  Any dielectric lens has a finite closed boundary and therefore is, in fact,
an open dielectric resonator capable of supporting resonant modes whose
Q-factor depends of the lens parameters (size, shape, and material). The
hemielliptic lens, that is an essential building block of many mm-wave and THz
antennas, is not an exception: it supports the so-called halfbowtie (HBT)
resonances that can strongly affect performance of such antennas. In this paper
we illustrate the interplay between the optical and modal features in the
electromagnetic behaviour of hemielliptic lenses and highlight the drastic
influence of the HBT resonances on radiation characteristics of lens antennas.
We also discuss the difficulties associated with accurate description of the
resonant phenomena in compact-size hemielliptic lenses with conventional
techniques and provide recommendations on how to minimize the parasitic impact
of HBT resonances on the antenna performance.
