Low-Permittivity Core Design Rule and Thermal Switching of Negative Refractive Index in Metal-Insulator-Metal Waveguides at Visible Wavelengths

Metal-insulator-metal (MIM) waveguides supporting backward-wave surface plasmon polariton modes can achieve negative effective refractive index at visible wavelengths. Prior theoretical work by Dionne et al. (2006) established Ag/GaP/Ag (core permittivity ~11) as the benchmark geometry, predicting a figure of merit (FOM) of ~20 using an idealized Drude silver model. Here we show that when experimentally measured Ag di- electric data from Johnson and Christy (1972) is used, which includes interband absorp- tion absent from Drude models, the optimal core material changes qualitatively. Low- permittivity cores such as Si3N4 (permittivity ~4.0) outperform high-permittivity cores (GaP, permittivity ~10.86) by a factor of 32 in FOM. The root cause is that interband losses in real silver narrow the spectral margin over which the SPP resonance condition is satisfied for high-permittivity cores. We map the full MIM design space (8 core di- electrics, 10 thicknesses, 2 metals) and identify Ag/Si3N4/Ag at d = 15 nm as the optimal non-switchable configuration (FOM = 8.33 at 380 nm). We further demonstrate thermally switchable negative refractive index by incorporating VO2, a phase-change material with a metal-insulator transition at 68 degrees C, into the core. An Ag/Si3N4/VO2/Si3N4/Ag hybrid at d = 12 nm with 50% VO2 volume fraction achieves FOM = 3.07 at 525 nm in the insulating state, with complete suppression of the negative-index mode in the metallic state – the first predicted switchable negative-index MIM device at visible wavelengths. All results employ exclusively published experimental dielectric functions.