  Propagation properties of light in optomechanical waveguides arrays (OMWAs)
are studied for the first time, to the best of our knowledge. Due to the strong
mechanical Kerr effect, the optical self-focusing and self-defocusing phenomena
can be realized in the arrays of subwavelength dielectric optomechanical
waveguides with the milliwatt-level incident powers and micrometer-level
lengths. Compared with the conventional nonlinear waveguide arrays, the
required incident powers and lengths of the waveguides are decreased by five
orders of magnitude and one order of magnitude, respectively. Furthermore, by
adjusting the deformation of the nanowaveguides through a control light, the
propagation path of the signal light in the OMWA can be engineered, which could
be used as a splitting-ratio-tunable beam splitter. This work provides a new
platform for discrete optics and broadens the application of integrated
optomechanics.
