Genetic optimization of terahertz metamaterial absorber for improved absorption and quality factor

Terahertz metamaterial absorbers are typically comprised of an array of sub-wavelength meta-atoms, a dielectric spacer layer and a ground plane. The absorption and quality factor are two of the most important performance metrics for various advanced applications, such as THz communication, sensing, and imaging. However, a large number of structural parameters in the meta-atom make the design approach based on physical intuition and parameter sweep impractical and difficult. In this paper, we report an intelligent design methodology based on the genetic algorithm that facilitates the optimization of an air-spaced terahertz metamaterial absorber to improve its absorption and quality factor. The presented approach starts by randomly generating the size parameters of the meta-atom, and it iteratively obtains the optimized design of the dual narrow band terahertz metamaterial perfect absorber. The quality factor for the two near unity-absorption peaks are 23.8 at 0.5 THz and 60.3 at 0.7 THz, respectively. The device was fabricated using the surface and bulk-micromachining processes, and the measured absorption spectra agrees well with the simulated results. Not limited to this proof-of-concept demonstration, this methodology can be applied to all metamaterial-based photonic systems achieving efficient forward optimization design.


Introduction
Terahertz metamaterial absorbers (TMAs) consist of a sub-wavelength meta-atom layer, a dielectric spacer, and a ground plane, which can be resonant with incident electromagnetic (EM) waves at a specific frequency achieving perfect absorption characteristics [1].It has shown great potential in various scientific and technical applications, such as THz sensing, imaging, and filtering [2].For most practical narrow-band applications, the absorption and quality factor (Q) are two key performance indicators [3].Multi-narrow-band TMAs are developed by employing the meta-atoms including several same geometric shapes with different sizes [4], and the number of size parameters in a unit cell will increase substantially.However, the conventional optimal structure design is a time-consuming process and shows low design efficiency.It is fairly difficult to obtain the optimized result through the brute-force parameter sweep method based on the trial-and-error strategy [5].This can be attributed to the weak and limited human brainpower in terms of complicated high-dimensional problems [6].
One way to overcome this limitation is to design the sophisticated meta-devices utilizing artificial intelligence (AI) techniques [7].Up to date, AI algorithms applied for meta-atom optimization can be classified into two categories, including traditional optimizations (such as genetic algorithm (GA), topological optimization (TO), and particle swarm optimization (PSO)) and Artificial neural network (ANN) models [8].Different from ANN models, traditional optimizers can achieve efficient forward optimization without building a huge database and complicated training.Therefore, traditional optimizations are more appropriate for solving medium-sized design tasks (e.g., ≈ ten variables) [9].
In this work, we proposed an air-spaced dual narrow band TMA with high absorption and quality factor optimized by a GA approach.After 32 iterations of 6 size parameters, the performance of our device meets the expected optimal requirements.Two distinct absorption peaks are observed at 0.5 THz (Q1 = 23.8) and 0.7 THz (Q2 = 60.3),respectively.The novel methodology based on GA optimization exhibits superior efficiency compared to the more commonly used design approaches.

Design and simulation
A schematic drawing of our designed air-spaced dual-band TMA is shown in Figure 1(a).An array of metal resonators (150 nm thick) was patterned on a high resistivity (HR) silicon layer (>10 4 Ω•cm).The resonator has a pair of metal strips with different lengths to support THz resonances at two frequencies, as shown in Figure 1(b).The top chip is bonded to a bottom gold-coated substrate by a patterned adhesive layer.Figure 1(c) shows that the air gap between the top and the bottom chip is 6 μm.The six size parameters of the meta-atom that need to be optimized, including the period of the meta-atom (P), the distance between two metal strips (D), the gap (g1) and width (w1) of strip 1, and the gap (g2) and width (w2) of strip 2, are introduced in the caption of Figure 1.The TMA in this work was designed and optimized using a novel design method based on GA.The methodology is composed of two parts: a parametrized EM finite element model (FEM) implemented in CST Microwave Studio and a GA implemented in MATLAB.In the first step, the total number of the population and the length of the individual genes were initialized as 20 and 53, respectively.Our goal is to obtain double near-unity absorption peak with high quality factor at 0.5 THz and 0.7 THz. Figure 2 demonstrates the results of GA-optimized absorption for the 1st, 11th, 21st and 32nd generations respectively, and the inset illustrations show the corresponding meta-atom structures.The absorption of the 32nd generation at 0.5 THz and 0.7 THz is 0.978 (Q1 = 23.8) and 0.985 (Q2 = 60.3),respectively.The performance of optimized TMA reached the expected design requirements.

Fabrication and measurement
The device was fabricated by surface, bulk micro-machining processes, and flip-chip bonding as shown in Figure 3(a)-3(g) [10].Figure 3(h) and 3(i) illustrate the image of a fabricated air-spacer absorber and the microscopy image of the meta-atom array.When the incident THz pulse is parallel to the metal strip pair, two absorption peaks can be observed at 0.515 THz (0.9451) and 0.702 THz (0.9244).The full width at half maximum for peak 1 and peak 2 are approximately 30 GHz (Q1≈17.2) and 19 GHz (Q2≈36.9),respectively.When the incident THz pulse is perpendicular to the metal strip pair, the absorption is about zero in the range from 0.4 to 0.8 THz.The differences between the experimental and simulated results may arise from the fabrication error.

Conclusion
In this paper, we introduced a novel design approach based on GA optimization by describing the optimization process for an air-spaced dual narrow band TMA with high absorption and quality factor as a study case.Our devices showcased two near-unity absorption peaks at 0.5 THz (Q1 = 23.8) and 0.7 THz (Q2 = 60.3) in the EM spectra, respectively.We fabricated the device through the surface and bulk-micromachining processes, and characterized its terahertz absorption.The simulation results and experimental results exhibit a high degree of agreement.This high-efficiency design method can also be extended to the optimization of many other metamaterial-based systems.

Figure 1 .
Figure 1.(a) Schematic drawing of the assembling of the air-spacer absorber.(b) The schematic and (c) cross section of the metamaterial unit cell.

Figure 3 .
Figure 3. Fabrication process flow of the device: (a) LPCVD SiNx, (b) ICP etching, (c) Lift-off, (d) KOH etching, (e) Au evaporation, (f)-(g) Flip-chip bonding.(h) Photograph of the TMA.(i) The microscopy image of the meta-atom array.The fabricated devices were characterized by a THz time-domain spectroscopy at normal incidence.The measured time-domain reflection signals were plotted in Figure 4(a) and converted to the frequency-domain signals using the Fourier transform.The reflection spectrum of air was listed as a reference.Then, the frequency-domain signals with different polarizations of the incident THz pulse were normalized with the reference signal, as shown in Figure 4(b).When the incident THz pulse is parallel to the metal strip pair, two absorption peaks can be observed at 0.515 THz (0.9451) and 0.702 THz (0.9244).The full width at half maximum for peak 1 and peak 2 are approximately 30 GHz (Q1≈17.2) and 19 GHz (Q2≈36.9),respectively.When the incident THz pulse is perpendicular to the metal strip pair, the absorption is about zero in the range from 0.4 to 0.8 THz.The differences between the experimental and simulated results may arise from the fabrication error.

Figure 4 .
Figure 4. (a) The measured time-domain reflection signals.(b)The measured absorption spectra with different polarizations of the incident THz pulse.