“ Lensters ” at mm-wave frequencies

The use of capacitive metal-mesh structures on polypropylene substrates is routinely used in far infrared astronomy for the purpose of spectral low-pass filtering. The transmission of these filters well below their cut-off frequency follows the well known behavior of a Fabry-Perot etalon due to the fairly achromatic nature and finite thickness of the embedding substrate. We show how it is possible to reproduce to a good level of precision, the predicted transmission of an embedded stack of layers of a given square-geometry using Transmission Lines when compared to HFSS simulations. We then use the Fabry-Perot etalon model to invert their spectral behavior to extract an effective index of refraction corresponding to the mesh geometry and device thickness. This injective mapping allowed us to design a Gradient Index lens based on a fixed spacing (or grid) while varying the mesh filling factor. Measurements of such a flat lens-filter (or lenster) are shown.