Figure 3. Absorptivity of the metamaterial versus incidence angle.

Simulated absorptivity of the tungsten/hafnium dioxide metamaterial described in Fig. 2 as a function of wavelength of incident light and as a function of the angle of incidence, taking into account both s- and p- polarizations. The simulation is performed using the transfer matrix formalism assuming optical properties of tungsten from Roberts⁵², and that hafnium dioxide can be treated as a dispersionless dielectric with a relative dielectric constant of 3.88. The figure shows that the designed topological transition produces largely angularly independent thermal absorptivity up to the blackbody limit (white region in the colour plot) over a narrow spectral bandwidth suited to use with low-bandgap photovoltaic cells³³,³⁴,³⁵,³⁶. According to Kirchhoff's law and since the transmission through the metamaterial stack is negligible, the expected emissivity is considered identical to the calculated absorptivity. Because of the low coupling of modes between vacuum and hyperbolic regime of the metamaterial thermal radiation in the mid-infrared is strongly suppressed. Note that our approach is fundamentally different from structural resonances in metasurfaces and bandgap effects in photonic crystals.