  Bound states in the continuum (BICs) and exceptional points (EPs) have been
the subjects of recent intensive research as they exhibit exotic phenomena that
are significant for both fundamental physics and practical applications. We
investigated the emergence of the Friedrich-Wintgen (FW) type BIC and the EP in
a dielectric waveguide comprising a metal grating, focusing on their dependence
on the grating thickness. The BIC emerges at a branch near the anti-crossing
formed of the two waveguide modes, for a grating of any thickness. With the
grating-thickness change, the anti-crossing gap varies and the branch at which
the BIC appears flips. We show that, when the slit is single mode, the BIC
appears at the crossing between the two waveguide modes in the empty-lattice
(zero slit-width) limit, while the results satisfy the criteria for the branch
at which the BIC appears in the previous reports. In addition, we find that the
EP appears near the BIC in the same device only on selecting the grating
thickness. The BIC and EP in the dielectric waveguide comprising a metal
grating, particularly with such tunability, are expected to result in the
development of functional and high-performance photonic devices in addition to
being a platform for the fundamental research of non-Hermitian systems.
