1. Introduction

Light absorption plays an important role in many applications, including radiometer, stealth technology, thermal emission, optical switch and modulator [1–12]. For traditional metal conductive film, due to impedance mismatch between metal and free space, its absorption in the microwave range is very low [13]. Although reducing the thickness of film can improve the match performance and enhance the absorption efficiency, its maximum absorption is limited to 50%, which cannot be broken under the ultra-thin approximation [13].

In 2008, Landy et al. [1] proposed the concept of metamaterials perfect absorbers based on the electromagnetic resonance, and about nearly 100% perfect absorption of the electromagnetic wave can be achieved in a specific frequency. Electromagnetic metamaterials are artificially constructed structures or composite materials with extraordinary electromagnetic properties that are not available in natural materials, and attract more and more attention in recent years [14,15]. As 2D version of metamaterials, metasurfaces of deeply subwavelength thickness can dramatically modify the amplitude, phase and polarization of light [16–21]. Many metamaterial absorbers have been widely researched from visible to infrared frequencies [1,2,5–11]. However, the metamaterial absorbers have a typical drawback in the working wavelength and absorption efficiency which are determined by the original structure and difficult to control flexibly. This drawback seriously impairs its performance as an optical switch or a modulator.

The way of the coherent perfect absorption (CPA) could provide a solution for the above mentioned problem, in which the absorption of light is controlled by two coherent beams with equal intensities propagating in opposite directions [22–32]. With the influence of absorption and interference, the absorption of light can be dynamically tuned from 0% to 100% by simply changing the relative phase of two incident beams, and thus the metasurface can achieve the transitions from transparent states to opaque states [23,24,33,34]. A typical coherent perfect absorber is a FP dielectric cavity in which all the incident energy can be captured and dissipated inside the cavity. Up to now, many structures are presented to achieve CPA, including thin films [25,28,30,34–36], grating [37], metal-insulator-metal structure [38]. However, as a time-reversal laser [22], many coherent perfect absorbers of above metasurfaces and metamaterials only work at a single frequency, and thus the absorption bandwidth is narrow and the expanding to multi-band or broadband is difficult. The narrow bandwidth severely limits its broadband applications, such as solar energy absorption for thermal photovoltaic [39] and microwave absorption for electromagnetic stealth [40] that require a wide absorption band. Therefore we urgently need to find a way to achieve multi-band or broadband coherent perfect absorption.

Until now, many efforts have been done to achieve this goal, including thin resistive sheet with ultrabroadband absorption spectrum which was originally proposed in [20] and later demonstrated in [41]. Others structures include a metasurface with four different periodically arranged meta-atoms [42], and multilayered split rings [43]. But these absorbers still cannot satisfy the multiband applications. For instance, because the bandwidth of resistive sheet is always very broad, it cannot retain the light transparent of other frequencies that are not required. Moreover, the bandwidth of metasurface proposed in [42] is still very narrow. The structure of multilayered split rings is quite complicated which increases the difficulty of industrial manufacturing.

In this paper, we propose a metasurface composed by the unit cells in which four-sized column patches are separated by a dielectric layer that can achieve CPA in four separated frequencies. By simply adjusting the structure parameters, we can obtain a broadband CPA of which absorption rates at these frequencies are greater than 90% and can be flexibly tuned by phase modulation. The absorption performance of oblique incidence is also studied. When increasing the incidence angle, the absorption is slightly reduced for transverse electric (TE) polarization but it is not varied for transverse magnetic (TM) polarization. In order to improve its performance as a beam splitter, we optimize the structure parameters for the case of oblique incident and obtain strong absorption for both TE and TM polarizations at the incident angle of 45°. The CPA frequencies of our metasurface can be tuned within a wide frequency range and extended easily to the other desired frequencies.

2. Structure

As shown in Fig. 1, the metasurface suggested in this paper consists of three layers where two metallic patterned films with thickness$d$are separated by a dielectric spacer with thickness$h$. Gold is used as metallic material and experimental value of dielectric constant is applied [44]. At a frequency of 100 THz, the real part of the dielectric constant is −339.13, and the imaginary part is 60.09, respectively. The dielectric spacer is chosen as Al₂O₃ and the permittivity is 2.92 at frequencies around 100 THz. The period of each unit cell is$p(p=2.4\text{μm})$. The gold film in each unit cell is etched into four-sized column patches with radius$r_1,r_2,r_3,r_4$and the thickness$d=40\text{nm}$. Two counter-propagating coherent beams along$\pm z$with the same amplitudes and different phases are used as excitations. Our simulation and calculation are based on commercial software Computer Simulation Technology Microwave Studio (CST MWS) and the corresponding formula in [37], respectively.

 

Fig. 1 Schematic of the metasurface which is illuminated by two counter-propagating coherent beams along$\pm z$. View of the unit cell where two patterned gold films with thickness$d$are separated by a Al₂O₃ dielectric spacer with thickness$h$. Geometrical parameters are the period$p$in both x and y-directions, the radius of four column patches$r_1,r_2,r_3,r_4$.

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3. Single-band CPA

For illustration, we first calculate the coherent absorption of a metasurface in which the column patches have the same radius in a unti cell ($r_1=r_2=r_3=r_4=r$). For the metasurface in our paper, there are many parameters that can be changed, such as gold film thickness, dielectric layer thickness and the radius of column patches. For simplicity, the thickness of the gold film remains 40nm throughout the optimization. For the single-band CPA, we keep the radius of column patches constant and optimize the thickness of the dielectric layer to achieve 100% perfect absorption. The optimized parameters of $h=115\text{nm}$and $r=0.34\text{μm}$are used to satisfy the condition of CPA and the phase difference of the two coherent beams is set to$\pi$for simplicity. In the metamaterial perfect absorber theory, both reflection and transmission coefficients must be weakened ($\left|r\right|=\left|t\right|=0$) [1], but the CPA is completely different which requires meet two conditions: (i) forward and backward waves are of the same amplitudes and (ii) reflection and transmission coefficients have same amplitudes ($r=t$) and$n\pi$phase difference with$n$being an arbitrary integer when illuminated by a single beam [37]. The absorption spectra is shown in Fig. 2(a) and from it, we can see that the maximum absorption is 99.9% at$f=109.5\text{THz}$.

 

Fig. 2 (a) Coherent absorption spectra for a metasurface in which the column patches have the same radius in a unti cell$r_1=r_2=r_3=r_4=r=0.34\text{μm}$, where the inset depicts the schematic of the proposed subunits. (b) Amplitudes of transmission (Red dotted line) and reflection coefficients (Blue solid line) for a single beam incident normally upon the metasurface. (c) The corresponding phases of transmission and reflection coefficients. (d) Coherent absorption spectra with$r$varying from 0.3 to 0.38µm, where arrows indicate the direction of spectral movement.

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The reason why the absorption peak occurs at the frequency of 109.5 THz can be understood from Figs. 2(b) and 2(c), which show the amplitudes of reflection and transmission coefficients and the corresponding phases when a single beam incident, respectively. We can see that the reflection coefficient is equal to the transmission coefficient at two frequencies of 109.5 THz and 193.5 THz where the first condition of CPA is satisfied. Only at the frequency of 109.5 THz, where the phase difference is 1.479° closed to 0, the second condition of CPA is also satisfied and a maximum absorption is obtained. When$f=193.5\text{THz}$, the phase difference is 260.73° and does not meet the second CPA condition, therefore there is no obvious absorption peak even though $r=t$. Changing the radius from$0.3-0.38\text{μm}$, the simulation results are shown in Fig. 2(d). We can find that when the radius is reduced, the absorption peak moves toward high frequencies while moving to the low frequencies when the radius increases. This relationship can provide a useful reference for us to design multi-band CPA devices. In the following, we will study the size effects of the columnar patches on absorption spectra.

4. Multi-band CPA

When we add the number of columns with different radius in a unit cell, the number of absorption peaks will also increase which can be seen in Figs. 3(a)-3(c). Now we consider a metasurface composed of four-sized column patches in a unit cell with $r_1=0.44\text{μm},$ $r_2=0.32\text{μm},r_3=0.36\text{μm},r_4=0.4\text{μm,}$respectively. Because the absorption peak frequency is affected by the radius of the metal patches, the simulations on the combinations of different metal patches radius in a unit cell are performed repeatedly to achieve identifiable multiple peaks, and thus the optimized radius parameters were obtained. To meet the condition of CPA, the thickness of the dielectric layer is tuned to 235nm through the same optimization process as single-band CPA. Their coherent absorption spectrum is shown in Fig. 3(d). Nearly perfect coherent absorption occurs at the frequencies of $f_1=90\text{THz}$, $f_2=96.9\text{THz}$, $f_3=104.7\text{THz}$and $f_4=114.6\text{THz}$.

 

Fig. 3 Simulated coherent absorption spectra of proposed multi-band metasurface in which the number of columns is different in a unit cell. (a) A column with radius$r_1$; (b) Two columns with radius$r_1,r_2$; (c) Three columns with radius$r_1,r_2,r_3$; (d) Four columns with radius$r_1,r_2,r_3,r_4$. The four peaks CPA occurs at four frequencies for$f_1=90\text{THz},f_2=96.9\text{THz},$ $f_3=104.7\text{THz,}{f}_4=114.6\text{THz}$with absorption rates of 99.34%, 95.46%, 95.06%, 98.83%, respectively. The bottom four figures are the magnetic field distribution in the center of the dielectric layer at each resonant frequency in which the (e)$f_1=90\text{THz}$; (f)$f_2=96.9\text{THz}$; (g) $f_3=104.7\text{THz}$; (h) $f_4=114.6\text{THz}\text{.}$

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The physical mechanism for the appearance of the four absorption peaks can be explained as follows. The unit cell is composed by four subunits. At a specific frequency of each subunit, the current in the upper and lower metal patches flows in the opposite direction, which forms a current loop and produces a strong magnetic resonance coupling with the magnetic field of the incident light [38, 43]. Here, the magnetic resonance results in a significantly enhanced of the magnetic field in the dielectric layer so that light is completely absorbed by the metaurface, which can be seen from Figs. 3(e)-3(h). As described above, metal patches have different radius corresponding to different magnetic resonance response frequencies. Each magnetic resonance is independent of the others, and the total light response on the metasurface is a linear superposition of four-sized subunits.

For the previous metasurface in [42], its response frequencies are 23.86 THz, 25.2 THz, 26.36 THz and 27.47 THz, respectively. The response range is 3.61 THz, this narrow band limits its potential application. Our design can extend the range to 24.6 THz and maintain a high absorption at each frequency. Despite multi-layer structure in [43] can also achieve multi-band absorption, its manufacturing process is complex. Our structure is superimposed by horizontal, which can be simplified in the process and maintain it ultra thin.

5. Broadband CPA

In our suggestion metasurface, based on the physical mechanism of multi-band CPA, broadband CPA can be obtained when we change the radius of the four metal column patches in a unit cell. Use the same optimization process as multi-band CPA, adjust the radius of the metal patches to move several absorption peaks closer together, and then optimize the thickness of the dielectric layer to obtain the perfect absorption. The broadband absorption spectrum is shown in Fig. 4(a) and the optimized parameters are$r_1=0.37\text{μm},$$r_2=0.33\text{μm,}$ $r_3=0.34\text{μm},r_4=0.36\text{μm}$and $h=185\text{nm}\text{.}$ The bandwidth is enhanced as the frequency range for the absorption rate greater than 90%. Compare with the single-band absorption in Fig. 2(a) of which the bandwidth is 2.7 THz, the bandwidth of the broadband CPA is 9 THz which is expanded to more than three times. Furthermore, compared with the former absorber in [42], our broadband design here also increases the bandwidth by 2.5 times and always maintains more than 90% absorption within the desired frequency range.

 

Fig. 4 (a) A broadband coherent absorption spectra (Black solid line) when the optimized parameters are$r_1=0.37\text{μm},r_2=0.33\text{μm},r_3=0.34\text{μm},r_4=0.36\text{μm},h=185\text{nm}$and a single-band coherent absorption spectra (Red dotted line) with$r=0.34\text{μm},h=115\text{nm}\text{.}$ (b) Dependence of the absorption spectra on the polarization angles at normal incidence.

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Then we investigate the absorption spectra at different polarization angles ($\varphi$), and it is clear that the absorption is almost constant due to the symmetry of the structure when the polarization angle changes [45]. This indicates that the absorber is polarization-independent at normal incidence.

As mentioned above, coherent perfect absorber has a significant advantage that when the structure is fixed, the absorbance can be tuned by changing the phase difference of two coherent input beams. The phase modulation of coherent absorption in our suggestion structure is shown in Fig. 5(a). When the phase difference varies from 0° to 360°, the absorption of the entire broadband changes at the same time. Thus we can simultaneously tune the broadband absorption rate from 0 to 1, between completely transparent state to completely absorbed state. The phase modulation of absorption for our designed metasurface is useful as a broadband absorption modulator.

 

Fig. 5 (a) Coherent absorption of the metasurface as a function of frequency and phase difference, the black and brown dotted lines refer to the absorption at the frequencies of 106.5THz and 112.8THz, respectively. (b) Phase modulation of absorption at $f=106.5\text{THz}$ (Black dotted line) and$f=112.8\text{THz}$(Brown dotted line).

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In order to better show the modulation ability of our metasurface, we show the coherent absorption as a function of phase difference at two peak frequencies 106.5 THz and 112.8 THz in Fig. 5(b). The modulation depth is defined as the ratio of the maximum absorption rate and minimum value [37], which represents the modulation capability of the absorber. It is 38.49 and 32.89 in our structure, respectively (see Table 1).

Table 1. The Calculated Maximum and Minimum Absorption Rate and Modulation Depth at the Two Peak Frequencies

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Actually, taking into account the possible deviations in the experimental production, the thickness of the dielectric layer cannot be exactly equal to 185nm. Therefore, we investigate the effect of dielectric layer thickness varying on broadband absorption. As shown in Fig. 6(a), it is easy to find that when the thickness varies from 180nm to 205nm, the coherent absorption is not significantly reduced. The peaks are always maintained at more than 97% which can be considered to be effective from the point of view of the absorber application. In this way, we provide a useful reference range for the thickness in the experiment.

 

Fig. 6 (a) Coherent absorption of the metasurface as a function of frequency and the thickness of dielectric layer. (b) Absorption spectra for different dielectric constants of the dielectric layer.

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In our suggestion CPA, the dielectric material is chosen to be Al₂O₃ and the dielectric constant ($\epsilon$) is 2.92 in the frequency range we calculated. Then we will study the effects of different dielectric constants on absorption. From Fig. 6(b), we can see that there are still some absorption peaks when the dielectric constant varies and the only difference is the shift of the peak frequencies. In other words, the peak frequencies are dependent on the material of dielectric layer. This relationship introduces a frequency tunable capability for the metasurface we designed, and the absorption peaks can be moved to other interested frequencies.

6. Oblique Incidence

The potential applications of angle-independent absorption are also very important, and thus we study the absorption properties of our suggestion CPA under oblique incidence for both TE and TM polarizations. As shown in Figs. 7(a) and 7(b), for TM polarization, the increased incidence angle ($\theta$) has no significant effect on the coherent absorption performance, and the absorbance always remains greater than 96% at the resonant frequencies for the incident angle varying from $0°$to $80°$. These trends are very similar to those in other suggestion perfect metamaterial absorbers [46]. While for TE polarization, the absorption at large incidence angle is deteriorated. When the angles are less than$40°$, the absorbance decreases slightly and remains 96%. With the increase of the incident angle beyond $40°$, the peak absorption decreases significantly and becomes 44% at $\theta =80°$.

 

Fig. 7 Coherent absorption of the metasurface as a function of frequency and incidence angle for (a) TE polarization, and (b) TM polarization. (c) TE polarization and (d) TM polarization wave incident on the metasurface in$x-z$plane with an incident angle of $\theta$ to z-direction.

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Figures 7(c) and 7(d) are the sketch figures which are helpful for understanding the physical mechanism of the above results. As demonstrated above, light absorption is mainly due to magnetic resonance. For TM polarization, when the incident angle increases, the magnetic field component in XY plane remains unchanged and does not affect the magnetic resonance intensity. However, this is completely different for TE polarization, the magnetic field component in XY plane is weakened with the increase of the incident angle. The transform in the intensity of the magnetic field component is similar to the cosine curve. When the incident angle increases, the magnetic field intensity in XY plane is drastically reduced, and therefore the incident magnetic field can no longer effectively support magnetic resonance [47].

As a beamsplitter for practical application, high absorption at the incidence angle of 45° is expected. Because in the case of normal incident, the incident beam coincides with the outgoing beam, as shown in Fig. 8(a), and thus the two beams cannot effectively be separated. However, when the beams are oblique incident, for example$\theta =45°$, the incident beams are completely separated from the outgoing beams in horizontal and vertical directions on the optical path, as shown in Fig. 8(b). And in this case the metasurface can be effectively used as a splitter. Therefore we need to optimize the absorption performance at $\theta =45°$ for TE polarization.

 

Fig. 8 Optical path diagram of two coherent beams incident on the metasurface. (a) Normal incidence and (b) Oblique incidence. P_in1 and P_in2 refer to the input beams, P_out1 and P_out2 represent output beams.

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Using the same procedure as before, the geometrical parameters are optimized with $h=205\text{nm},r_1=0.38\text{μm},r_2=0.35\text{μm},r_3=0.36\text{μm},r_4=0.37\text{μm}$. Figures 9(a) and 9(b) show the coherent absorption spectra of the optimized metasurface for TE and TM polarizations, respectively. Absorbance is greater than 90% at the frequencies from 101.7 to 107.4 THz for TE polarization at$\theta =45°$. The bandwidth is 5.7 THz which has been improved compared with the initial metasurface for which bandwidth is 3 THz. Importantly, the absorption for TM polarization is no significantly decreased. In addition, the broadband resonance frequencies are tunable. We simply reduce the radius of metal column patches to $r_1=0.37\text{μm},r_2=0.34\text{μm},r_3=0.35\text{μm},r_4=0.36\text{μm}$while the other parameters are unchanged, the absorption peak shifts to high frequencies for both TE and TM polarizations in Figs. 9(c) and 9(d). These trends are very similar to the absorption in a single-sized metasurface shown in Fig. 2(d), which again confirms that the broadband CPA is a linear superposition of single-band CPA. When the radius increases, the absorption peak shifts to low frequencies. This effect of radius provides a way to tune the absorption frequency. Thus we can obtain high absorption at any desired frequency using this metasurface.

 

Fig. 9 Coherent absorption for TE (a)(c) and TM polarization (b)(d) when the incidence angle is 45°. The optimized parameters are $r_1=0.38\text{μm},r_2=0.35\text{μm},r_3=0.36\text{μm,}$$r_4=0.37\text{μm}$for (a)(b),$r_1=0.37\text{μm},r_2=0.34\text{μm},r_3=0.35\text{μm},r_4=0.36\text{μm}$for (c)(d). The black solid line represents the optimized result while the red dotted line represents the unoptimized result in each graph.

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It should be mentioned that coherent absorption at $\theta =45°$can also be tuned by changing the phase difference of the two incident beams. Therefore, as a splitter or absorption modulator we can use one beam to modulate the output light intensity of the other from 0 to 100%. Finally, there is an interesting thing when we extend the simulation frequency to 300 THz to calculate coherent absorption of the metasurface. At large incidence angles, other absorption peaks occur at higher frequencies around 210 THz and 218 THz [Fig. 10(a)], which are related with the interplay of localized and delocalized plasmon resonances. The mechanism can be explained using Bragg scattering theory [38,48]. The angle-dependent absorption at high frequencies can be used to achieve the modulation of the point source. The light at large incident angles is absorbed and point source just can be incident at small angles, as shown in Fig. 10(b). The modulation may provide helpful guidance for potential optical application.

 

Fig. 10 (a) Coherent absorption of the metasurface as a function of frequency and incidence angle for TM polarization in a wide range of frequencies. (b) The modulation of the point source. The black dotted arrows indicate the absorbed light while the red solid arrows indicate the reserved light.

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7. Conclusion

In conclusion, we have designed a multi-band three-layered metasurface composed of unit cells in which four-sized metal column patches are separated by a dielectric layer and calculated coherent absorption spectra. The different radius of the four column patches in a unit cell results in four magnetic resonances at different frequencies. The resonant frequency is influenced by the radius of metal patches, and broadband absorption can be achieved by optimized parameters. The absorption is polarization independent and the bandwidth in our design is significantly enhanced compared with the single-band absorbers. This may be used on solar cells or other broadband absorbers in the future. Furthermore, by changing the phase difference of the two coherent incident beams, absorption can be modulated from 2.58% to 99.56% at 106.5 THz, 3.03% to 99.90% at 112.8 THz, respectively. Finally, we have studied the effect of the incident angle on absorption. Due to weakened magnetic resonance, the absorption is significantly reduced for TE polarization when angle increases. The optimized structure at $\theta =45°$can be used as a beamsplitter. Because of the high absorbance at large incident angles, our metasurface can also be used to modulate point source at high frequencies.