  We calculate the angular dependence of the radiation-zone output power and
electric polarization of stimulated terahertz amplified radiation (STAR)
emitted from a $dc$ voltage applied across cylindrical and rectangular stacks
of intrinsic Josephson junctions. During coherent emission, a spatially uniform
$ac$ Josephson current density in the stack acts as a surface electric current
density antenna source, leading to an harmonic radiation frequency spectrum, as
in experiment, but absent in all cavity modesl of cylindrical mesas. Spatial
fluctuations of the $ac$ Josephson current cause its fundamental mode to lock
onto the lowest finite energy cylindrical cavity mode, causing it to resonate,
leading to a non-uniform magnetic surface current density radiation source, and
a non-trivial combined fundamental frequency output power with linear
polarization We also present a model of the superconducting substrate, and
present results for rectangular mesas.
