Nonlinear Maximization of the Sum-Frequency Component from Two Ultrasonic Signals in a Bubbly Liquid

Techniques based on ultrasound in nondestructive testing and medical imaging analyze the response of the source frequencies (linear theory) or the second-order frequencies such as higher harmonics, difference and sum frequencies (nonlinear theory). The low attenuation and high directivity of the difference-frequency component generated nonlinearly by parametric arrays are useful. Higher harmonics created directly from a single-frequency source and the sum-frequency component generated nonlinearly by parametric arrays are attractive because of their high spatial resolution and accuracy. The nonlinear response of bubbly liquids can be strong even at relatively low acoustic pressure amplitudes. Thus, these nonlinear frequencies can be generated easily in these media. Since the experimental study of such nonlinear waves in stable bubbly liquids is a very difficult task, in this work we use a numerical model developed previously to describe the nonlinear propagation of ultrasound interacting with nonlinearly oscillating bubbles in a liquid. This numerical model solves a differential system coupling a Rayleigh–Plesset equation and the wave equation. This paper performs an analysis of the generation of the sum-frequency component by nonlinear mixing of two signals of lower frequencies. It shows that the amplitude of this component can be maximized by taking into account the nonlinear resonance of the system. This effect is due to the softening of the medium when pressure amplitudes rise.