Abstract
The super resolution effect with virtual image was discovered about ten years ago using micron-sized transparent spherical dielectric particles. However, within the range of the corresponding size parameters, the simple approximation of geometric optics is not valid. Correct description of the virtual image needs the wave theory. Here we developed a novel theoretical method based on the wave theory of virtual image formation within a transparent dielectric sphere and discussed a few unusual effects arising in the frame of the wave theory.
Highlights
The lenses of microscopes and telescopes have a characteristic size R of about centimeter scale
The super resolution effect with virtual image was discovered about ten years ago using micron-sized transparent spherical dielectric particles
We developed a novel theoretical method based on the wave theory of virtual image formation within a transparent dielectric sphere and discussed a few unusual effects arising in the frame of the wave theory
Summary
The lenses of microscopes and telescopes have a characteristic size R of about centimeter scale. It means that a typical size parameter, q = 2πR/λ, for these devices in the optical range of spectrum exceeds q >> 102 -103. Magnification M of virtual image within the dielectric sphere at q >102 follows well the geometrical optics approximation, M = n/(2-n) (here n is a refractive index) while the resolution of virtual image in a transparent sphere is restricted by diffraction limit ∆x ∼ λ/2n. In the present paper we discuss the theory, suggested in [19], in more detail, including the situations out of the limit of geometrical optics, e.g., at n → 2 where magnification has singularity, M → ∞
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