Focusing by a single lens based on an optically thinner medium

Abstract

This paper investigates the focusing properties by a single lens, based on the optically thinner medium (OTM). The lens model is of a plano-concave shape, made from the OTM with a refractive index of 0.5 at the wavelength λ=6.328e-4mm, named the plano-concave OTM thick lens. Any geometrical approximation is not included in the deducing process, which ensures that the full geometrical aberrations are included. The intensity distribution, in its focal region, can be calculated by the Huygens-Fresnel integral formula, using the phase and intensity distributions on the reference plane. The on-axis intensity distribution in the focal region of the plano-convex optically denser medium (ODM) thick lens is given correctly. The intensity distribution in the focal region of the plano-concave OTM thick lens is plotted in two dimensions, no symmetry about the focal plane. The plano-concave OTM thick lens has smaller on-axis spherical aberration than the plano-convex ODM thick lens has, when they have the same aperture radius, equal curvature radius (not including the sign), and equal medium index difference quantity (not including the sign also) from the environmental medium air. The radial resolution, around the near end peak in the focal region of the plano-concave OTM thick lens with its total spherical aberration, breaks down the traditional diffraction limit. Therefore the planoconcave OTM thick lens will exhibit its practical super resolution abilities, if the diffraction focused spot can be filtered off, or further more if the energy outside the near end peak can be moved into it.