Fig. 1 Mini-BIC modes. (a) Schematic of a mini-BIC (region A) surrounded a photonic bandgap (PBG, region B). (b) A continuous band (TE-A) of an infinitely large PhC with periodic boundary condition (left) turns into a set of discrete modes under the PBG boundary condition (right). (c) The momentum distribution of each mode is highly localized to points that form a square lattice in the momentum space with a spacing of . Modes are labeled as , according to their momentum peak positions in the first quadrant at . (d) The near-field mode profiles of four modes through (left) and their far-field emission patterns (right).
Fig. 2 Maximizing the Qs of mini-BICs by properly arranging topological charges in the momentum space. (a) Multiple BICs appear on bulk band TE-A in momentum space, in which ones with topological charges compose an octagonal-shaped topological constellation, denoted by the radius . When unit cell periodicity a varies from 526.8 (W) to 534.0 nm (Z), the topological constellation shrinks, merges, and annihilates to a single topological charge (upper panel). The quality factor Q for each unit cell design is shown in the lower panel. (b) The quality factor Q of modes, through , as functions of periodicity a (upper axis) and topological constellation (lower axis). Q for (red line) maximizes when its quantized momentum matches the topological constellation , corresponding to case X (a=529.1 nm) in (a). Similar maxima are also observed for (blue) and (black) under other designs, when matches and , respectively.
Fig. 3 Fabricated sample and experimental setup. (a–d) Scanning electron microscope images of the fabricated samples from top and side views. The photoresist and underlying layer are removed before measurements. The chosen structural parameters correspond to case X in Fig. 2a to maximize Q for mode . (e) Schematic of the
experimental setup. L, lens; RFP, real focal plane; PD, photodiode; POL, polarizer; BS, beam-splitter; Lens L2 and L3 are confocal.
Fig. 4 Observation of mini-BIC modes. (a) The far-field emission patterns (x=y-polarized and overall) of modes through , measured with a camera (gray color map), show good agreements with simulation results (hot color map). (b) Middle panel: measured scattered light intensity as the laser wavelength scans from 1570 to 1590 nm. Four clear peaks are observed and identified as through . The Q of reaches (left panel). In the same sample, the Qs of and are measured as and , respectively (right panel).
Fig. 5 Demonstration of mini-BIC robustness against fabrication errors. (a) Measured resonance wavelengths (circles) in samples with different periodicities a show good agreements with simulation results (dashed lines). (b) Measured Qs (circles) in samples with different periodicities a (upper axis) and therefore different topological constellation (, lower axis). Polynomial fittings are shown in solid lines. Each curve reaches its maximum value when the matching condition is satisfied, as is shown on the dashed vertical line. (c) The statistical histogram of measured Qs of in 87 samples shows that our mini-BICs have good robustness.