Abstract
In this paper， we propose an RLC equivalent circuit model theory which can accurately predict the spectral response and resonance characteristics of metamaterial absorption structures， extend its design， and characterize the parameters of the model in detail. By employing this model， we conducted computations to characterize the response wavelength and bandwidth of variously sized metamaterial absorbers. A comparative analysis with Finite Difference Time Domain （FDTD） simulations demonstrated a remarkable level of consistency in the results. The designed absorbers were fabricated using micro-nano fabrication processes， and were experimentally tested to demonstrate absorption rates exceeding 90% at a wavelength of 9.28 µm. The predicted results are then compared with test results. The comparison reveals good consistency in two aspects of the resonance responses， thereby confirming the rationality and accuracy of this model.
Infrared detection technology involves multiple disciplines and fields. The uncooled infrared detectors have been used in infrared thermal imaging， energy harvesting， and heat emitters by virtue of their low cost， low power consumption， and small siz
In recent years， the emergence of metamaterials has attracted a great deal of attention. Metamaterials are artificially produced composite materials with unique electromagnetic properties not found in nature. The fundamental unit is composed of subwavelength dimensions. By altering the structural dimensions， shape， and spatial arrangement of individual subwavelength basic units， control over the overall or local optical field is achieved at the subwavelength scale. Additionally， it is possible to regulate the dielectric constant and magnetic permeability of composite structures， endowing them with characteristics of nearly perfect absorption in specific frequency bands. This particular electromagnetic property has excellent potential in various applications， including metamaterial absorbers （MAs）， photonic crystals， plasmonic resonance， skin effect enhancement， stealth technology， et
The most common structure of MAs consists of metal-insulator-metal with a thickness of only subwavelength dimensions. This structure leverages surface plasmons （SPs） at subwavelength scales to achieve strong light-matter interactions. Simultaneously， it realizes ideal absorption responses by reducing reflection and eliminating transmission. In 2008， Landy et al. proposed MAs in microwave band for the first time and achieved greater than 88% absorption at 11.5 GHz by experiment
This work introduces long-wavelength infrared window metamaterial absorbers that can be integrated into uncooled infrared detectors. It elucidates the absorption mechanism and resonance principles， followed by design and experimental validation. We simultaneously expanded the RLC equivalent circuit model. By predicting resonance characteristics， including wavelength response and full width at half maximum （FWHM）， and comparing them with FDTD simulation results， the rationality of the model was validated. The impact of the structural parameters of the designed MAs on resonance response was analyzed. In the end， we fabricated the MAs by micro-nano fabrication processes and conducted tests using a Fourier Transform Infrared Spectrometer （FTIR）. The absorption rate of the sample at 9.28 µm was more than 90%. The test results were compared and validated against the predictions of the RLC circuit， further confirming the feasibility and relevance of the model. This paper comprehensively elucidates the resonant behavior of MAs， providing a profound and intuitive analysis of the resonance response mechanism. The study offers design guidance for the development of efficient and cost-effective novel uncooled infrared detection technologies.
The proposed metal-insulator-metal （MIM） three-layer MAs structure is shown in
Fig. 1 MIM-MAs infrastructure and related performance： （a） schematic of the proposed structure of MIM-MAs； （b） optical parameters of AlN and Mo； （c） absorption， reflectivity and transmittance curves of the MAs structure
图1 MIM-MAs基础结构和相关性能：（a） 所提出MIM-MAs结构示意图；（b） AlN和Mo材料的光学参数；（c） MAs结构的吸收、反射和透射响应示意图
| Parameter | Symbol | Value |
|---|---|---|
| Period | P［µm］ | 3.6 |
| Characteristic length （width） | w［µm］ | 2.6 |
| Thickness of top metallic pattern | tAu［nm］ | 50 |
| Thickness of dielectric spacer | tAlN［nm］ | 200 |
| Thickness of bottom metallic pattern | tMo［nm］ | 100 |
When a specific infrared light irradiation to the nanometer metal surface， the incident light （surface electromagnetic wave） and the top layer of metal in the free electron element interact to form surface plasmons （SPs）， the occurrence of surface plasmon resonance （SPR）. This phenomenon induces an electric dipole resonance， which excites the coupling effect between the underlying metal plates through the subwavelength dielectric layer gap， generating a reverse oscillating current and exciting a magnetic dipole. These electric and magnetic dipoles resonate synergistically， effectively dissipating the incident light and achieving high absorption in the target spectral range.
According to the law of conservation of energy， the MAs absorptivity formula is A=1-R-T， where A， R， and T are absorptivity， reflectivity， and transmittance， respectively. When the thickness of the underlying metal Mo is greater than the skinning depth of the LWIR window， the light cannot penetrate， and the transmittance T is approximated to be 0. Therefore， its absorptivity is A=1-R. The designed MAs are simulated and analyzed using FDTD software. In the simulation， the light source propagates as a plane wave along the z-axis direction with perfectly matched layer （PML） boundary conditions and periodic boundary conditions along the x and y directions. The dielectric constant and refractive index parameters of the Au material are taken from the literature data of Pali
Due to the central symmetry of the designed top nanostructures， the wavelength responses obtained are the same when both transverse magnetic （TM） and transverse electric （TE） waves are used for incidence. In the simulation， the absorption spectrum response is obtained using transverse magnetic （TM） wave incidence， as shown in
In order to explore and clarify the mechanism of perfect absorption of MAs in more depth， the electric and magnetic field distributions of the designed MAs at 9.62 µm were computationally characterized and analyzed， as shown in
Fig. 2 Mapping of electric and magnetic field distributions at MAs absorption peak： （a） x-y plane and （b） x-z plane electric field distributions； （c） x-y plane and （d） x-z plane magnetic field distributions； （e） x-y plane and （f） x-z plane power density distributions
图2 MAs吸收响应处的电场和磁场分布图：（a） x-y平面和（b） x-z平面电场分布；（c） x-y平面和（d） x-z平面磁场分布；（e） x-y平面和（f） x-z平面功率密度分布
The distribution of the electromagnetic field indicates the combination of localized surface plasmon resonance modes and dipole resonance modes， satisfying the wave vector matching condition of the incident electromagnetic wave. The energy of the incident electromagnetic wave can be effectively confined within the intermediate dielectric layer， as shown in Figs.
Based on the MAs absorption mechanism， we employ an RLC equivalent circuit model to elucidate the physical mechanisms and resonance effects related to the excitation of localized surface plasmon resonance and magnetic dipole resonance. Sakurai et al. and Lee et al. have developed equivalent circuit models for characterizing the geometric effects of MA
Underneath each subwavelength metal nanostructure exists an independent magnetic field distribution， and these distributions are mutually independent. It can be assumed that the entire device is connected by an equivalent circuit composed of multiple RLC lumped elements. The RLC equivalent circuit model of the extended single subwavelength cell is shown in
| , | (1) |
| , | (2) |
Fig. 3 Proposed equivalent circuit model structure： （a） schematic diagram of the RLC equivalent circuit model for MIM-MAs； （b） real and imaginary parts of the relative impedance of the equivalent circuit model
图3 等效电路模型结构：（a） MIM-MAs结构等效电路模型示意图；（b） 等效电路模型相对阻抗的实部和虚部
where ε0 （≈8.854×1
| , | (3) |
where µ0 （=4π×1
Due to the interaction of electric field vectors， the current loop at the metal interface is excited， resulting in the resonance of magnetic dipoles. Assuming negligible influence from other factors， all the work done by the current is entirely converted into magnetic field energy. Taking a single MAs structure as an example， the magnetic flux ψ and the increase in magnetic energy dWm for an RLC circuit can be described as follows：
| , | (4) |
| , | (5) |
where is the mutual inductance coefficient.The current in this circuit is assumed to start from zero， and the loop current increases by the same percentage γ， i.e.， di=Idγ. After integration， the magnetic field energy Wm converted from the work done by the current loop in a single RLC equivalent circuit is expressed as：
| , | (6) |
when only one circuit exists， M11 is equal to L1， representing the inductance within a single current loop. The relationship between the total mass Me of the moving charges， the drift velocity v when free electrons drift， and the kinetic energy generated by the internal electrons in the metal can be described as follows：
| , | (7) |
| , | (8) |
| . | (9) |
As shown in Equations （
| , | (10) |
| . | (11) |
Therefore， by energy conservation， the kinetic energy generated by the motion of electrons is equal to the magnetic field energy converted by the work done by the current， i.e.，
| , | (12) |
| , | (13) |
| , | (14) |
| . | (15) |
The above RLC lumped circuit elements are all represented using fundamental equivalent formulas for the geometric parameters and material properties of MAs structures. This approach plays an important role in guiding the design and optimization of MAs. Simultaneously， the structure model and physical mechanism of MAs can be reverse-designed and analyzed through backward deduction and iterative computations. The relative impedance Zri（ω） and the reflection coefficient R（ω） of the equivalent circuit model can be described a
| , | (16) |
| , | (17) |
where Zt（ω） and Z0 are the total set element impedance and free space impedance， respectively. As shown in
To further substantiate the accuracy of the RLC equivalent circuit model， we calculated resonance conditions for different top subwavelength metal nanostructure widths and periods within this model. The relevant parameters of its associated R， L， and C components have been included in
| w （μm） | λFDTD （μm） | λRLC （μm） | Cm （F） | Cg （F） | Lm （H） | Le （H） | L | Rc （Ω） | Rg （Ω） |
|---|---|---|---|---|---|---|---|---|---|
| 2.2 | 8.97 | 8.91 |
1.25×1 |
4.62×1 |
1.26×1 |
6.43×1 |
1.22×1 | 0.45 | 1.23 |
| 2.3 | 9.16 | 9.17 |
1.48×1 |
4.74×1 |
1.26×1 |
6.65×1 |
1.18×1 | 0.43 | 1.20 |
| 2.4 | 9.32 | 9.27 |
1.84×1 |
4.84×1 |
1.26×1 |
6.98×1 |
1.16×1 | 0.34 | 1.13 |
| 2.5 | 9.46 | 9.43 |
2.04×1 |
5.02×1 |
1.26×1 |
7.12×1 |
1.12×1 | 0.38 | 1.21 |
| 2.6 | 9.63 | 9.61 |
2.21×1 |
5.19×1 |
1.26×1 |
7.38×1 |
1.08×1 | 0.41 | 1.26 |
| 2.7 | 9.75 | 9.76 |
2.33×1 |
5.52×1 |
1.26×1 |
7.54×1 |
1.01×1 | 0.41 | 1.13 |
| 2.8 | 9.87 | 9.89 |
2.48×1 |
5.71×1 |
1.26×1 |
7.63×1 |
0.96×1 | 0.40 | 1.12 |
| 2.9 | 9.99 | 10.04 |
2.73×1 |
6.11×1 |
1.26×1 |
7.92×1 |
0.84×1 | 0.39 | 1.10 |
| 3.0 | 10.09 | 10.17 |
2.88×1 |
6.36×1 |
1.26×1 |
8.18×1 |
0.78×1 | 0.39 | 1.09 |
| 3.1 | 10.20 | 10.29 |
3.03×1 |
6.77×1 |
1.26×1 |
8.67×1 |
0.69×1 | 0.40 | 1.08 |
| 3.2 | 10.31 | 10.37 |
3.36×1 |
6.69×1 |
1.26×1 |
8.96×1 |
0.65×1 | 0.38 | 1.07 |
Fig. 4 Comparison of RLC circuit model prediction results and FDTD simulation results： At P=3.6 µm， （a） resonant wavelength and （c） FWHM for different values of w are as follows； At w=2.6 µm， （b） resonant wavelength and （d） FWHM for different values of P are as follows
图4 RLC电路模型预测结果与FDTD仿真结果对比：在P=3.6 µm时不同w值的（a） 谐振波长和（c） FWHM；在w=2.6 µm时不同P值的（b） 谐振波长和（d） FWHM
Calculations and comparisons were conducted for the FWHM in the absorption response， as shown in Figs.
Fig. 5 Preparation by MIM-MAs process： （a） process steps for fabrication of MAs； （b） SEM image of the fabricated MAs； （c） tested MAs absorption response （orange points） versus the absorption response predicted by the RLC equivalent circuit model （blue points）
图5 MIM-MAs工艺制备：（a） 制备MAs工艺步骤；（b）所制备MAs的SEM图像；（c）测试MAs的吸收响应（橙色）与RLC等效电路模型预测的吸收响应（蓝色）对比
The structure comprises a square array of nanostructures， with geometric dimensions outlined in
According to the test results， the manufactured MAs samples exhibit an absorption peak at 9.28 µm， where the absorption rate exceeds 90%. The obtained result exhibits slight discrepancies when compared with the predictions from the RLC circuit model. Upon comparing the results， it is evident that the absorption peak in the test results undergoes a blueshift， accompanied by a slight decrease in absorption rate. This phenomenon can be attributed to two terms. First of all， due to insufficient metal surface treatment during the preparation process， some metals are taken away by the photoresist tape during the stripping process， which reduces the width of the square gold nanostructure. Secondly， in terms of material parameters， the optical material constants represented in the circuit model are slightly different from those measured in actual machining. Consequently， this results in deviations in both the wavelength and absorption rate of the absorption peaks.
At wavelengths of 5.94 µm and 11.25 µm， parasitic peaks with absorption rates below 40% are present. This is attributed to the incomplete removal of residual photoresist on the MAs surface during the lift-off process. The residual photoresist adheres to the metal surface， leading to the appearance of local parasitic peaks and exerting a certain influence on the test results. In the subsequent preparation process， the optimization of processing steps and parameters can effectively prevent the occurrence of the aforementioned issues. Overall， the RLC equivalent circuit model provides a good prediction for MAs.
In this study， a theoretical model and experimental validation of MIM metamaterial absorbers that can be integrated with an uncooled infrared detector are presented. The RLC equivalent circuit model is extended and designed to explain and analyze the physical mechanism and resonance effect of MAs in depth based on the geometrical effect of the structure. The model successfully predicted the resonant characteristics， including the resonance frequency and FWHM. The designed MAs structures were fabricated using micro-nano processing techniques and subjected to FTIR testing. The results indicate that absorption rates exceeding 90% were achieved at a wavelength of 9.28 µm. Comparing the predicted results of this model with the FDTD simulation calculation results and test results， a better resonance response match is obtained， which further verifies the rationality and accuracy of the model. This study contributes to an in-depth understanding of the wavelength response and resonance mechanism of MAs and guides the design and optimization of metamaterial absorbers.
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