# Ultrathin Six-Band Polarization-Insensitive Perfect Metamaterial Absorber Based on a Cross-Cave Patch Resonator for Terahertz Waves

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{eff}(ω) and permeability µ

_{eff}(ω) can be equivalent, and thus an impedance can be matched to free space [1,2,3,4,5,6,7,8,9,26]. For this fundamental EM resonance, the electric response stems from the excitation of the electric resonators by the electric field [5,6,7]. The magnetic response is usually provided by pairing the top layer with a metal ground plane or metal wire for an external magnetic field. The strong local EM resonance usually restricts the unique responses to only a single narrow-band absorption, which greatly affects its applications, particularly for biological sensing, thermal imaging, and spectroscopic detection. Thus, simple and effective designs of high-performance multi-band PMMAs are also necessary.

## 2. Structure Design and Simulation

_{x}= p

_{y}= 75 μm, l = 68 μm, g = 1 μm, t

_{s}= 3.8 μm. The unit–cell structure of the PMMA is periodic along the x and y axes, with periods of 75 μm to avoid diffraction at the normal incidence for frequencies up to 4 THz. In our interesting frequency range (0.8–3.2 THz), the metal elements (CCPR structure and ground plane layer) are made of a lossy copper film with a frequency-independent conductivity σ = 5.8 × 10

^{7}S/m and a thickness of 0.6 μm, which is much larger than the typical skin depth in the terahertz regime (to avoid transmission through the ground plane metallic film). GaAs with a complex dielectric constant of ε = 12.9 + 0.0774i was selected as the dielectric spacer between two metallic layers.

## 3. Results and Discussion

_{1}, f

_{2}… f

_{6}) can be observed clearly. From Figure 2b–g, at resonant frequencies of f

_{1}= 1.13 THz, f

_{2}= 1.56 THz, f

_{3}= 1.77 THz, f

_{4}= 2.18 THz, f

_{5}= 2.85 THz, and f

_{6}= 3.14 THz, the absorbance A(ω) is about 90.5%, 94.4%, 98.7%, 96.2%, 95.4%, and 95.2%, respectively. The corresponding electric thickness of the PMMA is about λ

_{1}/70, λ

_{2}/50, λ

_{3}/45, λ

_{4}/36, λ

_{5}/28, and λ

_{6}/25, respectively (the λ

_{i}is the resonance wavelength, where i = 1, 2, 3…6). Thus, our designed PMMA possesses an ultrathin thickness compared with the operation wavelength (<λ/25, at 3.14 THz). In addition, it also exhibited a frequency selectivity of the six-band PMMA, since the bandwidth of perfect absorption is very narrow and the off-resonance absorption is very small (A(ω) < 5%). The peak absorption at different resonant frequencies corresponds to the nature of the different resonance modes, which will be illustrated and classified by analyzing the distributions of the electric fields of the unit–cell structure. It can be conjectured that the high-level absorption of those six resonance peaks is attributable to the higher-order multipolar plasmon resonances of the CCPR structure. It can be found that the absorption frequency band for the six-peak PMMA is relatively narrow compared with the previous PMMAs [5,6,7,8,11,12,36,37]. It is expected that the proposed PMMA has a significantly higher Q factor than the previous ones.

_{1}= 1.13 THz, f

_{2}= 1.57 THz, f

_{3}= 1.77 THz, f

_{4}= 2.18 THz, f

_{5}= 2.83 THz, and f

_{6}= 3.14 THz), the FWHM bandwidth is about 0.0167 THz, 0.0139 THz, 0.0219 THz, 0.0219 THz, 0.0251 THz, and 0.0286 THz, respectively. Thus, the corresponding Q factor is about Q

_{1}= 67.48, Q

_{2}= 113.19, Q

_{3}= 80.6, Q

_{4}= 77.39, Q

_{5}= 112.67, and Q

_{6}= 109.53, respectively. From the above results, the high-level absorption with high Q factor only occurs at resonant frequencies. The Q factor of the previous MMs structure for sensing applications is usually relatively lower (Q factor < 20) [21,22,23,40], in contrast, our proposed PMMA has a relatively higher Q factor (>60). Especially, it can be expected that our proposed PMMA can serve as a highly sensitive sensor for phase imaging of prohibited drugs, detection of combustible, toxic and harmful gases, and biological sensing, due to its high Q factor. In addition, it can be expected that the proposed structure of the PMMA is insensitive to the polarization state of the incident terahertz wave, due to the high geometric rotational symmetric of the unit–cell structure.

^{°}to 45

^{°}, owing to the rotational symmetry of the unit–cell structure of the PMMA, as shown in Figure 3a,b. Obviously, under normal incidence, the absorbance under different polarization angles remains unchanged for both the transverse electric(TE) and the transverse magnetic (TM) modes. This means that the designed PMMA can keep the absorption stability for normal incident terahertz waves with different polarization in practical application. It should be noticed that the first absorbance can be kept unchanged for both the TE and the TM mode, when the angle of the incident wave is below 65

^{°}. The absorbance performance of the higher-resonant frequencies (for example, second resonance, third resonance…and sixth resonance frequency) will deteriorate with the increase of the incident angle (θ > 30

^{°}), due to the higher-order multipolar plasmon resonance (not shown).

_{z}) of the electric field of the incident wave is mainly concentrated on the patch edges, gap edges, and corners of the metallic CCPR structure. As shown in Figure 4a, at the lowest frequency (f

_{1}= 1.13 THz) the electric field is mainly concentrated on the corners of the upper and lower triangle areas of the CCPR structure, indicating an excitation of quadrupolar resonance. This means that the upper and lower triangle areas of the resonator structure can strongly couple with the electric field and supply quadrupolar resonances, which can be interpreted by a simple dipole–dipole interaction along the electric field direction [38,39,43,44]. For the second frequency (f

_{2}= 1.56 THz), as shown in Figure 4b, the upper and lower areas of the CCPR structure and the greater part of the triangle section generate the half-wave resonance mode, coupling strongly to the electric field. Similarly to the lowest mode (f

_{1}), the CCPR structure at the second mode (f

_{2}) supplies hexapolar resonance. In effect, the electric field distributions revealing quadrupolar and hexapolar resonances correspond to the nature of localized surface plasmon (LSP) behaviors [56,57]. Figure 4c shows that for the third resonant frequency (f

_{3}= 1.77 THz) the electric field (E

_{z}) distribution is mainly concentrated on the upper, middle and lower areas of the CCPR structure, showing an excitation of multiple half-wavelength charge oscillations in the structure corresponding to the first higher-order mode [34]. Essentially, the higher-order modes occurring at the higher frequencies are due to the fact that the dimension of the CCPR structure is larger than the multiple of a half-wavelength of the resonant modes [8,11,34,36,39]. Similarly, as shown in Figure 4e, the E

_{z}distribution at the fifth frequency (f

_{5}= 2.85 THz) reveals the next higher-order excitation of multiple half-wavelength charge oscillations in the CCPR structure. The E

_{z}distributions for the higher-order mode possesses a finite dipole moment for these two modes (f

_{3}and f

_{5}), which is much like the fundamental dipole resonance response [30]. At the other frequencies (f

_{4}= 2.18 THz and f

_{6}= 3.14 THz), as shown in Figure 4d,f, the E

_{z}distributions reveal decapole and octadecapole excitations of the CCPR structure [57]. It can be seen that the resonant electric fields associated with the multipolar modes (f

_{4}and f

_{6}) are highly localized on the CCPR structure as well as highly enhanced in comparison to fields at nearby frequencies. It should be noted that the excitations of the propagating surface plasmon (PSP) also contribute to the formation of the absorption peaks (f

_{4}and f

_{6}) [57]. This also means that the fourth and sixth absorption peaks (f

_{4}and f

_{6}) originate from the combination of the high-order LSP and PSP resonance of the designed CCPR structure [57]. Therefore, this six-band perfect absorption of the PMMA is realized easily, based on the combination of the PSP resonance and the high-order multipolar response of the CCPR structure. These results suggest a new approach for designing a multi-band PMMA by integrating different resonance modes in a single patterned structure.

_{s}of the dielectric layer. Taking a further step, we studied the influences of geometric parameters of the unit–cell structure on the resonance absorption properties of the proposed PMMA.

_{1}, f

_{2}, f

_{3}, f

_{4}, f

_{5}, and f

_{6}), which will decrease with the increase of the l. The absorption peaks of the resonance modes f

_{1}and f

_{3}will remain almost unchanged, and those of the f

_{2}and f

_{4}will increase slightly, while the ones of the other resonances (f

_{5}and f

_{6}) will decrease slightly with the increase of the l. In addition, it should be noted that another peak close to f

_{6}can be observed clearly when the CCPR length is greater than 68 μm (>68 μm), revealing that the higher-order resonance mode is excited in this case. However, the absorbance of the resonant frequency close to f

_{6}is relatively small (<70%). According to the equivalent LC resonance circuit theory, the resonant frequency can be expressed as ${f}_{i}=\frac{1}{2\pi \sqrt{LC}}$, where the equivalent capacitance C and inductance L are mainly determined by the geometric parameters (l, g, and t

_{s}) of the unit–cell structure of the PMMA [51,52,58]. The C will increase with the increase of the l, thus resulting in a decrease of the multiple resonant frequencies.

_{1}, f

_{2}, f

_{3}, f

_{4}, f

_{5}, and f

_{6}) drift to the higher frequency, and the absorption peaks remain almost unchanged when the parameter g was changed from 1 μm to 1.4 μm. Although the resonance modes (f

_{3}and f

_{6}) also shift to the higher frequency, the absorption peak of mode f

_{6}will decrease with the increase of the CCPR gap width g. It also can be easily understood that C will decrease with the increase of the CCPR gap width g, thus resulting in an increase of multiple resonant frequencies, which is different to the change of the l.

_{s}on the absorption, and Figure 8 shows the calculated absorbance of the PMMA with different t

_{s}(t

_{s}= 3.7 μm, 3.8 μm, 3.9 μm) while the other geometric parameters were unchanged. From Figure 8b–d, it is obvious that the resonance absorption frequencies (f

_{1}, f

_{2}, f

_{3}, and f

_{4}) drift to the lower frequency, and the absorption peak remains unchanged at a high level when changing the parameter t

_{s}from 3.7 μm to 3.9 μm. Although the absorption frequencies (f

_{5}and f

_{6}) also shift to the higher frequency, the absorption peaks will increase with the increase of the dielectric layer thickness t

_{s}, as shown in Figure 8e. In this case, when increasing the dielectric layer thickness t

_{s}, the L will increase, thus the multiple resonant frequencies will decrease accordingly.

_{s}) of the unit–cell structure. We could adjust the absorption peaks and frequencies by changing these parameters. Although all changes of the parameters almost affect the resonant frequency absorption peak, the designed PMMA still remains high absorption level (A(ω) > 90%) at resonance. These results further confirm that the frequencies of the designed six-band PMMA could meet different application needs, especially in sensors.

## 4. Conclusions

_{1}, f

_{2}…f

_{6}) revealed that the high-level absorption originated from the PSP and the higher-order multipolar plasmon resonance response of the square cross-cave patch structure. Furthermore, the resonance absorption properties of our design can be adjusted by varying the geometric parameters of the unit–cell structure, which gives considerable freedom to shift or change the operation frequencies of the PMMA to meet different application needs. In addition, the simple design of the six-band PMMA is easily fabricated using the conventional photolithography process and metallization process steps [59,60]. In our next work, we will perform an experiment for our designed PMMA for practical sensing application. The aforementioned advantages of the six-band PMMA make it a good candidate in some potential applications of thermal imaging, wavelength selective radiators, thermal bolometers, biosensors, and so on.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Schematic of the designed six-band polarization-insensitive terahertz perfect metamaterial absorber (PMMA): (

**a**) 2D array, (

**b**,

**c**) front view and perspective view of the unit cell.

**Figure 2.**(

**a**) The absorption spectra of the proposed six-band PMMA, (

**b**–

**g**) the absorbance spectra under different resonant frequency domain.

**Figure 3.**Dependence of the absorption spectra on the polarization angles of the normal incident terahertz wave for the proposed PMMA: (

**a**) transverse electric (TE) mode and (

**b**) transverse magnetic (TM) mode.

**Figure 4.**Distributions of the z-component (E

_{z}) of the electric field for the proposed PMMA at frequencies of (

**a**) f

_{1}= 1.13 THz, (

**b**) f

_{2}= 1.56 THz, (

**c**) f

_{3}= 1.77 THz, (

**d**) f

_{4}= 2.18 THz, (

**e**) f

_{5}= 2.85 THz, and (

**f**) f

_{6}= 3.14 THz, respectively.

**Figure 5.**Distributions of power loss density in the middle dielectric layer for the proposed PMMA at frequencies of (

**a**) f

_{1}= 1.13 THz, (

**b**) f

_{2}= 1.56 THz, (

**c**) f

_{3}= 1.77 THz, (

**d**) f

_{4}= 2.18 THz, (

**e**) f

_{5}= 2.85 THz, and (

**f**) f

_{6}= 3.14 THz, respectively.

**Figure 6.**(

**a**) Dependence of the absorption spectra of the proposed PMMA on the size changes of the cross-cave patch resonator (CCPR) length l (l = 68 μm, 69 μm, 70 μm), (

**b**–

**e**) dependence of the absorbance spectra on the l at different frequency domains.

**Figure 7.**(

**a**) Dependence of the absorption spectra of the proposed PMMA on the size changes of the CCPR gap width g (g = 1 μm, 1.2 μm, 1.4 μm), (

**b**–

**e**) dependence of the absorbance spectra on the g at different frequency domain.

**Figure 8.**(

**a**) Dependence of the absorption spectra of the proposed PMMA on the size changes of the dielectric layer thickness t

_{s}(t

_{s}= 3.7 μm, 3.8 μm, 3.9 μm), (

**b**–

**e**) dependence of the absorbance spectra on the t

_{s}at different frequency domain.

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Cheng, Y.Z.; Huang, M.L.; Chen, H.R.; Guo, Z.Z.; Mao, X.S.; Gong, R.Z.
Ultrathin Six-Band Polarization-Insensitive Perfect Metamaterial Absorber Based on a Cross-Cave Patch Resonator for Terahertz Waves. *Materials* **2017**, *10*, 591.
https://doi.org/10.3390/ma10060591

**AMA Style**

Cheng YZ, Huang ML, Chen HR, Guo ZZ, Mao XS, Gong RZ.
Ultrathin Six-Band Polarization-Insensitive Perfect Metamaterial Absorber Based on a Cross-Cave Patch Resonator for Terahertz Waves. *Materials*. 2017; 10(6):591.
https://doi.org/10.3390/ma10060591

**Chicago/Turabian Style**

Cheng, Yong Zhi, Mu Lin Huang, Hao Ran Chen, Zhen Zhong Guo, Xue Song Mao, and Rong Zhou Gong.
2017. "Ultrathin Six-Band Polarization-Insensitive Perfect Metamaterial Absorber Based on a Cross-Cave Patch Resonator for Terahertz Waves" *Materials* 10, no. 6: 591.
https://doi.org/10.3390/ma10060591