Multipolar propagators near a corrugated surface: Implication for local-probe microscopy

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Abstract
The response field of a nonplanar surface to a fluctuating multipolar moment is obtained from two different approaches within the quasistatic approximation. In the first one, a continuous picture of matter is used, and the dynamic character of the substrate is included in the bulk local dielectric constant of the solid. The second method is based on a discrete description of matter in which the surrounding dielectric is introduced from a self-consistent matrix equation. The response field and the corresponding field gradients are then used for defining a general expression of the nth-order multipolar propagator between two points outside the corrugated surface of a solid body. In the case of a continuous description, corrections to the results for a perfectly planar surface are derived in terms of the Fourier transform of the topography function limiting the surface. We show how the multipolar response functions can be used to express in a very compact form various physical effects relevant in experimental situations (physisorption energy, dispersion attractive force, scattered intensity, etc.) Finally, the continuum model is used to discuss the structure sensitivity of the atomic-force microscope in the attractive range.