Figure 1. Frequency-dependent directional angles of the hyperbolic polaritons propagating inside the hBN.

Solid lines in (a,b) the critical angle θ of the HPs as a function of the frequency ω in the Type-I (760<ω<825 cm⁻¹, ɛ_t>0 and ɛ_z<0) and Type-II (1,360<ω<1,610 cm⁻¹, ɛ_t<0 and ɛ_z>0) hyperbolic bands of the hBN. (c–h) Simulated electric-field distribution (|E_z|) at various frequencies. The directional angles evaluated from these simulations are plotted in a,b (colour dots) for comparison: θ=16° (c, at ω=761 cm⁻¹), θ=2° (f, at ω=1,613.8 cm⁻¹), θ=45° (d,g; at ω=778.2 cm⁻¹ and ω=1,527 cm⁻¹) and θ=60° (e,h; at ω=795 cm⁻¹ and ω=1,459.6 cm⁻¹). Scale bar, 1 μm (c).