**6. Coherent metamaterial absorbers**

It is known that one of drawbacks of a typical metamaterial absorber is that the absorptivity is commonly fixed after the initial design of the metamaterial absorber. As a consequence, it is not suitable for environments that require the flexible tunability of absorption. The presence of coherent perfect absorption (CPA) is a solution for this issue [82, 83]. Mathematically, CPA corresponds to a zero eigenvalue of the scattering matrix S at a specific frequency, which can be regarded as the time-reversed lasing at threshold. The perfect absorption can be achieved by utilizing the destructive interference in a standing wave system formed by two counterpropagating beams [84]. Moreover, the absorptivity in such a system can be modulated from nearly 0 to 100% by solely adjusting the phase difference between the two counter-propagating incident beams [85]. Owing to this dynamic configurability of absorptivity, such absorbers are very attractive for applications in transducers, modulators, and electromagnetic switches.

The concept of CPA was first presented theoretically by Chong et al. [82] and experimentally demonstrated by the same group later [83]. Since then, CPA phenomena have been observed in epsilon-near-zero metamaterials [86], slow light waveguides [87], a metasurface consisting of metallic cross antennas [88], and a Fano resonance plasmonic system [84], just to name a few.

Most of the coherent metamaterial absorbers are based on metallic subwavelength resonators. However, recent researches revealed that CPA could also be achieved in metal-free metamaterials or metasurfaces. Zhu et al. [89] designed a mono-layer fishnet structure made of all dielectric ceramic, which has a thickness of two levels smaller than the operating wavelength. They demonstrated that CPA could be found in such a structure and the absorptivity is controllable within a wide range from 0.38 to 99.85% through phase modulation. A similar monolayer fishnet structure made of water could also be used for achieving high coherent absorption at multiple frequency bands [90]. Moreover, due to intrinsic high loss in water, the CPA could be designed with wider bandwidths.

Unlike perfect metamaterial absorbers that require strong electric and magnetic resonances resulting from the artificially structured resonators, few recent works reported that CPA can also be found in naturally existing layer materials with deep subwavelength thickness. Li et al. [89] presented that ultra-thin conductive films could be used for achieving CPA. As demonstrated experimentally, broadband coherent absorption with relative bandwidth close to 100% at microwave frequencies was observed in a conductive film, having a thickness of 1/1000 of the working wavelength. The CPA phenomena in thin graphene and MoS2 layers were also investigated [60, 91]. The tunable conductivity in graphene or MoS2 allows such a coherent absorber to be more flexible in working frequency, which could be controlled by adjusting the chemical doping rate or bias voltage.
