  We examine the mechanical eigenmodes of a quartz tuning fork (QTF) for the
purpose of facilitat- ing its use as a probe for multi-frequency atomic force
microscopy (AFM). We perform simulations based on the three-dimensional finite
element method (FEM) and compare the observed motions of the beams with
experimentally measured resonance frequencies of two QTF systems. The com-
parison enabled us to assign the first seven asymmetric eigenmodes of the QTF.
We also find that a modified version of single beam theory can be used to guide
the assignment of mechanical eigen- modes of QTFs. The usefulness of the QTF
for multi-frequency AFM measurements is demonstrated through photo-induced
force microscopy (PiFM) measurements. By using the QTF in different con-
figurations, we show that the vectorial components of the photo-induced force
can be independently assessed, and that lateral forces can be probed in true
non-contact mode.
