Focusing by a single lens based on an optically thinner medium

摘要

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 refractive index 0.5 at wavelength λ=6.328e-4mm, named the plano-concave OTM thick lens. Any geometrical approximation is not included in deducing, which ensures that the full geometrical aberrations are included. The intensity distribution, in its focal region, can be calculated by Huygens-Fresnel integral, 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 geometrical focal plane. The plano-concave OTM thick lens has smaller focal depth 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 half width at the full maximum(HWFM) of the radial intensity distribution, on the near end peak plane in the focal region of the planoconcave OTM thick lens with its total spherical aberration, is smaller than that of the Airy disk and breaks down the traditional diffraction limit. Therefore the plano-concave OTM thick lens will exhibit its focusing ability breaking down the traditional diffraction limit, if the energy outside the near end peak can be moved into it.