Quantum theory and virtual photon model of near-field optics

We point out that recent experimental results exemplify the need for quantum theoretical treatment of optical near-field problems, as well as the need for an intuitive model that provides clear insights into near-field optical systems. In this context, the virtual photon model as an intuitive model is discussed, and a quantum theoretical formulation of an optical near-field system is proposed on the basis of the projection-operator method. Special attention is paid to nanometric probe tip and quantum-mechanical sample systems such as atoms, molecules, and quantum dots. The effective probe tip-sample interaction is derived from the microscopic viewpoint; this interaction is essential for describing such phenomena as atom guidance and manipulation, or local excitation of a single quantum dot. The relationship to the virtual photon model is also discussed by focusing on the latter's empirical assumption of Yukawa-type interaction between the probe tip and sample. The key points are that a probe tip exists near the sample, and that the electron energies in the probe tip or sample are inversely proportional to the square of its size, owing to the confinement effect. Several applications and the future prospects of our theory are also briefly outlined.