  We propose sub-harmonic resonant optical excitation with femtosecond lasers
as a new method for the characterization of phononic and nanomechanical systems
in the gigahertz to terahertz frequency range. This method is applied for the
investigation of confined acoustic modes in a free-standing semiconductor
membrane. By tuning the repetition rate of a femtosecond laser through a
sub-harmonic of a mechanical resonance we amplify the mechanical amplitude,
directly measure the linewidth with megahertz resolution, infer the lifetime of
the coherently excited vibrational states, accurately determine the system's
quality factor, and determine the amplitude of the mechanical motion with
femtometer resolution.
