  Optical near-fields of small dielectric particles are of particular
importance and interests for nanoscale optical engineering such as field
localization, fabrication, characterization, sensing and imaging. This paper
represents a systematic investigation on the focusing characteristics (focal
length, field enhancement, spot size) for a given refractive-index microsphere
(n=1.6) with a varying size parameter across the range of pi<q0<20*pi.
Conditions for super-resolution foci were analysised in details. Particularly
strong super-resolution foci with spot size falling at least 50% below the
diffraction limit were identified and possible new applications were suggested.
To understand how the super-resolution conditions could be scaled to other
refractive-index particles or background medium, principles of field-invariant
parameters scaling (size, wavelength, and refractive index) were revealed and
demonstrated with example cases. It offers the new freedom to choose particles
and background medium to gain super-resolution at any frequency across the
whole electromagnetic spectrum.
