  We propose tunable nonlinear antennas based on an epsilon-near-zero material
with a large optical nonlinearity. We show that the absorption and scattering
cross sections of the antennas can be controlled dynamically from a nearly
superscatterer to a nearly superabsorber by changing the intensity of the laser
beam. Moreover, we demonstrate that a hybrid nonlinear antenna, composed of
epsilon-near-zero and high-index dielectric materials, exhibits nonreciprocal
radiation patterns because of broken spatial inversion symmetry and large
optical nonlinearity of the epsilon-near-zero material. By changing the
intensity of the laser, the radiation pattern of the antenna can be tuned
between a bidirectional and a unidirectional emission known as a Huygens
source. Our study provides a novel approach toward ultrafast dynamical control
of metamaterials, for applications such as beam steering and optical limiting.
