Nonlinear dynamics of acoustic bubbles excited by their pressure dependent subharmonic resonance frequency: oversaturation and enhancement of the subharmonic signal

The acoustic bubble is an example of a highly nonlinear system which is the building block of several applications and phenomena ranging from underwater acoustics to sonochemistry and medicine. Nonlinear behavior of bubbles, and most importantly 1/2 order subharmonics (SH), are used to increase the contrast to tissue ratio (CTR) in diagnostic ultrasound (US) and to monitor bubble mediated therapeutic US. It is shown experimentally and numerically that when bubbles are sonicated with their SH resonance frequency (fsh=2fr where fr is the linear resonance frequency), SHs are generated at the lowest excitation pressure. SHs then increase rapidly with pressure increase and reach an upper limit of the achievable SH signal strength. Numerous studies have investigated the pressure threshold of SH oscillations; however, conditions to enhance the saturation level of SHs has not been investigated. In this paper nonlinear dynamics of bubbles excited by frequencies in the range of fr<f<2fr is studied for different sizes of bubbles (400nm-8 micron). We show that the SH resonance frequency is pressure dependent and decreases as pressure increases. When a bubble is sonicated with its pressure dependent SH resonance frequency, oscillations undergo a saddle node bifurcation from a P1 or P2 regime to a P2 oscillation regime with higher amplitude. The saddle node bifurcation is concomitant with over saturation of the SH and UH amplitude and eventual enhancement of the upper limit of SH and UH strength (e.g. $\approx$ 7 dB in UH amplitude). This can increase the CTR and signal to noise ratio in applications. Here, we show that the highest non-destructive SH amplitude occurs when f~=1.5-1.8fr.