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We develop a new, simple and non-destructive method to precisely measure the thickness of thin wall micro bubble resonators (MBRs) by using internal aerostatic pressure sensing. Measurement error of 1% at a bubble wall thickness of 2 μm is achieved. This method is applicable to both thin wall and thick wall MBR with high measurement accuracy.
© 2016 Optical Society of America
1. Introduction
Very recently, micro bottle or bubble resonators have attracted more and more attention in the field of sensing [1–5], low-threshold laser [6], cavity quantum electrodynamics (QED) [7], and nonlinear optics including stimulated Raman scattering [8], stimulated Brillouin scattering [9], Kerr optical switching [10] and four wave mixing [11], due to their support of ultrahigh quality factor (Q) and small mode volume (V) whispering gallery modes (WGMs). Typically, hollow structured micro bubble resonators (MBRs) with microfluidic channel become excellent sensors to detect biomolecules [2], refractive index (RI) [1], temperature [12] and gas pressure changes [13]. The sensing ability relies on the portion of electromagnetic field distributed in the core of MBR, which depends on the wall thickness of MBR for a given mode. Thus, optimized wall thickness with an appropriate mode provides significant improvement of sensitivity in sensing [14, 15]. The wall thickness is also important in nonlinear optics and optical dynamics to engineer geometric dispersion for hyper-parametric frequency conversions [11]. Besides, the coupling strength of plasmonic mode and photonic mode in plasmonic MBR can be adjusted by wall thickness [16].
Previous determination of wall thickness is mainly by theoretical models [13] or destructive methods [6,17]. Recently, Cosci et al used a confocal reflectance microscopy to measure the wall thickness of MBR with a resolution of 1.78 μm, limited by the longitudinal resolution of microscopy [18].
In this paper, we develop a convenient and non-destructive method to precisely measure the micro bubble resonator thickness by internal pressure sensing. Experimental results show that the measurement uncertainty is about 1%, or 0.02 μm as a minimum. Theoretical calculation also shows that the method is applicable for MBRs with either thin or thick wall thickness.
2. Experimental characterization
The MBRs were fabricated from a pressurized silica microcapillary (Polymicro Technology) by heating with a standard fusion splicer [11]. The initial thickness, T, of microcapillary plays a vital role to the wall thickness of MBR. So, to control the geometrical features of MBRs, especially the wall thickness, microcapillaries were etched before fabrication, which can be considered as a rough control to the wall thickness. Further, in order to obtain MBRs with different radius and wall thickness from a microcapillary with certain T, a gradually expanding method was employed.
Assuming that the volume of the shell of capillary is conserved during the fabrication process, the wall thickness of MBR mainly depends on the radius. It provides an access to indirectly adjust the wall thickness of the MBR, provided that the radius can be controlled in fabrication. In order to form a controllable bubble shape with an appropriate wall thickness, we extended our previous technique of fabrication, focusing on a combination of relatively low pressure and multiple heating and compression steps. Thus, the radius of MBR can be increased gradually, and the wall thickness decreased accordingly. In this way, the target wall thickness of MBR can be achieved by gradually increasing the radius to an appropriate value.
A group of silica capillaries with the same outside radius of 65 μm and different T was used to fabricate MBRs with different radii. The radii and wall thicknesses of MBRs shown in Fig. 1 were determined by an optical microscope. The monomial fitting curve as a guide line shows the required radii for various target wall thicknesses using capillaries with different T. Sometimes a large MBR is not easy to fabricate, limited by the arc discharge area of the splicer. Alternatively, hydrofluoric acid can be used to etch the inner wall of MBR and thinner wall MBR can be obtained with a moderate radius.
Fig. 1 Different radii and wall thicknesses of the MBRs fabricated from silica capillaries with a radius of 65 μm and different initial thicknesses (T). The monomial fitting curve as a guide line was employed to estimate the geometrical features of MBRs and indirectly control the wall thicknesses of MBRs during fabrication.
We used aerostatic tuning of WGM resonance to measure the wall thickness of an MBR. The internal pressure on the MBR shifts the WGM resonance for the following two reasons. One is the RI change due to the stress in pressurized MBR. The other is the MBR size change. As a result, the total shift of the resonant wavelength λ is given by [13, 19, 20]
where in which a, b are the outer and inner radius of bubble shell, pi and po are the internal and external pressures, n0 is the RI of the microbubble; the elastic-optic constant, shear and bulk moduli are C = 4 × 10−12 m2/N, G = 31 × 109 Pa and K = 41 × 109 Pa, respectively for silica. From Eqs. (1)-(3), one can see that the resonance shifts linearly with the internal pressure pi. The internal pressure sensitivity Sp for microbubble is:where v is the resonant frequency, and the geometrical parameter χ isThe thickness of the MBR can thus be determined as:where is a constant.Therefore, once pressure sensitivity Sp is measured, wall thickness t can be deduced. Figure 2 shows the calculated pressure sensitivity versus thickness t and outer radius a of the MBR. For two MBRs with identical size, the one with a thinner wall possesses larger pressure sensitivity. On the other hand, for MBRs with similar wall thickness, pressure sensitivity is larger for a larger size MBR.
The internal pressure sensitivity Sp is obtained experimentally by coupling a tapered fiber to the MBR and measuring its resonant wavelength shift induced by internal pressure change. Light from a tunable single frequency diode laser (Anritsu Tunics Plus CL) at 1.55 μm is launched into the tapered fiber, and the transmitted light is detected by a photodiode (PD) connecting to an oscilloscope (TEKTRONIX TDS3012). One end of the stem of MBR is sealed and the other is connected to a pressure source. The WGMs is monitored by finely scanning over a 6 GHz range and recording for different pressures.
Figure 3(a) plots the transmitted light spectra from an MBR when its internal pressure changes. The MBR has an outer radius a = 112.5 μm. As the pressure increased, the resonant mode shifts to a lower frequency (redshift) because of the increment of both the radius of MBR and the RI of silica. Figure 3(b) plots the resonant frequency shift versus pressure. A linear fit gives a pressure sensitivity of 6.21 GHz/bar with standard error of 0.10 GHz/bar.
Fig. 3 (a) Transmitted spectra at different internal pressures, (b) Dependence of the frequency with internal pressure.
According to the error transfer formula:
the uncertainty of thickness u(t) depends on the uncertainties of a and Sp. For a given MBR, a can be measured by optical microscope with u(a)/a around 0.4%, and the measured u(Sp)/Sp is about 1.6%. Thus u(t)/t can be deduced by Eq. (7) to be around 1-2%.Table 1 summarizes data from eight MBR samples, from which we can see that the thickness uncertainty is less than 0.25 μm, one order of magnitude smaller than that measured by confocal reflectance microscopy [18], and the smallest uncertainty is only about 0.02 μm.
Table 1. Statistics Data of Eight MBR Samples for Determination of MBR Thickness
Pressure sensitivity depends on size and thickness of MBR as predicted in Fig. 2. For two MBRs with identical size, the one with a thinner wall possesses larger pressure sensitivity. On the other hand, for MBRs with similar wall thickness, pressure sensitivity is larger for a larger size MBR.
3. Theoretical comparison
In addition to pressure sensing, RI [14], surface thickness and temperature sensing [12] can be used alternatively to deduce MBR wall thickness, because all these types of sensing rely on the portion of electromagnetic field distributed in the core of the MBR, which depends on the wall thickness. In the following, we theoretically compare the adaptability of wall thickness by pressure, RI, surface thickness and temperature sensing.
In the calculation, the outer radius of the MBR is fixed as 120 μm. For internal pressure sensing, the core of MBR is filled with air, while for RI, surface thickness and temperature sensing, the core of MBR is filled with water. The pressure sensitivity of fundamental mode with different wall thickness is calculated and shown in Fig. 4(a). For RI sensing, the resonant wavelength for different core RI is numerically calculated based on the Mie scattering theory [14] and the RI sensitivity SRI with different wall thickness is shown in Fig. 4(b). For surface thickness sensitivity SS, the sensitivity of WGM frequency shift to the change of thickness of MBR wall, the internal surface thickness is assumed to be etched gradually and the surface thickness sensitivity at different wall thickness of MBR is shown in Fig. 4(c). The temperature sensitivity ST is:
where ηcore, ηwall and ηair are the portion of the optical field located in the core, wall and air, which are determined based on Mie scattering theory; κcore = −1 × 10−4 K−1 and κwall = 6.4 × 10−6 K−1 are the thermo-optic coefficient of water and silica, respectively; ηair and κair are both very small comparing with those of core and wall and are thus negligible; neff is the effective index of the calculated fundamental mode. The calculated temperature sensitivity is shown in Fig. 4(d). Except pressure sensitivity, the other three sensitivities vs. the thickness of MBR are fitted with exponential curves. The RI, surface thickness and temperature sensitivity all reach a constant value when t > 5 μm, which means the thickness measurement can hardly be carried out for MBR with thick wall. However, the pressure sensitivity is still as high as 1 GHz/bar even for t = 15 μm. And the relative error for sample #2 in Table 1 (wall thickness 15 μm) is only 0.36%. Higher order radial modes have higher sensitivities because more modal field distributed in the core. As an example, RI sensitivity of the 3rd order radial mode (blue line) is plotted in Fig. 4(b), which is higher than that of fundamental mode with the same t. However, the sensitivity goes unchanged at t > 6 μm. Thus, even using higher order radial modes, the thickness measurements by RI, surface thickness and temperature sensitivity still have limited sensing range. Meanwhile internal aerostatic pressure sensing is applicable for MBR with both thin and thick wall thickness.Fig. 4 Pressure (a), RI (b), surface thickness (c) and temperature (d) sensitivity of fundamental modes vs. the thickness of MBR. RI sensitivity of 3rd order radial mode is also given in (b).
4. Conclusion
We developed a method to precisely measure the micro bubble resonator thickness by using internal aerostatic pressure sensing. Measurement uncertainty is on sub-micrometer scale and the smallest uncertainty is only 0.02 μm. We also made a theoretical comparison of measuring the wall thickness by other sensing schemes, including RI, surface thickness and temperature sensing. Theoretical calculation on determining wall thickness precision by other sensing schemes, including RI, surface thickness and temperature sensing, supports that this method allows deriving wall thickness for MBRs with both thin wall and thick wall. Our study may help to evaluate the performance of MBR with precise wall thickness on sensing, nonlinear optics and opto-plasmonics.
Funding
National Natural Science Foundation of China (NSFC) (11474070, 61327008, 11074051); Specialized Research Fund for the Doctoral Program of Higher Education (20130071130004).
References and links
1. S. Berneschi, D. Farnesi, F. Cosi, G. N. Conti, S. Pelli, G. C. Righini, and S. Soria, “High Q silica microbubble resonators fabricated by arc discharge,” Opt. Lett. 36(17), 3521–3523 (2011). [CrossRef]
2. X. Zhang, L. Liu, and L. Xu, “Ultralow sensing limit in optofluidic micro-bottle resonator biosensor by self-referenced differential-mode detection scheme,” Appl. Phys. Lett. 104(3), 033703 (2014). [CrossRef]
3. M. Sumetsky, Y. Dulashko, and R. S. Windeler, “Super free spectral range tunable optical microbubble resonator,” Opt. Lett. 35(11), 1866–1868 (2010). [CrossRef]
4. M. Li, X. Wu, L. Liu, X. Fan, and L. Xu, “Self-referencing optofluidic ring resonator sensor for highly sensitive biomolecular detection,” Anal. Chem. 85(19), 9328–9332 (2013). [CrossRef]
5. Y. Yang, J. Ward, and S. N. Chormaic, “Quasi-droplet microbubbles for high resolution sensing applications,” Opt. Express 22(6), 6881–6898 (2014). [CrossRef]
6. W. Lee, Y. Sun, H. Li, K. Reddy, M. Sumetsky, and X. Fan, “A quasi-droplet optofluidic ring resonator laser using a micro-bubble,” Appl. Phys. Lett. 99(9), 091102 (2011). [CrossRef]
7. Y. Louyer, D. Meschede, and A. Rauschenbeutel, “Tunable whispering-gallery-mode resonators for cavity quantum electrodynamics,” Phys. Rev. A 72(3), 031801 (2005). [CrossRef]
8. Y. Ooka, Y. Yang, J. Ward, and S. N. Chormaic, “Raman lasing in a hollow, bottle-like microresonator,” Appl. Phys. Express 8(9), 092001 (2015). [CrossRef]
9. Q. Lu, S. Liu, X. Wu, L. Liu, and L. Xu, “Stimulated Brillouin laser and frequency comb generation in high-Q microbubble resonators,” Opt. Lett. 41(8), 1736–1739 (2016). [CrossRef]
10. M. Pöllinger and A. Rauschenbeutel, “All-optical signal processing at ultra-low powers in bottle microresonators using the Kerr effect,” Opt. Express 18(17), 17764–17775 (2010). [CrossRef]
11. M. Li, X. Wu, L. Liu, and L. Xu, “Kerr parametric oscillations and frequency comb generation from dispersion compensated silica micro-bubble resonators,” Opt. Express 21(14), 16908–16913 (2013). [CrossRef]
12. J. M. Ward, Y. Yang, and S. N. Chormaic, “Highly sensitive temperature measurements with liquid-core microbubble resonators,” IEEE Photonics Technol. Lett. 25(23), 2350–2353 (2013). [CrossRef]
13. R. Henze, T. Seifert, J. Ward, and O. Benson, “Tuning whispering gallery modes using internal aerostatic pressure,” Opt. Lett. 36(23), 4536–4538 (2011). [CrossRef]
14. H. Li and X. Fan, “Characterization of sensing capability of optofluidic ring resonator biosensors,” Appl. Phys. Lett. 97(1), 011105 (2010). [CrossRef]
15. G. Huang, V. A. Bolaños Quiñones, F. Ding, S. Kiravittaya, Y. Mei, and O. G. Schmidt, “Rolled-up optical microcavities with subwavelength wall thicknesses for enhanced liquid sensing applications,” ACS Nano 4(6), 3123–3130 (2010). [CrossRef]
16. Q. Lu, M. Li, J. Liao, S. Liu, X. Wu, L. Liu, and L. Xu, “Strong coupling of hybrid and plasmonic resonances in liquid core plasmonic micro-bubble cavities,” Opt. Lett. 40(24), 5842–5845 (2015). [CrossRef]
17. Y. Yang, S. Saurabh, J. M. Ward, and S. N. Chormaic, “High-Q, ultrathin-walled microbubble resonator for aerostatic pressure sensing,” Opt. Express 24(1), 294–299 (2016). [CrossRef]
18. A. Cosci, F. Quercioli, D. Farnesi, S. Berneschi, A. Giannetti, F. Cosi, A. Barucci, G. N. Conti, G. Righini, and S. Pelli, “Confocal reflectance microscopy for determination of microbubble resonator thickness,” Opt. Express 23(13), 16693–16701 (2015). [CrossRef]
19. T. Ioppolo and M. V. Ötügen, “Pressure tuning of whispering gallery mode resonators,” J. Opt. Soc. Am. B 24(10), 2721–2726 (2007). [CrossRef]
20. Y. Yang, S. Saurabh, J. Ward, and S. N. Chormaic, “Coupled-mode-induced transparency in aerostatically tuned microbubble whispering-gallery resonators,” Opt. Lett. 40(8), 1834–1837 (2015). [CrossRef]
