## Abstract

Coherent perfect absorber (CPA) is a novel strategy proposed and demonstrated for solving the challenge to attain efficient control of absorption by exploiting the inverse process of lasing. The operation condition of CPA results in narrow-band, which is the main limitation obstruct it from practical applications. Here, we demonstrate a CPA with tunable operation frequency employing the liquid metal made reconfigurable metasurface. The flow of liquid metal is restricted with a plastic pipe for realizing a controllable liquid metal cut-wire. The adjustable electric dipolar mode of the reconfigurable cur-wire metasurface ensures that the quasi-CPA point can be dynamically controlled; the measured CPA under proper phase modulation is in good agreement with the simulation results. The proposed CPA system involving liquid metal for dynamic control of operation frequency will have potential applications and may stimulate the exploitation of liquid based smart absorption control of optical waves.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

Engineering the absorption of materials and associated processes are of great interests in both fundamental physics and practical applications [1–3]. Recently, coherent perfect absorber (CPA) was proposed for solving the challenge to attain efficient control of absorption by exploiting the inverse process of lasing [4–7]. However, the operation conditions of CPA always result in narrow operation band, which is one of the main aspects hindering it from practical applications. In a CPA system, the absorptive medium illuminated by two counter-propagating coherent light beams can either be homogenous [8–11] or structured resonator [12–14] for improving the modulations on the coherent light beams. CPA provides coherence of light as an extra freedom for suppressing the scattering of light beams and localizing the light in the absorptive medium for complete absorption. The CPA has aroused huge interests and been discovered in many kinds of photonic structures ranging from microwave regime to visible light.

Metasurface, a class of metamaterial with few functional layers [15–24], is made of rationally designed microstructures with extraordinary properties that cannot be found in natural mediums. The powerful control capability of light of metasurface has been demonstrated in realizing light fields with arbitrary local amplitude, phase, polarization, spatial distributions [25–30]. The metasurface is selected to achieve absorbers in a specific frequency band primarily because of its ultra-thin profile, simple structure, and diverse functions. The subwavelength metasurfaces have been intensively utilized for ultra-thin absorbers with enhanced performance [31,32]. The dispersive response of the metasurface can be specifically designed for blocking the scattering of light at the interface between the metasurface and outside space, meanwhile the pathway of light in the metasurface should also be properly designed for realizing perfect absorption [33–42]. By introducing the concept of CPA, the reflection and the transmission through the metasurface can be efficiently suppressed by coherently modulating the scatterings of the counter-propagating beams [43,44]. It is highly desirable to extend the operation band of these resonant structures based meta-devices by introducing tuning mechanisms, and there have been a lot of works related to dynamic or tunable metamaterials [45–50]. Nevertheless, it is difficult to achieve coherent suppression of scatterings in a wide frequency range [51], in that the operation band of CPA is rather limited for applications demanding wide band. In this paper, we propose a coherent perfect absorber based on liquid metal made metasurface. The fluidity of the liquid metal can be exploited for simply adjusting the geometry of metasurface [52,53], which is helpful in realizing a dynamical controllable CPA as well as various active manipulation functions beyond solid metasurfaces.

## 2. Results and discussion

The schematic diagram for the proposed CPA based on liquid metal metasurface is presented in Fig. 1. Two important structure parameters w and m represents length and position of the liquid metal rod, respectively. The substrate is teflon with a dielectric constant of 2.65 and the loss angle tangent is 0.0004. The dimensions of the substrate are 47.54×22.14×1 mm^{3}. An input beam *P _{0}* is firstly splitted into two counter-propagating beams with equal intensity through a power divider and then the two beams are guided to illuminate the metasurface in the counter-propagating configuration. The amplitudes of the scattered output beams for the input coherent optical beams (with amplitudes of

*I*and

_{+}*I*) from the metasurface at two sides are

_{-}*O*and

_{+}*O*, respectively.

_{-}The complex scattering coefficients (*O _{±}*) of the liquid metal-based metasurface can be written as follows (here we set both the amplitudes of the input beams as I since the beams coming from the power divider are of equal intensity):

*S*is the scattering matrix, (

_{g}*t/r*)

_{+}and (

*t/r*)

_{-}are scattering elements of forward (irradiate towards positive direction of

*z*-axis) and backward (irradiate towards negative direction of

*z*-axis) beams. Since the liquid metal-based metasurface is reciprocal and symmetric, the scattering matrix can be simplified and the amplitudes of the scattering coefficients would be CPA requires the scattering coefficients being suppressed: $|{{O_ + }} |= |{{O_ - }} |= 0.$ So the CPA condition $tI{e^{i{\varphi _ + }}} = - rI{e^{i{\varphi _ - }}}$ can be derived from Eq. (2), implying that the CPA can be demonstrated at the frequency where the scattering coefficients fulfills $|r |= |t |.$ This frequency is defined as the quasi-CPA point which ensures the realization for CPA under incidences with proper phase modulation.

It is crucial to get the quasi-CPA point of metasurface firstly. We calculated the scatterings ($|r |$ and $|t |$) of the metasurfaces with an electromagnetic solver based on the Finite-Difference Time-Domain (FDTD) method, the transmission and reflection spectra of a metasurface (with w = 22 mm, m = 6 mm) is shown in Fig. 2(a). It is obvious there exists a frequency (of 4.97 GHz) fulfills the condition $|r |= |t |,$ the point is the intersection of the sample’s transmission curve and reflection curve and we call it quasi-CPA point.

It is known that the CPA can be achieved when two incident coherent modulated lights have a specific phase difference. Figure 2(b) shows the normalized scattering coefficients at the quasi-CPA frequency (blue line) and a frequency near the quasi-CPA point (orange line) as a function of phase modulation($\Delta \varphi$). It can be seen that specific phase modulation ($\Delta \varphi = 1.44\pi$) on the input coherent beams leads to significant reduction of the scattering outputs even to zero at the quasi-CPA frequency. The scattering of coherent beams can be perfectly suppressed for absorption at the quasi-CPA point while the suppression of scatterings cannot be perfectly realized for CPA outside the quasi-CPA point.

To demonstrate the reconfigurable feature of the proposed liquid metal based metasurface CPA. Liquid metal based metasurfaces were prepared with dielectric substrate and plastic pipes with exactly the same dimensions as in numerical simulations. Liquid metal alloy (eutectic gallium-indium, EGaIn) was injected into the tiny pipes and restricted or controlled with connected peristaltic pumps. Photographs of the experimental setup used for characterizing the sample is shown Figs. 3(a) and 3(b), the two sides of a standard waveguide (WR-187) are connected to a power divider through cables of same model with stabilized amplitude and phase for coherent and counter propagating electromagnetic beams on the sample (Fig. 3(c)) . We first choose a set of parameters as w = 22 mm and m = 6 mm as that used in case study of Fig. 2. As shown in Fig. 3(d), we can see from the measured transmission and reflection spectra a quasi-CPA point is at the frequency of 5.21 GHz, at which the necessary condition for complete coherent scattering suppression was achieved. The CPA can be realized at the frequency with proper phase modulation as will be discussed later.

The proposed reconfigurable metasurface can be easily tuned by exploiting the fluidity of the liquid metal in tiny pipes for tunable CPA. We first consider the geometric tunability of the liquid metal-based CPA. It was found that the length and position to center of the simple liquid metal rod structure are crucial in influencing the scatterings of metasurface and thus the quasi-CPA point. The scattering coefficients for metasurfaces with liquid rods at different positions (i.e. m = 0 mm, 2 mm, 4 mm, and 6 mm; the length was fixed as w = 22 mm) are presented in Fig. 4 (left: numerical simulations; right measured data), the solid and dashed curves represent transmission and reflection spectra, respectively. There is an electric dipolar resonance in the measured frequency range, which induced significant modulation on the scattering coefficients. The quasi-CPA point associated to the dipolar resonance lies just in the measuring band of the waveguide. Both the numerical and experimental results show that the quasi-CPA point moves to low frequency (from 5.95 GHz to 5.21 GHz in experiments) as the rod moves away from the center, the red-shift of the resonant frequency or dispersion of the electric dipolar mode is due to the inhomogeneous field of the waveguide mode in the experimental setup which is similar to the results of previous study (blue-shift for the magnetic mode) [54].

Then the length of the liquid metal rod is further studied for the tunability of the quasi-CPA. Figure 5 shows the simulated (Figs. 5(a) and 5(c)) and experimentally measured (Figs. 5(b) and 5(d)) scattering coefficients for liquid metal rod with different length (w = 19 mm, 20 mm, 21 mm, 22 mm) and the position fixed as m = 6 mm. Similarly to the previous case, an electric dipolar resonance exists for all the samples, the resonance can be tuned to low frequency by increasing the length of the rod. The associated quasi-CPA can be tuned in a larger range as in simulations, and an additional quasi-CPA appears in the working range of the experimental setup as in Fig. 4(d). The experimental results agree well with the simulated ones as can be seen from these results in Fig. 4 and Fig. 5, and both of them shows that the operation frequency or quasi-CPA point can be flexibly tuned by controlling the geometric size and placement in the measurement setup.

One step further, we continuously to put proper modulation on the phase difference for counter-propagating beams for direct observation of perfect suppression of scatterings and CPA. We used a power divider and two identical-length coaxial cables to divide the incident wave from into two equal-amplitude coherent beams. The two beams fed into the waveguide are completely coherent in the setup. Then we can get proper phase modulation by changing the position of the sample in the waveguide. Thus we can control appearance or vanishment of the CPA by changing position of substrate. And by exploiting the liquid fluidity and geometric tunability of liquid metal based metasurface, we have realized a switching and dynamic regulation of the quasi-CPA. The blue solid and dashed curves Fig. 6 represent the transmission or reflection spectra for several cases or samples: (a) no liquid metal rod; (b) w = 19 mm, m = 6 mm; (c) w = 22 mm, m = 4 mm; (d) w = 21 mm, m = 5 mm; (e) w = 21 mm, m = 6 mm.

For the case without liquid metal rod, there is no quasi-CPA point, and we did not measured suppression of reflection as well as the CPA. For the cases taking from Fig. 4 and Fig. 5, indeed perfect suppression of reflection from the sample can be achieved at the CPA points as shown in Figs. 6(b)–6(e), i.e. the coherent beams cannot escaping from the absorbing channel of the liquid metal-based metasurface, which corresponds to complete absorption or CPA. There are deep valleys of reflection coefficient below −25 dB corresponding to the absorption are higher than 99%.

## 3. Conclusion

In summary, we demonstrate a simple metasurface made of liquid metal alloy for controllable coherent perfect absorber. The operation frequency of CPA can be tuned by various geometric properties due to the liquid fluidity and geometric tunability of the liquid metal-based metasurface. Moreover, the properties of the proposed coherent modulator can be enriched by exploiting complex metasurface design, and it is compatible with the microfluidic chips for functional devices in terahertz range [52,55]. The proposed liquid metal metasurface for coherent manipulation is also promising in steerable detections, sensing, and signal processing since liquid metal possess metallic properties and fluidity simultaneously.

## Funding

National Natural Science Foundation of China (11674248, 11674266, 11774057, 61505164, 61771402); Hong Kong Scholars Program (XJ2017006); Natural Science Foundation of Shaanxi Province (2017JM6094, 2018JM6024); Shenzhen Science and Technology Innovation Commission (JCYJ20170817162221169);Fundamental Research Funds for the Central Universities (3102017zy033, 3102018jgc008).

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