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Abstract
The coexistence of transmission mechanisms, including Fabry-Perot (FP), Mach-Zehnder (MZ), and anti-resonant (AR), is demonstrated via a silica capillary-based cascaded structure. The analysis for MZ shows that one pathway is formed by the beam refracted into the silica capillary cladding from the air core, rather than being transmitted into the cladding directly at the splicing interface. Using the ray optics method, the two coexistence conditions are derived for FP and MZ, and for FP, MZ and AR, respectively. The existence percentages of the three mechanisms can be obtained using the fast Fourier transform. Finally, the coexistence of multiple transmission mechanisms is applied for independent multi-parameter sensing with the FP-based temperature sensitivity of 10.0 pm/°C and AR-based strain sensitivity of 1.33 nm/N. The third mechanism MZ interference can assist in verifying changes in both the temperature and axial strain. This shows the possibility to optimize the transmission spectra for independent multi-parameter sensing by tailoring the existence percentages of different mechanisms.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Fiber optic sensors demonstrate outstanding advantages over traditional sensors, such as anti-electromagnetic interference, corrosion resistance, high flexibility, high radiation resistance, compact size, and low cost [1]. In the past decades, various optical fiber sensor configurations have been developed, such as long-period fiber gratings (LPFGs) [2], fiber Bragg gratings (FBGs) [3,4], Fabry-Perot interferometers (FPIs) [5], Mach-Zehnder interferometers (MZIs) [6], anti-resonant (AR) reflecting optical waveguides [7], and Sagnac interferometers [8]. In general, fiber grating-based sensors show great superiority in distributed remote sensing. Interferometer-based sensors have a simple fabrication process and high sensitivity. Their diverse structures are suitable for different application scenarios and requirements, and they are fabricated based on various specialty optic fibers. Recently, great efforts have been directed toward the simple and integrated structure in order to realize multi-parameter sensing on a single sensor.
The silica capillary, which is the simplest AR reflecting optical waveguide, has attracted significant attention because it provides a reliable platform for realizing different transmission mechanisms for multiple sensing parameters. It consists of an air core and layer of cladding with a high refractive index. The spectral characteristics are governed by the refractive index and thickness of the first high-refractive-index layer (i.e., the silica capillary cladding) [9]. Owing to the inherent hollow core, silica capillary has been a unique research platform for in-line micro-cavity in the air core as it can confine light and be filled with liquids, gases, or other materials [10–12]. The device provides a long distance over which the interaction of light with matter can occur, enabling a high sensitivity and a low detection limit. Additionally, the silica capillary can also achieve high compression factors, high transmission coefficients, and high beam quality [13–15]. To date, different sensing parameters have been measured, such as temperature [16], surface refractive-index [15], bio-sensing parameters [17], bending [18], pressure [19], humidity [20], pH [21], magnetic field intensity [22], strain [23], and liquid level [24]. Multi-parameter sensing has also been realized [25–28]. More than one transmission mechanism can exist in silica capillary-based sensors, which are related to the different designed structures [29,30], special processing [19–21], or splicing methods [31,32]. A hybrid-structured optical fiber sensor is fabricated, which consisted of three transmission mechanisms, that is, FP, MZ and AR [27]. The device is able to measure the curvature, temperature, and transverse load with low crosstalk and high sensitivity. However, a structure with an air bubble and an up-taper has a complex structure compared with a cascaded structure. To develop a simple and integrated sensing device, the coexistence of transmission mechanisms in the silica capillary-based cascaded structure shows value for investigation due to its meaningful application in sensing.
In this paper, we investigate the FP, MZ and AR mechanisms in silica capillary-based cascaded structures with small inner diameter (ID). Fabrication of the device is carried out by fusion splicing a section of silica capillary between two single mode fibers (SMFs). The critical lengths for the coexistence conditions are analyzed using the ray optics method, moreover, numerical simulations and experiments are carried out to verify the coexistence of mechanisms in structures with different silica capillary IDs and lengths. Then, the existence percentages of the three mechanisms are analyzed that can be obtained using the fast Fourier transform. Finally, the coexistence of multiple transmission mechanisms for independent multi-parameter sensing is realized experimentally for ambient temperature and axial strain.
2. Principle and simulation
Figure 1(a) depicts the schematic diagram of a cascaded structure with a flat-fusion surface. The inner diameter of the silica capillary, denoted as ID, is larger than the core diameter of SMF, denoted as 2r, which is 9 µm. Owing to the structural symmetry, it only shows one side of the SMF and silica capillary. The light is input from the SMF on the left side, transmitted in the capillary, and output from the SMF on the right side. The refractive indices of the silica capillary air core, SMF core and silica capillary cladding are n0=1.000, n1=1.452 and n2=1.447 at the wavelength of 1300 nm in simulations, respectively. The numerical aperture (NA) of SMF is $\sqrt {{n_1}^2 - {n_2}^2} $, and the maximum incident angle θ0 from the SMF to the silica capillary is ${\sin ^{ - 1}}\sqrt {{n_1}^2 - {n_2}^2} $. Here, the analysis for MZ shows that one pathway is formed by the beam refracted into the silica capillary cladding from the air core at point A, rather than being transmitted into the cladding directly at the splicing interface [18]. Another pathway is formed by the beam transmitted forward in the air core. The critical length L0 for the occurrence of MZ mechanism using the ray optics method can be written as Eq. (1). When light reaches the interface between the silica capillary core and cladding, some light is refracted into the silica capillary cladding to form one or more zigzag pathways. The length between the two refracted points A and B is denoted as L1, and is written as Eq. (2). Two critical lengths, L0 and L0 + L1, are small and on the order of tens to hundreds micrometers. ID and the thickness of the silica capillary cladding d, have a great influence on the critical length, and thus, a precise analysis is necessary. In order to refine the work, we consider that the output light is emitted from the core boundary of the SMF instead of the case in which the output light is emitted from the center of the SMF core [33].
Fig. 1. (a) Schematic of optical pathways in cascaded structure with a flat-fusion surface and the transmission mechanisms for different silica capillary lengths. (b) Energy intensity of cascaded structures with different silica capillary IDs. (c) A partial zoom-in view of the energy distribution in the device with silica capillary ID of 15 µm and length of 150 µm.
The length of silica capillary is an important parameter for the transmission mechanism in a cascaded structure. Only the FP mechanism exists in the structure when the silica capillary length L is smaller than L0, as shown in the pink shade of Fig. 1(a). The intensity of the FP interference decreases gradually as the silica capillary length increases. The FP and MZ mechanisms coexist when the silica capillary length is between L0 and L0 + L1, whereby the beam is refracted into the silica capillary cladding from the air core but not refracted into the core in a zigzag pathway. When the silica capillary length is larger than L0 + L1, it satisfies the critical condition for forming the AR mechanism. However, not all light is refracted into the air core after a zigzag pathway transmitted in the cladding. Light with a resonant wavelength still exists in the cladding, which provides the possibility for MZ mechanism. Therefore, the FP, MZ and AR mechanisms can coexist when the silica capillary length is larger than L0 + L1.
In addition to the length of the silica capillary, ID is also a significant parameter in transmission. The mode field diameter (MFD) is a significant parameter for fibers. The simulated MFD of SMF is 10.2 µm at 1550 nm, which represents the width of the fundamental mode in an SMF. The fundamental mode field is not only concentrated in the core of fiber, but also some energy is transmitted through the cladding. Some contour maps of cascaded structures are simulated to compare different silica capillary IDs of 10 µm, 15 µm and 20 µm with the same length of 150 µm. The light energy intensity in the core of SMF and silica capillary is monitored as shown in Fig. 1(b). For the structure where the silica capillary ID is 10 µm, the light energy in the core is much less than that of the other structures. Because the value of MFD is larger than 10 µm, substantial light is transmitted into the cladding, and the relative energy intensity in the silica capillary core is smaller. Some high-order modes are excited at the fusion point between SMF and silica capillary. The larger ID of the silica capillary, the greater number of high-order modes are contained. The loss coefficient of the high-order mode is larger than that of the fundamental mode [34]. Many more high-order modes are dissipative and cause a significant loss in the silica capillary core with increasing silica capillary ID. Additionally, the simulations show an oscillation of power intensity, as shown in Fig. 1(b), and the period corresponds to the difference in efficient refractive index [35]. For the two-beam interference model, the output interference light intensity can be expressed as $I = {I_1} + {I_2} + 2{I_1}{I_2}\cos \varphi $, where I1 and I2 represent the light intensities of two different modes, or two beams along the different pathways participating in the interference. ${\varphi}$, the phase difference, is distinct for the different transmission mechanisms. When the transmission mechanism is MZ, the phase difference can be written as ${\varphi _{MZ}} = 2\pi ({n_2} - {n_0})L/\lambda $. Similarly, the phase difference is ${\varphi _{FP}} = 4\pi {n_0}L/\lambda$ in the FP interference and ${\varphi _{AR}} = 4\pi d\sqrt {{n_2}^2 - {n_0}^2} /\lambda $ for the AR mechanism, where $\lambda $ is the wavelength in vacuum. The oscillation period is approximately 4.2 nm in Fig. 1(b), which corresponds to the MZ mechanism. To provide a proof-of-concept demonstration, the energy distribution in the device with a silica capillary ID of 15 µm and length of 150 µm is simulated, and a partial zoom-in view is shown in Fig. 1(c). The critical length L0 can be roughly estimated and is close to the theoretical result calculated using Eq. (1).
The cascaded structures with different silica capillary lengths and IDs are simulated using the beam propagation method (BPM) for the transmission spectra, as shown in Fig. 2. The equations for the free spectral range (FSR) of the three mechanisms are as follows.
where m is the resonance order, which is an integer. λm and λm+1 are the resonance wavelengths for m and m+1 orders, respectively. Notably, the efficient optical path difference of MZ is smaller than (n2-n0)L in Eq. (4) because the pathway in the cladding starts at point A rather than at the splicing point, as shown in Fig. 1(a). When the silica capillary length is larger than the order of thousands of microns, L0 can be negligible. However, it will have impact on FSRMZ when silica capillary length is as small as tens of microns. The calculated FSRMZ using Eq. (4) is labeled with all length in Fig. 2, and they are all larger than the calculated FSR in the simulated transmission spectra, indicating that MZ is generated not at the interface of SMF and capillary.Fig. 2. Simulated transmission spectra for cascaded structures with different silica capillary parameters. Silica capillary ID of 10 µm with length (a) 70 µm, (b) 795 µm and (c) 1000 µm, respectively. Silica capillary ID of 15 µm with length (d) 50 µm, (e) 200 µm and (f) 550 µm, respectively.
The calculated L0 values are smaller than 50 µm for structures with silica capillary IDs of 10 µm and 15 µm according to Eq. (1). The MZ mechanism exists when the silica capillary length is slightly larger than the corresponding L0, as shown in Figs. 2(a) and (d). With increasing silica capillary length, some interesting phenomena occur. For the structure with a silica capillary ID of 10 µm, light in two different pathways is coupled at the second fusion splicing point, and MZ interference is formed. The AR wavelength light is refracted into the air core after transmission in a long silica capillary [36]. MZ and AR mechanisms can coexist in the transmission spectra when the silica capillary length is larger than L0 + L1, as shown in Figs. 2(b) and (c). However, the FP mechanism is not visible clearly in the transmission spectra because it only accounts for a small relative percentage. The structures with a silica capillary of 15 µm demonstrate similar behavior. MZ and AR mechanisms coexist when the silica capillary length is 200 µm, while MZ could not be monitored when the length is 550 µm, as shown in Figs. 2(e) and (f). AR mechanism would be dominated as the silica capillary length increases.
3. Experiment and result
As described above, the silica capillary ID is small in the cascaded structure with a flat-fusion surface and its length is smaller than 1000 µm. Therefore, a fine preparation is necessary for fabricating the device. A schematic of the experimental setup for the preparation process and measurement is shown in Fig. 3. The outer diameter of the silica capillary (after removing polymer coating layer) is about 125 µm and the IDs are selected as 10 µm (TSP010150) and 15 µm (TSP015150). Initially, a section of SMF (SMF-28) is spliced with a small ID silica capillary using suitable fusion parameters [37]. A short and precise silica capillary length is required. A precise cleaver with a micrometer screw is used to control the silica capillary length and a charge-coupled device (CCD) assisted in monitoring the process closely. The silica capillary is cut after adjusting to obtain a proper length, as shown in the inset of Fig. 3(b). Then, the cut structure is spliced with another section of SMF using the corresponding fusion program. A wideband light source (ASE, Amonics, ASLD-CWDM-5-B-FA) and an optical spectrum analyzer (OSA, Yokogawa, AQ6370B) are connected to the two ends of the cascaded structure for real-time monitoring of the transmission spectrum, as shown in Fig. 3(d).
Fig. 3. Illustration showing the fabrication of cascaded structures. (a) Splicing a section of SMF with the small ID silica capillary. (b) Controlling the silica capillary length on the precise cleaver with a spiral micrometer alongside a CCD to assist with precise monitoring clearly. Inset shows cutting of the silica capillary after adjusting to a proper length. (c) Splicing the structure with another SMF. (d) Experimental setup for transmission spectra of cascaded structures.
Devices are fabricated with different silica capillary IDs and lengths, which are similar to the simulated structures. The transmission spectra are shown in Fig. 4. The light in the fundamental mode is transmitted with a glancing incident angle from the air core into the high-refractive-index cladding. It requires the diameter of the air core to be sufficiently large, so that the silica capillary ID satisfies $ID \gg \lambda /2{n_0}$[38]. A significant reflection can be produced with the glancing incident angle and non-continuity of the refractive index. Therefore, the AR mechanism can exist in the cascaded structure with silica capillary ID of 10 µm. When the silica capillary length is longer than critical length L0 + L1, AR and MZ mechanisms coexist as shown in Figs. 4(b) and (c). Due to the collapse, only the MZ mechanism can be observed in the transmission spectra when the silica capillary length is 69 µm, as shown in Fig. 4(a).
Fig. 4. Experimental transmission spectra for cascaded structures with different silica capillary parameters. Silica capillary ID of 10 µm with length (a) 69 µm, (b) 795 µm and (c) 991 µm, respectively. Silica capillary ID of 15 µm with length (d) 51 µm, (e) 175 µm and (f) 513 µm, respectively.
For devices with a silica capillary ID of 15 µm, FP mechanism exists with a small extinction ratio and the MZ mechanism exists as the envelope of FP as shown in Fig. 4(d), where the silica capillary length is 51 µm. Figure 4(e) shows that MZ and AR mechanisms coexist in the device with a silica capillary length of 175 µm. This coincides with the simulations and theoretical theory analysis. When the silica capillary length increases to 513 µm, the AR mechanism dominates in the transmission spectrum, as shown in Fig. 4(f). These results match the corresponding simulations. It is also observed that experimental results show difference from corresponding simulations in Fig. 2. The potential reason for the difference is mainly related to surface collapse between SMF and silica capillary during fusion splicing process. Furthermore, surface collapse will introduce transmission loss and spectrum changes, including decreasing of FP extinction ratio [33] and shifts of resonant wavelengths.
4. Analysis and discussion
The coexistence of the three transmission mechanisms occurs under different conditions. The transmission spectrum superposition can be written as
where 0≤${\eta_n}$≤1 is the existence percentage of the corresponding transmission mechanism in the interference spectrum, and n is 1, 2 and 3, respectively. The existence percentages can be calculated using the fast Fourier transform (FFT). TFP, TMZ and TAR are the normalized transmissions of FP, MZ and AR, respectively.Figure 5(a) shows the FFT spectrum for the structure with a silica capillary length of 175 µm and ID of 15 µm. The optical path differences of three dominant peaks are calculated corresponding to the MZ, AR and FP mechanisms. The intensities of peaks in the FFT spectrum correspond to the normalized transmission mechanism intensities, that is, the existence percentages of the corresponding mechanisms. The transmission spectra for the three mechanisms are simulated separately without loss, as shown in Fig. 5(b). The superposition of three transmission spectra is shown in Fig. 5(c). This is similar to the corresponding experimental results shown in Fig. 5(d), which is the same as that in Fig. 4(e).
Fig. 5. (a) FFT spectrum for a silica capillary ID of 15 µm and length of 175 µm. Simulated transmission spectra for (b) three mechanisms with different existence percentages, and (c) a superposition of (b). (d) Labeled experimental transmission spectrum of the cascaded sensor. The inset shows the optical microscope image of the device.
The existence percentage of the transmission mechanism is a key parameter that has a significant influence on the variation in spectral shape. In general, the existence percentages of the three mechanisms are related to the silica capillary ID and length, and vary regularly in the proposed cascaded structures. The existence percentage of FP decreases with increasing silica capillary length. If there is an obvious collapse surface between the silica capillary and SMF, the existence percentage of FP may decrease. The existence percentage of MZ increases as the silica capillary length increases in the range L0 to L0 + L1. If there is an obvious collapse, the existence percentage of MZ increases. When the silica capillary length is larger than L0 + L1, the existence percentage of MZ decreases while that of AR increases. The existence percentage of AR dominates in the transmission spectra when the silica capillary length is significantly longer than a few thousand microns. Therefore, tailoring the silica capillary ID and length can regulate the transmission spectral shape and this can help in increasing the extinction ratio, or achieving Vernier effect-like spectra [39].
5. Multi-parameter sensing
The different transmission mechanisms can coexist in a device with a certain length of silica capillary cascaded between two SMFs, as verified above. Multi-parameter sensing can be realized based on different existing mechanisms that can be monitored in a transmission spectrum. Experimental measurements are performed on both the temperature and axial strain. By further deriving Eqs. (3), (4) and (5), the temperature sensitivities of the three mechanisms can be obtained as follows.
It can be deduced that the temperature sensitivity depends on the thermo-optical and thermal expansion coefficients of air and silica glass. For the silica cladding around room temperature, the thermo-optical and thermal expansion coefficients are 0.55×10−6 /°C and 6.45×10−6 /°C, respectively [40]. The thermo-optical coefficient of air is −9.29×10−7 /°C according to the Ciddor Equation. The efficient optical pathway for MZ interference LMZ is smaller than the silica capillary length and LMZ=L-L0. Therefore, the theoretical temperature sensitivity of the FP, MZ and AR mechanisms can be calculated as −0.54 pm/°C, 8.67 pm/°C and 11.5 pm/°C, respectively. It could be observed that temperature sensing based on AR has the highest sensitivity of the three.
For axial strain sensing, the sensitivities of the three mechanisms are obtained as follows.
The strain sensitivities of FP and MZ are mainly determined by the refractive indices of air and silica glass. SS,AR is mainly affected by $\Delta d/\Delta S$, which is smaller than $\Delta L/\Delta S$ in the small ID silica capillary according to Poisson’s ratio. By tailoring the capillary ID and length, the strain sensitivity can be changed accordingly. When silica capillary with an ID of 15 µm and length of 175 µm is applied, the theoretical strain sensitivity of FP, MZ and AR mechanisms can be calculated as 1.62 nm/N, 1.32 nm/N and −0.32 nm/N, respectively. Given the fact that SS, FP >SS, MZ >SS, AR and ST, AR >ST, MZ >ST, FP, the sensor with proposed parameters can be applied for strain and temperature sensing based on FP and AR mechanism, respectively. The optical microscope image of the sensor is shown in the inset of Fig. 5(d). Three points, PFP, PMZ and PAR, in the transmission spectrum are monitored within three different ranges, which correspond to the FP, MZ and AR mechanisms, respectively.
To demonstrate the temperature and strain sensing capability of the device, the fabricated sensor is characterized in a temperature chamber and strain testing environments. The temperature measurement setup is similar to that shown in Fig. 3(d), in which the sensor is placed in a temperature-controlled box. The ambient temperature range is set from 0 °C to 100 °C in steps of 10 °C. On the other hand, the strain measurement setup is as follows. The sample is fixed on a translation stage with two fiber clamping points located 58 cm apart. A tensile axial strain is applied to the cascaded sensor by moving the translation stage away from the fixed one in a step of 0.01 mm at the room temperature. A tensiometer is used to record the axial strain at the stage. The axial strain on the sensor is determined to vary between 0 and 1 N.
Figures 6(a) and (b) show the full range transmission spectra during temperature and strain testing, separately. The difference between two spectra in transmission losses could be related to different experimental setups and ambient environment changes. When testing the temperature and strain response based on FP, the device is characterized by wavelength tracking instead of transmission intensities change. As such, impact on transmission loss is relatively low as shown in Figs. 6(c) and (d). The wavelength corresponding to point PFP does not shift with increasing temperature, as shown in Fig. 6(e). In contrast to the temperature sensing, the point PFP has a significant redshift at a sensitivity of 1.33 nm/N with increasing axial strain, as shown in Fig. 6(f), which is close to the theoretical value of 1.62 nm/N. The deviation between experimental and theoretical results could be related to the surface collapse of silica capillary [23]. Therefore, FP mechanism can realize strain sensing independently with zero-temperature crosstalk in the sensor.
Fig. 6. Full range transmission spectra evolutions under (a) different temperatures and (b) different axial strains. Zoom-in spectra for the point PFP under (c) different temperatures and (d) different axial strains. Response of point PFP to (e) ambient temperature and (f) axial strain.
The experimental results of point PAR at different temperatures and axial strains are shown in Figs. 7(a) and (b), respectively. Because of the different thermo-optic coefficients between the silica capillary cladding and air core, the wavelength corresponding to point PAR has an obvious redshift compared with point PFP. As shown in Fig. 7(c), the temperature sensitivity is 10.0 pm/°C, which is closely aligned with the theoretical result. In contrast, the wavelengths shift slightly with increasing axial strain, as shown in Fig. 7(d). This is because the silica capillary cladding thickness d is as thick as 55 µm, which determines the resonant wavelength for AR, and a small strain force has little effect on its variation. Therefore, the AR mechanism can realize temperature sensing nearly independently with low strain crosstalk in the sensor.
Fig. 7. Transmission spectrum evolutions of point PAR with (a) different temperatures and (b) different axial strains. Response of point PAR to (c) ambient temperature and (d) axial strain.
The MZ mechanism is sensitive to both temperature and axial strain because MZ is generated by the two beams, that is, one is in air and the other is in the silica capillary cladding. The transmission spectra of the point PMZ under different temperatures and axial strains are shown in Figs. 8(a) and (b), respectively. The fitted lines in Figs. 8(c) and (d) show that the temperature sensitivity is 8.20 pm/°C and the axial strain sensitivity is 1.21 nm/N, which match the theoretical results. Considering the high strain sensitivity and low temperature influence based on FP, as well as the high temperature sensitivity and strain insensitivity for AR, the FP and AR mechanism are applied for axial strain and temperature sensing, respectively. The MZ mechanism can be used to verify the change in ambient temperature or axial strain, and it can optimize the peak of AR to make a great extinction ratio for sensing. Additionally, the existence percentage of different transmission mechanisms can be adjusted by tailoring the silica capillary parameters, which can obtain different transmission spectra. It can be used to realize multi-parameter sensing based on different transmission mechanisms.
Fig. 8. Transmission spectrum evolutions of point PMZ with (a) different temperatures and (b) different axial strains. Response of point PMZ to (c) ambient temperature and (d) axial strain.
6. Conclusion
In summary, the coexistence of three transmission mechanisms, FP, MZ and AR, is investigated theoretically and demonstrated experimentally in a silica capillary-based cascaded structure. Two critical lengths are obtained by the ray optics method, which correspond to the coexistence conditions for FP and MZ, and for FP, MZ and AR, respectively. The existence percentages of the three mechanisms can be obtained by FFT, which has a significant influence on the transmission spectral shape. Furthermore, the coexistence of multiple transmission mechanisms is applied for independent multi-parameter sensing with the FP-based temperature sensitivity of 10.0 pm/°C and AR-based strain sensitivity of 1.33 nm/N. The third mechanism MZ interference can assist in verifying changes in both the temperature and axial strain. This provides the possibility to optimize the transmission spectra for independent multi-parameter sensing by tailoring the existence percentages of different mechanisms. Besides the temperature and strain, the silica capillary-based cascaded structure can be also used for refractive index sensing, liquid level and curvature measurements.
Funding
National Natural Science Foundation of China (61675126, 61875116, 62022053); Natural Science Foundation of Shanghai (18ZR1415200); Open Project Program of Wuhan National Laboratory for Optoelectronics (2018WNLOKF014); 111 Project (D20031).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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