Optical Refractive Index of Massive Particles and Physical Meanings of Left-handed Media

TL;DR

This paper derives the refractive index for de Broglie waves in potential fields, clarifies the physical meaning of negative refraction, and links electromagnetic wave behavior in left-handed media to antiphotons, aiding understanding of photonic crystals.

Contribution

It introduces a new expression for the refractive index of de Broglie waves and explains the physical significance of negative refraction in left-handed media.

Findings

Negative refractive index corresponds to antiphoton behavior.

Electromagnetic waves in left-handed media behave like antiphotons.

Complex vector field theory aids in understanding wave propagation in photonic crystals.

Abstract

In this Letter the expression for the refractive index of de Broglie wave in the presence of a potential field is obtained and based on this, the physical meanings of negative index of refraction is revealed. We demonstrate that the electromagnetic wave propagation in a left-handed medium with negative refractive index behaves just like that of antiphotons, which is required of the complex vector field theory. It is believed that the complex vector field theory is helpful in considering the wave propagation and photonic band gap structure in the left-handed medium photonic crystals with a periodicity in negative and positive index of refraction.