Non-Euclidean cloaking for light waves

TL;DR

This paper analyzes non-Euclidean cloaking for light waves, demonstrating that such cloaks perform effectively beyond geometrical optics, especially at higher frequencies, approaching perfect invisibility in the limit.

Contribution

It provides analytical and numerical analysis of wave propagation in non-Euclidean cloaks, showing improved performance at higher frequencies beyond geometrical optics.

Findings

Cloak performs well beyond geometrical optics regime.

Nearly perfect cloaking for frequencies related to spherical harmonics.

Performance improves with increasing wavenumber, approaching ideal behavior.

Abstract

Non-Euclidean geometry combined with transformation optics has recently led to the proposal of an invisibility cloak that avoids optical singularities and therefore can work, in principle, in a broad band of the spectrum [U. Leonhardt and T. Tyc, Science 323, 110 (2009)]. Such a cloak is perfect in the limit of geometrical optics, but not in wave optics. Here we analyze, both analytically and numerically, full wave propagation in non-Euclidean cloaking. We show that the cloaking device performs remarkably well even in a regime beyond geometrical optics where the device is comparable in size with the wavelength. In particular, the cloak is nearly perfect for a spectrum of frequencies that are related to spherical harmonics. We also show that for increasing wavenumber the device works increasingly better, approaching perfect behavior in the limit of geometrical optics.