Fig. 2: Brightening of dark excitons with BICs.

a The band structure of a PhC slab that supports a symmetry-protected on-Γ BIC with a zero-degree incident angle. The blue bands are the transverse magnetic mode-like (TM-like) bands whereas the red bands are the transverse electric mode-like (TE-like) bands. Only four of the bands (solid lines) can be observed under p-polarized incident light. The PhC only supports the on-Γ BIC to illustrate the dark exciton brightening. b The simulated (left) and the measured (right) angle-resolved reflection spectra mapping of the PhC slab. It is clear to see the two on-Γ BICs at wavelengths 694 nm and 750 nm, respectively. c Electric-field profile \({{{{{{\bf{E}}}}}}}_{{{{{{\bf{z}}}}}}}/{{{{{{\bf{E}}}}}}}_{{{{{{\bf{0}}}}}}}\) of the on-Γ BICs, plotted on the top surface of the PhC slab (top) and the y = −r/2 slice (bottom). d The reflection spectrum with an oblique incident angle of 3° is shown by the black dashed line, while the maximum local electric field amplitude enhancement ratio on the top of the PhC slab is plotted in red. WSe₂ monolayer was considered. e The PL spectra of dark excitons and bright excitons. The blue spectrum was taken when the pump laser matched the on-Γ BICs at the wavelength of 694 nm (on-BIC) whereas the red spectrum was taken when the pump laser was at the wavelength of 647 nm (off-BIC). f A log plot of the power dependence of PL intensity of dark excitons. The black line is a fit of the dark exciton emissions exhibiting a linear power dependence. The fitted slop α is 0.9 indicating the PL stem from dark excitons rather than bi-excitons.