⇦Chinese Physics Letters, 2017, Vol. 34, No. 11, Article code 117801 Design of Broadband Metamaterial Absorbers for Permittivity Sensitivity and Solar Cell Application * Hai-Long Huang(黄海龙), Hui Xia(夏辉)**, Zhi-Bo Guo(郭智博), Ding Xie(谢定), Hong-Jian Li(李宏建) Affiliations School of Physics and Electronics, Central South University, Changsha 410083 Received 5 May 2017 *Supported by the National Natural Science Foundation of China under Grant No 61275174, and the Research Fund for the Doctoral Program of Higher Education of China under Grant No 20100162110068.
**Corresponding author. Email: xhui73@csu.edu.cn Citation Text: Huang H L, Xia H, Guo Z B, Xie D and Li H J 2017 Chin. Phys. Lett. 34 117801 Abstract A broadband and ultra-thin absorber for solar cell application is designed. The absorber consists of three layers, and the difference is that the four split ring resonators made of metal gold are encrusted in the gallium arsenide (GaAs) plane in the top layer. The simulated results show that a perfect absorption in the region from 481.2 to 684.0 THz can be obtained for either transverse electric or magnetic polarization wave due to the coupling effect between the material of GaAs and gold. The metamaterial is ultra-thin, having the total thickness of 56 nm, which is less than one-tenth resonance wavelength, and the absorption coefficients at the three resonance wavelengths are above 90%. Moreover, the effective medium theory, electric field and surface current distributions are adopted to explain the physical mechanism of the absorption, and the permittivity sensing applications are also discussed. As a result, the proposed structure can be used in many areas, such as solar cell, sensors, and integrated photodetectors. DOI:10.1088/0256-307X/34/11/117801 PACS:78.66.-w, 78.66.Bz, 81.05.Zx, 42.25.Bs, 88.40.hj © 2017 Chinese Physics Society Article Text Electromagnetic (EM) metamaterials (MMs) are artificially built media with exotic EM properties, such as negative electric permittivity, negative magnetic permeability, and negative refraction index,[1-3] and have attracted considerable interest in practical applications such as super-lensing,[4] optical cloaking,[5] energy harvesting,[6] and other optical devices.[7-11] Recently, a 'perfect' absorber with near-unity absorption can be realized by an MM which was first proposed by Landy et al.[12] Subsequently, many different structures of the metamaterial absorbers (MMAs) have been proposed in different frequency ranges, including microwave,[13] terahertz,[14] infrared,[15] and optical regions.[16] However, most of these structures only have one perfect absorption point in a specific frequency, which results in a narrow absorption bandwidth. To increase the bandwidth, great efforts have been made by many researchers. For example, Shen et al.[17] designed an absorber using a resistive film, which can obtain the perfect absorption above 90% in the frequency range 3.9–26.2 GHz. Chen et al.[18] presented a broadband MMA based on lumped elements in microwave regions, and a broad absorption bandwidth of 1.5 GHz can be obtained. Zhang et al.[19] proposed a magnetic-type MMA with needlepoint-shape pattern, and the results show that this structure can expand the absorption bandwidth by more than 65%. Unfortunately, the above-mentioned methods are not easy to implement in higher frequencies such as terahertz, infrared, and optical regions. For example, it is very difficult to fit many different sizes of arrays in the same plane and relative complicated fabrication process using the lumped elements in the absorber. In addition, using the multilayer structure is another way to increase the absorption bandwidth,[20,21] but this approach will increase the total thickness of the absorber. As we know, the thickness of the MMA is a crucial factor which should be carefully considered in the design process. Therefore, it is desired and necessary to design a perfect-absorption MMA with the reduced thickness, which is less than one-tenth resonance wavelength with the absorption coefficient above 90% at the resonance wavelength. Nowadays, MMAs are widely used in some applications such as energy harvesting and sensors whose operating frequency is located from 400 THz to 750 THz, which is the visible light frequency region.[22] Therefore, designing the MMA with the characteristics of broadband, polarization-insensitive, and wide-angle is in urgent need for the solar cell applications. For example, Patrick and Cumali[23] studied a perfect MMA with two distinct absorption peaks of 99.9% at 543.7 THz and 99.0% at 663.7 THz. However, the absorption bandwidth needs to be further broadened so as to ensure the more efficient solar energy collection. The accurate sensing of permittivity or refraction index for different surrounding media by MMA needs to be considered in much higher frequencies. Specifically, an obvious shift in the position of the absorption peak for a given MMA will confirm the permittivity of different media. In this Letter, an ultrathin and broadband MMA based on hybrid materials in the top layer is proposed for the aim of increasing the absorption bandwidth effectively. The results show that a high absorption over 90% can be obtained from 481.2 to 684.0 THz for either transverse electric (TE) or transverse magnetic (TM) polarized wave due to the coupling effect between the gold and gallium arsenide (GaAs). In addition, the effective medium theory, the electric field and surface current distributions are adopted to explain the physical mechanism of the high absorption. Finally, the permittivity sensing of the proposed MMA for different surrounding media is discussed. Therefore, this structure can pave a way for obtaining the multiband (or broadband) MMA in infrared and optical regions.
cpl-34-11-117801-fig1.png
Fig. 1. Schematic illustration of the unit cell of the three-layer metamaterial absorber: (a) front view, (b) left view, and (c) perspective view.
Figure 1 shows the schematic diagram of the proposed MMA structure. This structure consists of three layers: a hybrid layer, a dielectric spacer, and a metal ground plate. The top layer (hybrid layer) is a slot GaAs plane and four split ring resonators (SRR) are to be encrusted in it. SiO$_2$ is set as the dielectric spacer to separate the hybrid layer and the bottom metal layer, and its relative permittivity and dielectric loss tangent are 3.9 and 0.025, respectively. The lossy gold (Au) is chosen to be the metal, and its electric conductivity is $4.09\times10^{7}$ S/m. The other geometric parameters are listed as follows: $P_{x}=P_{y}=520$ nm, $g=5$ nm, $w=50$ nm, $D=30$ nm, $t=10$ nm, $h_{1}=15$ nm, $h_{2}=26$ nm, and $h_{3}=15$ nm. Our results are obtained through a full wave EM simulation based on the finite integration technique (FIT) owing to its accuracy in results and its suitability for the study of high frequency.[24] In the $x$ and $y$ axes, the unit cell boundary conditions are used, and open space boundary conditions are applied in the $z$ direction. Absorption $A$, transmittance $T$, and reflection $R$ of the MMA satisfy the following relationship $A=1-T-R=1-|S_{21}|^{2}-|S_{11}|^{2}$. Due to the metallic background, the transmission coefficient of the MMA is zero as the thickness of the gold is much larger than its skin depth. Therefore, the expression can be changed into $A=1-R=1-|S_{11}|^{2}$. According to the effective medium theory, the relative impedance $Z$ of MMA reads[25] $$\begin{align} Z=\,&\sqrt {\frac{(1+S_{11})^2-S_{21}^2}{(1-S_{11})^2-S_{21}^2}} =\frac{1+S_{11}}{1-S_{11}},~~ \tag {1} \end{align} $$ $$\begin{align} A=\,&1-R=1-\frac{Z-1}{Z+1}=\frac{2}{Z+1}\\ =\,&\frac{2[{\rm Re}(Z)+1]}{[{\rm Re}(Z)+1]^2+{\rm Im}(Z)^2}\\ &-i\frac{2{\rm Im}(Z)}{[{\rm Re}(Z)+1]^2+{\rm Im}(Z)^2}.~~ \tag {2} \end{align} $$ Thus the perfect absorption can be obtained if the real part of the relative impedance equals to the free-space value, ${\rm Re}(Z)=1$, and the imaginary part approaches to zero, ${\rm Im}(Z)=0$.
cpl-34-11-117801-fig2.png
Fig. 2. (a) Absorption spectra of the proposed absorber. (b) Two comparison absorbers at normal incidence. (c) Calculated real and imaginary parts of the effective impedance of the absorber.
Figure 2(a) plots the absorption curves of the proposed MMA under normal incidence. It can be seen that the absorption spectrum shows three resonance points, which are $f_{1}=511.2$ THz, $f_{2}= 606.0$ THz, and $f_{3}=651.6$ THz with the absorption coefficients of 99.7%, 97.3%, and 97.1%, respectively. The corresponding absorption bandwidth can reach 202.8 THz, from 481.2 to 684.0 THz in the term of that the absorption is larger than 90%. We can also find that the same absorption efficiency can be obtained for TE and TM polarization waves. In Fig. 2(b), compared with the absorption curves of two different MMA structures (i.e., metal-SiO$_{2}$-metal (black line), slot GaAs-SiO$_{2}$-metal (red line)), it is clear that the absorption efficiency is decreased significantly especially at high frequencies. More specifically, only one resonance peak with a low absorption efficiency of 40.5% at 598.7 THz can be obtained using slot GaAs in the top layer (red line). The absorption spectrum of metal-SiO$_{2}$-metal shows traditional dual resonance points, the maximum absorption is only 92.7% at 660.2 THz, and the effective absorption bandwidth is very narrow. However, if we put these two structures in the same MMA, the absorption curve will be shown in Fig. 2(a). Thus we can obtain that the wider absorption bandwidth can be realized using the hybrid materials in the top layer. According to Eq. (1), the relative impedance $Z$ of the MMA can be obtained based on the $S$ parameters. As shown in Fig. 2(c), the real part of the relative impedance is near unity (${\rm Re}(Z)\approx 1$) and the imaginary part is close to zero (${\rm Im}(Z)\approx 0$) at the three resonant points, and the value of the reflectance at normal incidence will approach to zero. However, in our proposed structure, the smallest value of reflectance is 0.026 at the second resonance point ($f_{2}=606.0$ THz) shown in Fig. 2(a). As a result, the mismatched impedance of the imaginary part has a slight influence on realizing perfect absorption.
cpl-34-11-117801-fig3.png
Fig. 3. Electric field ($|E|$) and real ($E_z$) distributions at the three resonance points.
To better understand the physical mechanism of the high absorption, the distributions of the electric field ($|E|$) and real ($E_z$) in the MMA are shown in Fig. 3. Figures 3(a$_{1}$)–3(a$_{3}$) show the absolute value of the electric field ($|E|$) at the three resonant points for TE wave. We can see that the electric field is mainly localized and concentrated at some part of the absorber, but the strength of the electric field is much stronger in the gap between the SRRs and the slot GaAs plane than the other area around. As shown in Figs. 3(c$_{1}$)–3(c$_{2}$), in the case of the TM wave, we can also see that the most electric field distributes at the gap between these two materials. Therefore, the much wider absorption bandwidth is derived from the coupling effect between the material of gold and GaAs. As shown in Figs. 3(b$_{1}$)–3(b$_{3}$) and 3(d$_{1}$)–3(d$_{3}$), the real electric field ($E_z$) distribution means that the opposite charges mainly distribute in the left and right parts of the gap between the gold and GaAs, which is inspired by the electric dipoles resonance in the metal SRRs. This strong EM resonance makes the EM energy be consumed in the MMA, resulting in the perfect absorption and wide absorption bandwidth.
cpl-34-11-117801-fig4.png
Fig. 4. Surface current distributions at the three resonance points.
To further explore the absorption mechanism of the broadband MMA, we investigate the surface current distributions at the three resonance points, which are $f_{1}=511.2$ THz, $f_{2}=606.0$ THz, and $f_{3}=651.6$ THz. The results are shown in Fig. 4. It is noted that the distributions of the surface currents are symmetric at the resonance points, which is similar to the LC resonator.[26] However, the intensity of the surface current at three resonance points is distinct, especially at the point $f_{3}=651.6$ THz. Specifically, the currents are mainly distributed in every split ring resonator (SRR), rather than concentrating in the diagonal SRRs at the points $f_{1}=511.2$ THz and $f_{2}=606.0$ THz. As shown in Figs. 4(a$_{1}$) and 4(b$_{1}$), in the case of TE wave at the low resonant frequency, the surface currents on the top layer mainly flow along the direction of the arrow, and on the bottom layer the surface currents are in the opposite direction. Thus the anti-parallel surface currents form an equivalent current loop, which can be regarded as a magnetic dipole that exhibits magnetic resonance. However, we can find that the parallel currents will be formed between the two adjunction SRRs in the top layer and the electric resonance is excited. Thus the perfect absorption at the three resonance points is derived from the coupling effect of electric and magnetic resonance. The surface current distributions of the MMA for TM polarization wave are similar to that in the TE wave, which can be regarded as that in the TE polarization wave when the structure is rotated with 90$^{\circ}$ around the $z$ direction.
cpl-34-11-117801-fig5.png
Fig. 5. The absorption curves of the proposed absorber at oblique incidence: (a) TE wave, and (b) TM wave.
Figure 5 shows the absorption curves of the MMA based on oblique incidence. It is noted that the absorption spectra show a clear red shift at the first resonance peak (low-frequency resonance point) with the increase of the incidence angle. As for the TE polarization wave, the largest incidence angle can reach 40$^{\circ}$ when the absorption coefficient is over 90%. However, for the TM polarization wave, the largest incidence angle for absorption above 90% will reach 50$^{\circ}$. Figure 5(b) shows the absorption curves for the TM polarization wave under oblique incidence, and it is shown that this structure has a narrower absorption bandwidth with the increase of the incidence angle when the absorption is larger than 90%. In addition, we find that the position of the first resonance point ($f_{1}=511.2$ THz) will maintain unchanged with the increase of the incidence angle, especially for TM wave. However, for the second ($f_{2}=606.0$ THz) and third ($f_{3}=651.6$ THz) resonance points, the position will change obviously. Thus the first resonance point is the best choice for the sensing application. For permittivity sensing, a thin layer (15 nm in thickness) of different permittivities is placed on the top of the MMA. Figure 6(a) depicts the absorption spectra for five different permittivity media. It is clearly observed that when the permittivity of the sensing medium is increased from 2 to 10, the position of the resonance points with the absorption coefficient 90% will be red shifted, and the perfect absorption bandwidth is decreased. For example, when the permittivity of the sensing medium is increased to 10, the 90% absorption frequency is red shifted to 592.4 THz. To explore the sensitivity of the proposed sensor with respect to the different permittivities, the relation curve between the frequency shift and the different permittivities is shown in Fig. 6(b). It can be seen that the frequency shift increases almost linearly with the permittivity. In other words, a strong shift in the 90% absorption point is caused by the large permittivity of the medium. Therefore, the proposed MMA may be used as a sensor for permittivity sensing.
cpl-34-11-117801-fig6.png
Fig. 6. (a) The simulated results for the absorption coefficient under different permittivity sensing media. (b) Simulated data and fitting curve.
cpl-34-11-117801-fig7.png
Fig. 7. The absorption efficiency of MMA for different temperature $T$.
The complex-valued relative permittivity of GaAs is given by the Lyoyd,[27] $$\begin{align} \varepsilon (\omega )=\,&\varepsilon _{\rm L} (\omega )+\frac{i\sigma (\omega )}{\omega \varepsilon _0},~~ \tag {3} \end{align} $$ $$\begin{align} \varepsilon _{\rm L} (\omega )=\,&\varepsilon _\infty +(\varepsilon _{\rm s} -\varepsilon _\infty )\frac{\omega _{{\it \Gamma} 0}^2}{\omega _{{\it \Gamma} 0}^2 -\omega ^2-i\omega {\it \Gamma}},~~ \tag {4} \end{align} $$ $$\begin{align} \sigma (\omega )=\,&\frac{Nq^2}{m^\ast} \frac{\tau}{1-i\omega {\it \Gamma}},~~ \tag {5} \end{align} $$ where $\omega$ is the angular frequency, $\omega_{{\it \Gamma} O}$ is the ${\it \Gamma}$O-photon angular frequency, $\varepsilon _{\rm s}$ is the static permittivity, $\varepsilon _{\infty}$ is the high-frequency permittivity, and $\tau$ is the damping constant. The intrinsic carrier density $N$ of GaAs can be given as follows: $$\begin{align} N=5.76\times 10^{20}T^{1.5}\exp \Big(-\frac{0.26}{2k_{_{\rm B}} T}\Big),~~ \tag {6} \end{align} $$ where $k_{_{\rm B}}$ is the Boltzmann constant, and $T$ is the temperature in Kelvin. According to the above expressions and parameters, the complex permittivity of GaAs can be calculated under different $T$. Figure 7 shows the absorption performance of the structure for various temperatures. It can be seen that the absorption performance has a slight change at various temperatures. Thus this feature enables us to use absorbers for the solar cell application. In conclusion, a broadband and ultra-thin absorber based on hybrid materials use in the top layer has been proposed in the visible region. The numerical results show that the absorption curve of the MMA exhibits three resonance points in the range of 481.2–684.0 THz in terms of absorption larger than 90%, which are $f_{1}=511.2$ THz, $f_{2}=606.0$ THz, and $f_{3}=651.6$ THz with the absorption coefficients of 99.7%, 97.3%, and 97.1%, respectively. The wider absorption bandwidth and high absorption are derived from the coupling effect between the material of gold and GaAs. In addition, the absorption mechanism for TE and TM polarized waves are investigated by analyzing the distributions of the surface current and electric field. This structure can be used as a sensor for determining the permittivity of the different surrounding media. Thus this broadband MMA can be a good candidate for applications of solar cell, sensors and cloaking in optical regions. References Experimental Verification of a Negative Index of RefractionTHE ELECTRODYNAMICS OF SUBSTANCES WITH SIMULTANEOUSLY NEGATIVE VALUES OF $\epsilon$ AND μComposite Medium with Simultaneously Negative Permeability and PermittivityA NOVEL DUAL-BAND METAMATERIAL ABSORBER AND ITS APPLICATION FOR MICROSTRIP ANTENNAFlexible metamaterial absorbers for stealth applications at terahertz frequenciesHighly efficient selective metamaterial absorber for high-temperature solar thermal energy harvestingAspect ratio control and sensing applications for a slot waveguide with a multimode stubTheoretical analysis of ultrahigh figure of merit sensing in plasmonic waveguides with a multimode stubSensing Application in Fano Resonance With T-Shape StructureSensing analysis based on plasmon induced transparency in nanocavity-coupled waveguideTunable ultra-wide band-stop filter based on single-stub plasmonic-waveguide systemPhonon-Driven Ultrafast Exciton Dissociation at Donor-Acceptor Polymer HeterojunctionsBandwidth-enhanced dual-band dual-layer polarization-independent ultra-thin metamaterial absorberGraphene metamaterial for multiband and broadband terahertz absorberOmnidirectional and polarization insensitive nearly perfect absorber in one dimensional meta-structurePolarization-Independent Absorber Based on a Cascaded Metal–Dielectric Grating StructureAn extremely wideband and lightweight metamaterial absorberDesign, fabrication and measurement of a broadband polarization-insensitive metamaterial absorber based on lumped elementsLow frequency needlepoint-shape metamaterial absorber based on magnetic mediumBroadband multi-layer terahertz metamaterials fabrication and characterization on flexible substratesWide-angle, polarization-independent and dual-band infrared perfect absorber based on L-shaped metamaterialPlasmonic materials for energy: From physics to applicationsDesign and characterization of a dual-band perfect metamaterial absorber for solar cell applicationsMicrowave absorption properties of Ag naowires/carbon black compositesElectromagnetic parameter retrieval from inhomogeneous metamaterialsPolarization-Independent, Thin, Broadband Metamaterial Absorber Using Double-Circle Rings Loaded with Lumped ResistancesGeneralized conductivity model for polar semiconductors at terahertz frequencies
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