Broadband terahertz metamaterial absorber based on sectional asymmetric structures

We suggest and demonstrate the concept and design of sectional asymmetric structures which can manipulate the metamaterial absorber’s working bandwidth with maintaining the other inherent advantages. As an example, a broadband terahertz perfect absorber is designed to confirm its effectiveness. The absorber’s each cell integrates four sectional asymmetric rings, and the entire structure composed of Au and Si3N4 is only 1.9 μm thick. The simulation results show the bandwidth with absorptivity being larger than 90% is extended by about 2.8 times comparing with the conventional square ring absorber. The composable small cell, ultra-thin, and broadband absorption with polarization and incident angle insensitivity will make the absorber suitable for the applications of focal plane array terahertz imaging.

In 2011, Tao et al. from Boston University proposed a metamaterial absorbing enhanced optical-readout bimaterial cantilever pixels for Microwave and Terahertz (THz) wave imaging 1 . Since then, the bimaterial cantilever focal plane array (FPA) imaging sensor integrated with metamaterial absorber has gained increased attention owing to its many distinctive properties [2][3][4][5] . In 2012, Alves et al. reported a micro-electro-mechanical systems (MEMS) bimaterial THz sensor operating at 3.8 THz. Its pixels integrated metamaterial absorber and the measurement showed that the fabricated absorber has nearly 90% absorption at 3.8 THz 2,3 . In 2013 and 2014, they improved their design and the absorption achieved near 100% at 3.8 THz and the responsivity is around 1.2 deg/μ W 4,5 . In 2015, Ma et al. demonstrated an infrared bimaterial cantilever focal plane array integrated with metamaterial absorber to enhance the infrared imaging performance 6 .
The metamaterial absorbers provide unprecedented ability to absorb energy of electromagnetic waves. The absorbed energy heats bimaterial cantilever to deform its optical-readout structure. To increase the sensitivity and reduce the response time of the cantilever sensor, relatively thin absorber which is compatible with MEMS-based bimaterial fabrication process is required 3 . To improve the imaging resolution, the sensor's unit cell should be small enough 4 . To enhancing dynamic range of the deformable cantilever sensor, the broadband absorption with polarization insensitivity and incident angle insensitivity is important. However, it is a great challenge to simultaneously meet all the aforementioned properties (ultra-thin, small cell, and broadband), especially in the THz frequency range.
To overcome the limitations of prior works, we suggest the concept of sectional asymmetric metamaterial structures which can manipulate specific device's working bandwidth with maintaining the inherent advantages of the device. In the following a broadband THz absorber based on the structures will be demonstrate to confirm this idea. The absorber integrates four sectional resonators into a small cell with inheriting the complete resonator's advantages of polarization insensitivity and incident angle insensitivity, while the bandwidth with absorptivity being larger than 90% is extended to about 2.8 times. Its entire structure which is compatible with MEMS-based fabrication is only 1.9 μ m thick. The small cell, ultra-thin, and broadband absorption will make the absorber suitable for the applications of optical-readout bimaterial cantilever focal plane array imaging sensor 4,5 , or some electrical-readout imaging sensors such as microbolometer sensor [25][26][27] and pyroelectric sensor 28 .

Principle and Design
The basic idea of sectional asymmetric structures can be explained in such a simple way that multiple sectional structures in one cell result in coupling of multiple resonant frequencies. It will extend the bandwidth effectively by combing the frequency responses. As an example, Fig. 1 describes the design process of a sectional asymmetric cell. First of all, choosing one complete metamaterial structure as basic structure as is shown in Fig. 1(a). And then, dividing the symmetrical structure into sections and varying the characteristic size of each section as shown in Fig. 1(b,c). Finally, compose these asymmetric sections into a new unit cell and the cell is called sectional asymmetric cell which is shown in Fig. 1(d).
Next, we proposed a broadband THz absorber based on the above example to verify its effectiveness. The basic structure is a simple square ring resonator which has advantages of polarization insensitivity and incident incidence angle insensitivity 12 . Figure 2    dielectric film (t = 1.7 μ m thick); the bottom layer is Au ground (0.1 μ m thick). The thermal, mechanical, and optical properties of Au and Si 3 N 4 make the absorber suitable for applications of bimaterial cantilever focal plane array optical readout imaging 29 .
The physical concepts and explanation of the bandwidth broadening are as follows: 1) To realize perfect absorption the impedance of the absorber should be matched to that of free space, for example: μ = ε then Z = (μ /ε ) 1/2 = 1, which ε stands for the normalized electric permittivity, μ is the normalized magnetic permeability, and Z represents the normalized free space impedance. The sectional square ring (Au bracket) is an example of electric ring resonator (ERR) and couples strongly to uniform electric fields, but negligibly to a magnetic field. By adding a ground plane, the magnetic component of the incident electromagnetic wave induces a current in the sections of the ERR that are parallel to the direction of the E-filed. The electric and magnetic response can then be tuned independently. The ERR determines the electric response while the dielectric type and thickness between the ERR and the ground plane determines the magnetic response. 2) In this design, the resonant frequency of the absorption peak is mainly determined by the outer side length P of basic square rings. Therefore, we integrate four sectional square rings with different size (P 1 -P 4 ) to support multiple resonant modes closely positioned together in the absorption spectrum. By tuning the thickness of the dielectric film, the sectional asymmetric structure can be impedance-matched to free space at each resonant frequency and absorption broadening is achieved.
To provide a further interpretation, the Transmission line model of the sectional asymmetric metamaterial cell is described in Fig. 2(b). R stands for electromagnetic loss of the Si 3 N 4 dielectric film. The four sectional square rings are equivalent to four parallel RLC circuit. R 1 , R 2 , R 3 , R 4 represent ohm resistance of the four Au sectional rings. L 1 , L 2 , L 3 , L 4 stand for equivalent inductance and C 1 , C 2 , C 3 , C 4 are equivalent capacitance of the four sectional rings, respectively. According to the RLC circuit model, the resistance will not affect the resonance frequency, so we omitted it for simplicity. The inductance and capacitance can approximately describe the resonance of sectional asymmetric structures. The inductance of each sectional square ring can approximately be given by L i ~ (t/w) · P i , where t is thickness of the Si 3 N 4 dielectric film, w is the width of the sectional ring, P i is the outer side length of the basic square ring. The capacitance can be expressed by C i ~ (P i · w)/t. Then the resonance frequency of the specific sectional ring is given by 30,31 : Here i represent the sectional ring resonators. The Equation 1 demonstrates that the resonance frequency f is an approximate linear function of 1/P i . Therefore, four sectional square rings will correspond to four resonance frequencies. The bandwidth of the absorber will be broadened by optimizing and adjusting the four outer side lengths P 1 , P 2 , P 3 , and P 4 .

Results and Discussions
The proposed absorber can be regarded as an effective media and characterized by a complex electric permittivity ε and complex magnetic permeability μ . The resonance structures couple strongly to the electric or magnetic fields and match the impedance Z = (μ /ε ) 1/2 to free space to minimize the reflectance. The absorber's reflectance and transmission can be acquired by simulating the complex frequency dependent S parameters, S 11 and S 21 7 . Then, the absorptivity A is calculated by where R = |S 11 | 2 and T = |S 21 | 2 are the reflectance and transmission, respectively. In our design the transmission T is zero because of the Au ground. Therefore, the absorptivity can be given by A = 1−R. We modeled the sectional asymmetric structures and simulated the electromagnetic characteristics by the commercial 3D electromagnetic simulator CST Studio Suite 2012. The thickness of its Si 3 N 4 dielectric film is 1.7 μ m and the dielectric constant is 8. The material of the sectional ring is Au with an electric conductivity 4.6 × 10 7 s/m and the thickness of the ring is 0.1 μ m. The unit cell boundary condition with Floquet-port was used to simulate the absorption spectra, because the Floquet mode can be applied to any periodical array whether mirrored or rotated. The absorptivity curve of sectional asymmetric absorber is shown in Fig. 3(a) and there are four absorption peaks A1 = 99.2%, A2 = 96.4%, A3 = 99.3%, and A4 = 81.3% corresponding to four resonance frequencies 4.7 THz, 4.82 THz, 4.96 THz, and 5.13 THz, respectively. The bandwidth with absorptivity being larger than 90% is about 364 GHz. Figure 3(b) is the resonance current distributions in one cell at different absorption peaks. It shows that the sectional square ring1 primarily contributes to absorption peak A1, the ring2 contributes to absorption peak A2, the contributions of ring3 and ring4 corresponding to absorption peak A3 and A4, respectively. Moreover, we provide the absorption spectrum in the situation of only having isolated Au bracket (quarter sectional ring) in Fig. 3(a). The four absorption spectra are all narrowband and the absorption peaks are located at 4.706 THz, 4.784 THz, 5.014 THz, and 5.222 THz respectively. It's worth mentioning that the maximum absorptivity of the isolated Au bracket absorber is only about 90% and lower than the counterpart (about 99%) of their combination. The results demonstrate that the sectional asymmetric structure can realize better impedance-matched to free space by the coupling of four isolated Au brackets effectively.
Furthermore, as a comparison we modeled an absorber based on a complete square ring structure. The period of its unit cell is 22 μ m and the outer side length of the square ring is P 4 = 18 μ m. The layer and materials are the same as the proposed sectional asymmetric broadband absorber. Figure 3(c) shows its absorptivity curve. The bandwidth with absorptivity being larger than 90% is only about 126 GHz. The bandwidth of sectional asymmetric structure absorber is about 364/126 = 2.8 times than that of complete square ring structure absorber. In application of focal plane array THz imaging, the sensor integrated absorber should be insensitive to the incidence angles, especially for the optical-readout cantilever sensor which will deflect angles owing to the bimaterial thermal effect, and the absorber should be polarization insensitive to maximize the absorption. To evaluate these characteristics, we simulated the absorption spectra of sectional asymmetric broadband absorber in different polarization angles and incidence angles by the CST2012. Figure 4(a) shows the absorptivity curves at various polarization angles for the normal incident radiation. Figure 4(b) depicts the calculated average curve of the absorptivities according to the various polarization angles. The polarization angle ϕ is defined as the angle between electric field E and positive x axis and depicted as the inset in Fig. 4(b). The equation for calculating average absorption curve of Fig. 4(b) is given by  The major metrics to define polarization-insensitive are 1) the absorptivity; 2) the resonance frequency. The absorbers which are sensitive to polarization will have severer absorptivity decline and resonance frequency shift 7 in different polarization directions. For the polarization-insensitive absorbers, although they cannot realize uniform absorption exactly at different polarizations and most of polarization-insensitive absorbers will show differences between neighboring polarizations, but the polarization-insensitive absorbers can keep relative high absorption and the resonance frequency will not be offset too much in different polarization directions. As is shown in Fig. 4, although the absorptivity has fluctuation when ϕ sweeps from 0° to 170°, the simulation results show that the proposed structure provides relative high absorptivity (The range of values is about 60~99% ) and keeps broadband absorptions (resonance frequency almost no shift) at different polarization angles. Furthermore, the calculated average absorption according to the polarization angles (ϕ = 0°, ϕ = 10°, … . ϕ = 160°, ϕ = 170°) also shows broadband high absorption in the same frequency range. Figure 5(a) describes how the absorptivity changes for different incidence angles which increase with a step of 10 degrees from 0° to 40° for the TE (Transverse Electric) radiation. Figure 5(b) shows how the absorptivity changes for the TM (Transverse Magnetic) radiation. The incidence angle θ is defined as the angle between wave vector k and the surface normal of the absorber and is depicted as the insets.
According to the Fig. 5, the absorptivity decreases a little when ϕ sweeps from 0° to 40° for the TE wave. Meanwhile, the absorptivity increases and has frequency shift when ϕ sweeps from 0° to 40° for the TM wave. Although the absorptivity has fluctuation, the simulation results demonstrate that the absorber keeps the characteristic of broadband absorption at various oblique incident angles.

Conclusion
The paper proposed the concept of sectional asymmetric structures. They can manipulate specific device's working bandwidth with maintaining the properties of the basic structure. To verify its effectiveness a broadband THz absorber was designed and evaluated numerically. Each cell of the absorber integrates four sectional square rings with approximate resonance frequencies. The entire structure composed of Au and Si 3 N 4 is only 1.9 μ m thick. The simulation results show its bandwidth with absorptivity being larger than 90% is extended to about 2.8 times comparing with the classic square ring absorber.
We believe the sectional asymmetric structures have two distinctive advantages: 1) manipulating specific device's working bandwidth while maintaining the inherent advantages of the complete structure; 2) not increasing size of the structure and thickness of the device. Therefore, it will be suitable for the focal plane array THz imaging sensors such as optical-readout bimaterial cantilever sensors or some electrical-readout sensors (microbolometer sensors and pyroelectric sensors).

Methods
Design of the sectional asymmetric metamaterial structures. There are four steps to design a normal sectional asymmetric structure (or cell). The first step is choosing one complete resonance structure as basic structure. The second step is dividing the symmetrical structure into sections. The third step is varying the characteristic size of each section. The fourth step is composing these asymmetric sections into a new structure (cell). Then, we called it sectional asymmetric metamaterial structure. It should be mentioned that the selected basic structure in the first step should be multiple symmetric structures, such as square ring, hexagonal ring, circular ring, or elliptical ring and so on.
We take another simple example to demonstrate the design method. This example is also a metamaterial absorber made of Au and Si 3 N 4, but its basic structure is circular ring. The absorber comprises three layers: the top layer is an array of sectional asymmetric Au resonators (0.1 μ m thick); the middle layer is Si 3 N 4 dielectric film (1.8 μ m thick); the bottom layer is Au ground (0.1 μ m thick). Figure 6(a) shows one cell based on a complete circular ring. After the aforementioned four steps, the Fig. 6(d) describes the final sectional asymmetric unit cell which integrates four circle sections with four resonance frequencies. The outer radiuses of four circle rings are 9.6 μ m, 9.4 μ m, 9.2 μ m, and 9 μ m, respectively. The gaps between the sectional rings are 2.1 μ m and the width of the sectional circle ring is 3 μ m. The period of one metamaterial cell is the same as the proposed sectional asymmetric square ring absorber (22 μ m). Figure 1(e) depicts the absorptivity curve of the metamaterial absorber simulated by CST 2012. The absorber's bandwidth with absorptivity being larger than 90% is about 390 GHz, but its entire thickness is only 2 μ m. In addition it's worth mentioning that we can broaden the absorption spectra using more sectional rings, or narrow the absorption spectra using fewer sectional rings.
Numerical simulation. We modeled the cell structures and simulated their electromagnetic characteristics by the commercial 3D electromagnetic simulator CST Studio Suite 2012. We use auto meshing technology and (b) Absorptivity curves at various oblique incident angle θ for the TM radiation. The incidence angle θ is defined as the angle between wave vector k and the surface normal of the absorber and is depicted as the insets.
frequency-domain solver to acquire S-parameter. The unit cell boundary condition with Floquet-port was used to simulate the absorption spectra, because the Floquet mode can be applied to any periodical array whether mirrored or rotated. The resonance current distributions were obtained based on the Field Monitor technology of the CST at certain frequencies. The thickness of Si 3 N 4 dielectric film is 1.7 μ m and its dielectric constant is 8. The material of the sectional ring is Au with an electric conductivity 4.6 × 10 7 s/m and the thickness of the ring is 0.1 μ m.