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Abstract
In this paper, we proposed an axially slow-variation microbubble resonator fabricated by an improved arc discharge method and applied to axial strain sensing. The prepared resonators are characterized by ultra-thin wall thickness and axial slow-variation. The wall thickness was experimentally measured to reach 938 nm and maintain a quality factor of an optical mode as large as $\textrm{7}\mathrm{.36\ \times 1}{\textrm{0}^\textrm{7}}$. The main factors affecting the strain sensitivity of the microbubble resonators are investigated theoretically and experimentally. Experimentally, the maximum sensitivity measured was 13.08pm/µε, which is three times higher than the microbubble resonators without this method. The device is simple to prepare and possesses ultra-thin wall thickness. It is promising for applications in high-precision sensing, such as single molecule and biological sensing.
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1. Introduction
Optical whispering gallery modes (WGMs) resonators have been widely studied and applied in the past decades due to their ultra-high quality factor (Q) and extremely small mode volume. WGMs have been applied in a variety of fields such as nonlinear optics [1–3], low-threshold la-ser [4] and cavity quantum electrodynamic [5]. In addition, because WGMs greatly enhance the light-matter interaction [6], they have the obvious advantages of increased sensing sensitivity [7] and reduced detection limit in high-precision sensing [8]. WGMs resonators are available in different geometrical shapes such as microsphere [9], microbottle [10], microdisk [11], microtube [12], and microbubble [13]. Among these shapes, microbottle, microtube, and microbubble have a natural rod-like structure, which is very suitable for high-precision axial strain sensing.
For strain sensing, the first experimental study of force-induced resonance wavelength displacement using microsphere resonators was performed by Ioppolo et al. [14] in 2009. In recent years, structures such as microtube, microbottle, and microbubble have demonstrated the feasibility of WGMs strain tuning. In 2019, Qin et al. [15] proposed a solid resonator consisting of a double vial structure and obtained a strain sensitivity of 1.7pm/µε by monitoring the upper and lower bimodal peaks. Although this solid resonator is simpler in terms of fabrication steps, its strain sensitivity is lower compared to the hollow structure due to its structural limitation when the same strain is applied. In 2021, Guo et al. [16] demonstrated a hollow peanut-shaped resonator, and the experimental results showed that the highest sensitivity reached 6.96pm/µε. However, the fabrication of this particular structure requires complex steps, which leads to a time-consuming and low success rate of the experimental process. To address the above technical challenges, we innovatively propose an improved arc discharge method for preparing microbubble resonators. This method requires only a commercial single-mode fiber fusion splicer, which is simple and has a high success rate.
In this study, we introduce an axially slow-variation microbubble resonator (ASMBR) fabricated by an improved arc discharge method for strain sensing. Characterized by its ultra-thin wall and axially slow-variation, the ASMBR demonstrates increased axial strain sensitivity. We have systematically investigated the main factors affecting the strain sensitivity of microbubble resonators. Experimentally, we have achieved a notable strain sensitivity of up to 13.08pm/µε. The experimental results show that our ASMBR offers a threefold sensitivity enhancement over microbubble resonators and a tenfold improvement compared to microtube resonators. More importantly, our proposed method greatly reduces the wall thickness and radius of microbubble resonators, which is expected to be generalized to the field of single molecule [17] and biological [18] sensing.
2. Fabrication and experimental setup
A commercial silica capillary TSP075150 (150$\mathrm{\mu m}$ outer diameter, 75$\mathrm{\mu m}$ inner diameter) was required to fabricate the ASMBR. The polymer coating on the capillary was removed by hydroxide flame prior to resonator fabrication. The coating residue was then wiped off with alcohol to obtain a pure silica capillary. The outer diameter of the removed capillary was 125µm and the wall thickness was 25µm. The capillary was heated and melted using an arc discharge generated by a commercially available single-mode fiber fusion splicer. High pressure air was pumped into the capillary using a homemade pressurization system. Prior to starting the fabrication process, we used the fusion splicer to melt and seal one end of the capillary tube.
The specific fabricate process is shown in Fig. 1. First, the other end of the capillary tube is connected to a pressurizing device and an atmospheric pressure of about 120KPa is delivered to the inside of the capillary tube. The motor of the fusion splicer was controlled to apply tensile force to both ends of the capillary tube. At the same time, the fusion capillary was heated with a discharge time of 300 ms and a discharge intensity of -3bit, as shown in Fig. 1(a). This step created a waist tapered region to reduce the wall thickness of the capillary. To counteract the hydrostatic pressure [19], high-pressure air is pumped into the tube. The pressure inside the capillary tube should be precisely controlled. When the pumped air pressure is less than the hydrostatic pressure, the capillary shrinks and increases the wall thickness; when the pumped air pressure is greater than the hydrostatic pressure, the capillary expands and creates a bulge. This step is repeated to precisely control the wall thickness and diameter of the capillary tube to achieve the desired state. In the second step, as shown in Fig. 1(b), the tensile force applied to the capillary tube was stopped and the discharge was continued with the tube filled with high-pressure air. After the axial force is canceled, the capillary tube is mainly pressurized by the internal high-pressure air. In this case, after heating by multiple arc discharges, the tapered waist region of the capillary tube gradually forms a bottle-shaped bulge. Finally, the capillary tube gradually expands to form an axially slow-variation microbubble resonator, as shown in Fig. 1(c).
Fig. 1. (a)-(c) Schematic diagram of the fabrication process for the ASMBR. (d) Optical microscope photograph of the ASMBR.
Unlike the method of preparing microbubble resonator using a CO2 laser [20] and heating with a hydroxide flame [21], we used a fusion splicer to fabricate the waist region with a shorter length and a distinctly tapered feature. In this case, the closer to the center of the waist, the thinner capillary wall thickness. Thus, ASMBR fabricated using our proposed method have a smaller wall thickness at the center of the cavity compared to the sides. It should be noted that this is relative to microbubble resonators fabricated on capillaries with constant wall thickness. Microbubble resonators fabricated using our method have smaller radius and wall thicknesses and are characterized by a slow-variation in the axial direction. In the axial direction, the change in wall thickness is more pronounced, and the closer the region to the center of the resonant cavity, the thinner the wall thickness.
In order to test the mechanical strain properties of the fabricated ASMBR, we used an experimental system as shown in Fig. 2 to excite the resonator WGMs and test the strain sensing properties. To excite the WGMs, we fabricated the tapered fibers with a diameter of 1-2µm by Heat and Pull method [22]. A tunable laser with a center wavelength of 1550 nm and the tunable range of 0.233 nm was used as the pump laser, and the pump laser was passed through a polarization controller and then through an adjustable attenuator to control the pump power. Too high power of the pump light can lead to thermal effects in the resonator [23], affecting its sensing performance. The laser power output from the adjustable attenuator is controlled to be below 1 mW, and the incoming tapered fiber power is preferably around 500µW. The pump laser from the attenuator is coupled to the resonator through a tapered fiber to excite the WGMs, which is converted to an electrical signal by a photodetector and input to an oscilloscope for real-time monitoring and acquisition of the resonance spectrum. The microbubble resonator is fixed to two precision translation stages (Newport M-561D-XYZ) at each end. One of them is fixed, and the axial strain is applied to the resonator by adjusting the high-precision adjuster (Newport DS-4F) of the other one. The two stages were placed vertically at a distance of L = 10 cm, with the minimum displacement scale of ΔL = 20 nm and the minimum strain of εL = ΔL/L = 0.2µε. The inset shows a high-resolution micrograph of the tapered optical fiber coupled to the ASMBR.
Fig. 2. Experimental setup for the strain-tuning and transmission spectrum of the ASMBR. TL, tunable laser; AFG, arbitrary function generator; OSC, oscilloscope; PC, polarization controller; VOA, variable optical attenuator; TS, translation stage; PD, photoelectric detector.
3. Discussion and results
3.1 ASMBR characterization
The exact wall thickness of ASMBR was determined by scanning electron microscopy (SEM). The ASMBR was first mechanically ruptured and then placed vertically into the electron microscope cavity. The results are shown in Fig. 3(a). It can be observed that the wall thickness of the ASMBR varies relatively uniformly in the equatorial plane, with the minimum wall thickness of 938 nm. The optical field distribution of the resonant modes of the ASMBR axial quantum number q = 0, 1, 2, and 3 is simulated using the finite element analysis software COMSOL, and the results are shown in Fig. 3. In the simulation setup, the ASMBR radius is set to 40µm and the wall thickness is set to 1µm. Figure 3(c) shows a schematic diagram of the resonance wavelength shift that occurs after the resonators are subjected to axial strain. When the axial strain increases, the radius of the equatorial plane of the resonators decreases causing a blue shift of the resonant wavelengths. Figure 3(d) shows the transmission spectrum excited using the experimental system shown in Fig. 2. The tapered fiber is coupled at the maximum diameter of the ASMBR, and the coupling efficiency is improved by adjusting the coupling distance. Its theoretical Q can reach about $\textrm{7}\mathrm{.36\ \times 1}{\textrm{0}^\textrm{7}}$ calculated by Lorentz fitting, as shown in Fig. 3(e).
Fig. 3. (a) An SEM image of the ASMBR snapped in the middle. The measured minimum wall thickness is 938nm. (a) Typical optical field distributions for different axial quantum numbers in ASMBR simulated by COMSOL. (c) Schematic diagram of resonance wavelength shifts due to strain applied to resonators. (d) Transmission spectra excited by a tapered fiber coupled to an AGMBR. (e) The enlarged view of the black rectangular region in (c) is fitted by Lorentz.
3.2 Numerical simulation
When axial mechanical stretching of a hollow bottle-shaped resonator, the main contribution to the shift in its resonance spectrum is given by the amount of change in its equatorial radius $\varDelta \textrm{R}$. Neglecting relatively small changes in refractive index [24–25], the shift in the resonant wavelength can be derived from the equation:
according to the equation: given in the literature [25], the radius change that occurs when a microbubble resonator with a wall thickness of h and an equatorial radius of R is stretched by a uniformly distributed perpendicular force F can be calculated. where E and v denote the Young's modulus and Poisson's ratio of the material, respectively.The modes of the bottle-shaped resonator can be characterized by the azimuthal quantum number m, the radial quantum number p and the axial quantum number q. The theoretical resonant wavelength can be expressed as [26]:
By using the above equation, we can theoretically calculate the relationship between the resonant wavelength shift and the radius change for different quantum numbers. The theoretical calculation results are shown in Fig. 4(b). From the figure, we can see that the wavelength shift occurring in the low-order axial mode is larger in the case of equal amount of radius change.
Fig. 4. (a) Strain sensitivity versus wall thickness and outer radius of microbubble resonators. (b) Radius reduction of bottled-shape resonator versus wavelength shift for different axial quantum numbers.
Figure 4(a) shows the theoretically calculated strain sensitivity versus the wall thickness and outer radius of the microbubble resonator. From the figure, we can conclude that two microbubble resonators of similar dimensions with smaller wall thicknesses are able to achieve greater strain sensitivity. On the other hand, in the case of two microbubble resonators with similar wall thicknesses, the smaller size of the microbubble resonator will have greater strain sensitivity. As we mentioned in the previous section, the microbubble resonators fabricated using our proposed method will have smaller wall thicknesses and radius. This will greatly increase the axial strain sensitivity of the resonator.
3.3 Experimental results
Prior to applying axial stress, the coupling state of the tapered fiber to the ASMBR must be precisely adjusted. It is crucial that the tapered fiber remains in direct contact with the resonator throughout the experiment. However, the fiber should be allowed a slight relaxation to prevent its displacement relative to the resonator during axial stretching. We conducted strain sensing experiments on AGMBR using the experimental setup in Fig. 2. Since the fabricated microbubble resonator possesses a large variation of wall thickness in the axial direction. In order to obtain the response of the resonator to the amount of strain change at different positions of the resonator. We excited the WGMs at different diameters of the AGMBR by adjusting the coupling position of the tapered fiber to the resonator. And the strain response of the resonant spectra at different diameters of the ASMBR was observed and recorded.
The experimental results are shown in Fig. 5. As shown in Fig. 5(a)-5(c), the resonance wavelength shifts at different diameters of the AGMBR when it experiences gradually increasing axial strain. As the strain increases, the resonance wavelength gradually shifts upward in the direction of the shorter wavelength. This is due to the fact that the radius of the resonator decreases gradually with the gradual increase in strain. In the selection of resonant modes for tracking, we prioritize modes that not only exhibit a high Q factor but also demonstrate stability and the capability to endure the entire process of axial strain being applied. Figure 5(a) and (b) show the variation of the resonance wavelength as the resonator undergoes the process from 0-24$\mathrm{\mu \varepsilon }$ when the tapered fiber is coupled at the edge of the ASMBR with diameters of 129.74µm and 134.96µm, respectively. The strain sensitivities at the edge of the resonator were obtained by linear fitting and were 4.02pm/µε and 4.53pm/µε, respectively. After that, we moved the tapered fiber to the center of the resonator at the maximum diameter (diameter of 153.45µm) and applied strains from 0-9µε to the ASMBR. The evolution of the traced transmission spectra is shown in Fig. 5(c). As expected, the thin-walled feature in the central region of the resonator improves the strain sensitivity to 13.08pm/µε. The difference in strain sensitivity reaches a factor of three, which we attribute to the altered structure of the ASMBR caused by the improved fabrication process. The microbubble resonator was fabricated at the capillary tapered waist region, which causes the wall thickness of the resonator to undergo a greater variation in the axial direction. Figure 5(d) shows the tapered fiber coupling at different diameters of the ASMBR versus the experimentally measured strain sensitivity. Locations with larger resonator diameters will have higher strain sensitivity.
Fig. 5. Spectral evolution of the traced resonance peak with a tapered fiber coupled at different diameters D of the resonators. (a) D = 129.74µm, (b) D = 134.96µm, (c) D = 153.45µm. The arrows in the figure are used to mark the modes we have traced. (d) Relationship between the diameter and strain sensitivity of the ASMBR.
We believe that this is mainly due to the fact that locations with larger diameters tend to have smaller wall thicknesses. This causes a difference in the amount of radius change in the equatorial plane of the resonator when the same amount of strain change is applied, i.e., the smaller the wall thickness the larger the radius change.
After that, we focus on the evolution of the excited WGMs under increasing strain when the tapered fiber is coupled at the maximum diameter of the ASMBR. As shown in Fig. 6(a), the resonance spectra change as the axial strain increases from 0 to 21µε. We traced three modes and labeled them in the figure. It is observed that the transmittance of all three modes decreases, which is due to the fact that there is a slight decrease in the radius of the equatorial plane of the resonator with increasing axial strain leading to an increase in the coupling distance to the tapered fiber. The resonance points of these three modes are linearly fitted to the applied strain and the results are shown in Fig. 6(b). The strain sensitivities of modes 1-3 are 13.08pm/µε, 11.68pm/µε, and 8.78pm/µε, respectively. A significant differentiation of the strain sensitivities of the multiple resonance modes is observed in one transmission spectrum.
Fig. 6. (a) Evolution transmission spectra of ASMBR under applied strain from 0µε to 21µε. (b) Wavelength-strain dependence of Mode-1, Mode-2 and Mode-3.
Analysis of Fig. 6(a) reveals that the strain sensitivities for modes 1-3 are ${\textrm{S}_{\textrm{M}1}}$: ${\textrm{S}_{\textrm{M}2}}:\; {S_{M3}}$= 1.48:1.33:1. According to the previous theoretical calculations, this closely aligns with the sensitivity ratios ${\textrm{S}_{q0}}$: ${\textrm{S}_{\textrm{q}2}}:\; {S_{q7}}$= 1.4991:1.3537:1, associated with the axial quantum numbers q = 0, 2, and 7. These observations suggest that the differences in sensitivity among modes 1-3 might be attributable to variations in their axial quantum numbers. From the experimental results, we can conclude that to improve the strain sensitivity of the hollow bottle-shaped resonators, we can realize it not only by decreasing the wall thickness and radius, but also by tracing the low-order axial modes.
As a comparison, we fabricated a microtube resonator (MTR) and a microbubble resonator (which has a similar curvature compared to the ASMBR) using silica capillaries TSP075150. And strain sensing experiments were performed under the same experimental conditions, respectively. The microtube resonator was obtained by removing the polymer coating on the capillary surface and using the procedure in Fig. 1(a). The microbubble resonator was fabricated using the Fuse-and-Blow method [27], with a maximum diameter of 195µm, and a theoretical wall thickness of 7µm. The results of the comparative experiments are shown in Fig. 7. The strain sensitivity of the microtube resonator was measured to be 1.26pm/µε which is higher than the previously reported result [28]. We attribute this to the fact that our fabrication technique reduces the wall thickness and radius of the resonator. The strain sensitivity of the microbubble resonator was measured to be 3.33pm/µε. The strain sensitivity of the microbubble resonator is mainly affected by the outer radius of the wall thickness. A larger wall thickness and outer radius both lead to a smaller strain sensitivity. As can be seen from the figure, the strain sensitivity of our reported resonator (ASMBR) is improved by an order of magnitude with respect to the microtube, and by a factor of three with respect to the microbubble resonator of similar curvature.
Fig. 7. Comparison of strain sensitivity of microtube resonator (MTR), microbubble resonator (MBR) and the ASMBR.
Table 1 lists the strain sensitivities of other previously reported WGMs resonators with our proposed ASMBR. The table shows that our proposed sensor possesses higher sensitivity. This indicates that the microbubble resonator fabricated by our proposed improved arc discharge method are capable of achieving high sensitivity for strain sensing.
Table 1. Sensitivity of WGMs strain sensors
According to Table 1 our proposed device not only successfully reduces the size of the resonators but also enhances their sensitivity. Our refined method for fabricating microbubble resonators significantly reduces their wall thickness and decreases the resonator diameter. This procedure is straightforward and utilizes only a single fusion splicer.
4. Conclusion
In summary, our work details an improved arc discharge method for fabricating axially slow-variation microbubble resonators tailored for strain sensing. Our method significantly reduces the wall thickness of the resonators. SEM measurements confirm the wall thickness of the ASMBR as low as 938 nm. We have thoroughly examined the factors influencing strain sensitivity, achieving the maximum sensitivity of 13.08pm/µε. With its ultra-thin wall thickness and straightforward preparation steps, ASMBR is expected to be extended to high-precision sensing fields.
Funding
National Natural Science Foundation of China (62101230); Natural Science Foundation of Jiangxi Province (20224BAB202006, 20232ACB212008, 20232BAB212016, 20232BCJ23096); Chinese Aeronautical Establishment (2018ZC56006); Jiangxi Provincial Department of Education Science and Technology Project (GJJ200915).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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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