Isotropic transformation optics: approximate acoustic and quantum cloaking

TL;DR

This paper presents a method to create approximate acoustic and quantum cloaks using isotropic, nonsingular materials, overcoming previous anisotropic and singular design challenges, with applications in quantum mechanics.

Contribution

It introduces a novel approach to approximate cloaking with isotropic, nonsingular parameters applicable to acoustic and quantum waves, expanding transformation optics techniques.

Findings

Approximate cloaking achieved with isotropic, nonsingular parameters.

Cloaking effective outside a discrete set of frequencies or energies.

Supports almost trapped states near Neumann eigenvalues.

Abstract

Transformation optics constructions have allowed the design of electromagnetic, acoustic and quantum parameters that steer waves around a region without penetrating it, so that the region is hidden from external observations. The material parameters are anisotropic, and singular at the interface between the cloaked and uncloaked regions, making physical realization a challenge. We address this problem by showing how to construct {\sl isotropic and nonsingular} parameters that give {\sl approximate} cloaking to any desired degree of accuracy for electrostatic, acoustic and quantum waves. The techniques used here may be applicable to a wider range of transformation optics designs. For the Helmholtz equation, cloaking is possible outside a discrete set of frequencies or energies, namely the Neumann eigenvalues of the cloaked region. For the frequencies or energies corresponding to the Neumann eigenvalues of the cloaked region, the ideal cloak supports trapped states; near these energies, an approximate cloak supports {\sl almost trapped states}. This is in fact a useful feature, and we conclude by giving several quantum mechanical applications.