Time delays and energy transport velocities in three dimensional ideal cloaking

TL;DR

This paper explicitly derives the energy transport velocity distribution in a 3D ideal cloak, revealing peculiar behaviors such as constant velocities along certain lines and zero velocities at the inner boundary, leading to infinite time delays.

Contribution

It provides the first explicit analysis of energy transport velocities in a 3D ideal cloak, highlighting unique velocity distributions and their implications.

Findings

Velocity along a line to the origin is constant

Velocity approaches zero at the inner boundary

Infinite time delays occur within geometric optics approximation

Abstract

We obtained the energy transport velocity distribution for a three dimensional ideal cloak explicitly. Near the operation frequency, the energy transport velocity has rather peculiar distribution. The velocity along a line joining the origin of the cloak is a constant, while the velocity approaches zero at the inner boundary of the cloak. A ray pointing right into the origin of the cloak will experience abrupt changes of velocities when it impinges on the inner surface of the cloak. This peculiar distribution causes infinite time delays for the ideal cloak within a geometric optics description.