Anisotropic Response in Metamaterials with Elliptically Perforated Plates: Applications to Near-Field Radiative Heat Transfer

TL;DR

The paper addresses how to engineer anisotropy in metamaterial plates to control near-field radiative heat transfer (NFRHT) by perforating slabs with elliptical cylinders. It develops a Maxwell-Garnett-type effective medium theory to obtain a biaxial dielectric tensor and uses fluctuational electrodynamics to compute NFRHT between two such slabs, exploring dependence on ellipse eccentricity $e$, orientation, filling fraction $f$, and gap $L$. Key findings show that increasing $e$ broadens Reststrahlen-band resonances and can enhance the total heat flux up to an optimal eccentricity due to anisotropy-induced modal overlap, with high $e$ causing saturation and dilution effects; the orientation and anisotropy enable directional control of heat transfer. The framework is applicable to realistic pore sizes ($a imes a ightarrow 50$–$60$ nm) and separations ($L ightarrow 100$ nm), offering a practical route to directional thermal metamaterials and anisotropic thermal management at the nanoscale.

Abstract

Metamaterials with tunable optical properties provide a versatile platform for controlling electromagnetic interactions at the nanoscale. This study explores the anisotropic thermal behavior of metamaterials composed of planar plates perforated with periodic arrays of cylinders possessing elliptical cross sections. In contrast to conventional circular perforations, elliptical geometries inherently break rotational symmetry, introducing anisotropy in the effective electromagnetic and thermal response of the structure. Using a fluctuation electrodynamics framework combined with full-wave numerical simulations, we quantify the near-field radiative heat transfer between such elliptically perforated plates as a function of ellipse orientation, aspect ratio, and separation distance. The results reveal that elliptical perforations enable enhanced spectral and directional control of evanescent mode coupling and surface polariton excitation, leading to significant modulation of the near-field heat flux. These findings highlight the potential of geometrically engineered anisotropy for advanced thermal management and energy conversion applications, and offer new design strategies for the development of thermally functional metamaterials operating in the near-field regime.

Figures (9)

• Figure 1: Schematics of the system under study, including a front view of the slabs. Two parallel slabs with parallel perforations that can be of circular cross section or elliptical cross section. The cylinders are randomly placed and occupy a volume fraction $f$. The angle $\phi$ is measured with respect the $y$ axis, as indicated.
• Figure 2: The real (top) and imaginary parts (bottom) of the effective dielectric function of a slab along the $x$ and $y$ axes, with cylindrical perforation of different eccentricity. The slab is made of SiC and the holes are empty (air). The frequency is normalized to $\omega_0=10^{14}$ rad$\cdot$s$^{-1}$. The perforations are assumed to be randomly distributed.
• Figure 3: Anisotropy of the dielectric function $\Delta_{\epsilon}=|\epsilon_{xx}-\epsilon_{yy}|$ as a function of frequency for different filling fractions and at a fixed eccentricity of $e=0.67$. As the value of $f$ decreases the anisotropy also decreases.
• Figure 4: Transmission coefficient for two parallel slabs with cylinders of circular cross section. (a) SiC with no holes $f=0$ and (b) with circular cylinders and volume fraction $f=0.1$. The perforations are assumed to be randomly distributed.
• Figure 5: Spectral heat flux $S_{\omega}$ for SiC slabs ($f=0$) and for perforated slabs with the same filling fraction of $f=0.1$ but different cross section circular (dashed line), elliptical with $e=0.67$ solid line and $e=0.8$ long-dashed line. The separation between the plates is $L=100$ nm. The perforations are assumed to be randomly distributed.