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.

Optical bound states in the continuum (BICs) have recently stimulated a research boom, accompanied by demonstrations of abundant exotic phenomena and applications. With ultrahigh quality (Q) factors, optical BICs have powerful abilities to trap light in optical structures from the continuum of propagation waves in free space. Besides the high Q factors enabled by the confined properties, many hidden topological characteristics were discovered in optical BICs. Especially in periodic structures with well-defined wave vectors, optical BICs were discovered to carry topological charges in momentum space, underlying many unique physical properties. Both high Q factors and topological vortex configurations in momentum space enabled by BICs bring new degrees of freedom to modulate light. BICs have enabled many novel discoveries in light–matter interactions and spin–orbit interactions of light, and BIC applications in lasing and sensing have also been well explored with many advantages. In this paper, we review recent developments of optical BICs in periodic structures, including the physical mechanisms of BICs, explored effects enabled by BICs, and applications of BICs. In the outlook part, we provide a perspective on future developments for BICs.

In this Letter, Ti–Si bilayer was deposited on white silk to achieve coloration of the silk. By controlling the thickness of the Ti layer and Si layer, the saturation and the hue of the color on the silk could be preciously modulated, respectively. The structural colors on the silk could cover the major colors in the International Commission on Illumination 1931 chromaticity diagram, and it exhibits good durability, which is demonstrated by rubbing and stretching treatments. The developed textile coloration method may provide an eco-friendly technology in the silk dyeing industry.