Abstract
In this paper, we present a numerical modal study of a simple slab, made of an uniaxial anisotropic material having an "epsilon-near-zero" (ENZ) dielectric function, surrounded by vacuum. We use two Drude models with a different plasma frequency for the direction parallel and perpendicular to the slab surface as toy models to study the effect of uniaxial anisotropy of type I (∊‖ > 0, ∊⊥ < 0) and type II (∊‖ < 0, ∊⊥ > 0) on the different electromagnetic modes of the system. In addition to the so-called ENZ mode, studied in detail by Campione et. al [ Phys. Rev. B91, 121408(R) (2015)], the slab can support quasi-confined (QC) mode in the type I and type II anisotropy frequency ranges. We show that those modes exhibit a strong electric field enhancement, caused by the ENZ character of the dielectric function. In strong contrast with the ENZ mode, QC modes can have a strong electric field enhancement for thick slabs, with a Fabry-Perot-like electromagnetic field distribution spanning over the whole slab thickness. This opens the way for large electric field enhancement in thick slabs with QC ENZ modes. Thick slabs also allow metamaterial designs, giving the possibility to engineer the anisotropy of the effective dielectric function, opening interesting perspectives for the control of field enhancement of the ENZ QC modes and their integration in operating devices, such as detectors, sources, or modulators.
Highlights
In their pioneering work [1], Engheta and co-workers predicted the tunneling of electromagnetic energy through narrow channels with the use of material having a dielectric function close to zero
The QC modes were mostly discussed in the framework of electron-phonon interaction in GaN/AlGaN quantum heterostructure and more recently in the context of hyperbolic materials [28,29] and quantum transport in graphene supported by h-BN [30] where they are referred to as Hyperbolic Phonon Polaritons (HPP)
The dielectric function of a quantum well (QW) with intersubband transitions can be described by an anisotropic tensor, where the electrons in the well are described by a Drude model in the direction perpendicular to the QW growth direction, and by a resonant term in the growth direction describing intersubband transitions
Summary
In their pioneering work [1], Engheta and co-workers predicted the tunneling of electromagnetic energy through narrow channels with the use of material having a dielectric function close to zero (epsilon-near-zero, or ENZ). Strategies to enhance the ENZ properties by loss-compensation have been proposed [18] Another important topic is the electromagnetic modes supported by thin slabs of ENZ materials. In particular a rule of thumb was given for the slab thickness limit: d λp/50, where λp is the wavelength corresponding to the plasma frequency for a simple Drude model This appears as a significant limitation when using the mode to enhance the electrical field for absorption or non linear effect, as the volume of the active material is significantly reduced. We extend this theoretical work by considering an uniaxial anisotropic slab with ENZ properties.
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