  A broadband opto-mechanical phase shifter for photonic integrated circuits is
proposed and numerically investigated. The structure consists of a
mode-carrying waveguide and a deformable non-mode-carrying nanostring, which
are parallel with each other. Utilizing the optical gradient force between
them, the nanostring can be deflected. Thus the effective refractive indices of
the waveguide is changed with the deformation, and further causes a phase
shift. The phase shift under different geometry sizes, launched powers and
boundary conditions are calculated and the dynamical properties as well as the
thermal noise's effect are also discussed. It is demonstrated that a $\pi$
phase shift can be realized with only about 0.64 mW launched power and 50 $\mu
m$ long nanostring. The proposed phase shifter may find potential usage in
future investigation of photonic integrated circuits.
