Boundary-value problems in near-field optical microscopy and optical size resonances

Abstract

We have solved a boundary-value problem for a ball probe interacting with a flat dielectric surface in an external optical radiation field. This interaction gives rise to the optical size resonance at frequencies significantly different from the natural frequencies of two-level atoms both in the medium and in the probe with allowance for the local field corrections. These resonances depend significantly on the distance from the probe center to the surface, on the ball probe size, on the concentration of two-level atoms in the probe and in the medium, on the spectral line width, and on the atomic inversion. The field strengths inside and outside the ball probe and a semiinfinite dielectric medium have been calculated in the near-field and wave zones. It is shown that the proposed electrodynamic theory of optical near-field microscopy agrees with the results of experimental measurements.