[Paper Review] Acoustic cloaking: geometric transform, homogenization and a genetic algorithm

Lucas Pomot, Cédric Payan+2 more|arXiv (Cornell University)|Apr 12, 2019

Metamaterials and Metasurfaces Applications37 references32 citations

TL;DR

The paper presents a general process to design anisotropic inhomogeneous metamaterials via coordinate transformations, and uses homogenization plus a genetic algorithm to realize acoustic cloaks with practical microstructures.

ABSTRACT

A general process is proposed to experimentally design anisotropic inhomogeneous metamaterials obtained through a change of coordinate in the Helmholtz equation. The method is applied to the case of a cylindrical transformation that allows to perform cloaking. To approximate such complex metamaterials we apply results of the theory of homogenization and combine them with a genetic algorithm. To illustrate the power of our approach, we design three types of cloaks composed of isotropic concentric layers structured with three types of perforations: curved rectangles, split rings and crosses. These cloaks have parameters compatible with existing technology and they mimic the behavior of the transformed material. Numerical simulations have been performed to qualitatively and quantitatively study the cloaking efficiency of these metamaterials.

Motivation & Objective

• Motivate and formalize how coordinate transformations create anisotropic inhomogeneous media for acoustic waves.
• Propose an inverse homogenization workflow to realize transformed media with feasible microstructures.
• Demonstrate cloaking designs using 1D laminar and 2D rectangular lattice microstructures compatible with existing fabrication.
• Quantify cloaking efficiency across frequencies and compare different microstructure designs.

Proposed method

• Revisit the Helmholtz equation and form-invariance under coordinate transformations yielding anisotropic inhomogeneous parameters (α and β).
• Apply a non-linear cylindrical transformation to generate an annular cloaking region with constant β and anisotropic α.
• Use homogenization theory to retrieve effective medium parameters from microstructured lattices (1D laminar and 2D rectangular lattices).
• Formulate an inverse homogenization problem solved by a genetic algorithm to match the homogenized parameters to those from the transformation.
• Employ a conformal map to transfer microstructures from (r,θ) to (x,y) coordinates for practical realization.
• Assess cloaking efficiency numerically by comparing transformed and reference homogeneous fields over frequency.
• Explore additional microstructures (split ring resonators, Celtic cross) to test robustness and resonance effects.

Experimental results

Research questions

• RQ1 How can a geometrical transformation be used to create an acoustic cloaking region and what are the resulting material parameters?
• RQ2 Can homogenization plus a genetic algorithm reproduce the transformed medium with feasible microstructures?
• RQ3 What are the quantitative cloaking performances of different microstructures (1D laminar vs 2D rectangular) across frequencies?
• RQ4 How do more exotic microstructures affect cloaking efficiency and resonance phenomena?

Key findings

• The transformed medium parameters are α = a J J^T det J and β = b det J, with a constant det J for the chosen non-linear transformation.
• An inverse homogenization approach using a genetic algorithm can identify microstructures that mimic the transformed anisotropic medium.
• 1D laminar lattices and 2D rectangular lattices can produce cloaks composed of concentric layers with isotropic perforations that approximate the transformed material.
• Rectangular lattice designs require less extreme parameter ranges than laminar lattices, improving experimental feasibility.
• Cloak efficiency is high at low frequencies but decreases at higher frequencies due to homogenization limits and resonances.
• Exotic microstructures (split ring resonators, Celtic cross) show reduced performance at higher frequencies due to resonance and geometric imperfections.