Fig. 2: Optical characterisation for the BIC cavity, SPE and their weak coupling.

a Experimental (left) and calculated (right) angle-resolved unpolarised reflectance spectra of the designed TiO₂ nanopillar array showing vertical magnetic dipole BIC resonance at \({E}_{{{{{{\rm{BIC}}}}}}} \sim\) 2.107 eV at angle \(\theta=\) 0°. b Top view and c side view of the electric-field distribution at the BIC frequency in the nanopillars. The direction of the electric field is represented by red arrows. d Experimental resonance energies (green squares) and full-width at half-maximum (FWHM) (light-brown circles) of the BIC mode observed in (a) as a function of \(\theta\). The corresponding fitting curves (solid lines) are obtained using the BIC model discussed in the SI. e Typical photoluminescence (PL) spectrum of carbon-related SPEs showing the zero-phonon-line (ZPL) peak at \(\sim\)2.092 eV, and a phonon side-band (PSB) at \(\sim\)1.919 eV. f Angle-resolved PL spectra in a weak coupling regime, showing a PL enhancement of the SPE. The cavity mode and the SPE PL position are shown by the white dashed lines. g PL spectra of the coupled SPE extracted from (f) at −8.18° (black squares) and the uncoupled SPE (grey circle) under the same measurement conditions. The PL spectrum of the weakly coupled SPE is fitted by single Lorentzian (green solid line), and the PL intensity is represented by the area under the fitting curve (green shaded area).