  Bound states in the continuum (BICs) are localized states existing within a
continuous spectrum of delocalized waves. Emerging multilayer photonic
integrated circuit (PIC) platforms allow implementation of low index 1D guided
modes within a high-index 2D slab mode continuum; however, conventional wisdom
suggests that this always leads to large radiation losses. Here we demonstrate
low-loss BIC guided modes for multiple mode polarizations and spatial orders in
single- and multi-ridge low-index waveguides within a two-layer heterogeneously
integrated electro-optically active photonic platform. The transverse electric
(TE) polarized quasi-BIC guided mode with low, <1.4 dB/cm loss enables a
Mach-Zehnder electro-optic amplitude modulator comprising a single straight
Si3N4 ridge waveguide integrated with a continuous LiNbO3 slab layer. The
abrupt optical transitions at the edges of the slab function as compact and
efficient directional couplers eliminating the need for additional components.
The modulator exhibits a low insertion loss of 2.3 dB and a high extinction
ratio of 25 dB. The developed general theoretical model may enable innovative
BIC-based approaches for important PIC functions, such as agile spectral
filtering and switching, and may suggest new photonic architectures for quantum
and neural network applications based on controlled interactions between
multiple guided and delocalized modes.
