Green’s function formulation for third-harmonic generation microscopy

We report a theoretical study of third-harmonic generation (THG) microscopy by use of a Green’s function formulation. The third-harmonic signal under a tight-focusing condition is calculated for samples with various shapes and sizes. Our results show that THG signals can be efficiently generated at a sizable interface perpendicular or parallel to the optical axis or from a small object with a size comparable to the width of the axial excitation intensity profile. The signal-generation mechanism of THG microscopy is explained by a modified phase-matching condition, uk3 2 3(k1 1 Dkg)ul ! p, where Dkg is the wave vector mismatch induced by the Gouy phase shift of the focused excitation field. The relation of the THG power and radiation pattern to the orientation of an interface is investigated. A comparison between signal generation in THG microscopy and that in coherent anti-Stokes Raman scattering microscopy is given. © 2002 Optical Society of America OCIS codes: 190.4160, 180.5810, 180.6900, 190.4380.