Optimal Design of Broadband, Low-Directivity Graded Index Acoustic Lenses for Underwater Applications

TL;DR

This paper presents an optimization-based design method for broadband, low-directivity underwater acoustic lenses using metamaterials, enabling practical implementation with improved control over wave focusing.

Contribution

It introduces a novel large-scale optimization scheme for designing low-directivity acoustic lenses from metamaterials, directly linking desired refractive indices to practical lattice structures.

Findings

Optimized lenses achieve broadband, low-directivity performance.

The Lagrangian approach simplifies large-scale optimization.

Homogenized models match finite element simulations effectively.

Abstract

Manipulating underwater pressure waves is crucial for marine exploration, as electromagnetic signals are strongly absorbed in water. However, the multi-path phenomenon complicates the accurate capture of acoustic waves by receivers. Although graded index lenses, based on metamaterials with smoothly varying properties, successfully focus pressure waves, they tend to have high directivity, which hinders practical application. This work introduces three 2D acoustic lenses made from a metamaterial composed of solid inclusions in water. We propose an optimization scheme where the pressure dynamics is governed by Helmholtz's equation, with control parameters affecting each lens cell's density and bulk modulus. Through an appropriate cost function, the optimization encourages a broadband, low-directivity lens. The large-scale optimization is solved using the Lagrangian approach, which provides an analytical expression for the cost gradient. This scheme avoids the need for a separate discretization step, allowing the design to transition directly from the desired smooth refractive index to a practical lattice structure. As a result, the optimized lens closely aligns with real-world behavior. The homogenized numerical model is validated against finite elements, which considers acoustic-elastic coupling at the microstructure level. When homogenization holds, this approach proves to be an effective design tool for achieving broadband, low-directivity acoustic lenses.