# Robust Conformal Perfect Absorber Involving Lossy Ultrathin Film

^{*}

## Abstract

**:**

## 1. Introduction

_{1.5}Sb

_{0.5}Te

_{1.8}Se

_{1.2}(BSTS) film on the top, an absorptance of >95% can be achieved, covering a wavelength ranging from 470 to 1000 nm with a bandwidth of 72%. It is found that the excellent absorption performance is maintained for a wide incident angle of up to 50°, which can be readily applied to curved surfaces. We believe the conformal perfect absorbers can find wide applications in optoelectric devices.

## 2. Results and Discussion

_{2}middle layer, and an optically thick metal aluminum (Al) substrate is used to block all the transmission. The dielectric constant of the SiO

_{2}and Al are described by fitting the Palik data in Lumerical’s material library, while the dielectric function of the BSTS film is taken from ref. [27]. Figure 1 shows the real and imaginary parts of the dielectric constant of the BSTS film, which supports a zero real part at a wavelength of ~670 nm. Notably, the imaginary part is very considerable, which results in a high heat dissipation rate.

_{2}are optimized to be 5 and 100 nm, respectively. A plane wave is normally incident on the structure. Significantly, the absorption can be as high as 95%, covering the wavelength ranging from 470 to 1000 nm with a bandwidth of 72%, as the solid black line shows in Figure 2. Furthermore, a high absorptance of >99% can be maintained in a considerable wavelength band ranging from 500 to 918 nm with a bandwidth of 58% centered at the wavelength of 710 nm, which is close to the ENZ wavelength of 670 nm.

_{11}and S

_{21}represent the reflection and transmission coefficients of the system, respectively. Here, S

_{11}can be extracted from the simulation and S

_{21}= 0 due to the optically thick Al substrate. As shown in Figure 2, the high absorption band matches well with the wavelength range of the impedances of the vacuum for both the ZIM and MZIM structures. Therefore, the outstanding absorption performance can be attributed to the impedance matching between the environment and the entire structure. The lossy BSTS layer will then take charge of energy dissipation in the entire system. In the near infrared range, the decrease in the absorptance of the ZIM structure can be mainly contributed to the larger mismatch in impedance caused by the larger positive dielectric constant. However, for the MZIM structure, the resonance initiated by the top Al block still works well, and therefore the corresponding absorptance remains higher.

_{2}layer. As depicted in Figure 4a, when there is no BSTS layer, the low absorptance mainly results from the loss of the Al substrate, with a maximum of less than 25%. However, the absorptance is significantly increased when a layer of BSTS film is added. As the thickness of the BSTS film increases, the absorptance reaches an optimized performance when t

_{BSTS}= 5 nm—i.e., a high absorptance and considerable bandwidth. Meanwhile, the central wavelength of the absorption curve remains pinned at ~670 nm as the thickness of the BSTS film varies. As the thickness of the BSTS layer increases further, the absorptance of ~670 nm shows a more pronounced decline. Essentially, the thickness of the BSTS layer is critically responsible for the trade-off between light penetration and structure absorption. The reduction in absorption for the thicker BSTS film arises from the stronger blocking effect, which weakens the interaction strength between the incident energy and the structures.

_{2}has a slight influence on the absorptance. As shown in Figure 4b, by varying the thickness of the SiO

_{2}layer from 70 to 120 nm, the absorption band slightly shifts, but the absorptance maintains as high as 90% in a broadband, which indicates a fine robustness to the variation in the spacer. In particular, when the thickness of SiO

_{2}is 100 nm, the bandwidth of absorptance >99% is optimized, with a center close to the ENZ wavelength.

_{2}, and Al substrate—are designed with the same sinusoidal function, the vertical thicknesses (along z-axis) of BSTS and SiO

_{2}are 5 and 100 nm, respectively. As a result, the thickness of each layer along the normal direction to the surface changes with the coordinates, as schematically shown in the inset of Figure 6. Only the thicknesses at the top and bottom of the curvature are 5 and 100 nm for BSTS and SiO

_{2}, respectively, whereas the layer is thinner than the optimized parameters in planar ZIM. Remarkably, although the absorption decreases at the short and long wavelength sides of the spectrum, the absorption of the proposed curved ZIM structure changes slightly with the surface morphology variation at the center band ~670 nm for both TM and TE-polarized incidences. As shown in Figure 6, the absorptance remains higher than 90% even when α is 60°. More importantly, the excellent absorption performance is immune from the variations in the thickness of the BSTS and SiO

_{2}layer. Therefore, the proposed ZIM structure could find wide applications as a conformal perfect absorber, with great simplification in comparison with structural metamaterials [31].

_{2}layer for a planar multilayer design, which can be regarded as the geometry angle being 0. The low absorptance (~49.6%) mainly arises from the negligible absorption in the SiO

_{2}layer. In contrast, the absorptance of the curved surface increases remarkably, which is >60% even when α = 60°. Such a remarkable increase in absorption can be understood from the perspective of field distributions. For planar structure, the field is uniformly distributed in the along x-axis. However, the spatial distributions of electric and magnetic field varies as the geometry angle increases. As shown in Figure 7(a1–a6), as the geometry angle increases, the electric field gradually exhibits standing-wave-like distributions in the dielectric layer and inside the top valley separately. The deeper valley could support higher-order standing waves. Furthermore, the electric field tends to be sucked into the gap for lager geometry angles. A similar standing-wave-like distribution is also applied to magnetic field, albeit being mainly confined to the dielectric layer. A shallow valley enhances the field confinement and thus lengthens the interaction strength between the incident light and dissipation layer. As shown in Figure 7(c1), in addition to the BSTS layer, incident energy starts to be dissipated at the surface of the Al substrate. Consequently, the total absorptance increases to 90% when α = 10°. The absorptance is further boosted up to 97% as α increases to 30°. However, as α increases to 40°, part of the electric field is confined to the valley, which holds a dipole-like feature. Therefore, the energy gets easier to be radiative to the far field and the absorptance decreases. As a results, less energy is dissipated in the BSTS layer, as shown in Figure 7(c4). The absorptance degrades further as α increases to 50° due to the stronger radiative effect. Nevertheless, the absorptance increases again when α = 60°, which results from an inefficient radiation since the field goes deeper inside the valley.

_{2}layer, which results in the energy dissipation at the SiO

_{2}/Al interface. In comparison with the field distribution at 428 nm, the standing wave-like effect can be negligible at the long wavelength side. In addition, the distribution of absorption area is almost continuous at the center part of valley, which further confirms the absence of the standing wave-like effect. Therefore, as the geometry angle increases, the absorptance decreases monotonically due to the strong scattering by the large slope of valleys. A similar trend also occurs for TE-polarized illumination.

_{2}can be readily deposited on Al substrate. It is also believed that a 5 nm-thick BSTS film could be possible. As shown in our previous work, a 5 nm-thick Bi

_{2}Te

_{3}, another type of topological insulator, can be fabricated in an experiment [33]. Therefore, the proposed perfect absorber in this work could be fabricated in the future.

## 3. Conclusions

_{2}layers. The realized perfect conformal absorber using ZIM structures could act as a promising role for a wealth of absorption-related applications. Moreover, the involvement of ENZ can also open an exciting avenue to designing metamaterials for robust and enhanced optical functionalities.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Real (black line) and imaginary (red line) parts of the permittivity of the Bi

_{1.5}Sb

_{0.5}Te

_{1.8}Se

_{1.2}(BSTS) film. The real part of the permittivity is close to zero at a wavelength of 670 nm.

**Figure 2.**Comparison of the absorptance and impedance for different structures. The thicknesses of the BSTS film are SiO

_{2}t

_{BSTS}= 5 nm and t

_{SiO2}= 100 nm, and the Al substrate is optically thick to block the light transmission. In the MZIM structure, 30 nm-high and 20 nm-wide Al wire arrays are positioned on the top, with a periodicity of 100 nm. The upper grey dashed line indicates an absorptance of 95%, while the lower one specifies an impedance of 1.

**Figure 3.**Distributions of the (

**a**) electric field amplitude, (

**b**) phase, and (

**c**) absorptance as a function of the wavelength for the ZIM structure. The dashed lines are plotted to indicate the interface between different materials. Here, t

_{BSTS}= 5 nm and t

_{SiO2}= 100 nm.

**Figure 4.**Dependence of the absorptance of the ZIM structure on the thickness of (

**a**) the BSTS layer by fixing t

_{SiO2}= 100 nm and (

**b**) the SiO

_{2}layer by fixing t

_{BSTS}= 5 nm. Linear polarized light is normally incident on the ZIM structure. Dashed lines represent an absorptance of 90%.

**Figure 5.**Dependence of the absorptance of the ZIM structure on the incident angle under the illumination of (

**a**) TM and (

**b**) TE-polarized incident lights. Here, t

_{BSTS}= 5 nm and t

_{SiO2}= 100 nm. Insets show the simulation configurations.

**Figure 6.**Dependence of the absorptance of a conformal structure on the geometric angle α under the illumination of (

**a**) TM and (

**b**) TE-polarized incident lights. Here, t

_{BSTS}= 5 nm and t

_{SiO2}= 100 nm. Note: the thickness is measured along the z-axis in the following simulations. The surface curvature is defined as z = Asin (2πx/p), where the periodicity p is 314 nm and A is the amplitude. The geometry angle can thus be defined as α= atan (4A/p).

**Figure 7.**Calculated distributions of the normalized electric field (

**a1**–

**a6**), normalized magnetic field (

**b1**–

**b6**), and absorption (

**c1**–

**c6**) at 428 nm as the geometry angle α increases from 10° to 60° under the illumination of TM-polarized light propagating along the z-axis. Here, t

_{BSTS}= 5 nm and t

_{SiO2}= 100 nm.

**Figure 8.**Calculated distributions of the normalized electric field (

**a**,

**b**), normalized magnetic field (

**c**,

**d**), and absorption (

**e**,

**f**) at wavelengths of 808 and 1000 nm when the geometry angle α is 50° under the illumination of TM-polarized light propagating along the z-axis. Here, t

_{BSTS}= 5 nm and t

_{SiO2}= 100 nm.

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**MDPI and ACS Style**

Zhang, L.; Wang, K.; Chen, H.; Zhang, Y. Robust Conformal Perfect Absorber Involving Lossy Ultrathin Film. *Photonics* **2020**, *7*, 57.
https://doi.org/10.3390/photonics7030057

**AMA Style**

Zhang L, Wang K, Chen H, Zhang Y. Robust Conformal Perfect Absorber Involving Lossy Ultrathin Film. *Photonics*. 2020; 7(3):57.
https://doi.org/10.3390/photonics7030057

**Chicago/Turabian Style**

Zhang, Lei, Kun Wang, Hui Chen, and Yanpeng Zhang. 2020. "Robust Conformal Perfect Absorber Involving Lossy Ultrathin Film" *Photonics* 7, no. 3: 57.
https://doi.org/10.3390/photonics7030057