Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: Structure of the electromagnetic field. i

We consider the diffraction occurring when light is focused by a lens without spherical aberration through a planar interface between materials of mismatched refractive indices, which focusing produces spherical aberration. By means of a rigorous vectorial electromagnetic treatment that was previously developed for this problem [Torok et al., J. Opt. Soc. Am. A 12, 325 (1995)], the diffraction integrals are transformed into a form that is computable. Time-averaged electric energy density distributions in the region of the focused probe are numerically evaluated for air-glass and air-silicon interfaces as a function of lens numerical aperture and probe depth corresponding to a wide range of spherical aberration. Two-dimensional lateral (x -y) and meridional (x -z) electric energy density plots show how the energy, the size, and the position of the various axial and lateral maxima changed, providing new information concerning the above two important optical systems. The treatment also shows that the use of a lens without spherical aberration to focus into a second material is formally equivalent to the use of a lens with spherical aberration and a reduced solid semiangle to focus into a single material.