Fig. 1. Focusing of in-plane hyperbolic PhPs.

(A) IR dielectric function of α-MoO₃ for the hyperbolic reststrahlen band studied in this work (shaded region). (B) IFC of in-plane hyperbolic PhPs in a 165-nm-thick α-MoO₃ slab at an illuminating wavelength λ₀ = 11.05 μm. PhPs with high-|$\overrightarrow{k}$| wave vectors are indicated by ${\overrightarrow{k}}_{\mathrm{H}}$, together with their Poynting vector $\overrightarrow{S}$. (C) Color plot (z component of the Dyadic Green’s function) for the density of electromagnetic modes in k-momentum space (k_x, k_y) generated by a point dipole on α-MoO₃ (λ₀ = 11.05 μm). The dashed yellow line represents the pattern of the field emitted by the dipole as a function of the polar angle. (D) Near field, |E_z|, calculated analytically for two vertical point dipoles on α-MoO₃. A focal spot is obtained upon interference of ray-like PhPs with ${\overrightarrow{k}}_{\mathrm{H}}$ wave vectors (dashed circle). (E) Simulated near field, Re(E_z), produced by a metal Au disk nanoantenna: The excitation and interference of PhPs with ${\overrightarrow{k}}_{\mathrm{H}}$ wave vectors lead to a focal spot (yellow dashed circle). The right inset shows the analogous case for an in-plane isotropic medium using a rod-like metal nanoantenna with a concave extremity. The left inset shows the electric field amplitude, |E_z|², along the dashed red line (normalized to the intensity at the white cross). (F) Simulated near field, Re(E_z), for a discrete distribution of point electric dipoles localized along the periphery of a virtual disk: A convex interference pattern and focal spot (cyan dashed circle) are revealed, resembling the results obtained in (E).