  Transformation optics methods and gradient index electromagnetic structures
rely upon spatially varied arbitrary permittivity. This, along with recent
interest in millimeter-wave lens-based antennas demands high spatial resolution
dielectric variation. Perforated media have been used to fabricate gradient
index structures from microwaves to THz but are often limited in contrast. We
show that by employing regular polygon unit-cells (hexagon, square, and
triangle) on matched lattices we can realize very high contrast permittivity
ranging from 0.1-1.0 of the background permittivity. Silicon micromachining
(Bosch process) is performed on high resistivity Silicon wafers to achieve a
minimum permittivity of 1.25 (10% of Silicon) in the WR28 waveguide band,
specifically targeting the proposed 39 GHz 5G communications band. The method
is valid into the THz band.
