  Non-Hermitian (NH) photonics has attracted considerable attention from
researchers owing to exotic properties that originate from the parity-time
($\mathcal{PT}$) phase transition and exceptional points (EPs). To date, the
$\mathcal{PT}$ phase transition, EPs, and circling around EPs have been
investigated in many photonic systems. However, few studies focused on the
singular nature of the EP eigenstates of the Hamiltonian matrices. Moreover,
the switching of an EP eigenstate based on the sign of the coupling constant
and its manifestation in physical phenomena have not yet been investigated. In
this paper, we propose and numerically demonstrate a unidirectional radiation
phenomena manifested by the formation of Huygens dipoles using the singular EP
eigenstates in coupled plasmonic systems. Two types of EPs corresponding to
positive and negative signs of the coupling constants are realized using
dipole-dipole coupling. We show that the Huygens dipole is formed at the EP
condition and its radiation direction can be controlled by choosing the sign of
the coupling. The unique photonic functionality, which originates directly from
the singular eigenstate at the EP uncovers a new aspect of NH photonic physics
and devices.
