Fig. 2: Gradient effective refractive indices enabled by dielectric environment engineering.
From: A lithography-free approach to polaritonic Luneburg lenses
a Calculated dispersion relations of phonon polaritons in air/hBN/SiO2 and PMMA/hBN/SiO2 three-layer structures. Insets show simulated field distributions at the frequency (ω) of 1500 cm−1, with the hBN slab thickness (dhBN) set to 50 nm. b Polariton momentum (q) and effective refractive index (neff) as a function of PMMA thickness (dPMMA) in an air/PMMA/hBN/SiO2 four-layer structure. Inset shows the gradually decreasing polariton wavelengths across a PMMA taper. c Calculated neff as a function of dPMMA at different frequencies. d Tuning neff through adjustments in both dhBN and dPMMA. Dependence of the maximum refractive index (\({n}_{{{{\rm{eff}}}}}^{\max }\)) on the dielectric permittivities of the dielectric layer (εdl, e) and the substrate (εsub, f), under the approximation of the infinite dielectric layer thickness \(\left({d}_{{{{\rm{dl}}}}}\to {\infty }\right)\). Red curves respectively indicate the dielectric permittivities of PMMA (εPMMA) and SiO2 (\({\varepsilon }_{{{{\rm{Si}}}}{{{{\rm{O}}}}}_{2}}\)) employed in theoretical analysis.
