As a perfect graphene absorber without any external mirrors, we proposed asymmetric slot-assisted grating structures supporting two degenerate resonant modes of the guided-mode resonances (GMR) and the quasi-bound states in the continuum (quasi-BIC). The GMR mode functions as an internal mirror in conjunction with the background scattering, while the quasi-BIC, which is responsible for perfect graphene absorption, stems from the horizontal symmetry breaking by an asymmetric slot. By properly shifting the slot center from the grating center, the leakage rate of quasi-BIC can be controlled in such a way as to satisfy the critical coupling condition. We provide a comprehensive study on the coupling mechanism of two degenerate resonant modes for a one-port system mimicking the resonance. We also numerically demonstrated that our proposed grating structures show an excellent reflection-type modulation performance at optical wavelength ranges when doped double-layer graphene is applied. Due to the perfect absorption at the OFF state, a high modulation depth of ~50 dB can be achieved via a small Fermi level variation of ~0.05 eV. To obtain the lower insertion loss at the ON state, the higher Fermi level is required to decrease the graphene absorption coefficient.
