Coupling the Thermal Acoustic Modes of a Bubble to an Optomechanical Sensor

Academic Background

The acoustic behavior of bubbles in liquids has long been a significant research topic in physics and engineering. The vibrational modes of bubbles are not only closely related to acoustic phenomena in nature but also have broad applications in fields such as microfluidics and biosensing. The Minnaert breathing mode is the most well-known vibrational mode in bubble acoustics, describing the fundamental vibration behavior of bubbles in liquids. However, bubbles also support a series of higher-order acoustic modes, which, although theoretically predicted, have rarely been experimentally observed. Additionally, optomechanical sensors, as highly sensitive detection tools, can probe acoustic and vibrational properties at the microscale, providing a new platform for studying bubble acoustics.

This study aims to use optomechanical sensors to detect the acoustic modes of bubbles, particularly higher-order acoustic modes, and to explore the coupling effects between bubbles and sensors. The research not only deepens the understanding of bubble acoustics but also provides new insights for optimizing the performance of micro-mechanical oscillators.

Source of the Paper

This paper was co-authored by K. G. Scheuer, F. B. Romero, and R. G. Decorby, affiliated with Ultracoustics Technologies Ltd and the ECE Department at the University of Alberta. The paper was published in 2024 in the journal Microsystems & Nanoengineering, titled Coupling the Thermal Acoustic Modes of a Bubble to an Optomechanical Sensor.

Research Process and Experimental Design

Experimental Setup and Sensor Overview

The sensors used in the study are based on Fabry–Pérot optomechanical cavities with a “buckled-dome” structure, with a diameter of 100 micrometers and a cavity length of approximately 2.4 micrometers. The sensors support high-quality (Q-factor ~10^4) Laguerre–Gaussian optical modes in the 1550 nm wavelength range. The mechanical oscillator of the sensor is the buckled upper mirror, with its lowest-order radially symmetric vibrational modes in air centered at 2.5 MHz and 6 MHz, respectively.

The sensors operate in a thermomechanical noise-limited regime, with laser interrogation powers as low as 10–100 microwatts. Fluctuations in the ambient medium significantly contribute to the noise floor of these sensors, making them ideal for passive sensing of their acoustic environment. In the experiments, the reflected laser light was delivered to a high-speed photodetector, and power spectral density (PSD) plots were generated from sampled noise signals.

Bubble Acoustics

The acoustic properties of bubbles can be explained by the Minnaert breathing mode. For a spherical bubble, the resonant frequency can be estimated using the formula fm·r ≈ 3.3 m/s, where r is the bubble radius. Bubbles also support a series of higher-order acoustic modes, with resonant frequencies much higher than the Minnaert mode. Through numerical simulations (COMSOL) and theoretical analysis, the study predicted these higher-order acoustic modes and experimentally verified their existence.

Experimental Results

The study detected the acoustic modes of bubbles by placing them on optomechanical sensors. The experimental results showed that the acoustic modes of the bubbles appeared as a series of new resonant peaks in the sensor’s noise spectrum. These resonant peaks closely matched the frequencies of the bubble’s acoustic modes predicted by numerical simulations, confirming the existence of higher-order acoustic modes. Additionally, the study found that the acoustic modes of the bubbles could couple to the sensor through both air and water, indicating that higher-order acoustic modes can radiate sound waves.

Elastic Purcell Effect

The study also explored the Purcell effect modification of the sensor’s vibrational spectrum by the bubble environment. The experimental results showed that the bubble environment altered the sensor’s vibrational spectrum, manifesting as changes in resonance linewidths and frequency shifts. These phenomena are consistent with the Purcell effect, indicating that the bubble environment influences the sensor’s vibrational behavior by modifying the acoustic density of states (DOS).

Main Results and Conclusions

Experimental Verification of Bubble Acoustic Modes

The study experimentally observed the higher-order acoustic modes of bubbles for the first time, validating theoretical predictions. These higher-order acoustic modes have resonant frequencies much higher than the Minnaert mode, indicating that the acoustic behavior of bubbles is not limited to the fundamental breathing mode. The experimental results also showed that the acoustic modes of bubbles can couple to the sensor through both air and water, further confirming the sound radiation characteristics of higher-order acoustic modes.

Evidence of Elastic Purcell Effect

The study observed the elastic Purcell effect in the MHz frequency range for the first time. The experimental results demonstrated that the bubble environment significantly influenced the sensor’s vibrational spectrum by modifying the acoustic density of states. Specifically, the resonance linewidths narrowed, and the resonance frequencies shifted, consistent with the theoretical predictions of the Purcell effect.

Significance and Value of the Research

Scientific Value

This study experimentally verified the higher-order acoustic modes of bubbles for the first time, filling a gap in the experimental study of bubble acoustics. Additionally, the study observed the elastic Purcell effect in the MHz frequency range for the first time, providing new experimental evidence for research on acoustic and optomechanical coupling.

Application Value

The research findings have significant application value in fields such as microfluidics and biosensing. The acoustic properties of bubbles have broad application prospects in microfluidic systems, and the high sensitivity of optomechanical sensors provides new tools for these applications. Furthermore, the results offer new insights for optimizing the performance of micro-mechanical oscillators, particularly in terms of acoustic environment modification.

Highlights of the Research

1. First Experimental Verification of Higher-Order Acoustic Modes in Bubbles: The study observed the higher-order acoustic modes of bubbles for the first time using optomechanical sensors, validating theoretical predictions.
2. First Observation of Elastic Purcell Effect in the MHz Frequency Range: The study observed the elastic Purcell effect in the MHz frequency range for the first time, providing new experimental evidence for research on acoustic and optomechanical coupling.
3. Multi-Medium Coupling Effects: The study confirmed that the acoustic modes of bubbles can couple to the sensor through both air and water, indicating that higher-order acoustic modes can radiate sound waves.

Other Valuable Information

The study also explored the coupling effects between bubbles and sensors, finding that the bubble environment significantly influenced the sensor’s vibrational spectrum by modifying the acoustic density of states. These results provide new insights for future optimization of micro-mechanical oscillators, particularly in terms of acoustic environment modification.

Conclusion

This study used optomechanical sensors to detect the acoustic modes of bubbles, experimentally verifying the existence of higher-order acoustic modes for the first time and observing the elastic Purcell effect in the MHz frequency range. The findings not only deepen the understanding of bubble acoustics but also provide new tools and insights for applications in microfluidics, biosensing, and other fields.