Introduction to the theory of left-handed media

TL;DR

This paper explores the electromagnetic properties, phenomena, and potential applications of left-handed media, focusing on negative refractive index materials and their unique effects on wave propagation.

Contribution

It provides a comprehensive mathematical and physical analysis of left-handed media, covering fundamental effects, phenomena, and potential applications in optical and electromagnetic systems.

Findings

Reversal of Doppler effect in left-handed media

Negative refraction and its implications

Design of subwavelength resonators using left-handed materials

Abstract

This paper is devoted to investigating the physically interesting optical and electromagnetic properties, phenomena and effects of wave propagation in the negative refractive index materials, which is often referred to as the {\it left-handed media} in the literature. This paper covers a wide range of subjects and related topics of left-handed media such as many mathematical treatment of fundamental effects ({\it e.g.}, the reflection and the refraction laws on the interface between LH and RH media, the group velocity and energy density in dispersive materials, the negative optical refractive index resulting from a moving regular medium, the reversal of Doppler effect in left-handed media, the reversal of Cerenkov radiation in left-handed media, the optical refractive index of massive particles and physical meanings of left-handed media, the anti-shielding effect and negative temperature in left-handed media, {\it etc.}), and their some applications to certain areas ({\it e.g.}, three kinds of compact thin subwavelength cavity resonators (rectangular, cylindrical, spherical) made of left-handed media, the photon geometric phases due to helicity inversions inside a periodical fiber made of left-handed media, {\it etc.}).