Invisibility carpet in a channel with a structured fluid

TL;DR

This paper demonstrates how to design a structured fluid metamaterial that creates an invisibility carpet for surface liquid waves, enabling wave bending and mimetism in a channel.

Contribution

It introduces a mathematical framework for constructing operators with shared spectra using geometric transforms, applied to designing a feasible invisibility carpet for linear surface waves.

Findings

The structured metamaterial bends surface waves over a finite frequency range.

The approach uses spectral properties of operators with spatially varying coefficients.

The method enables mimetism between different domains in fluid wave propagation.

Abstract

We first note it is possible to construct two linear operators defined on two different domains, yet sharing the same spectrum using a geometric transform. However, one of these two operators will necessarily have spatially varying, matrix valued, coefficients. This mathematical property can be used in the design of metamaterials whereby two different domains behave in the same electromagnetic, acoustic, or hydrodynamic way (mimetism). To illustrate this property, we describe a feasible invisibility carpet for linear surface liquid waves in a channel. This structured metamaterial bends surface waves over a finite interval of Hertz frequencies.