Photonic transmittance in metallic and metamaterial Superlattices

TL;DR

This paper investigates electromagnetic wave transmission through metallic and metamaterial superlattices, revealing oscillating transmission characteristics, superluminal effects, and the conditions under which causality is preserved.

Contribution

It provides a detailed theoretical analysis of wave packet evolution in photonic superlattices, highlighting the effects of incidence angle, plasmon coupling, and superlattice structure on transmission.

Findings

Transmission oscillates with incidence angle and superlattice parameters.

Superluminal effects occur without causality violation.

Wave packet evolution matches theoretical predictions.

Abstract

We present here the transmission of electromagnetic waves through layered structures of metallic and left-handed media. Based on the theory of finite periodic systems, we show that besides the strong influence of the incidence angle, the low transmission characteristic of a single conductor slab, for frequencies $\omega$ below the plasma frequency $\omega_p$, becomes in this domain highly oscillating. Similarly, the well-established transmission coefficient of a single left-handed slab becomes highly resonant with superluminal effects in superlattices with more than one unit cell. We determine the space-time evolution of a wave packet through the $\lambda/4$ photonic superlattice whose transmission coefficient is a sequence of isolated and equidistant peaks with negative phase times. We show that the space-time evolution of a Gaussian wave packet, with centroid at any of these peaks, agrees with the theoretical predictions, and no violation of the causality principle occurs. We show that besides the strong influence of the incidence angle, the coherent coupling of the bulk plasmon modes and the interface surface plasmon polaritons lead to oscillating transmission coefficients, and depending on the parity of the number of unit cells $n$ of the superlattice, the transmission vanishes or amplifies as the conductor width increases. We determine the space-time evolution of a wave packet through the $\lambda/4$ photonic superlattice whose bandwidth becomes negligible, and the transmission coefficient becomes a sequence of isolated and equidistant peaks with negative phase times. We show that the space-time evolution of a Gaussian wave packet, with the centroid at any of these peaks, agrees with the theoretical predictions, and no violation of the causality principle occurs.