Virtual resonance and frequency difference generation by van der waals interaction

The ability to explore the interior of materials for the presence of inhomogeneities was recently demonstrated by mode synthesizing atomic force microscopy. Proposing a semiempirical nonlinear force, we show that difference frequency ω_- generation, regarded as the simplest synthesized mode, occurs optimally when the force is tuned to van der Waals form. From a parametric study of the probe-sample excitation, we show that the predicted ω_- oscillation agrees well with experiments. We then introduce the concept of virtual resonance to show that probe oscillations at ω_- can efficiently be enhanced.