Fig. 4

Natural hyperbolic materials vs. hyperbolic metamaterials. a Purcell factors and b propagation lengths for a 50 nm thick film of the TMD 2H-TaS₂ compared with a 100 nm thick hyperbolic metamaterial consisting of alternating Ag-SiO₂ films with a period of 20 nm (10 nm Ag—10 nm SiO₂). The dipole is placed a distance of h = 1 nm above the substrate. The Purcell factors were calculated using the transfer matrix method (full lines). The propagation lengths are shown for various in-plane wave vector components corresponding to wavelengths in the nanometer regime \(\left( {\lambda = 2\pi k_\parallel ^{ - 1}} \right)\)