Using infrared radiation suppression materials is regarded as an effective method to address the worsening thermal pollution owing to their favorable low-emission and radiation-cooling properties. According to the Stefan-Boltzmann law, the reduction of the thermal surface emissivity of a material can effectively suppress the infrared radiant energy. Metamaterial (MM) is an emerging branch of infrared radiation suppression materials with highly flexible spectral modulation capability and spectral designability. The infrared emission bandwidth and position will be precisely regulated by adjusting their pattern shapes and structure parameters, and thus the selective modulation of the infrared emission spectrum can be realized. However, due to the limitation of computer resources and computation power, it has always been challenging to directly obtain the infrared spectral response of millimeter-scale metamaterials through simulation software. Therefore, we hope to establish a computational model of the infrared spectral response of millimeter-scale metamaterials, which provides a novel approach for the design of broadband infrared radiation suppression functional devices.

In this paper, the mid- and far-infrared spectral response of millimeter-square metamaterials is simulated based on the time-domain finite-difference method. Combined with the electric field scattering effect, the impact of the marginal electric field strength distribution of the millimeter square pattern on the infrared reflectivity is analyzed. According to the traditional empirical formula, the computational model of the infrared spectral response of millimeter-square metamaterials is proposed. Using the full-wave electromagnetic simulation software FDTD and the parameter scanning method, the effects of the thicknesses of Au and SiO₂ on the infrared spectral response are investigated, and the optimal thicknesses of the reflector layer and the substrate layer are identified. Herein, two square metamaterials with the same filling ratio and different unit periods are designed. Then, this objective is discretized into independent solution units such as vertices, edges, and continuous media, while the x and y directions are set as PML and periodic boundary conditions, respectively. The infrared spectral response and electric field distribution of the millimeter-square metamaterial are obtained by iterative calculation and weighted superposition, and the influence of the electric field scattering effect on the spectral response in the mid- and far-infrared bands is verified. After that, the samples of the designed metamaterials are prepared in this paper by utilizing a stainless-steel mask plate and magnetron sputtering technology. In addition, the reflectance spectra of the samples in the full infrared band from 2 to 16 μm are measured using a Fourier transform infrared spectrometer.

The simulation results in Fig. 5 show that the infrared reflectance spectral trends of the two models are nearly close within the 2-16 μm band. However, in the range of 8-10 μm, the amplitude of the infrared reflectance spectra of MM1 is larger than that of MM2, with a peak reflectance of up to 83.58%. To interpret the physical mechanism underlying the above phenomenon, the electric field intensity distribution in the marginal scattering region of the metamaterial is simulated at the reflectance peak of 8.8 μm in Fig. 6. Due to the variation of the unit period, the electric field scattering effect in the marginal region leads to a slight difference in the amplitude of the infrared reflection spectrum. To verify the theoretical reliability of the model and the practical infrared radiation suppression characteristics, the measured infrared reflection spectra are shown in Fig. 7. As the cell size reduces, MM1 exhibits higher infrared reflectance performance, verifying that the electric field scattering effect in the marginal region contributes significantly to the millimeter-scale metamaterial infrared spectral response. The error between the theoretical and practical values is approximately 5%. Finally, Fig. 8 compares the results of this work with relevant studies, demonstrating the advantages of lower layer number, wider bandwidth, and lower emission.

A computational model of the infrared spectral response of millimeter-scale metamaterials is proposed to simulate the infrared reflectance spectra and electric field strength distribution of metamaterials. It can be found that when the filling ratio is identical, the decrease of the unit period leads to the enhancement of the marginal electric field scattering effect of the metamaterials, which improves their reflectance properties in the 8-10 μm long infrared wavelength band. Au square metamaterials are prepared using magnetron sputtering technology and stainless-steel mask plates. The reflectivity of the fabricated metamaterials exceeds 81.9% in the range of 2-16 μm middle and long infrared wavelength bands when the periodic cell is 0.5 mm. In addition, the infrared reflectivity even reaches 87.05% in the 8-10 μm wavelength range, which shows superior infrared radiation suppression properties of the sample. The infrared reflectance spectral trends obtained from the simulation and test are in good agreement. In conclusion, the computational model proposed in this paper effectively improves the design efficiency of millimeter-scale metamaterial infrared reflectors, which is promising in the field of broadband infrared radiation suppression functional device design.