1. Introduction

Utilizing the optical properties of whispering gallery microcavity for biosensing has been in research for years [1–7]. One of the important properties that hasn’t been fully investigated for sensing is the cavity optomechanical oscillation. In the past decade, cavity optomechanics [8–12] has been extensively explored to demonstrate a variety of optomechanical phenomena from optomechanical heating, cooling, optically induced spring, to various quantum mechanical phenomena [13–23]. The coherent regenerative optomechanical oscillation, being possible with the substantial optical force established at the cavity edge, has displayed pure spectral properties and unique back-action against thermal noises and is desirable for sensing applications. Its adoption to sensing, however, is limited in a gaseous environment [24–26]. The rare demonstration of such system in an aqueous environment lies in the fact that when a cavity is immersed in a liquid bath where a biospecimen dwells, the solution actuates strong viscous force against the cavity oscillation. This makes the optomechanical oscillation highly dissipative except in cases where a superfluid was adopted [27]. Up to date, the sole demonstration of an optomechanical system compatible to liquid solution is the bottleneck cavity where the liquid was injected to the inner tube of the cavity to circumvent the mechanical energy dissipation to the aquarium [28]. Although demonstration on sensing has been reported on this platform, the fact that the relative high mechanical oscillation frequency and large spatial separation between the optical mode and solution under test makes it less favorable in sensing applications compared to the microcavity reactive sensing established in previous experiments [1, 29].

To excite the cavity optomechanical oscillation in liquid, the optical quality factor of the microcavity must be maintained at a high value to establish a large intracavity power so that the dynamic back-action is strong enough for regenerative optomechanical oscillation. In our experiment, we demonstrated that by immersing a silica microsphere in heavy water for lower optical absorption at an operating wavelength around 970 nm, the optical quality factor of the microsphere can reach around ten million. Consequently, the condition was met and coherent regenerative optomechanical oscillation was observed.

2. Experiment results and discussions

The experiment setup is shown in Fig. 1(a). In our experiment, a Newport 6300LN external cavity tunable laser operating at 970 nm range was used as the pump source to drive the cavity oscillation. Throughout the experiment, the laser output power remained unchanged for a constant Schawlow-Townes limited laser frequency noise. To control the amount optical power delivered to the cavity, the laser output was regulated by a variable optical attenuator (VOA A) before entering a 99/1 optical directional coupler (OC A). The 99% port was connected to the input of a tapered optical fiber to deliver light to the silica microsphere under test. The micro-sphere was fabricated by melting a silica fiber tip into a 100 μm diameter sphere as shown in the micrograph of Fig. 1(a). The microsphere was immersed in heavy water (D₂O) and mounted on a nanopositioner to precisely control the coupling position between the microsphere and fiber taper. The intracavity optical power of the microsphere was interrogated by the same tapered fiber whose output was connected to a photodetector (New focus 1811) to convert transmitted the optical signal to electrical signal. The electrical signal was split by a 50/50 electrical splitter whose outputs were connected to an oscilloscope (Agilent DSO 90404A) and a real time spectrum analyzer (Tektronix RSA 3408B) for subsequent measurements.

 

Fig. 1 (a) Experiment setup. In the inset, the laser frequency noise spectrum measured by the reference interferometer (blue trace) was fitted by a sinc-square function (red dashed line). (b) Transmitted optical power as a function of probe laser wavelength detune. At a dropped optical power (defined as the optical power dropped into the cavity) close to the threshold power, the bottom left inset of the plot displayed a sinusoidal spectrum while at a high dropped power the spectrum displayed in the right inset of the plot was distorted by the high order harmonics. (c) Transmitted signal vs optical frequency detune (blue trace). The laser frequency was calibrated through the transmitted signal of the reference interferometer (green trace). The red dashed lines are least square fitting results.

Download Full Size | PDF

During the experiment, we linearly scanned the optical frequency of the probe laser using a waveform generator and adjusted the coupling between the tapered fiber and the microsphere such that the oscillation was observable in aquarium as shown in Fig. 1(b). The input optical power of the cavity was around 2.5 mW. As indicated in the insets, the oscillation was single mode when the optical power dropped in the cavity is slightly above the threshold power of coherent optomechanical oscillation while high order harmonics occurs at higher drop power level.

To measure the quality factor of a cavity optical resonant mode, the 1% output branch of the directional coupler was connected to a reference interferometer thermally stabilized in a foam box filled with ice water mixture. The transmitted optical signal from the interferometer was received by a balanced photo detector for real time laser frequency tracking. When the laser was in continuous wave (CW) mode, the spectrum of the electrical signal from the balanced photo detector was captured by an Agilent N9010A EXA signal analyzer. As shown in the top right inset of Fig. 1(a), the power spectrum of the signal displayed a sinc-square shape (blue trace). Note the spectrum was averaged over 100 measurements and calibrated by subtracting it from the dark current spectrum averaged over the same number of traces. A least square fit of the spectrum to a sinc-square function (red dashed trace) indicates the free spectral range Δν_FSR of the interferometer to be 21.3 MHz. We then scanned the optical frequency of the laser linearly and reduced the probe laser power till thermal broadening effects were not observable from the cavity transmission spectrum. As shown in Fig. 1(c), in the absence of thermal effects, transmitted signal from the cavity (blue trace, averaged over 100 traces) displayed a Lorentzian shape and the interferometer signal (green trace) has a sinusoidal shape with a periodicity equals to Δν_FSR. Therefore, by comparing the fitted curves of both spectra we obtained an intrinsic optical Q of 1.4 ×10⁷ when the microsphere was immersed in heavy water (D₂O). We measured the intrinsic quality factor by both up-scanning and down-scanning the laser wavelengths. Both measurements yield the same optical Q values, indicating the transmission spectrum was not affected by the thermal effects. Under the operation coupling condition, an intrinsic optical Q of 1.4 ×10⁷ was measured in heavy water, resulting an overall loaded optical Q of 9.8×10⁶.

In the next stage, we switched the laser to the continuous wave (CW) mode and the coupler (OC A) 1% output branch to an optical power meter. The amount of pump laser power delivered to the cavity was adjusted by the first variable optical attenuator (VOA A). To facilitate our measurement, we adjusted the second attenuator (VOA B) accordingly such that at off-resonance wavelength, the photodetector output voltage measured from the oscilloscope remains at a preset value of around 0.6 V regardless of the power delivered to the cavity. We then tuned the optical frequency of the laser toward cavity resonance frequency till the voltage at the photodetector dropped around 50%. Each radio frequency (RF) spectrum of the cavity transmitted signal Fig. 2 was captured by the real time spectrum analyzer. To improve the signal-to-noise ratio (SNR), each spectrum in Fig. 2(a) was averaged over 100 spectral traces collected seamlessly at the same drop power level while the traces of Fig. 2(b) was averaged over 500 times. From Fig. 2(a), the coherent oscillation is evident observing that the linewidth of the oscillation peak narrows rapidly when the optical power dropped to the cavity exceeds 1 mW. A detailed study of spectra in Fig. 2(a) indicates that the linewidth of the spectrum decreases gradually from 269 kHz when the dropped power is well below threshold (0.4 mW) to 61 kHz at a power level close to the threshold (1.0 mW). When the dropped power reaches 1.1 mW, the linewidth narrows down to 232 Hz rapidly. Note that the calculated linewidth on an averaged spectrum is broadened due to frequency jitter. A least square fit (red trace) to a single spectrum trace displayed as the blue trace in the inset yields a linewidth of 99 Hz, corresponding to a super mechanical quality factor Q_m = 3, 884. In Fig. 2(b) we further verify the generation of high order harmonics at high dropped optical power. As shown in the main plot, as many as 24 higher order harmonics peaks are visible over a frequency span of 10 MHz while the frequency doubling of the second harmonic is evident from the inset when the span is set to 1 MHz.

 

Fig. 2 (a) RF spectra at dropped power of 1.1 mW, 1 mW and 0.4 mW, least square fittings to the Lorentzian function indicate the linewidths of the optomechanical tones to be 232 Hz, 61 kHz and 269 kHz respectively. In the main plot, each spectrum was averaged over 100 spectral traces collected seamlessly at the same drop power level. The inset is the spectrum of single trace measurement. (b) In a separate measurement, as high as 24-th order harmonics was observed in a frequency span of 10 MHz. The dropped optical power is 2.6 mW. The inset further displayed the spectrum with a frequency span set at 1 MHz.

Download Full Size | PDF

In Fig. 3(a) we plotted the cavity mechanical energy normalized to its peak value (blue circle markers) as a function of the dropped power. As shown, the mechanical energy increases linearly with the dropped power at above a threshold power level. This further confirms the coherent nature of the mechanical oscillation. A linear fit to the mechanical energy (red dashed trace) reveals the threshold power to be 0.98 mW. In the inset of this figure, we plotted the peak frequency as a function of the dropped power. As shown, when below threshold the peak frequency drives gradually from 253 kHz at a dropped power of 0.3 mW to 370 kHz at 1 mW due to the optical spring effect [14]. A linear extrapolation to the peak frequency trace (red dashed line) predicts an intrinsic mechanic frequency of 199 kHz in the absence of optical force. To obtain the intrinsic mechanical quality factor Q_m, we plotted the linewidth (blue circles) as a function of the dropped power in Fig. 3(b). A linear fit (red dashed line) indicates an intrinsic linewidth of 431 kHz at zero dropped power level, yielding a Q_m of 0.5. Here the linewdith at each dropped power level was computed through a least square fitting of each RF spectrum to a Lorentzian function. At the lowest optical power around 0.3 mW, the spectrum significantly deviates from a Lorentzian shape, causing the estimated linewidth to be inaccurate. Therefore we exclude this data point from the linear fitting of linewidth displayed as red dashed line in Fig. 3(b). It is also worth mentioning that unlike those reported in the previous publication [28], the oscillation peak observed in the experiment was located at low frequencies around several hundred kHz.

 

Fig. 3 (a) Mechanical energy (normalized to the maximum value) as a function of the dropped power, a linear fit to the above threshold value shows a threshold power of 0.98 mW. The peak frequency as a function of the dropped power is displayed in the inset and a linear extrapolation predicts an intrinsic mechanical frequency of 198.7 kHz. (b) Mechanical linewidth vs dropped power indicates an intrinsic mechanical linewidth of 431 kHz and a mechanical quality factor of Q_m = 0.5 through linear extrapolation. Spectrogram of the optomechanical oscillation plotted in the inset indicates a 130 Hz standard deviation of the oscillation peak over a time span of 392 ms (The black line overlapped with the spectrogram is the peak frequency of the spectra calculated by the least square fitting).

Download Full Size | PDF

Finally we characterised the oscillation frequency stability by taking the spectrogram as displayed in the inset of Fig. 3(b). In this plot, the standard deviation of peak oscillation frequencies was computed to be 130 Hz over a time span of 392 ms. Note that such low frequency fluctuation makes the optomechanical oscillation an attractive tool for highly sensitive nanodetection.

3. Conclusion

In conclusion, we demonstrated the optomechanical oscillation of a silica microsphere immersed in heavy water. The intrinsic optical Q of microsphere was maintained above ten million in the aqueous environment. The high optical Q combined with sufficient overlap between cavity optical and mechanical modes makes it possible to establish a high intra-cavity optical force sufficient for optomechanical oscillation under the highly dissipative environment. It is worth noting that an optimum choice of pump laser wavelength may further reduce the optical absorption loss in water to increase the cavity optical Q for larger intracavity power. It may also increase the overlap between cavity optical and mechanical modes. Both effects will contribute to a lower oscillation threshold power. Therefore numerical verification of the optomechanical oscillation in aqueous environment is currently under investigation to determine the optimum pump laser wavelength for minimum threshold power and for better understanding of the system. Finally we believe that optomechanical oscillation in a buffered solution for biosensing applications is achievable with the use of higher power laser to overcome the excessive optical absorption from such solution. The established platform will find its applications in single particle mass-spectroscopy applications in future research.