  Recently, metasurfaces have gained popularity due to their ability to offer a
spatially varying phase response, low intrinsic losses and high transmittance.
Here, we demonstrate numerically and experimentally a silicon metasurface at
THz frequencies that converts a Gaussian beam into a Vortex beam independent of
the polarization of the incident beam. The metasurface consists of an array of
sub-wavelength silicon cross resonators made of a high refractive index
material on substrates such as sapphire and CaF$_2$ that are transparent at
IR-THz spectral range. With these substrates, it is possible to create phase
elements for a specific spectral range including at the molecular finger
printing around 10$~\mu$m as well as at longer THz wavelengths where secondary
molecular structures can be revealed. This device offers high transmittance and
a phase coverage of 0 to $2\pi$. The transmittance phase is tuned by varying
the dimensions of the meta-atoms. To demonstrate wavefront engineering, we used
a discretized spiraling phase profile to convert the incident Gaussian beam to
vortex beam. To realize this, we divided the metasurface surface into eight
angular sectors and chose eight different dimensions for the crosses providing
successive phase shifts spaced by $\pi/4$ radians for each of these sectors.
Photolithography and reactive ion etching (RIE) were used to fabricate these
silicon crosses as the dimensions of these cylinders range up to few hundreds
of micrometers. Large 1-cm-diameter optical elements were successfully
fabricated and characterised by optical profilometry.
