Fig. 3.

Geometry-invariant effects in ENZ thermal emission. (A) Sketch of the geometry and emission pattern at the ENZ wavelength, and (B) absorption cross-section for an incident plane-wave $\mathit{H}\left(\mathbf{r}\right)=\widehat{\mathit{z}}{H}_0\exp \left[-i{\omega }_{\text{ENZ}}\left(t-\widehat{y}\cdot \mathbf{r}/\text{c}\right)\right]$, corresponding to thermal emission in the −$\widehat{y}$ direction. The 2D geometry consists of a dielectric rod with three different cross-sections of area ${\lambda }_{\text{ENZ}}^2$ containing a germanium dielectric rod (${\epsilon }_{\text{Ge}}\approx 16$) of radius $r_p=0.096\hspace{0.17em}{\lambda }_{\text{ENZ}}$. Right triangle cross-section with catheti of length ${\lambda }_{\text{ENZ}}$ and $2{\lambda }_{\text{ENZ}}$ (black line), square cross-section of side ${\lambda }_{\text{ENZ}}$ (blue line), and $0.5{\lambda }_{\text{ENZ}}\times 2{\lambda }_{\text{ENZ}}$ rectangle cross-section (black line). The numerical results evidence geometry-invariant effects (a resonant spectral feature is observed at the same resonance frequency independently of the geometry of the external boundary keeping the same cross-sectional area) and beamforming capabilities (the emission patterns consist of one lobe per side of the body with emission strength proportional to the side of the triangle).