Non-resonant subwavelength imaging by dielectric microparticles

Recently a hypothesis explaining the non-resonant mechanism of subwavelength imaging granted by a dielectric microsphere has been suggested. In accordance to the hypothesis, the far-field image of a subwavelength scatterer strongly coupled to a microsphere by near fields is offered by the scatterer polarization normal to the sphere surface. The radiation of a closely located normally oriented dipole is shaped by the microsphere so that the transmitted wave beam has a practically flat phase front. Then this beam turns out to be imaging -- keeping the subwavelength information about the dipole location. However, this mechanism of subwavelength imaging was only supposed in our previous paper. In this paper, we present a theoretical study which confirms this hypothesis and better explains the underlying physics. In several scenarios of the imaging beam evolution either a flat or a slightly diverging phase front of the hollow wave beam formed by a microsphere enables the deeply subwavelength ($0.1-0.2\lambda$) resolution of two dipole sources. We numerically simulate one of these scenarios -- that one in which the focusing lens is located closer than the Rayleigh diffraction length to the beam-forming microsphere and represents a microsphere itself. In our simulations we replace a 3D microsphere by a 2D "sphere" (microcylinder) so that to use an available electromagnetic solver for dielectric microparticles of very large optical sizes. The physical mechanism of the imaging does not suffer of this replacement.