1. Introduction

Opto-mechanics of high-Q whispering-gallery modes (WGM) optical cavities has attracted wide attention in the past years. Benefitting from the unique characteristics of opto-mechanical coupling, microcavities have become a promising platform for cavity-assisted laser-cooling, quantum information processing, and mesoscopic quantum mechanics studying [1–9 ]. On the other hand, in this kind of opto-mechanical system, slight variations of many physical parameters such as force, mass, acceleration, displacement, are directly reflected as the vibration frequency shift, and can be measured from the transmitted optical power spectrum with high resolution through efficient opto-mechanical coupling. Detection of vibration frequency change allows many sensing applications, for example liquid, magnetometers, single-photon detectors [9–15 ].

Recently, WGM micro-bubble resonators (MBRs) with ultra-high Q and small mode volume are considered as excellent opto-microfluidic devices [16, 17 ], especially for optical sensing applications [18–20 ]. Their hollow structure provides a perfect structure for investigating microfluidic opto-mechanical properties as well [21–27 ]. The dependence of the mechanical vibrational frequency on liquid flowing in the MBRs has been found [22, 23, 25 ]. However, all the previous works focus either on the optical or opto-mechanical properties of MBRs. Here we show that combining optical resonance with opto-mechanical resonance properties provides important supplementary information. As an example, we demonstrate that optical/opto-mechanical cooperative sensing can be obtained by simultaneously monitoring optical and vibrational frequency change in a thin-wall MBR. The 2-D sensing scheme opens a door for multifunctional sensing applications.

2. Experiment

MBRs are fabricated by the fuse-and-blow technique [17, 19 ]. The outer diameter of MBRs is around 100 μm and the wall thickness is about 10 μm at the center of the bubble. MBR is coupled via a 2-3 μm tapered fiber in touch with it. The mechanical mode information reflects in the power spectrum of the transmitted light from the tapered fiber. When light is coupled to a specific whispering gallery mode, vibration of the resonator leads to a periodical transmitted light power change which can be detected by analyzing the power spectrum. Experimentally, light from a tunable single frequency diode laser (Anritsu Tunics Plus CL) at 1.55 μm is launched into the tapered fiber, the transmitted light is detected by a photodiode and the electric signal is sent to a frequency spectrum analyzer (Agilent Technologies E4402B) and an oscilloscope (Tektronix TDS3012) separately. The laser power was kept at 1 mW to ensure that optomechanical pump is at sub-threshold condition.

3. Results and discussions

Figure 1(a) is a typical opto-mechanical spectrum in a range of 15-18 MHz. Similar resonant spectrum can also be found in other works [22–27 ]. The mechanical mode is likely a breathing mode or radial vibrational mode. The quality factor of the mode in Fig. 1(a) is 1.9 × 10³. Other vibration modes also appear by changing the outer diameter and wall thickness of the MBR, or by changing the coupling conditions. Figure 1(b) shows an example that 3 mechanical modes can be identified by changing the coupling position.

 

Fig. 1 (a) Mechanical mode of an outer diameter 100 μm MBR with 10 μm wall thickness. Inset: Image of MBR and tapered fiber. (b) Vibrational spectrum of MBR with side pump (black line) and center pump (red line).

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Many factors have influences on the peak position of a mechanical mode in MBR, including sound speed, density, pressure and viscosity of liquid [25–27 ]. In the present work, we believe that the sound speed is the main factor. Mixed liquids with constant density and pressure are prepared to avoid the influence of density and pressure change on mechanical frequencies. Experimentally, this is realized by mixing aniline, methanol and carbon tetrachloride together. The physical properties of the three liquids can be found in [28–30 ] and are listed in Table 1 . With these, the sound speeds in the mixtures are calculated to be 1.05-1.35 km/s at a fixed density of 1.2 g/cm³. In the meantime, the viscosity of liquids changes between 0.98 cP and 2.48 cP (viscosity of mixed liquid is calculated by linearly adding fractional contribution of liquids). According to the dependence of mechanical frequency on viscosity as shown in Ref. 25, here the frequency shift due to the change of viscosity is negligible.

Table 1. Mechanical properties of different liquids [28–30]

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Figure 2(a) is the measured mechanical vibrational spectra with different liquid combinations. 3 mechanical modes can be found, and their resonant frequencies are between 8 and 13 MHz, obvious lower than that of an empty bubble due to the existence of the liquid. Figure 2(b) plots the relation of mechanical mode frequencies with sound speeds in liquid, all 3 mechanical mode frequencies increase in response to the increment of sound speeds in liquid. The slope of the plot represents the sensitivity of the mechanical modes to sound speed, it varies from 4.2 to 6.8 MHz/(km/s), and agrees with theoretical calculated results in Ref. 27. Take the experimental mean standard deviation of mechanical frequency of 0.45 kHz (see below the experimental results), which corresponds to a sound speed noise equivalent detection limit (NEDL) of 0.11 m/s, this means that 10² ppm toluene in CCl₄ is detectable. The variation of RI of this mixed liquid is of the order of 10⁻⁶ RIU, this leads to a conclusion that the detection limit of mechanical mode is equivalent to an RI detection limit of 10⁻⁶, which is a typical value for optical sensing [24].

 

Fig. 2 (a) Vibrational spectra with different liquids in the hollow tube of a MBR (outer diameter 150 μm and wall thickness 15 μm). The proportion in the figure shows volume ratio of the mixed solution (aniline: methanol: carbon tetrachloride). (b) The mechanical mode frequencies as a function of sound speed.

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A combination of WGM optical sensing and opto-mechanical sensing is capable to provide additional information of the liquid and help in determining composition change. Here we show the realization of a 2-D optical/opto-mechanical microfluidic sensor in a thin wall MBR.

An MBR with around 7 μm wall thickness and 190 μm outer diameter is fabricated. WGM optical spectrum is obtained by scanning input laser frequency through a WGM resonant line. We used mixture of CCl₄ /CS₂ /toluene as the testing liquid, its proportion ratio is accordingly 1:x:y. When WGM resonant frequency shift and mechanical mode frequency are plotted in the same figure, like that in Fig. 3(a) , each point in the figure represents one composition of liquids. As an example, when toluene is added into CCL₄ (mixture composition 1:0:y), an optical sensitivity of 18 nm/RIU is obtained by using a high quality factor (Q>10⁶) optical mode. A theoretical calculation of the resonant frequency shift versus RI by the same program used in [18, 20 ] (see Fig. 4 ) reveals that the WGM in this case is the 3rd order radial mode. Meanwhile the opto-mechanical sensitivity of the sound speed obtained is 3.8 MHz/(km/s), similar to that in the previous example in which mixtures of aniline/methanol/CCl₄ are used. In the inset of Fig. 3(a), we also plotted the variation of measured mechanical frequency of MBR filled with pure CCl₄. 10 measurement points give a mean standard deviation σ = 0.45 kHz, the variation may come from measurement error and slight environment change.

 

Fig. 3 (a) 2-D map of mechanical mode frequency and WGM resonant wavelength shift. Inset: variation of measured mechanical frequency of MBR filled with pure CCl₄, 10 measurements give a standard frequency variation of 0.45 kHz. (b) Mechanical mode frequency as a function of toluene proportion (T) when CCl₄/CS₂ has a fixed ratio of 1:0.176. Left inset: sound speed of the mixed liquids as a function of T. Right inset: optical resonance wavelength as a function of T.

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Fig. 4 Calculated radial optical mode sensitivity of a MBR with outer diameter around 190 μm and wall thickness of 6.8 μm.

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Note that in Fig. 3(a), when the ratio of CCl₄/CS₂ increases from 1:0 to 1:0.1, and then toluene is added, optical sensitivity becomes less and less. This is because RI of the CCl₄/CS₂ moves closer to that of toluene, thus larger amount of toluene is needed to change the RI of the mixture. Especially when CCl₄ and CS₂ have a volume ratio of 1:0.176, the mixture has almost the same RI as toluene. Therefore, RI of (CCl₄/CS₂)/toluene mixture at proportion 1: T is independent of T. As shown in the inset of Fig. 3(b), the optical mode frequency keeps at a constant when T changes. However, since sound speed in the mixed liquid is still different, as shown in left inset of Fig. 3(b), the difference in mechanical response is nonetheless significant. Consequently, as illustrated in Fig. 3(b), the mechanical mode frequency changes obviously with T. The sensibility of sound speed is 4.1 MHz/(km/s). On the other hand, when sound speed in the liquids is nearly the same but RI is different, results will appear as a horizontal line on the 2-D map. Thus the 2-D sensing map provides much more information than the conventional 1-D sensors.

4. Conclusions

In summary, we demonstrated that mechanical mode in an MBR can be used for sensing. The NEDL of opto-mechanical sensing is at the same level as that of optical sensor. A 2-D microfluidic sensing scheme is demonstrated by combining optical sensing and opto-mechanical sensing ability. The MBRs show great potential as excellent opto-mechanical microfluidic devices and can be used as a highly supplementary tool to conventional optical biological and chemical sensors.