Composite near-field superlens design using mixing formulas and simulations

Abstract

A slab with permittivity $-1$, relative to the environment, can be used as a near-field superlens (NFSL) for one polarization. To design a NFSL for any chosen visible wavelength, we investigate periodic silver–dielectric composites with effective permittivity close to $-1$. The initial design choices are based on the Maxwell Garnett mixing formula, and these are further refined using a combination of the Rayleigh formula and the Drude model for the complex permittivity of silver. The most promising composite turns out to be a silver slab with cylindrical air-holes occupying a volume fraction between 35 and 73%, which covers the whole visible range from 400 to 700 nm. The quasistatic accuracy of the predicted effective permittivity is verified using an accurate analytical solution, and the superlensing effect is demonstrated for one composite NFSL setup for violet light using numerical simulations. Finally, the correction required by nanoscale size effects on the permittivity function of silver is taken into consideration and its effect on the performance of the composite lens is estimated.