Fig. 2. Hyperbolic polaritonic crystals (PoCs) made of a periodically perforated α-MoO₃ slab.

a Schematic of a square-lattice PoC with the thickness (t) of 235 nm. b Scanning electron microscope (SEM) image of a square-lattice PoC with the periodicity (P) of 2.3 μm and diameter (d) of 0.6 μm. Red dashed square indicates the unit cell. Scale bar, 5 μm. c Calculated isofrequency contours (IFCs) of phonon polaritons (PhPs) and Fast Fourier Transform (FFT_cal) amplitude maps of the PoC. Grey circles represent reciprocal space points. The yellow, purple, and brown curves were calculated at 840, 892, and 925 cm^–1, respectively. d Optical permittivity (ε_x) of α-MoO₃ along the x direction. Inset, simulated hyperbolic wavefronts of PhPs in the α-MoO₃ slab excited by a point dipole (black dot). Scale bar, 3 μm. e Calculated absorption coefficients of the SiO₂ substrate, the plain α-MoO₃ slab supported by SiO₂, and the PoC. Black, yellow, purple, and brown dashed lines indicate the transverse optical (TO) phonon frequency and Bragg resonance frequencies. Inset, simulated electric field distribution around a single hole (white dot) in the α-MoO₃ slab excited by a plane wave. f Simulated electric field distribution (|E|) of the Bloch mode in a unit cell at the frequency of 872 cm^–1 (marked by the magenta dashed line in (h)). Scale bar, 1 μm. g The first Brillouin zone of the square-type PoC. h Calculated band structure of the PoC. Black arrows indicate the partially opened band gaps. Grey shaded areas represent the light cones.