Near-field focusing of the dielectric microsphere with wavelength scale radius

We focus on physically analyzing the origins of the numerical aperture (NA) and the spherical aberration of the microsphere with wavelength scale radius. We demonstrate that the microsphere naturally has negligible spherical aberration and high NA when the refractive index contrast (RIC) between the microsphere and its surrounding medium is about from 1.5 to 1.75. The reason is due to the spherical aberration compensation arising from the positive spherical aberration caused by the surface shape of the microsphere and the RIC and the negative spherical aberration caused by the focal shifts due to the wavelength scale dimension of the microsphere. We show that, only within the approximate region of 1.5 ≤ RIC ≤ 1.75 with the proper radius r of microsphere, the microsphere can generate a near-field focal spot with lateral resolution slightly beyond λ/2ns, which is also the lateral resolution limit of the dielectric microsphere. The r for each RIC can be obtained by optimizing r from 1.125λ/n o to 1.275λ/n o. Here λ, n s, and n o are the wavelength in vacuum and the refractive indices of microsphere and its surrounding medium, respectively. For the case of the near-field focusing, we also develop a simple transform formula used to calculate the new radius from the known radius of microsphere corresponding to the original illumination wavelength when the illumination wavelength is changed.