  We theoretically and experimentally demonstrate a multifrequency excitation
and detection scheme in apertureless near field optical microscopy, that
exceeds current state of the art sensitivity and background suppression. By
exciting the AFM tip at its two first flexural modes, and demodulating the
detected signal at the harmonics of their sum, we extract a near field signal
with a twofold improved sensitivity and deep sub-wavelength resolution,
reaching $\lambda/230$. Furthermore, the method offers rich control over
experimental degrees of freedom, expanding the parameter space for achieving
complete optical background suppression. This approach breaks the ground for
non-interferometric complete phase and amplitude retrieval of the near field
signal, and is suitable for any multimodal excitation and higher harmonic
demodulation.
