Resolution and polarization in apertureless near-field microscopy

We present numerical calculations of the electromagnetic fields produced ar ound a sharp metal tip held above a dielectric surface and illuminated from above by visible light. This geometry is that of an apertureless near-fiel d scanning optical microscope (A-NSOM). The electric fields produced by irr adiation are calculated using a real-space Green's function technique, also known as the frequency-domain method of moments. We investigate numericall y the convergence properties of this method with respect to the grid size u sed to discretize the equations and find that the usual criterion invoked t o ensure convergence does not apply inside small metallic scatterers; for t his reason, the fields near the border of the tip keep changing as we make the grid smaller and smaller. Although the calculations do not show converg ence (for the intensity of the fields near the borders of the probe), the i ntensity and the polarization of the field in other regions of space are co nverged; they do not change as the grid spacing is made smaller. When the t ip is five nanometers above a flat dielectric surface the field under the t ip is strongly enhanced in a region having a diameter of five nanometers, e ven though the end of the tip has lateral dimensions of order ten nm. The l ight intensity falls off rapidly as the tip-surface separation is increased and the region where the field is enhanced becomes larger. This implies th at illuminating very small areas with this device requires very good contro l of the tip height. Most of the results presented here are for an Al tip, but we have also performed calculations for tips made of sapphire, gold, si lver, and tungsten. For all probes, the field localization, and hence the N SOM resolution, depends only weakly on the tip composition, whereas the mag nitude of light intensity enhancement is strongly dependent on the dielectr ic properties of the tip. When the probe is very close to the surface, givi ng the best lateral resolution, the spatial variation of the electric field near the surface is quite complicated, and is different for different comp onents of the electric field vector; the polarization of the field under th e tip is not the same as the polarization of the incident far field or that of the field in the absence of the tip. Regardless of the incident polariz ation, the tip tends to make the induced electric field perpendicular to th e substrate. Moreover, different components of the field have different spa tial distributions; knowing the orientation of the field creates the possib ility of deducing the orientation of molecules adsorbed on the surface. (C) 2001 American Institute of Physics.