  We designed and simulated freestanding dielectric optical metasurfaces based
on arrays of etched nanoholes in a silicon membrane. We showed $2\pi$ phase
control and high forward transmission at mid-infrared wavelengths by tuning the
dimensions of the holes. We also identified the mechanisms responsible for high
forward scattering efficiency and showed that these conditions are connected
with the well-known Kerker conditions already proposed for isolated scatterers.
A beam deflector was designed and optimized through sequential particle swarm
and gradient descent optimization to maximize transmission efficiency and
reduce unwanted grating orders. Such freestanding silicon nanohole array
metasurfaces are promising for the realization of silicon based mid-infrared
optical elements.
