We proposed perfect absorbers of ultra-wide bandwidths based on prism coupling with wavelength-insensitive phase matching, which consists of three dielectric layers (Prism-Cavity-Air) with monolayer graphene embedded in the cavity layer. Due to inherent material dispersion of the dielectric layers, with the proper choice of the incidence angle and the cavity thickness, the proposed perfect absorbers can satisfy the phase matching condition over a wide wavelength range, inducing enormous enhancement of the absorption bandwidth. The requirement on the material dispersions of the prism and the cavity layer for the wavelength-insensitive phase matching over a wavelength range of the interest has been derived, and it has been demonstrated that the various kinds of materials can meet the requirement. Our theoretical investigation with the transfer matrix method (TMM) has revealed that a 99% absorption bandwidth of ~300 nm with perfect absorption at λ = 1.51 μm can be achieved when BK7 and PDMS are used as the prism and the cavity layer, respectively, which is ~7 times wider than the conceptual design based on the non-dispersive materials. The full width at half maximum of our designed perfect absorber is larger than 1.5 μm.
