Observation of accurately designed bound states in the continuum in momentum space

Bound states in the continuum(BICs) in artificial photonic structures have received considerable attention since they offer unique methods for the extreme field localization and enhancement of light-matter interactions.Usually, the symmetry-protected BICs are located at high symmetric points, while the positions of accidental BICs achieved by tuning the parameters will appear at some points in momentum space. Up to now, to accurately design the position of the accidental BIC in momentum space is still a challenge. Here, we theoretically and experimentally demonstrate an accurately designed accidental BIC in a two-coupled-oscillator system consisting of bilayer gratings, where the optical response of each grating can be described by a single resonator model. By changing the interlayer distance between the gratings to tune the propagation phase shift related to wave vectors,the position of the accidental BIC can be arbitrarily controlled in momentum space. Moreover, we present a general method and rigorous numerical analyses for extracting the polarization vector fields to observe the topological properties of BICs from the polarization-resolved transmission spectra. Finally, an application of the highly efficient second harmonic generation assisted by quasi-BIC is demonstrated. Our work provides a straightforward strategy for manipulating BICs and studying their topological properties in momentum space.