A perturbative diffraction theory of a multilayer system: applications to near-field optical microscopy SNOM and STOM

In the last years various scanning near-field optical microscopes (SNOM) have been developed leading to images with a lateral resolution far below the Rayleigh criterion. Theoretical studies are thus necessary to model the various SNOM and for interpreting experimental data which depend strongly on experimental conditions. In this paper, we propose a global theory that we apply to complex samples (multilayers), to general tip geometries and to various SNOM configurations. Of course, the electromagnetic coupling between tip and sample is taken into account. The model is based upon a macroscopic perturbation theory for calculating the diffracted fields in a multilayer rough structure. Maxwell equations are solved in the layers by invoking the boundary conditions and the Rayleigh hypothesis. When roughnesses are small compared to the wavelength, the Fourier spectrum of diffracted fields in each layer can be related to the incident field and layers roughnesses. Some results are presented. For scanning tunneling optical microscopes (STOM) configuration we study a same sample imaged by various kinds of tips. The influences of tip height and shape on images are also shown. When the sample is coated by a metal, a plasmon resonance strongly modifies the image. We also compare images of a same sample by three different SNOM set-ups. Far-field calculated images of a sub-micron sample imaged by a nano-source transmission SNOM are also obtained.