We present an analytical approach to the calculation of the linewidth and l
ineshift of an atom or molecule in the near field of a structured dielectri
c surface. For soft surface corrugations with amplitude lambda/50, we find
variations of the linewidth in the ten percent region. More strikingly, the
shift of the molecular resonance can reach several natural linewidths. We
demonstrate that the lateral resolution is of the order of the molecule-sur
face distance. We give a semiquantitative explanation of the outcome of our
calculations that is based on simple intuitive models. (C) 1998 Elsevier S
cience B.V. All rights reserved.