We propose a new type of apertureless scanning near-field optical microscop
e based on detection of the second-harmonic signal induced by or generated
at a probe tip. We discuss the image formation in this technique and presen
t numerical studies for different experimental circumstances. In two extrem
e cases this method is shown to be the nonlinear analogue of apertureless s
canning near-field optical microscopy based on local nanoscopic fluorescenc
e or scattering. (C) 2000 Published by Elsevier Science B.V. All rights res
erved.