Acoustic frequency combs using gas bubble cluster oscillations in liquids: a proof of concept

Abstract

We propose a new approach to the generation of acoustic frequency combs (AFC)-signals with spectra containing equidistant coherent peaks. AFCs are essential for a number of sensing and measurement applications, where the established technology of optical frequency combs suffers from fundamental physical limitations. Our proof-of-principle experiments demonstrate that nonlinear oscillations of a gas bubble cluster in water insonated by a low-pressure single-frequency ultrasound wave produce signals with spectra consisting of equally spaced peaks originating from the interaction of the driving ultrasound wave with the response of the bubble cluster at its natural frequency. The so-generated AFC posses essential characteristics of optical frequency combs and thus, similar to their optical counterparts, can be used to measure various physical, chemical and biological quantities.

Figure 1

(a) Schematic diagram of the suggested AFC generation. The oscillations of the bubble cluster are driven by a single-frequency ultrasound pressure wave. Acoustic waves scattered by the bubble cluster are recorded and post-processed to obtain a spectrum consisting of the equidistant peaks. (b) Schematic of the experimental setup. Bubbles are created in a stainless steel tank using a bubble generator. The driving pressure wave is emitted by an ultrasonic transducer. Waves scattered by the bubble are detected by a hydrophone. bf (c) Photograph of typical gas bubbles emitted by the bubble generator in a water tank with transparent walls at otherwise identical experimental conditions to those in the stainless steel tank. The diffuser of the bubble generator and other elements of the setup can be seen.

Figure 2

(a) Experimental spectra of a cluster of gas bubbles in water insonated with the 24.6 kHz sinusoidal signal of increasing pressure amplitude $\alpha =1.15$, 3.75, 4, 4.2, 4.3, 7.5 and 11.5 kPa. The frequency axis is normalised with frequency $f_0$ of the driving field. The detectable response frequency resolution is $\mathrm{\Delta }f/f_0=1.34\times {10}^{-4}$. The scattered pressure values (in dB) are shown along the vertical axis with the vertical offset of 30 dB between spectra. (b) Calculated spectra of a single gas bubble with 1.95 mm radius at the same driving pressure frequency and amplitudes as in the experiment. The vertical offset between individual spectra is 100 dB. In both panels, the vertical dashed lines mark the peaks at the natural frequency and its ultraharmonics (the left parts of the spectra) as well as the frequencies of the sideband peaks around the fundamental and second harmonic frequency of the driving signal.

Figure 3

(a) Measured acoustic response of the gas bubble cluster and (b) calculated acoustic response of a single equivalent bubble corresponding to a sinusoidal pressure wave with the frequency $f_0=24.6$ kHz and amplitude $\alpha =11.5$ kPa. In the calculation, the initial conditions were set to be $R(0)=R_0$ and $\frac{d}{\mathit{dt}}R(0)=0$, see Eq. (1). The time between the vertical dashed lines is $\mathrm{\Delta }T=1/f_{\mathit{nat}}\approx 0.6$ ms. The insets show the closeup of the waveforms and demonstrate the amplitude modulation (see the main text for more details.) Arbitrary pressure units are used in both panels to enable the comparison of the experimental and calculated data.

Figure 4

(a) Measured acoustic bubble cluster response corresponding to a sinusoidal driving pressure wave with the frequency $f_0=49.2$ kHz (twice the frequency in Fig. 3) and amplitude $\alpha =4.3$ kPa. The time between the vertical dashed lines is $\mathrm{\Delta }T=1/f_{\mathit{nat}}\approx 0.6$ ms.