  Photonic bound states in the continuum (BICs) are eigenmodes with an infinite
lifetime, which coexist with a continuous spectrum of radiating waves. BICs are
not only of great theoretical interest, but have a wide range of practical
applications, e.g. in the design of optical resonators. Here, we study this
phenomenon in a new integrated nanophotonic element consisting of a single
dielectric ridge terminating an abruptly ended slab waveguide. This structure
can be considered as an on-chip analogue of the Gires-Tournois interferometer
(GTI). We demonstrate that, in contrast to the conventional GTI, the proposed
integrated structure supports high-Q phase resonances and "conditional" BICs.
We develop a simple but extremely accurate coupled-wave model, which clarifies
the physics of the BIC formation and enables predicting their locations. We
show that the studied BICs are topologically protected and, for the first time,
investigate the strong phase resonance effect, which occurs when two BICs with
opposite topological charges annihilate.
