Analysis in temporal regime of dispersive invisible structures designed from transformation optics

TL;DR

This paper analyzes the temporal behavior of dispersive invisible structures based on transformation optics, deriving transient field expressions and confirming effects through numerical simulations.

Contribution

It provides a theoretical analysis of dispersion effects in transformation-optics-based cloaks, deriving transient field expressions and validating them with numerical simulations.

Findings

Transient fields decay as t^(-3/4) at large times

Cloak quality diminishes at short times but is preserved at large times

Dispersion effects are confirmed by numerical simulations

Abstract

A simple invisible structure made of two anisotropic homogeneous layers is analyzed theoretically in temporal regime. The frequency dispersion is introduced and analytic expression of the transient part of the field is derived for large times when the structure is illuminated by a causal excitation. This expression shows that the limiting amplitude principle applies with transient fields decaying as the power -3/4 of the time. The quality of the cloak is then reduced at short times and remains preserved at large times. The one-dimensional theoretical analysis is supplemented with full-wave numerical simulations in two-dimensional situations which confirm the effect of dispersion.