  In the field of cavity nano-optomechanics, the nanoresonator-in-the-middle
approach consists in inserting a sub-wavelength sized deformable resonator,
here a nanowire, in the small mode volume of a fiber microcavity. Internal
resonances in the nanowire enhance the light nanowire interaction which provide
giant coupling strengthes -- sufficient to enter the single photon regime of
cavity optomechanics -- at the condition to precisely position the nanowire
within the cavity field. Here we expose a theoretical description that combines
an analytical formulation of the Mie-scattering of the intracavity light by the
nanowire and an input-output formalism describing the dynamics of the
intracavity optical eigenmodes. We investigate both facets of the
optomechanical interaction describing the position dependent parametric and
dissipative optomechanical coupling strengths, as well as the optomechanical
force field experienced by the nanowire. We find a quantitative agreement with
recent experimental realization. We discuss the specific phenomenology of the
optomechanical interaction which acquires a vectorial character since the
nanowire can identically vibrate along both transverse directions: the
optomechanical force field presents a non-zero rotational, while anomalous
positive cavity shifts are expected. Taking advantage of the large Kerr-like
non linearity, this work opens perspectives in the field of quantum optics with
nanoresonator with for instance broadband squeezing of the outgoing cavity
fields close to the single photon level.
