Zitterbewegung-like effect near the Dirac point in metamaterials and photonic crystals

TL;DR

This paper explains a classical Zitterbewegung-like effect observed near the zero-refractive-index point in metamaterials and photonic crystals, linking asymmetrical transmittance spectra to temporal oscillations in transmitted pulses.

Contribution

It provides a classical interpretation of Zitterbewegung-like effects in metamaterials, connecting spectral asymmetry to pulse oscillations without relying on relativistic quantum mechanics.

Findings

Asymmetrical transmittance spectrum causes pulse asymmetry.

Temporal oscillations depend on pulse width and slab thickness.

Classical explanation aligns with quantum-inspired observations.

Abstract

We present a physical explanation of Zitterbewegung-like effect near the zero-refractive-index point in a metamaterial slab in this paper. Between the negative and positive refractive index regions centered at the zero-refractive-index point, the transmittance spectrum distribution of the metamaterial slab is asymmetrical. When a symmetrical pulse propagates through the metamaterial slab, its transmitted spectrum becomes asymmetrical due to the asymmetry of the transmittance spectrum of the slab, leading to a transmitted pulse with an asymmetrical temporal shape. The asymmetry manifests a kind of temporally tailed oscillations, i.e., the Zitterbewegung-like effect. Further, the effect of the temporal and spatial widths of pulse, and the thickness of metamaterial slab on the tailed oscillations of the transmitted pulse has also been discussed. Our results agree well with what the other researchers obtained on the strength of relativistic quantum concepts; however, the viewpoint of our analysis is classical and irrelevant to relativistic quantum mechanics.