On the transmittance of metallic superlattices in the optical regime and the true refraction angle

TL;DR

This paper investigates the optical transmittance and refraction angles in metallic superlattices, addressing anomalies caused by non-unitary assumptions and proposing a complex-angle approach that ensures flux conservation and accounts for absorption.

Contribution

It introduces a finite periodic systems theory for metallic superlattices valid for any number of layers, and develops a complex-angle formalism to accurately model optical properties including absorption.

Findings

Complex angles ensure flux conservation and proper energy accounting.

Anomalous parity effects are explained by absorption and loss phenomena.

New Fresnel and transmission coefficients are derived for improved modeling.

Abstract

Recently, an approach for metallic superlattices based on the finite periodic systems theory was introduced \cite{Pereyra2020}. Unlike most, if not all, of the published approaches that are valid in the $n \rightarrow \infty $ limit, the finite periodic approach is valid for any natural number $n$ and allows one to determine analytical expressions for scattering amplitudes and dispersion relations. It was shown, for frequencies below $\omega_{p}$ and large metallic-layer thickness, that under the common assumption that fields inside conductors move along the so-called "true" angle that defines the orientation of the constant-phase planes, anomalous results appear with an apparent parity effect. This issue is addressed here and it is shown that those results are due to the lack of unitarity and the underlying phenomena of absorption and loss of energy. Two compatible approaches are presented here to solve the lack of unitarity and to account for the absorption phenomenon. We show that by keeping the complex angles, the principle of flux conservation is fully satisfied, above and below $\omega_p$. This approach, free of assumptions, gives us light to improve the formalism when the real angle assumption is made. We show that by taking into account the induced currents and the requirement of flux conservation, we end up with an improved approach, with new Fresnel and transmission coefficients, fully compatible with those of the complex-angle approach.