On possible applications of media described by fractional-order models in electromagnetic cloaking

Abstract

The purpose of this paper is to open a scientific discussion on possible applications of media described by fractional-order (FO) models (FOMs) in electromagnetic cloaking. A 2-D cloak based on active sources and the surface equivalence theorem is simulated. It employs a medium described by FOM in communication with sources cancelling the scattered field. A perfect electromagnetic active cloak is thereby demonstrated with the use of a finite-difference time-domain method combined with a simulation algorithm of non-monochromatic wave propagation in the media described by FOM. The application of constitutive relations based on FOMs in Maxwell’s equations provides solutions which correspond to the results reported for the time-fractional diffusion-wave equation, which is non-relativistic, like the classical diffusion equation. This property is employed in the presented cloaking scheme for communication with active current sources around the cloak, which cancel the scattered field of an object inside the cloak. Although in the real world perfect invisibility is impossible to obtain due to the constraint of light speed, it is possible to obtain a perfect cloak in theoretical considerations by using FO formulation of electromagnetism. It is worth noticing that numerous literature sources experimentally confirm the existence of electromagnetic media described by FOMs; hence, the presented numerical results should hopefully stimulate further investigations related to applications of FOMs in electromagnetic cloaking.