We investigate the optical exceptional points (EPs) in the graphene incorporated multilayer metamaterial manifesting Fano resonance. The system is non-Hermitian and possesses EPs where both the eigenvalues and eigenvectors of the Hamiltonian coalesce. In the aid of Fano resonance, the reflection may reach minimum approaching to zero, resulting in the degeneration of both eigenvalues and eigenvectors and thus the emergence of EPs. The transmission and reflection of light through the metamaterial change sharply by varying slightly the incident wavelength and chemical potential of graphene in the parameter space when encircling the EPs. In addition, the unidirectional invisibility can be achieved at EPs. The study paves a way to precisely controlling the transmission and reflection through metamaterials and may find applications in optoelectronic switches, modulators, absorbers, and optical sensors.

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The concept of Fano resonance originally discovered in quantum systems has been introduced to the field of optics for the last decade and more. One distinctive feature of the resonance lies in its asymmetric line shape. Graphene metamaterials have attracted much attention for making tunable devices due to the controllable carrier density of graphene. As realizing Fano resonance in graphene metamaterials, asymmetric and tunable optical responses are usually observed in transmission or reflectance spectra. This Perspective is intended to review the current developments on Fano-resonant graphene metamaterials, which are divided into three categories based on the participation of graphene plasmon in Fano resonance. Later, discussions on the applications in sensors, switches, modulators, and slow-light devices are given, and a future perspective is proposed.

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