Fig. 1: Brillouin zone folding induced bound states in the continuum (BZF-BIC).

a Conceptual diagram of BZF-BICs. After introducing periodic perturbation, unit cell size (solid black box) is doubled, and guided modes (GM) are engineered as BZF-BICs. The Q factor of the quasi-BZF-BICs is continuously boosted in the momentum space by decreasing the periodic perturbation. In contrast, the Q factor of the quasi-ordinary BICs does not change. The Q factor enhancement of BZF-BICs compared to ordinary BICs is robust against disorders. b Schematic of terahertz photonic crystal (THz-PhC) slabs i) without perturbation, ii) with gap perturbation that the distance between two adjacent air holes in a unit cell is changed by ΔL, iii) with radius perturbation that the difference of every two air holes’ radius is changed by Δr. Both the gap perturbation and radius perturbation result in a period-doubling in the x direction. c Calculated transverse electric (TE) band structures of unperturbed and gap perturbed (perturbation factor α = 0.0167, ΔL = 1 μm) PhCs, respectively plotted with hollow blue circles and solid orange lines. The GMs at X point of unperturbed PhC, TE_m,X (m = 1 to 5), are marked with solid circles of different colors. They are folded into Γ point when gap perturbation is introduced. The bands of gap perturbed PhC are named TE_mn, where m represents the corresponding band of unperturbed PhC, and n = 1 (0) denotes that the bands are obtained with (without) band folding. The solid red line shows the light line of the unperturbed PhC. The shaded gray area without stripe pattern and light-brown area represent the 0^th-order and higher-order diffraction domains of the gap perturbed PhC, respectively. The inset shows that the original first Brillouin zone (FBZ) presented by the solid black box shrinks to its half size after the perturbation is introduced. The bands in the outer half area of unperturbed PhC’ FBZ (shaded blue area) are folded into the FBZ of gap perturbed PhC (dashed black box).