Universal Electromagnetic Waves in Dielectric

TL;DR

This paper investigates the universal electromagnetic wave behavior in dielectric materials characterized by fractional power-law susceptibility, deriving exact solutions to fractional differential equations that describe fractional damping effects across diverse materials.

Contribution

It introduces an exact solution for fractional differential equations governing electromagnetic fields in dielectrics with universal response, highlighting common wave features across various materials.

Findings

Electromagnetic fields exhibit fractional damping in dielectric media.

Universal response applies regardless of material composition.

Exact solutions to fractional equations are derived.

Abstract

The dielectric susceptibility of a wide class of dielectric materials follows, over extended frequency ranges, a fractional power-law frequency dependence that is called the "universal" response. The electromagnetic fields in such dielectric media are described by fractional differential equations with time derivatives of non-integer order. An exact solution of the fractional equations for a magnetic field is derived. The electromagnetic fields in the dielectric materials demonstrate fractional damping. The typical features of "universal" electromagnetic waves in dielectric are common to a wide class of materials, regardless of the type of physical structure, chemical composition, or of the nature of the polarizing species, whether dipoles, electrons or ions.