# Subwavelength guided modes for acoustic waves in bubbly crystals with a line defect

## TL;DR

This paper demonstrates that a line defect in a bubbly crystal acts as a waveguide for specific acoustic frequencies, supported by a new formula for defect mode frequencies and numerical validation.

## Contribution

It introduces an original formula for defect mode frequencies in bubbly crystal waveguides and numerically verifies wave localization along the line defect.

## Key findings

- Line defect creates localized waveguiding for certain frequencies.
- New analytical formula for defect mode frequencies.
- Numerical simulations confirm waveguiding behavior.

## Abstract

The recent development of subwavelength photonic and phononic crystals shows the possibility of controlling wave propagation at deep subwavelength scales. Subwavelength bandgap phononic crystals are typically created using a periodic arrangement of subwavelength resonators, in our case small gas bubbles in a liquid. In this work, a waveguide is created by modifying the sizes of the bubbles along a line in a dilute two-dimensional bubbly crystal, thereby creating a line defect. Our aim is to prove that the line defect indeed acts as a waveguide; waves of certain frequencies will be localized to, and guided along, the line defect. The key result is an original formula for the frequencies of the defect modes. Moreover, these frequencies are numerically computed using the multipole method, which numerically illustrates our main results.