Resolution and polarization in apertureless near-field microscopy

Abstract

We present numerical calculations of the electromagnetic fields produced around a sharp metal tip held above a dielectric surface and illuminated from above by visible light. This geometry is that of an apertureless near-field scanning optical microscope (A-NSOM). The electric fields produced by irradiation are calculated using a real-space Green’s function technique, also known as the frequency-domain method of moments. We investigate numerically the convergence properties of this method with respect to the grid size used to discretize the equations and find that the usual criterion invoked to ensure convergence does not apply inside small metallic scatterers; for this 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 convergence (for the intensity of the fields near the borders of the probe), the intensity and the polarization of the field in other regions of space are converged; they do not change as the grid spacing is made smaller. When the tip is five nanometers above a flat dielectric surface the field under the tip is strongly enhanced in a region having a diameter of five nanometers, even though the end of the tip has lateral dimensions of order ten nm. The light intensity falls off rapidly as the tip–surface separation is increased and the region where the field is enhanced becomes larger. This implies that illuminating very small areas with this device requires very good control 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, silver, and tungsten. For all probes, the field localization, and hence the NSOM resolution, depends only weakly on the tip composition, whereas the magnitude of light intensity enhancement is strongly dependent on the dielectric properties of the tip. When the probe is very close to the surface, giving the best lateral resolution, the spatial variation of the electric field near the surface is quite complicated, and is different for different components of the electric field vector; the polarization of the field under the 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 polarization, the tip tends to make the induced electric field perpendicular to the substrate. Moreover, different components of the field have different spatial distributions; knowing the orientation of the field creates the possibility of deducing the orientation of molecules adsorbed on the surface.