Analysis of imaging properties of a microlens based on the method for a dyadic Green's function

The dyadic Green's function (DGF) is applied to examine the effect of focal shift in a spherical microlens with the variation of the numerical aperture for a given Fresnel number when a monochromatic plane wave with x linear polarization is incident on the microlens. By comparing the results based on the method for the vector Kirchhoff diffraction theory [J. Opt. Soc. Am. A22, 68-76 (2005)], the effect of the spherical aberration on focal shift in a microlens is evaluated, and the influences of NA as well as the spherical aberration on the transverse electric energy density distribution in the focal plane are also investigated. In contrast with other vector formulations of imaging theory, which mainly focus on the focal shift in an aplanatic system, the DGF method is more practical and effective to locate the principal maximum energy density along the normal axis and to study transverse electric energy density distribution, because the actual shape of a microlens and the effects of aberrations are considered.