface, which can be calculated to be 0.04. superimposed spectrum will appear when the peak (dip) of the reflection spectrum of the Li represents the length of the F–P reference cavity; I0 is the incident light source intensity; reference cavity and the peak (dip) of the reflection spectrum of the sensing cavity overlap. λ0 is the central wavelength. It is well known that the maximum (minimum) value of the The FSR or FSR of the two reflection spectra can be defined as: r s superimposed spectrum will appear when the peak (dip) of the reflection spectrum of the 2 2 l l FSR = , FSR = (4) r s Dn L Dn L r r s s Photonics 2022, 9, 31 4 of 12 reference cavity and the peak (dip) of the reflection spectrum of the sensing cavity overlap. The FSRr or FSRs of the two reflection spectra can be defined as: λλ Photonics 2022, 9, 31 4 of 11 FSR== ,FSR (4) rs ΔΔ nL n L rr s s Due to the tiny difference between the length of reference cavity and sensing cavity, Due to the tiny difference between the length of reference cavity and sensing cavity, FSRr and FSRs is similar but not equal, which makes the spectrum of the paralleled FPIs FSR and FSR is similar but not equal, which makes the spectrum of the paralleled FPIs r s present an envelope. The FSR of the envelope can be expressed as: present an envelope. The FSR of the envelope can be expressed as: FSR ⋅ FSR rs FSR = (5) envelope FSR  FSR r s FSR − FSR rs FSR = (5) envelope FSR FSR j j r s With the changes of the external gas pressure, the RI of the gas in sensing FPI will With the changes of the external gas pressure, the RI of the gas in sensing FPI will change, while that of the reference FPI will remain the same so that a shift in the envelope change, while that of the reference FPI will remain the same so that a shift in the envelope spectrum will appear. The pressure sensitivity of the envelope spectrum is given by: spectrum will appear. The pressure sensitivity of the envelope spectrum is given by: ∂λ S = (6) P −envelope ¶l ∂P S = (6) Penvelope ¶P According to Equations (4) and (6), it can be concluded that the gas pressure sensi- According to Equations (4) and (6), it can be concluded that the gas pressure sensitivity tivity of the envelope spectrum at the central wavelength is: of the envelope spectrum at the central wavelength is:  ∂∂ Ln11 FSR ss r S =+ λ  (7) P −envelope m ¶L 1 ¶n 1 FSR s s r ∂∂ PLPn FSR−FSR S = l s+ sr s (7) Penvelope ¶P L ¶P n jFSR FSR j s s r s Compared with Equation (2), the gas pressure sensitivity is magnified M times by Compared with Equation (2), the gas pressure sensitivity is magnified M times by the the Vernier effect than that of single sensing FPI. The amplification factor is defined as: Vernier effect than that of single sensing FPI. The amplification factor is defined as: FSR P −envelope M == (8) Penvelope FSR SFSR −FSR M = P −sin gle = r s (8) S jFSR FSR j Psingle r s 3 3. . Ex Experimental perimental Re Results sults In order to investigate the influence of the F–P cavity length on the extinction ratio of In order to investigate the influence of the F–P cavity length on the extinction ratio of t the he interfer interference spect ence spectrrum, um, we we prepa prepared red the the F– F–PP ca cavity vity l lengths engthof s of 50 50/150/200/250/300 /150/200/250/300 μm, m, respectively. respectively. The The reflec reflection tion spectrum w spectrum was as test tested, ed, and and the results ar the results aree shown shown in in Figur Figure e 22. . 50 μm 150 μm 200 μm 35 250 μm 300 μm -5 -10 -15 -20 1400 1450 1500 1550 1600 Wavelength / nm Figure 2. Reflection spectrum of F–P cavities with different lengths. Figure 2. Reflection spectrum of F–P cavities with different lengths. As shown in Figure 2, as the cavity length increased from 50 to 300 m, the extinction As shown in Figure 2, as the cavity length increased from 50 to 300 μm, the extinction ratio of the reflection spectrum decreased accordingly. The reason is that the transmission ratio of the reflection spectrum decreased accordingly. The reason is that the transmission loss increased with the increase of the cavity length. The Vernier envelope with a high loss increased with the increase of the cavity length. The Vernier envelope with a high extinction ratio (>5 dB) required precise energy matching and cavity length matching. From extinction ratio (>5 dB) required precise energy matching and cavity length matching. Figure 2, a 150 m cavity length with suitable FSR and extinction ratio was selected as the sensing cavity in the following experiments. Before the pressure measurement of paralleled F–P cavities, the response of the single sensing cavity with the inner diameter of 50 m and the cavity length of 150 m was first tested. The sensing mechanism was that the change of the external pressure caused the variety of the RI in the F–P cavity, which led to the wavelength shift of the interference spectrum. According to the Edlen equation [35], n is a function of the pressure and Reflection, offset / dB Photonics 2022, 9, 31 5 of 12 Photonics 2022, 9, 31 5 of 12 From Figure 2, a 150 μm cavity length with suitable FSR and extinction ratio was selected From Figure 2, a 150 μm cavity length with suitable FSR and extinction ratio was selected as the sensing cavity in the following experiments. as the sensing cavity in the following experiments. Before the pressure measurement of paralleled F–P cavities, the response of the single Before the pressure measurement of paralleled F–P cavities, the response of the single sensing cavity with the inner diameter of 50 μm and the cavity length of 150 μm was first sensing cavity with the inner diameter of 50 μm and the cavity length of 150 μm was first tested. The sensing mechanism was that the change of the external pressure caused the Photonics 2022, 9, 31 5 of 11 tested. The sensing mechanism was that the change of the external pressure caused the variety of the RI in the F–P cavity, which led to the wavelength shift of the interference variety of the RI in the F–P cavity, which led to the wavelength shift of the interference spectrum. According to the Edlen equation [35], ns is a function of the pressure and the spectrum. According to the Edlen equation [35], ns is a function of the pressure and the −9 temperature as ns = 1 + (2.8793 × 10 × P)/(1 + 0.003671 × T). Thus, ∂ns/∂P can be regarded −9 temperature as ns = 1 + (2.8793 × 10 × P)/(1 + 0.003671 × T). Thus, ∂ns/∂P can be regarded the temperature as n = 1 + (2.8793  10  P)/(1 + 0.003671  T). Thus, ¶n /¶P can s −9 s as a constant (2.8791 × 10 ) at room temperature (25 °C). Combined with Equation (4), it −9 9 as a constant (2.8791 × 10 ) at room temperature (25 °C). Combined with Equation (4), it be regarded as a constant (2.8791  10 ) at room temperature (25 C). Combined with can be concluded that the drift of the interference spectrum is approximately linear with can be concluded that the drift of the interference spectrum is approximately linear with Equation (4), it can be concluded that the drift of the interference spectrum is approximately the increase of the gas pressure. The spectrum response and the wavelength shift of the the increase of the gas pressure. The spectrum response and the wavelength shift of the linear with the increase of the gas pressure. The spectrum response and the wavelength single FPI versus the gas pressure are shown in Figure 3, where we can observe that the single FPI versus the gas pressure are shown in Figure 3, where we can observe that the shift of the single FPI versus the gas pressure are shown in Figure 3, where we can observe resonant dip exhibited a red shift with the increase of gas pressure with a sensitivity of 4 resonan that the t dip resonant exhibited a red sh dip exhibitedift with a red shift the inc withrease the incr of g ease as pres of gas sur pr e essur with e a with sensitivity a sensitivity of 4 nm/MPa. The corresponding linearity was 99.9%. nm/MPa. The corresponding of 4 nm/MPa. The corresponding linearit linearity y was 99was .9%. 99.9%. Figure 3. Pressure response of single sensing cavity. (a) Reflection spectrum. (b) Linear fitting. Figure 3. Figure 3. Pres Pressur sure response of e response of sing single le sens sensing ing cavity cavity . ( . a () Ref a) Reflection lection spectru spectrum. m. (b (b ) L ) Linear inear fit fitting. ting. The paralleled FPI structure with the Vernier effect was fabricated to obtain the The paralleled FPI structure with the Vernier effect was fabricated to obtain the highly The paralleled FPI structure with the Vernier effect was fabricated to obtain the highly sensitive gas pressure sensor. The experimental setup for pressure measurement is sensitive gas pressure sensor. The experimental setup for pressure measurement is shown in highly sensitive gas pressure sensor. The experimental setup for pressure measurement is shown in Figure 4. The incident light from the BBS was guided into a 3-dB coupler and Figure 4. The incident light from the BBS was guided into a 3-dB coupler and was divided shown in Figure 4. The incident light from the BBS was guided into a 3-dB coupler and was divided into two parts. One part passed through the reference cavity and another into two parts. One part passed through the reference cavity and another part passed was divided into two parts. One part passed through the reference cavity and another part passed through the sensing cavity. The sensing cavity was put into the air pressure through the sensing cavity. The sensing cavity was put into the air pressure calibrator part passed through the sensing cavity. The sensing cavity was put into the air pressure calibrator (ALKT702, with the range and resolution of 0~10 MPa and 0.001 MPa), which (ALKT702, with the range and resolution of 0~10 MPa and 0.001 MPa), which had a pin calibrator (ALKT702, with the range and resolution of 0~10 MPa and 0.001 MPa), which had a pin hole connected to the outside, and then the pin hole was sealed up by sealant. hole connected to the outside, and then the pin hole was sealed up by sealant. The reflected had a pin hole connected to the outside, and then the pin hole was sealed up by sealant. The reflected lights were transmitted into an OSA by a 3-dB coupler. lights were transmitted into an OSA by a 3-dB coupler. The reflected lights were transmitted into an OSA by a 3-dB coupler. Figure 4. Experimental system for paralleled FPI sensor. Figure 4. Experimental system for paralleled FPI sensor. Figure 4. Experimental system for paralleled FPI sensor. To investigate the amplification factor, two prototypes were fabricated and experi- To investigate the amplification factor, two prototypes were fabricated and experi- To investigate the amplification factor, two prototypes were fabricated and experi- mentally tested: the lengths of reference and sensing HCFs in prototype 1 were 136 m mentally tested: the lengths of reference and sensing HCFs in prototype 1 were 136 μm mentally tested: the lengths of reference and sensing HCFs in prototype 1 were 136 μm and 147 m, while in prototype 2 were 186 m and 147 m, respectively. The reflection spectra are shown in Figure 5a, from which we can see that the FSRs of two prototypes were 91.3 nm and 27.2 nm. According to Equations (4) and (5), it can be calculated the- oretically that the FSRs of these two prototypes are 102.2 nm and 27.3 nm, respectively. Obviously, the experimental results agree well with the theoretical ones. Thus, as the cavity length difference (DL) decreases, the FSR of the envelope becomes larger, and according to Equation (8), the amplification factor will be larger, too. Figure 5b shows the simulated Photonics 2022, 9, 31 6 of 12 Photonics 2022, 9, 31 6 of 12 and 147 μm, while in prototype 2 were 186 μm and 147 μm, respectively. The reflection and 147 μm, while in prototype 2 were 186 μm and 147 μm, respectively. The reflection spectra are shown in Figure 5a, from which we can see that the FSRs of two prototypes spectra are shown in Figure 5a, from which we can see that the FSRs of two prototypes were 91.3 nm and 27.2 nm. According to Equations (4) and (5), it can be calculated theo- were 91.3 nm and 27.2 nm. According to Equations (4) and (5), it can be calculated theo- retically that the FSRs of these two prototypes are 102.2 nm and 27.3 nm, respectively. retically that the FSRs of these two prototypes are 102.2 nm and 27.3 nm, respectively. Obviously, the experimental results agree well with the theoretical ones. Thus, as the cav- Photonics 2022, 9, 31 6 of 11 Obviously, the experimental results agree well with the theoretical ones. Thus, as the cav- ity length difference (ΔL) decreases, the FSR of the envelope becomes larger, and accord- ity length difference (ΔL) decreases, the FSR of the envelope becomes larger, and accord- ing to Equation (8), the amplification factor will be larger, too. Figure 5b shows the simu- ing to Equation (8), the amplification factor will be larger, too. Figure 5b shows the simu- lated amplification factor under different cavity length differences. It can be obviously lated amplification factor under different cavity length differences. It can be obviously amplification factor under different cavity length differences. It can be obviously seen that seen that the amplification factor decreased with the increase of ΔL. seen that the amplification factor decreased with the increase of ΔL. the amplification factor decreased with the increase of DL. Figure 5. (a) Reflection spectrum of paralleled F–P cavities with different cavity length differences. Figure Figure 5. 5. ((a a)) Reflection spectr Reflection spectrum um of parallele of paralleled d F–P ca F–P cavities vities with with dif different cavi ferent cavity ty length differences. length differences. (b) Simulated amplification factor of different cavity length differences. (b) Simulated amplification factor of different cavity length differences. (b) Simulated amplification factor of different cavity length differences. In order to verify the number of the interference light of the two prototypes, Figure In order to verify the number of the interference light of the two prototypes, Figure 6 In order to verify the number of the interference light of the two prototypes, Figure 6 gives a Fast Fourier Transform (FFT) of the reflection spectrum in Figure 5a. As can be gives a Fast Fourier Transform (FFT) of the reflection spectrum in Figure 5a. As can be seen 6 gives a Fast Fourier Transform (FFT) of the reflection spectrum in Figure 5a. As can be −1 −1 seen in Figure 6a, there were two dominant peaks, 0.1199 nm and 0.1305 nm , indicating 1 1 −1 −1 in Figure 6a, there were two dominant peaks, 0.1199 nm and 0.1305 nm , indicating seen in Figure 6a, there were two dominant peaks, 0.1199 nm and 0.1305 nm , indicating that two kinds of interference might exist. According to Equation (4) and FSR = 1/f, it can that two kinds of interference might exist. According to Equation (4) and FSR = 1/f, that two kinds of interference might exist. According to Equation (4) and FSR = 1/f, it can −1 be calculated that the frequencies of the reference cavity and sensing cavity are 0.119 nm −1 it can be calculated that the frequencies of the reference cavity and sensing cavity are be calculated that the frequencies of the reference cavity and sensing cavity are 0.119 nm −1 and 0.129 2 nm 1 . Thus, these 1two peaks were formed by the interference of the reference 0.119 nm and−1 0.1292 nm . Thus, these two peaks were formed by the interference and 0.1292 nm . Thus, these two peaks were formed by the interference of the reference cavity and sensing cavity, respectively. From Figure 6b, we can also conclude the existence of the reference cavity and sensing cavity, respectively. From Figure 6b, we can also cavity and sensing cavity, respectively. From Figure 6b, we can also conclude the existence −1 of two dominant kinds of interference corresponding to the peaks of 0.1305 nm and conclude the existence of two dominant kinds of interference corresponding to the peaks −1 of of two dominant kinds of interference corresponding to the peaks of 0.1305 nm and −1 −1 −1 1 1 1 0.1642 nm , which are consistent with the theoretical values 0.1292 nm and 0.1639 nm . 0.1305 nm −1 and 0.1642 nm , which are consistent with the theoretical val −1 ues 0.1292 nm −1 0.1642 nm , which are consistent with the theoretical values 0.1292 nm and 0.1639 nm . −1 −1 1 1 Additionally, two tiny peaks located at 0.0119 nm in Figure 6a and 0.0342 nm in Figure and 0.1639 nm . Additionally, two tiny peaks located at 0.0119 nm in Figure 6a and −1 −1 Additionally, two tiny peaks located at 0.0119 nm in Figure 6a and 0.0342 nm in Figure 6b represent the envelope spectrum of superimposition in two prototypes. In conclusion, 0.0342 nm in Figure 6b represent the envelope spectrum of superimposition in two 6b represent the envelope spectrum of superimposition in two prototypes. In conclusion, the output spectra of these two prototypes are formed by two FPIs, namely multi-beam prototypes. In conclusion, the output spectra of these two prototypes are formed by two the output spectra of these two prototypes are formed by two FPIs, namely multi-beam interference. FPIs, namely multi-beam interference. interference. Figure 6. Spectral characteristics of the sensing structure. (a) Prototype 1. (b) Prototype 2. Figure 6. Spectral characteristics of the sensing structure. (a) Prototype 1. (b) Prototype 2. Figure 6. Spectral characteristics of the sensing structure. (a) Prototype 1. (b) Prototype 2. The responses of the two prototypes to the gas pressure are shown in Figure 7. From The responses of the two prototypes to the gas pressure are shown in Figure 7. From The responses of the two prototypes to the gas pressure are shown in Figure 7. From Figure 7a, we can observe that the envelope profile of prototype 1 suffered a red shift when Figure 7a, we can observe that the envelope profile of prototype 1 suffered a red shift Figure 7a, we can observe that the envelope profile of prototype 1 suffered a red shift the gas pressure increased from 0 to 1.2 MPa, corresponding to a gas pressure sensitivity of 45.76 nm/MPa and a linearity of 99.9%. The corresponding magnification was 11.44, which is basically consistent with the theoretical value under the 11 m cavity length difference in Figure 5b. The points are linearly fitted, as shown in Figure 7b. From Figure 7c, when gas pressure increased from 0 to 3 MPa, the envelope profile of prototype 2 showed a blue shift, corresponding to a gas pressure sensitivity of 15.08 nm/MPa and a linearity of 99.9%. The points are linearly fitted, as shown in Figure 7d. Photonics 2022, 9, 31 7 of 12 when the gas pressure increased from 0 to 1.2 MPa, corresponding to a gas pressure sen- sitivity of 45.76 nm/MPa and a linearity of 99.9%. The corresponding magnification was 11.44, which is basically consistent with the theoretical value under the 11 μm cavity length difference in Figure 5b. The points are linearly fitted, as shown in Figure 7b. From Figure 7c, when gas pressure increased from 0 to 3 MPa, the envelope profile of prototype Photonics 2022, 9, 31 7 of 11 2 showed a blue shift, corresponding to a gas pressure sensitivity of −15.08 nm/MPa and a linearity of 99.9%. The points are linearly fitted, as shown in Figure 7d. Figure 7. Figure 7. Re Response sponse of parall of paralleled eled F FPI PI sensor sensor tto o pressu pressur re. e. Pro Prototype totype 1: ( 1: (a a) Re ) Reflection flection spectru spectrum m unde under r different pressure; (b) linear fitting. Prototype 2: (c) The reflection spectrum under different pres- different pressure; (b) linear fitting. Prototype 2: (c) The reflection spectrum under different pressure; sure; (d) linear fitting. (d) linear fitting. To investig To investigate ate the the temper temperatur ature e crosstalk crosstalk,, th the e p parallel arallele ed d FPI str FPI stru uctur cture was placed e was placed int into o the temperature chamber (LICHEN, 202-00T, with a solution of 0.5 °C), which was heated the temperature chamber (LICHEN, 202-00T, with a solution of 0.5 C), which was heated ffr rom om 20 20 tto o 70 °C wit 70 C with h a an n int interval erval of 10 of 10 °C C un under der atm atmospheric ospheric pressure pressure. . F Figur igure e 8a 8a shows shows the the reflec reflection tion spec spectr trum um un under der d dif ifferen ferent t temper temperatur atures es, , and and F Figur igure e 8 8b b shows shows the the llinear inear fi fit t result of the envelope wavelength shifting. It is obvious that the envelope exhibited a little result of the envelope wavelength shifting. It is obvious that the envelope exhibited a little wavelength shifting with a sensitivity of 4.46 pm/ C because the thermo-optic coefficient wavelength shifting with a sensitivity of 4.46 pm/°C because the thermo-optic coefficient of air is so small that the temperature has little effect on RI of the air in the low temperature of air is so small that the temperature has little effect on RI of the air in the low temperature range [36]. Moreover, the slight difference of intensity is caused by fluctuation of the light range [36]. Moreover, the slight difference of intensity is caused by fluctuation of the light Photonics 2022, 9, 31 8 of 12 source power [37]. The temperature experimental results indicate that the proposed sensor source power [37]. The temperature experimental results indicate that the proposed sen- corresponded to a temperature crosstalk as low as 0. 097 KPa/ C. sor corresponded to a temperature crosstalk as low as 0. 097 KPa/°C. Figure 8. Figure 8. ( (a a)) Response Response of of par paralleled alleled F F–P–cavities P cavities to to temperatur temperatu e. (rb e. ( ) Linear b) Linear fitting of w fitting of wavelength avelength shift shift versus temperature. versus temperature. 4. Discussions The reason why the envelope moved in the opposite direction is explained as follows. For prototype 1, the sensing cavity length was larger than the reference cavity length so that the FSR of the sensing cavity was smaller than the FSR of the reference cavity. Proto- type 2 was just the opposite. Assuming that a peak of the envelope is located at λ0, when the sensing cavity spectrum shifts by |FSRr − FSRs|, the sensing FPI peaks in prototype 1 and prototype 2 will overlap with the λ0 − FSRr and λ0 + FSRr of the reference cavity, re- spectively. Therefore, the envelope moving directions of the two prototypes are different. The reflection spectra of the two sets of paralleled F–P cavities with different lengths were simulated to characterize the shift directions of the spectrum, as shown in Figure 9. The FSRs of reference cavity were set to be 8.1 nm and 7.4 nm, respectively, while that of the sensing cavity was 7.8 nm. Due to the tiny difference of FSRs, an envelope will be arisen by the superimposed spectra of two FPIs. From Figure 9a–c, when the FSR of the reference cavity is larger than that of the sensing cavity, with the increasing of the pressure, the drift direction of the envelope is consistent with the drift direction of the reflection spectrum of a single sensing cavity, and both are red-shifted. Moreover, when the FSR of the refer- ence cavity is smaller than that of the sensing cavity, the drift direction of the envelope is opposite to the drift direction of the reflection spectrum of a single sensing cavity, as shown in Figure 9d–f. Photonics 2022, 9, 31 8 of 11 4. Discussions The reason why the envelope moved in the opposite direction is explained as follows. For prototype 1, the sensing cavity length was larger than the reference cavity length so that the FSR of the sensing cavity was smaller than the FSR of the reference cavity. Prototype 2 was just the opposite. Assuming that a peak of the envelope is located at l , when the sensing cavity spectrum shifts by |FSR FSR |, the sensing FPI peaks in prototype 1 r s and prototype 2 will overlap with the l FSR and l + FSR of the reference cavity, r r 0 0 respectively. Therefore, the envelope moving directions of the two prototypes are different. The reflection spectra of the two sets of paralleled F–P cavities with different lengths were simulated to characterize the shift directions of the spectrum, as shown in Figure 9. The FSRs of reference cavity were set to be 8.1 nm and 7.4 nm, respectively, while that of the sensing cavity was 7.8 nm. Due to the tiny difference of FSRs, an envelope will be arisen by the superimposed spectra of two FPIs. From Figure 9a–c, when the FSR of the reference cavity is larger than that of the sensing cavity, with the increasing of the pressure, the drift direction of the envelope is consistent with the drift direction of the reflection spectrum of a single sensing cavity, and both are red-shifted. Moreover, when the FSR of the reference cavity is smaller than that of the sensing cavity, the drift direction of the Photonics 2022, 9, 31 9 of 12 envelope is opposite to the drift direction of the reflection spectrum of a single sensing cavity, as shown in Figure 9d–f. Figure 9. Simulated wavelength shift of pressure response. (a–c) The reflection spectra of the single Figure 9. Simulated wavelength shift of pressure response. (a–c) The reflection spectra of the single rreference ca eference cavity vity (150 (150 μm), m), single single sensing sensing cavity cavity (155 (155 μ m), m), and and paralle paralleled led F F–P –P cav cavii ties. ties. ( (d d– –f f)) The The reflection spectra of the single reference cavity (160 μm), single sensing cavity (155 μm), and paral- reflection spectra of the single reference cavity (160 m), single sensing cavity (155 m), and paralleled leled F–P cavities. F–P cavities. Besides, the performance comparisons among the reported pressure sensors are shown in Table 1. It is obvious that compared with [14,15,18], the sensitivity of our sensor was improved by an order of magnitude. Meanwhile, compared with [20,30–32,38,39], our sensor achieved a wide linear response range and good temperature influence resistance. Additionally, compared with other sensors, the preparation of the proposed structure can be completed by directly splicing the HCFs with different inner diameters by arc dis- charge technology, so it is simple to prepare and cost-effective. Table 1. Performance comparisons of different gas pressure sensors. Tempera- Linear Re- Structures Sensitivity ture Cross- Fabrication Refs. sponse Range talk Side-opened channel structure Anti-resonant 4.24 nm/MPa - 0–2 MPa Fs [14] Reflecting guidance with single-HCF 3.59 nm/MPa 7.5 KPa/°C 0–2 MPa Fs [15] Single-FPI with sub-micron silica diaphragm 1.036 nm/MPa 0.96 KPa/°C 0–2 MPa Coating [18] Dual FP cavities with composite diaphragm 30.2 nm/MPa - 0–0.4 MPa Coating [20] Cascaded MZIs with a micro-machined air cavity in 82.131 0.647 0–0.7 Mpa Fs [30] SMS * nm/MPa KPa/°C Cascaded FPIs in a glass capillary tube * 86.64 nm/MPa 5.18 KPa/°C 0–0.6 MPa Fs [31] Photonics 2022, 9, 31 9 of 11 Besides, the performance comparisons among the reported pressure sensors are shown in Table 1. It is obvious that compared with [14,15,18], the sensitivity of our sensor was improved by an order of magnitude. Meanwhile, compared with [20,30–32,38,39], our sensor achieved a wide linear response range and good temperature influence resistance. Additionally, compared with other sensors, the preparation of the proposed structure can be completed by directly splicing the HCFs with different inner diameters by arc discharge technology, so it is simple to prepare and cost-effective. Table 1. Performance comparisons of different gas pressure sensors. Temperature Linear Response Structures Sensitivity Fabrication Refs. Crosstalk Range Side-opened channel structure 4.24 nm/MPa - 0–2 MPa Fs [14] Anti-resonant Reflecting guidance with single-HCF 3.59 nm/MPa 7.5 KPa/ C 0–2 MPa Fs [15] Single-FPI with sub-micron silica diaphragm 1.036 nm/MPa 0.96 KPa/ C 0–2 MPa Coating [18] Dual FP cavities with composite diaphragm 30.2 nm/MPa - 0–0.4 MPa Coating [20] Cascaded MZIs with a micro-machined air 82.131 nm/MPa 0.647 KPa/ C 0–0.7 Mpa Fs [30] cavity in SMS * Cascaded FPIs in a glass capillary tube * 86.64 nm/MPa 5.18 KPa/ C 0–0.6 MPa Fs [31] Parallel-connected FPIs with gas hole * 47.76 nm/MPa 5.1 KPa/ C 0–0.45 MPa Fs [32] Separated structures using SI and FPI with a 31.73 nm/MPa - 0–1.6 MPa Coating [38] silver film * Paralleled FPIs with a thin layer of UV glue * 38.3 nm/MPa - 0.1–0.7 MPa Coating [39] Paralleled FPIs with HCF * 45.76 nm/MPa 0.097 KPa/ C 0–3 MPa Arc discharge This work * Representing the existence of the Vernier effect. 5. Conclusions In summary, we proposed a high sensitivity fiber gas pressure sensor based on paral- leled F–P cavities with the Vernier effect. The gas pressure sensitivity can be improved from 4 nm/MPa to 45.76 nm/MPa with an amplification factor of 11.44, and the corresponding linearity is 99.9%. Additionally, the sensor is resistant to the temperature fluctuation, and the temperature crosstalk is negligible in the gas pressure measurement process under the low temperature range. Benefitting from its characteristics of high sensitivity, low cost, good mechanical strength, and temperature resistance, this gas pressure sensor can find applications in more fields, especially in harsh-circumstance barometric monitoring. Author Contributions: Conceptualization, X.S., L.H., Y.L. and L.R.; methodology, X.S. and L.H.; software, X.W.; validation, H.S. and C.L.; formal analysis, X.S. and L.R.; investigation, L.H. and Y.L.; resources, L.H. and Y.L.; data curation, X.S. and L.H.; writing—original draft preparation, X.S.; writing—review and editing, X.S., L.H., H.S., Y.L. and L.R.; visualization, X.W. and C.L.; supervision, Y.L. and L.R. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the National Natural Science Foundation of China (11874133), the project of the central government supporting the reform and development of local colleges and universities (2020YQ01). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy. 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High Sensitivity Fiber Gas Pressure Sensor with Two Separated Fabry–Pérot Interferometers Based on the Vernier Effect

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hv photonics Article High Sensitivity Fiber Gas Pressure Sensor with Two Separated Fabry–Pérot Interferometers Based on the Vernier Effect 1 2 1 1 1 2 1 , Xiaokang Song , Liangtao Hou , Xiangyu Wei , Hang Su , Chang Li , Yan Li and Lingling Ran * College of Electronics Engineering, Heilongjiang University, Harbin 150080, China; 2191255@s.hlju.edu.cn (X.S.); 2181194@s.hlju.edu.cn (X.W.); 2191260@s.hlju.edu.cn (H.S.); 2191258@s.hlju.edu.cn (C.L.) Department of Optoelectronics Science, Harbin Institute of Technology at Weihai, Weihai 264209, China; 20b911012@stu.hit.edu.cn (L.H.); liy@hit.edu.cn (Y.L.) * Correspondence: ranlingling@hlju.edu.cn Abstract: A high sensitivity optical fiber gas pressure sensor based on paralleled Fabry–Pérot in- terferometers (FPIs) was demonstrated. One micro-cavity FPI is used as a reference FPI (FPI-1) to generate a Vernier effect and the other FPI (FPI-2) is used as a sensing tip. Both FPIs are connected by a 3-dB coupler to form a paralleled structure. The FPI-1 was fabricated by fusion splicing a piece of hollow core fiber (HCF) between two sections of single-mode fibers (SMF), whereas FPI-2 was formed by fusion splicing a section of HCF between SMF and a piece of HCF with a slightly smaller inner diameter for sensing pressure. The gas pressure sensitivity was amplified from 4 nm/MPa of single FPI to 45.76 nm/MPa of paralleled FPIs with an amplification factor of 11.44 and a linearity of 99.9%. Compared with the traditional fiber gas pressure sensors, the proposed sensor showed great advantages in sensitivity, mechanical strength, cost, and temperature influence resistant, which has potential in adverse-circumstance gas pressure sensing. Keywords: optical fiber sensor; gas pressure; Vernier effect; Fabry–Pérot interferometers; high sensitivity Citation: Song, X.; Hou, L.; Wei, X.; Su, H.; Li, C.; Li, Y.; Ran, L. High 1. Introduction Sensitivity Fiber Gas Pressure Sensor Optical fiber gas pressure sensors have been widely used in automatic production, with Two Separated Fabry–Pérot aerospace, military, and medical diagnosis fields due to their advantages of compactness, Interferometers Based on the Vernier Effect. Photonics 2022, 9, 31. https:// anti-interference, and high-accuracy [1–3]. Various optical fiber sensors, such as long-period doi.org/10.3390/photonics9010031 fiber gratings (LPFGs) [4,5], fiber Bragg gratings (FBGs) [6,7], Mach–Zehnder interferom- eters (MZIs) [8,9], and FPIs [10,11] have been developed to measure gas pressure, and Received: 23 November 2021 among them, FPI is very promising owing to its flexible manufacturing, easy operation, Accepted: 30 December 2021 and convenient combination. Published: 4 January 2022 The mechanism of FPI sensors for measuring gas pressure is to obtain the gas pressure Publisher’s Note: MDPI stays neutral variation tendency by observing the change of the fiber refractive index (RI) or the F–P cavity with regard to jurisdictional claims in length. In the open cavity structure, the F–P cavity is directly in touch with the external published maps and institutional affil- environment, and the gas pressure can be detected by monitoring the shift of the reflection iations. spectrum, which is induced by the change of the RI distribution [12,13]. In 2015, Wang et al. reported an F–P gas pressure sensor based on a side-opened channel structure, which realized the gas pressure sensitivity of 4.24 nm/MPa [14]. In 2016, Hou et al. demonstrated a gas pressure sensor based on an anti-resonant reflecting guidance mechanism with a single HCF, Copyright: © 2022 by the authors. whose gas pressure sensitivity was 3.59 nm/MPa [15]. In fact, the theoretical analysis reported Licensee MDPI, Basel, Switzerland. in [16] showed that the sensitivity of the open structure gas pressure sensor is low, which This article is an open access article is predicted to be less than 5 nm/MPa. However, by using the closed cavity structure, the distributed under the terms and gas pressure difference between inside and outside the cavity can result in the change of conditions of the Creative Commons the F–P cavity length so that the gas pressure can be retrieved by the spectral drifting under Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ this condition [17,18]. In 2019, Cui et al. reported an FPI gas pressure sensor fabricated 4.0/). by an exfoliated ultrathin graphene atomic layer, and a sensitivity of 9620 nm/MPa was Photonics 2022, 9, 31. https://doi.org/10.3390/photonics9010031 https://www.mdpi.com/journal/photonics Photonics 2022, 9, 31 2 of 11 obtained [19]. In 2021, Wang et al. utilized Ecoflex0030 silicone rubber/Polydimethylsiloxane as the end face of the closed F–P cavity, and a sensitivity of 30.2 nm/MPa was realized [20]. However, the mechanical strength and the measuring range of the closed cavity gas pressure sensor are always blamed due to the fact that the thin membrane attached at the fiber end can be easily cracked and further applications will be restricted. Therefore, ensuring a wide measurement range while still maintaining high sensitivity has always been the goal pursued in the field of gas pressure measurement. The Vernier effect has been proven to be an effective method to promote the sensitivity of an optical fiber sensor. The principle of the Vernier effect is to make two interferometers with small free spectral range (FSR) differences generate a superimposed spectrum, which will raise the sensitivity by measuring the response of the envelope. The key point of realizing the Vernier effect is to make FSRs of the two interferometers similar but not completely equal [21]. At present, the cascaded FPIs [22–24], cascaded MZIs [25,26], cascaded Sagnac interferometers (SIs) [27,28], and cascaded ring resonators [29] have successfully realized the Vernier effect. For gas pressure sensing, the Vernier effect based on MZIs [30] and FPIs [31] have been proposed and exhibited an ultra-high sensitivity of 82.131 nm/MPa and 86.64 nm/MPa, but the sensors were fabricated by a femtosecond laser (Fs), which greatly increased the cost and the difficulty of manufacturing, and the temperature crosstalk cannot be ignored. In this paper, a high sensitivity gas pressure sensor using paralleled FPIs based on the Vernier effect is demonstrated. Two separated F–P cavities with slight length difference are connected by a 3-dB coupler for sensing and referencing. The optical paths of these two FPIs are approximately equal, so the Vernier effect can be generated. By using the Vernier effect, the gas pressure sensitivity of the proposed sensor has been greatly improved. Experimental results show that gas pressure sensitivity is enhanced to 45.76 nm/MPa by the Vernier effect with an amplification factor of 11.44 and linearity of 99.9%. In addition, the reference FPI can be isolated from the sensing FPI and detection environment due to the separated structure. Thus, reference FPI cannot be affected by external environmental temperature. Only the temperature response of sensing FPI can be amplified, due to the extremely low thermo-optical coefficient and thermal expansion coefficient of air, leading to a temperature crosstalk of 0.097 KPa/ C. The proposed gas pressure sensor is expected to be used in broader areas for its high sensitivity, low cost, high mechanical strength, and temperature influence resistance. 2. Fabrication and Principle The schematic of the proposed gas pressure sensor is shown in Figure 1. It is con- structed by two paralleled F–P cavities. Figure 1a,c show the schematic of the two FPIs. The first F–P cavity fabricated by fusion splicing a section of HCF (Polymicro Technologies, TSP050125) between two sections of SMF (Corning, SMF28) is used as a reference, as shown in Figure 1a. The second is fabricated by fusion splicing a piece of HCF between SMF and HCF with the slightly smaller inner diameter in order to make the micro-cavity connect to the external environment for sensing the gas pressure, as shown in Figure 1c. Figure 1b,d are the microscope images of the two cavities. The core and the cladding diameters of SMF are 8.3 m and 125 m. The inner diameter and outer diameter of the first section of HCF in sensing FPI are 50 m and 125 m, and those of the second section of HCF in sensing FPI are 5 m and 125 m. Two FPIs are connected by a 3-dB coupler so that the incident light from the broadband light source (BBS, 1400–1600 nm) can be divided into two parts and the reflected light can be coupled into a 3-dB coupler, and then transmitted into an optical spectrum analyzer (OSA, with a resolution of 0.02 nm), as shown in Figure 1e. Photonics 2022, 9, 31 3 of 12 transmitted into an optical spectrum analyzer (OSA, with a resolution of 0.02 nm), as Photonics 2022, 9, 31 3 of 11 shown in Figure 1e. Figure 1. (a,c) Schematic of the two FPIs. (b,d) The microscope images of the two FPIs. (e) Schematic Figure 1. (a,c) Schematic of the two FPIs. (b,d) The microscope images of the two FPIs. (e) Schematic diagram of experimental setup with paralleled FPIs. diagram of experimental setup with paralleled FPIs. The single sensing FPI is shown in Figure 1c. The incident light beams were reflected The single sensing FPI is shown in Figure 1c. The incident light beams were reflected by two splicing surfaces S3 and S4 to form an optical path difference, and the generated by two splicing surfaces S3 and S4 to form an optical path difference, and the generated spectrum could be detected by OSA. The center wavelength of the m order interference dip spectrum could be detected by OSA. The center wavelength of the m order interference can be expressed as: dip can be expressed as: 4L l =  n (1) m s 2m + 1 4L λ=⋅ n (1) ms where L and n represent the length and the RI21 mof + the F–P sensing cavity, respectively. Since s s the gas pressure results in RI changes of the F–P cavity without influence on the cavity where Ls and ns represent the length and the RI of the F–P sensing cavity, respectively. length, the influence of the gas pressure on the cavity length variation can be ignored. The Since the gas pressure results in RI changes of the F–P cavity without influence on the gas pressure sensitivity can be derived as [32,33]: cavity length, the influence of the gas pressure on the cavity length variation can be ig- nored. The gas pressure sensitivity can ¶l be derive 4L d ¶n as [32,433]: n ¶L m s s s s S = =  + Psingle 2m+1 2m+1 ¶P ¶P ¶P (2) ¶n∂∂ λ ¶L44 Ln¶n n ∂L s s s ms s s s = l +  l m m S == ⋅ + ⋅ n ¶P L ¶P n ¶P P −singles s s ∂+ Pm21∂P 2m+1∂P (2)  ∂∂ nL ∂n Combining two FPIs with a 3-dB coupler, the total output light intensity can be ss s =+λλ≈  mm considered as a simple superposition of every single FPI output signal. The output light nP∂∂ L P n∂P ss s  intensity of two paralleled FPIs is given by [34]: Combining two FPIs with a 3-dB coupler, the total output light intensity can be con- sidered as a simple superposition of every single FPI output signal. The output light in- 1 4pL I(l) =  2R 1 cos I (3) å 0 tensity of two paralleled FPIs is given by [34]: 2 l i=1  1  4πL where R represents reflectance of the reflective surface, which can be calculated to be 0.04. IR λ =⋅ 21−cos I () (3)   0 2 λ L represents the length of the F–P reference i =1 cavity; I is the incident light source intensity;   0 i  0 l is the central wavelength. It is well known that the maximum (minimum) value of the where R represents reflectance of the reflective surface, which can be calculated to be 0.04. superimposed spectrum will appear when the peak (dip) of the reflection spectrum of the Li represents the length of the F–P reference cavity; I0 is the incident light source intensity; reference cavity and the peak (dip) of the reflection spectrum of the sensing cavity overlap. λ0 is the central wavelength. It is well known that the maximum (minimum) value of the The FSR or FSR of the two reflection spectra can be defined as: r s superimposed spectrum will appear when the peak (dip) of the reflection spectrum of the 2 2 l l FSR = , FSR = (4) r s Dn L Dn L r r s s Photonics 2022, 9, 31 4 of 12 reference cavity and the peak (dip) of the reflection spectrum of the sensing cavity overlap. The FSRr or FSRs of the two reflection spectra can be defined as: λλ Photonics 2022, 9, 31 4 of 11 FSR== ,FSR (4) rs ΔΔ nL n L rr s s Due to the tiny difference between the length of reference cavity and sensing cavity, Due to the tiny difference between the length of reference cavity and sensing cavity, FSRr and FSRs is similar but not equal, which makes the spectrum of the paralleled FPIs FSR and FSR is similar but not equal, which makes the spectrum of the paralleled FPIs r s present an envelope. The FSR of the envelope can be expressed as: present an envelope. The FSR of the envelope can be expressed as: FSR ⋅ FSR rs FSR = (5) envelope FSR  FSR r s FSR − FSR rs FSR = (5) envelope FSR FSR j j r s With the changes of the external gas pressure, the RI of the gas in sensing FPI will With the changes of the external gas pressure, the RI of the gas in sensing FPI will change, while that of the reference FPI will remain the same so that a shift in the envelope change, while that of the reference FPI will remain the same so that a shift in the envelope spectrum will appear. The pressure sensitivity of the envelope spectrum is given by: spectrum will appear. The pressure sensitivity of the envelope spectrum is given by: ∂λ S = (6) P −envelope ¶l ∂P S = (6) Penvelope ¶P According to Equations (4) and (6), it can be concluded that the gas pressure sensi- According to Equations (4) and (6), it can be concluded that the gas pressure sensitivity tivity of the envelope spectrum at the central wavelength is: of the envelope spectrum at the central wavelength is:  ∂∂ Ln11 FSR ss r S =+ λ  (7) P −envelope m ¶L 1 ¶n 1 FSR s s r ∂∂ PLPn FSR−FSR S = l s+ sr s (7) Penvelope ¶P L ¶P n jFSR FSR j s s r s Compared with Equation (2), the gas pressure sensitivity is magnified M times by Compared with Equation (2), the gas pressure sensitivity is magnified M times by the the Vernier effect than that of single sensing FPI. The amplification factor is defined as: Vernier effect than that of single sensing FPI. The amplification factor is defined as: FSR P −envelope M == (8) Penvelope FSR SFSR −FSR M = P −sin gle = r s (8) S jFSR FSR j Psingle r s 3 3. . Ex Experimental perimental Re Results sults In order to investigate the influence of the F–P cavity length on the extinction ratio of In order to investigate the influence of the F–P cavity length on the extinction ratio of t the he interfer interference spect ence spectrrum, um, we we prepa prepared red the the F– F–PP ca cavity vity l lengths engthof s of 50 50/150/200/250/300 /150/200/250/300 μm, m, respectively. respectively. The The reflec reflection tion spectrum w spectrum was as test tested, ed, and and the results ar the results aree shown shown in in Figur Figure e 22. . 50 μm 150 μm 200 μm 35 250 μm 300 μm -5 -10 -15 -20 1400 1450 1500 1550 1600 Wavelength / nm Figure 2. Reflection spectrum of F–P cavities with different lengths. Figure 2. Reflection spectrum of F–P cavities with different lengths. As shown in Figure 2, as the cavity length increased from 50 to 300 m, the extinction As shown in Figure 2, as the cavity length increased from 50 to 300 μm, the extinction ratio of the reflection spectrum decreased accordingly. The reason is that the transmission ratio of the reflection spectrum decreased accordingly. The reason is that the transmission loss increased with the increase of the cavity length. The Vernier envelope with a high loss increased with the increase of the cavity length. The Vernier envelope with a high extinction ratio (>5 dB) required precise energy matching and cavity length matching. From extinction ratio (>5 dB) required precise energy matching and cavity length matching. Figure 2, a 150 m cavity length with suitable FSR and extinction ratio was selected as the sensing cavity in the following experiments. Before the pressure measurement of paralleled F–P cavities, the response of the single sensing cavity with the inner diameter of 50 m and the cavity length of 150 m was first tested. The sensing mechanism was that the change of the external pressure caused the variety of the RI in the F–P cavity, which led to the wavelength shift of the interference spectrum. According to the Edlen equation [35], n is a function of the pressure and Reflection, offset / dB Photonics 2022, 9, 31 5 of 12 Photonics 2022, 9, 31 5 of 12 From Figure 2, a 150 μm cavity length with suitable FSR and extinction ratio was selected From Figure 2, a 150 μm cavity length with suitable FSR and extinction ratio was selected as the sensing cavity in the following experiments. as the sensing cavity in the following experiments. Before the pressure measurement of paralleled F–P cavities, the response of the single Before the pressure measurement of paralleled F–P cavities, the response of the single sensing cavity with the inner diameter of 50 μm and the cavity length of 150 μm was first sensing cavity with the inner diameter of 50 μm and the cavity length of 150 μm was first tested. The sensing mechanism was that the change of the external pressure caused the Photonics 2022, 9, 31 5 of 11 tested. The sensing mechanism was that the change of the external pressure caused the variety of the RI in the F–P cavity, which led to the wavelength shift of the interference variety of the RI in the F–P cavity, which led to the wavelength shift of the interference spectrum. According to the Edlen equation [35], ns is a function of the pressure and the spectrum. According to the Edlen equation [35], ns is a function of the pressure and the −9 temperature as ns = 1 + (2.8793 × 10 × P)/(1 + 0.003671 × T). Thus, ∂ns/∂P can be regarded −9 temperature as ns = 1 + (2.8793 × 10 × P)/(1 + 0.003671 × T). Thus, ∂ns/∂P can be regarded the temperature as n = 1 + (2.8793  10  P)/(1 + 0.003671  T). Thus, ¶n /¶P can s −9 s as a constant (2.8791 × 10 ) at room temperature (25 °C). Combined with Equation (4), it −9 9 as a constant (2.8791 × 10 ) at room temperature (25 °C). Combined with Equation (4), it be regarded as a constant (2.8791  10 ) at room temperature (25 C). Combined with can be concluded that the drift of the interference spectrum is approximately linear with can be concluded that the drift of the interference spectrum is approximately linear with Equation (4), it can be concluded that the drift of the interference spectrum is approximately the increase of the gas pressure. The spectrum response and the wavelength shift of the the increase of the gas pressure. The spectrum response and the wavelength shift of the linear with the increase of the gas pressure. The spectrum response and the wavelength single FPI versus the gas pressure are shown in Figure 3, where we can observe that the single FPI versus the gas pressure are shown in Figure 3, where we can observe that the shift of the single FPI versus the gas pressure are shown in Figure 3, where we can observe resonant dip exhibited a red shift with the increase of gas pressure with a sensitivity of 4 resonan that the t dip resonant exhibited a red sh dip exhibitedift with a red shift the inc withrease the incr of g ease as pres of gas sur pr e essur with e a with sensitivity a sensitivity of 4 nm/MPa. The corresponding linearity was 99.9%. nm/MPa. The corresponding of 4 nm/MPa. The corresponding linearit linearity y was 99was .9%. 99.9%. Figure 3. Pressure response of single sensing cavity. (a) Reflection spectrum. (b) Linear fitting. Figure 3. Figure 3. Pres Pressur sure response of e response of sing single le sens sensing ing cavity cavity . ( . a () Ref a) Reflection lection spectru spectrum. m. (b (b ) L ) Linear inear fit fitting. ting. The paralleled FPI structure with the Vernier effect was fabricated to obtain the The paralleled FPI structure with the Vernier effect was fabricated to obtain the highly The paralleled FPI structure with the Vernier effect was fabricated to obtain the highly sensitive gas pressure sensor. The experimental setup for pressure measurement is sensitive gas pressure sensor. The experimental setup for pressure measurement is shown in highly sensitive gas pressure sensor. The experimental setup for pressure measurement is shown in Figure 4. The incident light from the BBS was guided into a 3-dB coupler and Figure 4. The incident light from the BBS was guided into a 3-dB coupler and was divided shown in Figure 4. The incident light from the BBS was guided into a 3-dB coupler and was divided into two parts. One part passed through the reference cavity and another into two parts. One part passed through the reference cavity and another part passed was divided into two parts. One part passed through the reference cavity and another part passed through the sensing cavity. The sensing cavity was put into the air pressure through the sensing cavity. The sensing cavity was put into the air pressure calibrator part passed through the sensing cavity. The sensing cavity was put into the air pressure calibrator (ALKT702, with the range and resolution of 0~10 MPa and 0.001 MPa), which (ALKT702, with the range and resolution of 0~10 MPa and 0.001 MPa), which had a pin calibrator (ALKT702, with the range and resolution of 0~10 MPa and 0.001 MPa), which had a pin hole connected to the outside, and then the pin hole was sealed up by sealant. hole connected to the outside, and then the pin hole was sealed up by sealant. The reflected had a pin hole connected to the outside, and then the pin hole was sealed up by sealant. The reflected lights were transmitted into an OSA by a 3-dB coupler. lights were transmitted into an OSA by a 3-dB coupler. The reflected lights were transmitted into an OSA by a 3-dB coupler. Figure 4. Experimental system for paralleled FPI sensor. Figure 4. Experimental system for paralleled FPI sensor. Figure 4. Experimental system for paralleled FPI sensor. To investigate the amplification factor, two prototypes were fabricated and experi- To investigate the amplification factor, two prototypes were fabricated and experi- To investigate the amplification factor, two prototypes were fabricated and experi- mentally tested: the lengths of reference and sensing HCFs in prototype 1 were 136 m mentally tested: the lengths of reference and sensing HCFs in prototype 1 were 136 μm mentally tested: the lengths of reference and sensing HCFs in prototype 1 were 136 μm and 147 m, while in prototype 2 were 186 m and 147 m, respectively. The reflection spectra are shown in Figure 5a, from which we can see that the FSRs of two prototypes were 91.3 nm and 27.2 nm. According to Equations (4) and (5), it can be calculated the- oretically that the FSRs of these two prototypes are 102.2 nm and 27.3 nm, respectively. Obviously, the experimental results agree well with the theoretical ones. Thus, as the cavity length difference (DL) decreases, the FSR of the envelope becomes larger, and according to Equation (8), the amplification factor will be larger, too. Figure 5b shows the simulated Photonics 2022, 9, 31 6 of 12 Photonics 2022, 9, 31 6 of 12 and 147 μm, while in prototype 2 were 186 μm and 147 μm, respectively. The reflection and 147 μm, while in prototype 2 were 186 μm and 147 μm, respectively. The reflection spectra are shown in Figure 5a, from which we can see that the FSRs of two prototypes spectra are shown in Figure 5a, from which we can see that the FSRs of two prototypes were 91.3 nm and 27.2 nm. According to Equations (4) and (5), it can be calculated theo- were 91.3 nm and 27.2 nm. According to Equations (4) and (5), it can be calculated theo- retically that the FSRs of these two prototypes are 102.2 nm and 27.3 nm, respectively. retically that the FSRs of these two prototypes are 102.2 nm and 27.3 nm, respectively. Obviously, the experimental results agree well with the theoretical ones. Thus, as the cav- Photonics 2022, 9, 31 6 of 11 Obviously, the experimental results agree well with the theoretical ones. Thus, as the cav- ity length difference (ΔL) decreases, the FSR of the envelope becomes larger, and accord- ity length difference (ΔL) decreases, the FSR of the envelope becomes larger, and accord- ing to Equation (8), the amplification factor will be larger, too. Figure 5b shows the simu- ing to Equation (8), the amplification factor will be larger, too. Figure 5b shows the simu- lated amplification factor under different cavity length differences. It can be obviously lated amplification factor under different cavity length differences. It can be obviously amplification factor under different cavity length differences. It can be obviously seen that seen that the amplification factor decreased with the increase of ΔL. seen that the amplification factor decreased with the increase of ΔL. the amplification factor decreased with the increase of DL. Figure 5. (a) Reflection spectrum of paralleled F–P cavities with different cavity length differences. Figure Figure 5. 5. ((a a)) Reflection spectr Reflection spectrum um of parallele of paralleled d F–P ca F–P cavities vities with with dif different cavi ferent cavity ty length differences. length differences. (b) Simulated amplification factor of different cavity length differences. (b) Simulated amplification factor of different cavity length differences. (b) Simulated amplification factor of different cavity length differences. In order to verify the number of the interference light of the two prototypes, Figure In order to verify the number of the interference light of the two prototypes, Figure 6 In order to verify the number of the interference light of the two prototypes, Figure 6 gives a Fast Fourier Transform (FFT) of the reflection spectrum in Figure 5a. As can be gives a Fast Fourier Transform (FFT) of the reflection spectrum in Figure 5a. As can be seen 6 gives a Fast Fourier Transform (FFT) of the reflection spectrum in Figure 5a. As can be −1 −1 seen in Figure 6a, there were two dominant peaks, 0.1199 nm and 0.1305 nm , indicating 1 1 −1 −1 in Figure 6a, there were two dominant peaks, 0.1199 nm and 0.1305 nm , indicating seen in Figure 6a, there were two dominant peaks, 0.1199 nm and 0.1305 nm , indicating that two kinds of interference might exist. According to Equation (4) and FSR = 1/f, it can that two kinds of interference might exist. According to Equation (4) and FSR = 1/f, that two kinds of interference might exist. According to Equation (4) and FSR = 1/f, it can −1 be calculated that the frequencies of the reference cavity and sensing cavity are 0.119 nm −1 it can be calculated that the frequencies of the reference cavity and sensing cavity are be calculated that the frequencies of the reference cavity and sensing cavity are 0.119 nm −1 and 0.129 2 nm 1 . Thus, these 1two peaks were formed by the interference of the reference 0.119 nm and−1 0.1292 nm . Thus, these two peaks were formed by the interference and 0.1292 nm . Thus, these two peaks were formed by the interference of the reference cavity and sensing cavity, respectively. From Figure 6b, we can also conclude the existence of the reference cavity and sensing cavity, respectively. From Figure 6b, we can also cavity and sensing cavity, respectively. From Figure 6b, we can also conclude the existence −1 of two dominant kinds of interference corresponding to the peaks of 0.1305 nm and conclude the existence of two dominant kinds of interference corresponding to the peaks −1 of of two dominant kinds of interference corresponding to the peaks of 0.1305 nm and −1 −1 −1 1 1 1 0.1642 nm , which are consistent with the theoretical values 0.1292 nm and 0.1639 nm . 0.1305 nm −1 and 0.1642 nm , which are consistent with the theoretical val −1 ues 0.1292 nm −1 0.1642 nm , which are consistent with the theoretical values 0.1292 nm and 0.1639 nm . −1 −1 1 1 Additionally, two tiny peaks located at 0.0119 nm in Figure 6a and 0.0342 nm in Figure and 0.1639 nm . Additionally, two tiny peaks located at 0.0119 nm in Figure 6a and −1 −1 Additionally, two tiny peaks located at 0.0119 nm in Figure 6a and 0.0342 nm in Figure 6b represent the envelope spectrum of superimposition in two prototypes. In conclusion, 0.0342 nm in Figure 6b represent the envelope spectrum of superimposition in two 6b represent the envelope spectrum of superimposition in two prototypes. In conclusion, the output spectra of these two prototypes are formed by two FPIs, namely multi-beam prototypes. In conclusion, the output spectra of these two prototypes are formed by two the output spectra of these two prototypes are formed by two FPIs, namely multi-beam interference. FPIs, namely multi-beam interference. interference. Figure 6. Spectral characteristics of the sensing structure. (a) Prototype 1. (b) Prototype 2. Figure 6. Spectral characteristics of the sensing structure. (a) Prototype 1. (b) Prototype 2. Figure 6. Spectral characteristics of the sensing structure. (a) Prototype 1. (b) Prototype 2. The responses of the two prototypes to the gas pressure are shown in Figure 7. From The responses of the two prototypes to the gas pressure are shown in Figure 7. From The responses of the two prototypes to the gas pressure are shown in Figure 7. From Figure 7a, we can observe that the envelope profile of prototype 1 suffered a red shift when Figure 7a, we can observe that the envelope profile of prototype 1 suffered a red shift Figure 7a, we can observe that the envelope profile of prototype 1 suffered a red shift the gas pressure increased from 0 to 1.2 MPa, corresponding to a gas pressure sensitivity of 45.76 nm/MPa and a linearity of 99.9%. The corresponding magnification was 11.44, which is basically consistent with the theoretical value under the 11 m cavity length difference in Figure 5b. The points are linearly fitted, as shown in Figure 7b. From Figure 7c, when gas pressure increased from 0 to 3 MPa, the envelope profile of prototype 2 showed a blue shift, corresponding to a gas pressure sensitivity of 15.08 nm/MPa and a linearity of 99.9%. The points are linearly fitted, as shown in Figure 7d. Photonics 2022, 9, 31 7 of 12 when the gas pressure increased from 0 to 1.2 MPa, corresponding to a gas pressure sen- sitivity of 45.76 nm/MPa and a linearity of 99.9%. The corresponding magnification was 11.44, which is basically consistent with the theoretical value under the 11 μm cavity length difference in Figure 5b. The points are linearly fitted, as shown in Figure 7b. From Figure 7c, when gas pressure increased from 0 to 3 MPa, the envelope profile of prototype Photonics 2022, 9, 31 7 of 11 2 showed a blue shift, corresponding to a gas pressure sensitivity of −15.08 nm/MPa and a linearity of 99.9%. The points are linearly fitted, as shown in Figure 7d. Figure 7. Figure 7. Re Response sponse of parall of paralleled eled F FPI PI sensor sensor tto o pressu pressur re. e. Pro Prototype totype 1: ( 1: (a a) Re ) Reflection flection spectru spectrum m unde under r different pressure; (b) linear fitting. Prototype 2: (c) The reflection spectrum under different pres- different pressure; (b) linear fitting. Prototype 2: (c) The reflection spectrum under different pressure; sure; (d) linear fitting. (d) linear fitting. To investig To investigate ate the the temper temperatur ature e crosstalk crosstalk,, th the e p parallel arallele ed d FPI str FPI stru uctur cture was placed e was placed int into o the temperature chamber (LICHEN, 202-00T, with a solution of 0.5 °C), which was heated the temperature chamber (LICHEN, 202-00T, with a solution of 0.5 C), which was heated ffr rom om 20 20 tto o 70 °C wit 70 C with h a an n int interval erval of 10 of 10 °C C un under der atm atmospheric ospheric pressure pressure. . F Figur igure e 8a 8a shows shows the the reflec reflection tion spec spectr trum um un under der d dif ifferen ferent t temper temperatur atures es, , and and F Figur igure e 8 8b b shows shows the the llinear inear fi fit t result of the envelope wavelength shifting. It is obvious that the envelope exhibited a little result of the envelope wavelength shifting. It is obvious that the envelope exhibited a little wavelength shifting with a sensitivity of 4.46 pm/ C because the thermo-optic coefficient wavelength shifting with a sensitivity of 4.46 pm/°C because the thermo-optic coefficient of air is so small that the temperature has little effect on RI of the air in the low temperature of air is so small that the temperature has little effect on RI of the air in the low temperature range [36]. Moreover, the slight difference of intensity is caused by fluctuation of the light range [36]. Moreover, the slight difference of intensity is caused by fluctuation of the light Photonics 2022, 9, 31 8 of 12 source power [37]. The temperature experimental results indicate that the proposed sensor source power [37]. The temperature experimental results indicate that the proposed sen- corresponded to a temperature crosstalk as low as 0. 097 KPa/ C. sor corresponded to a temperature crosstalk as low as 0. 097 KPa/°C. Figure 8. Figure 8. ( (a a)) Response Response of of par paralleled alleled F F–P–cavities P cavities to to temperatur temperatu e. (rb e. ( ) Linear b) Linear fitting of w fitting of wavelength avelength shift shift versus temperature. versus temperature. 4. Discussions The reason why the envelope moved in the opposite direction is explained as follows. For prototype 1, the sensing cavity length was larger than the reference cavity length so that the FSR of the sensing cavity was smaller than the FSR of the reference cavity. Proto- type 2 was just the opposite. Assuming that a peak of the envelope is located at λ0, when the sensing cavity spectrum shifts by |FSRr − FSRs|, the sensing FPI peaks in prototype 1 and prototype 2 will overlap with the λ0 − FSRr and λ0 + FSRr of the reference cavity, re- spectively. Therefore, the envelope moving directions of the two prototypes are different. The reflection spectra of the two sets of paralleled F–P cavities with different lengths were simulated to characterize the shift directions of the spectrum, as shown in Figure 9. The FSRs of reference cavity were set to be 8.1 nm and 7.4 nm, respectively, while that of the sensing cavity was 7.8 nm. Due to the tiny difference of FSRs, an envelope will be arisen by the superimposed spectra of two FPIs. From Figure 9a–c, when the FSR of the reference cavity is larger than that of the sensing cavity, with the increasing of the pressure, the drift direction of the envelope is consistent with the drift direction of the reflection spectrum of a single sensing cavity, and both are red-shifted. Moreover, when the FSR of the refer- ence cavity is smaller than that of the sensing cavity, the drift direction of the envelope is opposite to the drift direction of the reflection spectrum of a single sensing cavity, as shown in Figure 9d–f. Photonics 2022, 9, 31 8 of 11 4. Discussions The reason why the envelope moved in the opposite direction is explained as follows. For prototype 1, the sensing cavity length was larger than the reference cavity length so that the FSR of the sensing cavity was smaller than the FSR of the reference cavity. Prototype 2 was just the opposite. Assuming that a peak of the envelope is located at l , when the sensing cavity spectrum shifts by |FSR FSR |, the sensing FPI peaks in prototype 1 r s and prototype 2 will overlap with the l FSR and l + FSR of the reference cavity, r r 0 0 respectively. Therefore, the envelope moving directions of the two prototypes are different. The reflection spectra of the two sets of paralleled F–P cavities with different lengths were simulated to characterize the shift directions of the spectrum, as shown in Figure 9. The FSRs of reference cavity were set to be 8.1 nm and 7.4 nm, respectively, while that of the sensing cavity was 7.8 nm. Due to the tiny difference of FSRs, an envelope will be arisen by the superimposed spectra of two FPIs. From Figure 9a–c, when the FSR of the reference cavity is larger than that of the sensing cavity, with the increasing of the pressure, the drift direction of the envelope is consistent with the drift direction of the reflection spectrum of a single sensing cavity, and both are red-shifted. Moreover, when the FSR of the reference cavity is smaller than that of the sensing cavity, the drift direction of the Photonics 2022, 9, 31 9 of 12 envelope is opposite to the drift direction of the reflection spectrum of a single sensing cavity, as shown in Figure 9d–f. Figure 9. Simulated wavelength shift of pressure response. (a–c) The reflection spectra of the single Figure 9. Simulated wavelength shift of pressure response. (a–c) The reflection spectra of the single rreference ca eference cavity vity (150 (150 μm), m), single single sensing sensing cavity cavity (155 (155 μ m), m), and and paralle paralleled led F F–P –P cav cavii ties. ties. ( (d d– –f f)) The The reflection spectra of the single reference cavity (160 μm), single sensing cavity (155 μm), and paral- reflection spectra of the single reference cavity (160 m), single sensing cavity (155 m), and paralleled leled F–P cavities. F–P cavities. Besides, the performance comparisons among the reported pressure sensors are shown in Table 1. It is obvious that compared with [14,15,18], the sensitivity of our sensor was improved by an order of magnitude. Meanwhile, compared with [20,30–32,38,39], our sensor achieved a wide linear response range and good temperature influence resistance. Additionally, compared with other sensors, the preparation of the proposed structure can be completed by directly splicing the HCFs with different inner diameters by arc dis- charge technology, so it is simple to prepare and cost-effective. Table 1. Performance comparisons of different gas pressure sensors. Tempera- Linear Re- Structures Sensitivity ture Cross- Fabrication Refs. sponse Range talk Side-opened channel structure Anti-resonant 4.24 nm/MPa - 0–2 MPa Fs [14] Reflecting guidance with single-HCF 3.59 nm/MPa 7.5 KPa/°C 0–2 MPa Fs [15] Single-FPI with sub-micron silica diaphragm 1.036 nm/MPa 0.96 KPa/°C 0–2 MPa Coating [18] Dual FP cavities with composite diaphragm 30.2 nm/MPa - 0–0.4 MPa Coating [20] Cascaded MZIs with a micro-machined air cavity in 82.131 0.647 0–0.7 Mpa Fs [30] SMS * nm/MPa KPa/°C Cascaded FPIs in a glass capillary tube * 86.64 nm/MPa 5.18 KPa/°C 0–0.6 MPa Fs [31] Photonics 2022, 9, 31 9 of 11 Besides, the performance comparisons among the reported pressure sensors are shown in Table 1. It is obvious that compared with [14,15,18], the sensitivity of our sensor was improved by an order of magnitude. Meanwhile, compared with [20,30–32,38,39], our sensor achieved a wide linear response range and good temperature influence resistance. Additionally, compared with other sensors, the preparation of the proposed structure can be completed by directly splicing the HCFs with different inner diameters by arc discharge technology, so it is simple to prepare and cost-effective. Table 1. Performance comparisons of different gas pressure sensors. Temperature Linear Response Structures Sensitivity Fabrication Refs. Crosstalk Range Side-opened channel structure 4.24 nm/MPa - 0–2 MPa Fs [14] Anti-resonant Reflecting guidance with single-HCF 3.59 nm/MPa 7.5 KPa/ C 0–2 MPa Fs [15] Single-FPI with sub-micron silica diaphragm 1.036 nm/MPa 0.96 KPa/ C 0–2 MPa Coating [18] Dual FP cavities with composite diaphragm 30.2 nm/MPa - 0–0.4 MPa Coating [20] Cascaded MZIs with a micro-machined air 82.131 nm/MPa 0.647 KPa/ C 0–0.7 Mpa Fs [30] cavity in SMS * Cascaded FPIs in a glass capillary tube * 86.64 nm/MPa 5.18 KPa/ C 0–0.6 MPa Fs [31] Parallel-connected FPIs with gas hole * 47.76 nm/MPa 5.1 KPa/ C 0–0.45 MPa Fs [32] Separated structures using SI and FPI with a 31.73 nm/MPa - 0–1.6 MPa Coating [38] silver film * Paralleled FPIs with a thin layer of UV glue * 38.3 nm/MPa - 0.1–0.7 MPa Coating [39] Paralleled FPIs with HCF * 45.76 nm/MPa 0.097 KPa/ C 0–3 MPa Arc discharge This work * Representing the existence of the Vernier effect. 5. Conclusions In summary, we proposed a high sensitivity fiber gas pressure sensor based on paral- leled F–P cavities with the Vernier effect. The gas pressure sensitivity can be improved from 4 nm/MPa to 45.76 nm/MPa with an amplification factor of 11.44, and the corresponding linearity is 99.9%. Additionally, the sensor is resistant to the temperature fluctuation, and the temperature crosstalk is negligible in the gas pressure measurement process under the low temperature range. Benefitting from its characteristics of high sensitivity, low cost, good mechanical strength, and temperature resistance, this gas pressure sensor can find applications in more fields, especially in harsh-circumstance barometric monitoring. Author Contributions: Conceptualization, X.S., L.H., Y.L. and L.R.; methodology, X.S. and L.H.; software, X.W.; validation, H.S. and C.L.; formal analysis, X.S. and L.R.; investigation, L.H. and Y.L.; resources, L.H. and Y.L.; data curation, X.S. and L.H.; writing—original draft preparation, X.S.; writing—review and editing, X.S., L.H., H.S., Y.L. and L.R.; visualization, X.W. and C.L.; supervision, Y.L. and L.R. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the National Natural Science Foundation of China (11874133), the project of the central government supporting the reform and development of local colleges and universities (2020YQ01). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy. 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Journal

PhotonicsMultidisciplinary Digital Publishing Institute

Published: Jan 4, 2022

Keywords: optical fiber sensor; gas pressure; Vernier effect; Fabry–Pérot interferometers; high sensitivity

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