Self-consistent model for second-harmonic near-field microscopy

A macroscopic self-consistent approach that allows one to describe image formation rigorously in second-harmonic (SH) scanning near-field optical microscopy is developed. The SH held is determined by taking consistently into account both the linear and nonlinear contributions in the effective current, i.e., the currents generated by the self-consistent fields at the fundamental frequency (FF) and SH frequency. The self-consistent problem for both frequencies is solved exactly with a new approach to the determination of the Green dyadic of the system. General expressions for the FF and SH fields are obtained in terms of the effective susceptibility of the probe-object system. Image formation in the illumination SH near-field microscopy is considered within the framework of the approach developed. Near-field optical FF and SH images are calculated for different polarization configurations and parameters of a rectangular object with nonlinear susceptibility We show that the polarization selection rules used in conventional (far-field) SH experiments cannot be applied for SH near-field microscopy and that the SH signal detected in the forbidden polarization configurations may become comparable with the signal in the allowed configurations.