Optimal Design of Infrared Wavelength‐Selective and Microwave Transmitting Bionic Metasurface

The radar and infrared (IR) compatible stealth technology is an important technology in the military field. Inspired by the special triangular‐shaped hairs from the Saharan silver ants, a bionic structure with IR wavelength‐selective emission and large microwave transmission simultaneously is presented. An algorithm based on the combination of Bayesian optimization and finite different time domain method is proposed for optimal design. The proposed structure is an indium tin oxide (ITO)‐hairs/ITO‐film/PET‐substrate structure. The IR wavelength‐selectivity is reached by the hair covered ITO film, and the microwave transmission is realized by patterning gap arrays on continuous films. After optimal calculation, the optimal bionic structure is obtained. The change of the structural parameters of the meta‐atom will lead to a change in microwave transmission. When p = 0.1 mm and w = 0.9 mm, the maximum and minimum transmittivity of the infrared stealth layer (IRSL) in 2–20 GHz are 0.972 and 0.764, respectively, while the estimated emissivity in 3–5, 5–8, and 8–14 µm wavebands are 0.592, 0.730, and 0.373, respectively. It illustrates that the IRSL maintains IR wavelength‐selective emission while maintaining high microwave transmission. This study provides a strategy for bionic structure applied in compatible stealth.


Introduction
[3][4] Radar and IR detection are two mostly employed approaches. [5,6]The aim of radar stealth is to reduce the radar cross-section of target by reducing the radar echo power or deflect the echo direction, and the key of IR stealth is to reduce or change the IR radiation characteristics of the target. [7,8]11] Generally, radar stealth materials or structures need low reflection and high absorption while IR stealth materials or structures require low emissivity means low absorptivity and high reflectivity. [5]t is difficult to realize IR and radar stealth simultaneously, because of their opposite working principles.Hybrid artificial metamaterials provide the possibility to realize compatible stealth in both radar and IR waveband, which is an effective approach for solving the problem of radar-IR compatible stealth.Zhong et al. proposed a structure to realize radar-IR bi-stealth by the combination of two metasurfaces that control the IR emission and microwave absorption, respectively. [6]Xu et al. designed a hybrid metasurface composed of radar absorber layer and IR shielding layer, which can achieve high microwave absorption and low IR emission. [7]Yang et al. designed a radar-IR bi-stealth structure composed of infrared camouflage layer with different IR emissivity and radar absorber with high radar absorptivity, which is below the infrared camouflage layer. [9]Zhang et al. proposed multilayered microwave-IR bi-stealth metasurface to achieve broadband absorption in microwave band and low emission in IR waveband. [12,13]The common feature of these researches is to achieve radar-IR compatible stealth by combining infrared shielding layer and radar absorber layer.The infrared shielding layer has low emissivity in IR band and allows the radar wave to transmit it, which is realized by patterning some gaps arrays on continuous high reflectivity materials.And the microwave could be absorbed by radar absorber layer below the infrared shielding layer.However, few works have paid attention to the wavelengthselectivity of infrared stealth layer (IRSL) for the compatible stealth structure.There are many reports on the wavelengthselectivity of single IR stealth.For example, Xu et al. proposed a radiative metasurface with visible tunability. [14]Pan et al. reported two simple photonic structures for multi-band infrared camouflage. [15]However, these single IR structures generally do not consider the compatibility of radar stealth.Saharan silver ants can inhabit extreme temperature conditions, which has been proved to benefit from their dense array of triangular hairs with wavelength-selectivity in the visible and near-infrared range. [16]Mimicking the photonic structure of their hairs, hair-like photonic structures with wavelength-selectivity can be designed. [17]nspired by the Saharan silver ants with triangular-shaped hairs, a bionic structure with IR wavelength-selective emission and large microwave transmission simultaneously is presented.An algorithm based on the combination of Bayesian optimization (BO) and finite different time domain (FDTD) methods is proposed for optimal design of the IR wavelength-selectivity.And the microwave transmission is realized by patterning gap arrays on continuous films.The influence of the structural parameters for the bionic structure on the IR wavelength-selectivity is researched.The optimal design is obtained by the combination of BO and FDTD methods.The microwave transmission of the IRSL is also investigated.

Design and Simulations
To achieve IR and radar compatible stealth, the key is to design an IRSL with high microwave transmittance.In this work, the IRSL is implemented by a bionic structure with IR wavelengthselectivity and microwave transmittance.Shi et al. [16] have proved that the reflectivity in visible and near-infrared ranges and the emissivity in the mid-infrared range of the ant's body surface are enhanced by their triangular hairs covered on their body surface.Sahara silver ants have unique hairs that can be considered as a photonic structure with wavelength-selectivity in multiband. [17]Inspired by Saharan silver ants, we will design an infrared wavelength-selective and microwave transmitting bionic structure.The proposed structure is an indium tin oxide (ITO)hairs/ITO-film/PET-substrate structure.This structure aims to exhibit high emittance in the 5-8 μm nonatmospheric window and low emittance in the 3-5 and 8-14 μm atmospheric window, and demonstrate high transmittance in microwave band that enables it to combine with other structures to achieve radar absorption.The optimal design is performed based on the combination of the BO method and FDTD method, and the flowchart is shown in Figure 1.

Numerical Simulations
The FDTD method is used to solve Maxwell's equations in bionic structure.In FDTD method, the Maxwell curl equations are discretized in the Yee cell space and solved to describe the radiation Comparing the present results with the simulation results in reference. [16]ocess. [18,19]Maxwell's curl equations in non-magnetic material can be expressed as: [20] { where E and H are the electric and magnetic fields, respectively,  r is the complex relative dielectric constant,  0 is the dielectric constant in vacuum, and μ 0 is the permeability in vacuum.Equation ( 1) is suitable for 3D study, while Maxwell's equations can split into two independent equations for 2D study.In the TE case, Maxwell's equations can be expressed as: [20] ⎧  The FDTD formulae with different scheme are available in any other reports, [18,19] and we will not repeat them here.The transmission   can be calculated by: [20]   = where S is the Poynting vector in the transmission plane (monitor plane), P ,in is the incident source power, and v is the surface normal.The reflectivity   can be obtained by placing a monitor in the reflection direction since   equals to   in reflection direction.
The ITO with surface resistance of 6 Ω per sq is deposited and patterned on dielectric substrate to construct the bionic metasurface.There are several materials that can be adopted as substrate, such as polyimide (PI), polyethylene terephthalate (PET), polymethyl methacrylate (PMMA), etc.We select the PET with a thickness of 0.125 mm and a permittivity of 3.0(1 -0.06i) [12] as substrate, which is flexible and transparent.The permittivity of ITO in IR band can be expressed by Drude model: [13] where  b = 3.95,  p = 3.07 × 10 15 rad s −1 , and  = 1.82 × 10 14 rad s −1 .ITO exhibits dielectric properties in visible and near IR band, while it behaves like a metal in the middle IR band.The continuous ITO film on the substrate is patterned with some gaps array, which enables the microwave to transmit through them.The smallest unit of the metasurface containing bionic structure is called meta-atom.The IR emissivity of the metasurface with gaps array can be calculated by the filling ratio of the meta-atom: [7,13] where  m is the emissivity of the bionic structure,  s is the emissivity of the dielectric substrate, and f m is the filling ratio of the bionic structure.Obviously, the emissivity is mainly dependent on the metallic filling ratio.By properly designing, a low IR emissivity could be realized.Thus, a periodic square patch structure unit with a high filling ratio was used to achieve high reflection of IR waves.

Implementation of the Bayesian Optimization
BO is a technique developed for optimizing time-consuming engineering simulations that guides the choice of experiments during materials design to find good design in as few explorations as possible. [21]By leveraging the surrogate model and the acquisition function, it can make informed decisions on where to sample next, reducing the number of costly evaluations required compared to other optimization methods.The central idea of BO is based on Bayes' rule: [22] p (y|x) = p (x|y) p (y) The tree-structured Parzen estimator (TPE) is used as a surrogate model in this work, which models p(x|y) by transforming generative process, replacing the distributions of the configuration prior with non-parametric densities. [23]The TPE defines p(x|y) as two densities: [23] p where l(x) is the density formed by using the observations, g(x) is the density formed by using the remaining observations, and y * is a threshold value.Expected Improvement (EI) is used as an acquisition function in this work.EI is an intuitive criterion and has been shown to work well in a variety of settings. [23]In TPE method, the derived EI is: [23] where  = p(y < y * ) is a quantile.On each iteration, the TPE method returns the candidate x * with the greatest EI.The details of TPE method are available in reference. [23]An open-source BO framework optuna is used in our research.

Validation
In order to verify the accuracy of the FDTD simulation for the bionic structure of Saharan silver ants, we compare the present results with the simulation results in the study by Shi et al. [16] In this validation, both the height and the width of the 2D triangular hair are set to 2 μm.The gap between the hair and the substrate is 0.6 μm.The refractive index of hair and substrate (chitin-protein complex) is set to 1.56.As shown in Figure 2, the comparison results are close, which verifies the accuracy of the FDTD simulation in this work.

IR Wavelength-Selectivity Demonstration
Here, the IR wavelength-selectivity for the bionic structure is investigated.The FDTD simulation model for the bionic structure is shown in Figure 3.The plane wave incident from the top of the metasurface.In the x-direction of the computational domain, the boundary conditions are set as periodic boundary.In the y-direction of the computational domain, boundary conditions are set as perfectly matched layer (PML).The FDTD simulation model in Figure 3 contains multiple periods, and only one period is required in the real simulation.
The transmission and reflection spectrums of ITO in IR band are calculated by FDTD method.It can be observed from Figure 4 that the reflectivity is ≈0.9, while the transmittivity is close to zero in 8-14 μm.Then the emissivity of the ITO film is ≈0.1 since it is equal to the absorptivity.It is indicating that thin ITO film has a great IR stealth property, while it does not have IR wavelength-selectivity.Next, we investigate the IR wavelengthselectivity of the bionic structure with triangular hair.The width and height of triangular hair are h 1 and h 2 , respectively.The height of the gap is h g .The effect of the structural parameters on the IR emission spectrum is investigated, and the results are shown in Figure 5. Compared to the ITO film, the bionic structure with hair exhibits significant wavelength-selective emission.As shown in Figure 5a, it can be seen that the structural parameters (h 1 and h 2 ) for the triangular hair significantly affect the IR emission spectrum of the bionic structure.As the size of the hair varies, the emission peak will shift as well, and the increases of widths and heights will lead to red-shifts. Figure 5b shows the gap size also affect the IR emission spectrum while the effect is not significant.It is illustrated that we could realize the IR wavelength-selectivity by bionic structure with triangular hairs.
In order to obtain the expected target emission spectrum, we combined the BO algorithm to optimize the design of bionic structure.In IR band, our target is to obtain high emission in 5-8 μm wavebands (non-atmosphere window) and low emission in 3-5 and 8-14 μm wavebands (atmosphere window).According to the proposed target, the figure-of-merit (FOM) for bionic structure is given as follow: where E b indicates the spectral blackbody intensity.  denotes the spectral emissivity. 1 = 3,  2 = 5,  3 = 8, and  4 = 14 μm.Our objective function is to maximize the FOM.
We consider the width and height of triangular to be 2-10 μm, and the gap size to be 0.1-2.0μm.The computational load is too heavy to calculate all the candidate structures.The applying of BO is beneficial to find the optimal result quickly in few numbers of computational steps.As shown in Figure 6a, the best value of FOM is 1.9128 and the maximum best trial is 1081.We can find that the optimization converged to the maximum FOM within 1500 trials, which demonstrates that BO has effective performance.The optimal structural parameters of the bionic structure are h 1 = 8.20, h 2 = 3.47, and h g = 0.37 μm.The spectral emissivity of the optimal structure is given in Figure 6b.It can be seen that the optimal bionic structure has low emissivity in 3-5 and 8-14 μm and high emissivity in 5-8 μm.The simulated emissivity from TE polarized light is close in 3-8 μm waveband and higher in 8-14 μm waveband when compared to TM polarized light.The average emissivity from non-polarized light in 3-5 and 8-14 μm wavebands are 0.52 and 0.25, respectively.The average emissivity from non-polarized light in 5-8 μm waveband is 0.69 and the maximum emissivity is 0.76 at 6.81 μm.

Microwave Transmission Demonstration
The electromagnetic responses of the ITO film in microwave band are also investigated.As shown in Figure 7, the reflectivity and transmittivity in microwave band are similar to those in IR band.The microwave reflectivity is ≈94% and the microwave transmittivity is close to zero in 2-20 GHz.The ITO film is almost no transmission.The microwave transmission is realized by patterning some gaps arrays on continuous ITO films.Figure 8a presents the top view of the IRSL that is composed of periodic bionic structure on a thin PET substrate.The smallest unit containing bionic structure is called meta-atom.In order to realize IR wavelength-selectivity and microwave transmission simultaneously, both the large bionic structure filling ratio and high microwave transmittivity should be considered.Figure 8b shows the microwave transmittivity (  ) of the IRSL as a function of slit width (p) and pattern width (w).When p = 0.2 mm and w = 0.8 mm, the filling ratio f m = 64%, the maximum and minimum transmittivity of the IRSL are 0.983 and 0.894, respectively.When p = 0.15 mm and w = 0.85 mm, the filling ratio f m = 72.3%, the maximum and minimum transmittivity of the IRSL are 0.978 and 0.839, respectively.When p = 0.1 mm and w = 0.9 mm, the filling ratio f m = 81%, the maximum and minimum transmittiv- ity of the IRSL are 0.972 and 0.764, respectively.It can be seen that the increase of filling ratio will lead to decrease of transmittivity.The high microwave transmission in in 2-20 GHz can be realizing by patterning gaps arrays on continuous films.The emissivity of PET substrate if 0.9. [13]The IR emissivity of the IRSL could be calculated according to Equation (5).The IR emissivity in 3-5, 5-8, and 8-14 μm wavebands of the IRSL are 0.657, 0.766, and 0.484, respectively, when the filling ratio is 64%.The IR emissivity in 3-5, 5-8, and 8-14 μm wavebands of the IRSL are 0.625, 0.748, and 0.430, respectively, when the filling ratio is 72.3%.The IR emissivity in 3-5, 5-8, and 8-14 μm wavebands of the IRSL are 0.592, 0.730, and 0.373, respectively, when the filling ratio is 81%.

Conclusion
In conclusion, a design of bionic structure with IR wavelengthselective emission and large microwave transmission is demonstrated.The results illustrate that the structural parameters of the bionic structure have effect on the IR emission spectrum.Then based on the combination of BO and FDTD methods, the design of the IR selective bionic structure is optimized to maximize the proposed FOM.The maximum FOM could be realized within calculations for less than 1500 structures.The optimal bionic structure is obtained with IR average emissivity of 0.52, 0.69, and 0.25 in 3-5, 5-8, and 8-14 μm wavebands, respectively, when the structural parameters are h 1 = 8.20, h 2 = 3.47, and h g = 0.37 μm.What is more, the microwave transmission of the IRSL is analyzed.By patterning gaps arrays on continuous films, the IRSL maintains IR wavelength-selective emission while maintaining high microwave transmission.When p = 0.1 mm and w = 0.9 mm, the filling ratio f m = 81%, the maximum and minimum transmittivity of the IRSL in 2-20 GHz are 0.972 and 0.764, respectively, while the estimated IR emissivity in 3-5, 5-8, and 8-14 μm wavebands of the IRSL are 0.592, 0.730, and 0.373, respectively.Our results also demonstrate the possibility of designing metasurface for specific applications via BO method.

Figure 1 .
Figure 1.Flowchart for optimal design of the bionic structure based on the combination of the BO method and the FDTD method.

Figure 2 .
Figure 2. Simulation validation.Comparing the present results with the simulation results in reference.[16]

Figure 3 .
Figure 3. FDTD simulation model for the bionic structure.

Figure 4 .
Figure 4.The simulated reflectivity and transmittivity of the ITO film in IR band.

Figure 5 .
Figure 5.The simulated emissivity characteristics of the bionic structure in IR band under a) different width and height of the triangular hair when h g = 0.6 μm, b) different gap size when h 1 = h 2 = 2 μm.

Figure 6 .
Figure 6.a) The search histories include objective value and best value for the optimization, and b) the spectral emissivity of the optimal bionic structure for TE, TM, and Non-polarizations.

Figure 7 .
Figure 7.The simulated reflectivity and transmittivity of the ITO film in microwave band.

Figure 8 .
Figure 8. a) The top view of the IRSL with bionic structure on the thin PET substrate.b) Transmission characteristic of the IRSL under different slit width and pattern width.