# Sub-wavelength focusing of acoustic waves in bubbly media

## TL;DR

This paper investigates how bubbly media can be used to achieve super-focusing of acoustic waves by analyzing wave scattering near the Minnaert resonance frequency, combining theoretical derivations and numerical experiments.

## Contribution

It introduces a new theoretical framework for modeling acoustic scattering in bubbly media and demonstrates super-focusing capabilities through numerical simulations.

## Key findings

- Super-focusing of acoustic waves is achievable in bubbly media.
- Derived scattering functions for single bubbles and multiple scattering approximations.
- Numerical experiments confirm super-focusing potential near Minnaert resonance.

## Abstract

The purpose of this paper is to investigate acoustic wave scattering by a large number of bubbles in a liquid at frequencies near the Minnaert resonance frequency. This bubbly media has been exploited in practice to obtain super-focusing of acoustic waves. Using layer potential techniques we derive the scattering function for a single spherical bubble excited by an incident wave in the low frequency regime. We then derive the point scatter approximation for multiple scattering by N bubbles. We describe several numerical experiments based on the point scatterer approximation that demonstrate the possibility of achieving super-focusing using bubbly media.