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The acoustic bubble is an example of a highly nonlinear system which is thebuilding block of several applications and phenomena ranging from underwateracoustics to sonochemistry and medicine. Nonlinear behavior of bubbles, andmost importantly 1/2 order subharmonics (SH), are used to increase the contrastto tissue ratio (CTR) in diagnostic ultrasound (US) and to monitor bubblemediated therapeutic US. It is shown experimentally and numerically that whenbubbles are sonicated with their SH resonance frequency (fsh=2fr where fr isthe linear resonance frequency), SHs are generated at the lowest excitationpressure. SHs then increase rapidly with pressure increase and reach an upperlimit of the achievable SH signal strength. Numerous studies have investigatedthe pressure threshold of SH oscillations; however, conditions to enhance thesaturation level of SHs has not been investigated. In this paper nonlineardynamics of bubbles excited by frequencies in the range of fr<f<2fr is studiedfor different sizes of bubbles (400nm-8 micron). We show that the SH resonancefrequency is pressure dependent and decreases as pressure increases. When abubble is sonicated with its pressure dependent SH resonance frequency,oscillations undergo a saddle node bifurcation from a P1 or P2 regime to a P2oscillation regime with higher amplitude. The saddle node bifurcation isconcomitant with over saturation of the SH and UH amplitude and eventualenhancement of the upper limit of SH and UH strength (e.g. $\approx$ 7 dB in UHamplitude). This can increase the CTR and signal to noise ratio inapplications. Here, we show that the highest non-destructive SH amplitudeoccurs when f~=1.5-1.8fr.

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