Coherent perfect absorber (CPA) was proposed as the time-reversed counterpart to laser: a resonator containing lossy medium instead of gain medium can absorb the coherent optical fields completely. Here, we exploit a monolayer graphene to realize the CPA in a non-resonant manner. It is found that quasi-CPA point exists in the terahertz regime for suspending monolayer graphene, and the CPA can be implemented with the assistant of proper phase modulation among two incident beams at the quasi-CPA frequencies. The graphene based CPA is found of broadband angular selectivity: CPA point splits into two frequency bands for the orthogonal $s$ and $p$ polarizations at oblique incidence, and the two bands cover a wide frequency range starting from zero frequency. Furthermore, the coherent absorption can be tuned substantially by varying the gate-controlled Fermi energy. The findings of CPA with non-resonant graphene sheet can be generalized for potential applications in terahertz/infrared detections and signal processing with two-dimensional optoelectronic materials.
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