Bound states in the continuum of infinite quality factor in finite unit cells

A theory based on the superposition principle is developed to uncover the basic physics of wave behavior in a finite grating of N unit cells. The theory reveals that bound states in the continuum (BICs) of infinite quality factor (Q-factor) can be supported by such a grating when perfect reflection is introduced at its boundaries. If geometrical perturbations are introduced into the structure, the dark BICs transform into bright quasi-BICs with finite Q-factor, maintaining spectral characteristics nearly identical to those of quasi-BICs supported by infinite gratings. When the boundaries are replaced with high-reflectivity metallic mirrors, the Q-factor of the resonant mode is reduced to be finite; however, it can be much larger than that in the corresponding nanostructure with open boundaries and can be tuned in a large range by varying the number of unit cells or boundary conditions.