Low Profile GRIN Lenses With Integrated Matching Using 3-D Printed Ceramic

In this paper, we investigate a shortened horn antenna with high gain that is enabled by a 3D-printed gradient index (GRIN) lens composed of high permittivity zirconia
$(ZrO_{2})$
. The baseline H-plane sectoral horn antenna is designed with length that is 1/3 of the optimal horn antenna and exhibits a low gain due to the high flaring rate of the horn. Increased gain is achieved by adding a flat GRIN lens at the horn aperture. High permittivity
$ZrO_{2}\,\,(\varepsilon _{r} = 23)$
enables lens miniaturization; however, when interfaced with air, reflections at the air interface increase the impedance mismatch. Two different methods for mitigating the reflections are studied. One is a simple
$\lambda /4$
matching layer that matches the bulk permittivity of
$ZrO_{2}$
to air. As expected, the
$\lambda /4$
layers reduce the reflections in part of the 13–18 GHz band but produce high reflection in other parts. The second approach is a GRIN lens with integrated tapered matching layer to match phase and impedance simultaneously. Three tapering methods are studied (exponential, Klopfenstein, linear) for impedance matching. Analytical expressions of the minimum thickness and permittivity distribution are derived. The lens is discretized for print and three types of unit cells are proposed to create a wide range of permittivities ranging from bulk ceramic to air. A
$ZrO_{2}$
lens prototype printed with an XJet Carmel 1400 is measured and results show good agreement with simulations, including gain performance equivalent to a horn of 2.4x longer length. The measured gain and beamwidth of the lens are 5.4dB higher and 52° narrower than those of the shortened horn alone at 15 GHz, respectively.