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Abstract
We propose a refractive index (RI) sensor based on a tapered hole-assisted dual-core fiber (HADCF). The sensor is fabricated by splicing a tapered HADCF between two single-mode fibers and operates on the coupling between the fundamental mode and the low-order mode in two cores. The HADCF is tapered to meet the phase matching condition between the fundamental mode (LP01) in the central core and the low-order mode (LP11) in the eccentric core. The tapered waist of the fiber becomes thinner; the coupling wavelength has a blue shift. Glycerin solutions of different RIs were injected into the air hole. The RI sensitivity of 936.69 nm/RIU is obtained in the RI range of 1.335-1.360. The multi-channel RI sensor cascaded by HADCFs with different taper lengths is obtained and can simultaneously measure the RI of different solutions. The proposed device has the advantages of high sensitivity, simple structure, and stable performance. The special microfluidic channel in the HADCF can protect the tested solution from external environmental pollution.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Refractive index (RI) sensors have received more attention in biological analysis, medical detection and environmental protection [1]. Optical fiber sensors have been widely used due to their high sensitivity, strong anti-electromagnetic interference ability, simple production, and small size. There are many methods to realize the RI sensors, such as tapered fibers [2,3], surface plasmon resonance (SPR) [4], long period fiber gratings (LPFGs) [5,6], fiber Bragg gratings (FBGs) [7,8], and interferometers [9–11]. The interaction between the evanescent field and the tested liquid can be enhanced by injecting liquid into built-in microfluidic channels of photonic crystal fibers (PCF) [12] or by polishing the cladding of PCF [13], thus a high RI sensitivity can be achieved. However, the preparation processes of such PCF-based devices are complex and their costs are high. The RI sensors based on multicore optical fibers were also widely investigated [14–16]. However, the guided mode in all solid multicore fiber sensor based on resonant coupling or interference between core modes is insensitive to the external environment. In order to enhance the RI sensitivity, various micro-processing technologies were used [14–18], including tilted FBGs [15] and the cladding etching [18]. The air hole was introduced into the fiber, and a dual-core fiber RI sensor based on the resonant coupling between fundamental modes was proposed [19]. The microfiber can generate a strong evanescent field and can obtain a high RI sensitivity in the tapered waist area. A RI sensor based on the dual-microfiber coupler with the Vernier effect achieved an ultra-high RI sensitivity of 126,540 nm/RIU [2]. However, the microfibers have some disadvantages such as low mechanical strength and fragile structure.
The multi-channel RI measurement is one of the development trends of RI sensor applications. The multi-channel RI sensor can detect multiple liquid samples simultaneously, with reducing sensor cost and size. The cascaded wavelength-multiplexed fiber sensors based on SPR offer enormous scope for multi-channel and multi-analyte detection [20]. The multiplexing of multiple tilted FBG SPR sensor in a single fiber was also demonstrated [21]. A multilayer-coated dual-channel SPR sensors based on a capillary structure and an etched side-hole fiber were presented [22,23]. In addition to the SPR effect, multi-channel RI measurements were also obtained using cascaded interferometers and special fibers. A temperature-compensated multipoint RI sensor combining cascaded Fabry-Perot cavity and frequency modulated continuous wave (FMCW) interferometry was obtained [24]. The dual-channel fiber refractometer based on intermodal interference from single-mode fiber (SMF) bending has RI sensitivities of 207 and 245 nm/RIU for two channels, respectively [25]. A helical LPG sensor in the dual-hole elliptical core fiber accomplished RI measurement in internal and external channels, respectively [26].
In this work, a RI sensor based on tapered hole-assisted dual-core fiber (HADCF) is proposed. The HADCF is composed of a central single mode core and an eccentric few mode core. The phase matching between LP01 mode in the central core and LP11 mode in the eccentric core is realized by taper technology. The maximum RI sensitivity is 936.69 nm/RIU. Multiple tapered HADCFs can be cascaded to form a multi-channel sensor for the simultaneous RI measurements of different solutions. The sensor has the advantage of high sensitivity, simple structure and easy realization. In addition, the sensor has stable performance and low temperature crosstalk due to special microfluidic channel, and can also protect the measured solution from external environmental pollution.
2. Structure and principle of optical fiber sensor
As shown in Fig. 1(a), the HADCF is composed of a center core, an air hole, an eccentric core suspended on the inner wall of the air hole, and the cladding. The suspended core with a diameter of 18.9 µm has a large contact with the cladding. The diameters of the cladding, air hole, and center core are 125 µm, 45 µm, and 7.9 µm, respectively. The distance between the centers of the two cores is 20.5 µm. The RIs of two cores are the same and the RI difference between the core and the cladding is 0.005. The center core of the HADCF is directly aligned with the cores of two SMFs by using a commercial fusion splicer, as shown in Fig. 1(b). The air hole does not collapse under the optimized current, so the loss induced by the splicing process can be ignored. Due to the small distance between the two cores, the resonant coupling will occur when the phase matching condition between the modes is satisfied. The dielectric materials around the two cores are different and two cores’ sizes are also different, therefore the resonant coupling only occurs when the propagation constants of the modes in two cores are equal or very close. The finite element method (FEM) is used to calculate the mode effective RIs of the guided modes in the two cores. The dispersion curves of the LP01 mode (cLP01) in the center core, the LP01 mode (eLP01) and the LP11 mode (eLP11) in the eccentric core in the HADCF are shown in Fig. 1(d), indicated by the solid lines. Due to the different sizes of the two cores, the central core only supports the fundamental mode, while the eccentric core supports two modes (LP01 and LP11) in the wavelength range of 1200-1700 nm. For the original HADCF with the cladding diameter of 125 µm, the calculated dispersion curves do not intersect and the two modes (cLP01 and eLP11) are phase-mismatched, therefore the energy coupling between two cores does not occur in the communication band.
Fig. 1. (a) Cross-section of the HADCF. Schematic configuration of the (b) untapered and (c) tapered HADCF. (d) The dispersion curves of cLP01, eLP01 and eLP11 modes for the different cladding diameters.
In order to satisfy the phase matching between the two cores in the communication band, the HADCF is tapered adiabatically. The diameters of the two cores, air hole, the cladding and the core spacing are decreased proportionally. The schematic diagram of the tapered HADCF is shown in Fig. 1(c). The dispersion curves of the LP01 mode in the central core, the LP01 mode and the LP11 mode in the eccentric core for the HADCF with different tapered waists are shown in Fig. 1(d). Since the air acts as the cladding of the eccentric suspended core, the slope of the mode dispersion curve of the eccentric core is obviously different from that of the center core. The slope of the eLP11 mode dispersion curve in the tapered HADCF is larger than those of cLP01 and eLP01. The propagation constants of the cLP01 mode and the eLP11 mode are equal at a certain wavelength in the communication band, and thus the phase matching condition is realized and the coupling between two modes occurs. The dispersion curves of cLP01 and eLP01 do not cross within the considered wavelength range, and the coupling between the fundamental modes can be eliminated. The incident light from the SMF propagates into the center core of the HADCF, and then the LP11 mode outputs from the suspended core of the HADCF at the phase matching wavelength. The intersection wavelength between the dispersion curves of eLP11 mode and cLP01 mode has a blue shift with decreasing waist diameter of the tapered HADCF, which is attributed to the larger drop in the effective RI of the eLP11 mode than that of the cLP01 mode with decreasing the diameter. As shown in Fig. 1(d), the coupling wavelengths are 1465 nm, 1337 nm, 1245 nm for the cladding diameters of 108 µm, 98 µm and 92 µm, respectively.
According to the coupled mode theory, the coupled mode equations of light propagation in two parallel cores can be expressed as:
The 3D beam propagation method (BPM) is used to calculate the beam propagation characteristics and the transmission spectrum of the tapered HADCF. The calculated beam propagation at 1467 nm for the tapered waist with the diameter of 108 µm is shown in Fig. 2(a). It can be clearly seen that the energy is coupled back and forth between the two cores. The coupling occurs between the LP01 mode in the central core and the LP11 mode in the eccentric core, rather than between the fundamental modes. The coupling length is defined as the minimum propagation distance, at which the maximum power is transferred from the one core to the other core. The coupling length is 2.44 mm in the tapered HADCF with the tapered waist of 108 µm. The field distributions on the end face of the fiber at one and two times of the coupling length are shown in the bottom and top insets of Fig. 2(a), respectively. At 2.44 mm, the energy is fully coupled to LP11 mode of the eccentric core, while the energy is in turn recoupled to LP01 mode of the central core at 4.88 mm. When the tapered HADCF length is an odd multiple of the coupling length, a resonance dip appears in the transmission spectrum of the central core due to the resonant coupling. The calculated transmission spectrum is shown in Fig. 2(b), where the coupling region length of the tapered HADCF is 7.32 mm that is 3 times the coupling length. Almost all energy is coupled into the suspended core at 1467 nm and a dip appears in the transmission spectrum, which is consistent with the dispersion curve. The small mismatch between the core of the SMF and the center core of the HADCF leads energy leakage into the cladding and ∼ 4 dB insertion loss is introduced.
Fig. 2. (a) The calculated beam propagation in the tapered HADCF with the waist of 108 µm at 1467 nm. (b) Transmission spectrum of the central core for the fiber with the length of 7.32mm.
3. Experimental results and discussions
The sensor is fabricated by splicing a small section of tapered HADCF between two SMFs. The central core of the HADCF and the core of SMFs are directly aligned by using a commercial fusion splicer, where there is no offset. Therefore, the preparation of the sensor is simple and the sensor has a good mechanical strength. The supercontinuum light source (SC-5, Yangtze Thornton Laser Co., Ltd.) is connected to input SMF, the output of SMF is connected to optical spectrum analyzer (OSA, AQ6375B, YOKOGAWA Inc.). The HADCF was tapered by the tapering machine. The pulling speed of the tapering machine is 0.02 mm/s, per-pull is 0.15 mm, the distance from the oxyhydrogen flame nozzle to the HADCF is 28 mm, and the hydrogen flow is 140 SCCM. The transmission spectrum of the HADCF with the pulling length of 3.5 mm is shown as the blue line in Fig. 3, where the pulling length is defined as the distance change between the two clamps of the taper machine. The longer the pulling length is, the thinner the diameter of the tapered waist is. The center wavelength and the 10 dB bandwidth of the resonant dip are 1466.92 nm and 95.2 nm, respectively, and the loss at the resonant dip is 17 dB. The measured bandwidth is larger than the calculated result in Fig. 2(b), which is interpreted as there is a transition zone with gradual fiber diameter at both ends of the actual taper waist, the measured spectrum is the superposition of the coupling peaks for the tapered fiber with different diameters, so the measured bandwidth is wider. In order to further decrease the bandwidth of the sensor, a larger effective RI difference between two modes near the phase matching wavelength is required, which can be achieved by two differently doped cores. The inset shows an observed optical field distribution on the fiber end at 1467 nm by an infrared CCD after the HADCF is tapered. It can be clearly seen that LP11 mode in the suspended core is excited. There are small ripples in the transmitted spectrum, which can be interpreted as a small size mismatch between the core of SMF and the center core of the HADCF, as a result it enables a part of energy of the core of the SMF to be coupled into the cladding of the HADCF and the weak interference is introduced.
Fig. 3. The transmission spectra of the tapered HADCF filled without and with liquid. The inset is the measured field distribution on the fiber end at 1467 nm.
The experimental setup for measuring the RI response of the sensor is shown in Fig. 4. Two microholes in the HADCF are drilled near the splicing joints, where the fiber is not tapered and has 125µm diameter, by a high-frequency CO2 laser with a maximum average output power of 10 W. The SMFs at both ends of the sample are fixed on the slide through the epoxy glue.
In the process of micro-hole machining, the air hole of the HADCF is adjusted to face the laser beam. The average output power of the CO2 laser is 0.35 W, and the scanning speed is 5.41 mm/sec. The diameter size of microholes is about 42 µm as shown in the inset of Fig. 4. The syringe needle covers one of the microholes, and the gap between the syringe needle and the microhole is sealed with epoxy glue. Finally, a microfluidic syringe pump is used to inject the solution into the air hole of the fiber at a fluid flow rate of 0.002 ml/s. Two microholes and air hole in the fiber together form a microfluidic channel to inject the mixed solution of glycerin and water with different concentrations.
The transmission spectrum of the tapered HADCF filled with deionized water is shown as the red line in Fig. 3. The resonant wavelength of the transmission spectrum shifts towards the long wavelength after filled water. The reason is that the material RI in the hole has a larger impact on the LP11 mode in the eccentric core. The effective refractive index of the LP11 mode in the eccentric core increases after filled liquid, while the effective refractive index of the LP01 mode in the center core is almost unchanged, so the intersection of the dispersion curves of these two modes shifts to long wavelengths. Therefore, the intersection wavelength between the dispersion curves of the cLP11 mode and the eLP01 mode has a red shift, which is consistent with the experimental result. The transmission spectra for different RI solutions are shown in Fig. 5(a), where the wavelength resolution of OSA is 0.5 nm. As the RI increases, the coupling dip shifts to the long wavelength. The relationship between the RI of glycerin and the center wavelength of the coupling dip is shown in Fig. 5(b). The shift of the coupling dip is linear with the RI. The sensitivities are 936.69 nm/RIU and 930.86 nm/RIU in the range of 1.335 to 1.360 for increasing and decreasing RI, respectively. As the RI rises and then falls, the dip wavelength can go back to the initial position. The RI sensitivity of the tapered HADCF sensor is higher than that of the untapered HADCF based on coupling between the fundamental modes in two cores [19]. The main reason is that the eccentric core becomes thinner after the tapering, and the evanescent field in the air hole is enhanced, resulting in a faster decrease in the effective RI of the LP11 mode. In contrast, the thinning of the fiber has a little effect on the effective RI of LP01 mode in the eccentric core. Therefore, the RI sensitivity of the proposed tapered HADCF sensor is higher.
Fig. 5. (a) The transmission spectra of the sensor for different RIs and (b) the relationship between the resonant wavelength and the RI.
It can be seen from the simulated results that the coupling dip shifts to the short wavelength with the decrease of the tapered waist diameter, i.e. the increase of the pulling length. Cascading two HADCFs with different pulling lengths together can form a multi-channel RI sensor. The multi-channel RI sensor can simultaneously measure the RIs of many different solutions. The two tapered HADCFs with different taper lengths are cascaded and the overall structure is SMF-DCF-SMF-DCF-SMF as shown in the inset in Fig. 6. A segment of SMF is added between the two tapered HADCFs, which can filter out the interference of cladding modes in the spectrum. The transmission spectrum of the cascaded tapered HADCF (sample A) with the pulling length L1 = 4.2 mm and L2 = 3.6 mm is shown as the blue line in Fig. 6, where the length of the SMF between the two couplers is 1.2 cm. The two coupling dips do not affect each other, increasing the length of the SMF has no effect on the transmission spectrum. The central wavelengths of two coupling dips are 1340 nm and 1447 nm, respectively. There are some ripples in the transmission spectrum due to the interference introduced by the core diameter mismatch. The two peaks are not fully separated and partially overlap. To completely separate the two peaks, the length difference between the tapered HADCFs needs to be increased. The transmission spectrum of the cascaded two tapered HADCFs (sample A′) with pulling lengths of L1′=4.2 mm and L2′=3.1 mm is shown as the red line in Fig. 6, and the central wavelengths of the two coupling dips are 1340 nm and 1587 nm, respectively. The two dips are clearly separated. There is no crosstalk between the two coupling dips, and the RI response of any one of the dips can be measured independently.
The RI sensitivity of the two dips can be measured separately or simultaneously. When one channel is used for RI sensing measurement, the other channel can be used as the reference channel for absolute measurement or temperature compensation. The multi-channel sensing is achieved when both channels are used simultaneously for RI sensing measurements. The glycerol solution with the RI range of 1.335-1.360 was injected into two tapered regions of the sample A. The experimental results are shown in Fig. 7. The RI sensitivities of the two coupling dips are 545.14 nm/RIU and 899.37 nm/RIU, respectively. The lower sensitivity of the short-wavelength coupling dip can be explained that the shorter the wavelength, the stronger the mode confinement capability in the core and the weaker the evanescent field.
The temperature characteristics of the tapered HADCF without solution filling were tested. The relationship between the temperature and resonant wavelength of the sample A is shown in Fig. 8. As the temperature increases from 20°C to 85°C, the proposed sensor is insensitive to the temperature. The change of the resonance wavelength of dip I is less than 0.9 nm as shown by the blue dots and the change in the resonant wavelength of dip II is less than 1.1 nm as shown by the red dots. The thermo-optic coefficient of the fiber material determines the temperature response of the sensor. When the temperature increases, the RI of the core and cladding decreases slightly and the coupling length changes accordingly. The energy in the center core reaches a minimum value at the dip wavelength and is almost zero. Therefore, the transmitted energy changes only slightly around the dip wavelength, and the change of the dip wavelength is very weak. Therefore, the proposed RI sensor has negligible temperature crosstalk.
4. Conclusions
In conclusion, we propose a RI sensor based on the coupling of the center core LP01 mode and the eccentric core LP11 mode in tapered HADCF. The HADCF with different tapered waists can satisfy the phase matching condition between two modes at different wavelengths. The coupling central wavelength has a blue-shift as the HADCF waist region becomes thinner. The coupling length of this sensor is very short and is only 2.44 mm, which is beneficial for sensor integration. Reducing the distance between the two cores of the HADCF can decrease the coupling length, thus the size of the sensor can be further reduced. The maximum RI sensitivity is 936.69 nm/RIU in the range of 1.335-1.360. By cascaded HADCFs with different pull lengths, a dual-channel sensor is achieved for simultaneous RI sensing measurements, thus the cost and size of the sensor is reduced. In addition, the sensor has a negligible temperature crosstalk. Therefore, the proposed sensor has the advantages of simple structure, good mechanical strength and stable performance, and has great potentials in biological analysis, medical detection methods and environmental protection.
Funding
National Natural Science Foundation of China (62175049, 62105077, U1931121); Natural Science Foundation of Heilongjiang Province (YQ2021F002, ZD2020F002); 111 Project to the Harbin Engineering University (B13015); Fundamental Research Funds for the Central Universities (3072022TS2501, 3072022CF2505, 3072021CFT2504).
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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