Wide-angle broadband absorber based on uniform-sized hyperbolic metamaterial

Yan-Lin Liao; Yan Zhao; Shan Wu; Sujuan Feng

doi:10.1364/OME.8.002484

1. Introduction

Metamaterials (MMs) [1], which are composed of artificial structured materials, have drawn a great deal of attention because of their exotic electromagnetic properties such as cloaking [2], super-lenses [3], negative refraction [4], asymmetric transmission [5] and absorbers [6]. In recent years, many researchers have focused on the metamaterials absorbers because they can be applied in solar cells [7,8], photodetector [9,10], thermo-photovoltaics (TPV) [11,12], and thermal emitters [13,14]. Since Landy et al. reported the first metamaterials absorber in 2008 [6], various absorbers with different structures have been developed for different application demand [15–23]. However, the absorption bandwidths of most metamaterials absorbers are narrow due to the intense electric and magnetic resonance. Such narrow bandwidths limit their applications such as detector and solar cell. To broaden the absorption bandwidth, several methods have been proposed such as interferences in metal-dielectric stacks [24,25], multiple resonances in metasurfaces [26,27], and impedance match design in multilayers [28,29]. On the other hand, hyperbolic metamaterials (HMM), which show dielectric response (i.e., positive permittivity) or metallic response (i.e., negative permittivity) in different directions, can be also used to achieve high absorption in broad continuous wavelengths by superposing the multiple slow-wave modes with tapering sawtooth structures [30]. Since Cui et al. proposed the first HMM absorber in 2012 [30], a variety of HMM absorbers have been proposed and demonstrated at different frequencies including microwave [31,32], terahertz [33], and infrared regions [34–38]. Recently, Lin et al. reported an ultra-broadband HMM absorber by exciting the multiple orders of slow-light resonant modes [39]. However, it is a challenge task to fabricate such absorbers with tapering sawtooth structures because the dose intensity should be carefully designed during the focused ion beam (FIB) milling process.

In this paper, we report a broadband absorber in the infrared regime by using uniform-sized hyperbolic metamaterial composed of the multilayer Au-ZnS gratings with different filling ratios. The simulation results show that the broadband absorption is originated from the multiple slow-wave modes. In addition, the absorption bandwidth can be engineered by adding or reducing Au-ZnS pairs. This broadband absorber is a good candidate for potential applications such as detection and phase imaging.

2. Results and discussion

Figure 1(a) shows the schematic diagram of the multilayer grating structure which is periodic in the x direction and infinite in the y direction. Figure 1(b) shows one unit cell of the multilayer grating structure which consists of m pairs of metal-dielectric films in the z direction. The materials of metal and dielectric are gold (Au) and zinc sulfide (ZnS), respectively. Gold is also used as the substrate material to effectively block the transmission. The incident wavelength $λ$ has units of micrometers in this paper. The permittivity of ZnS in the infrared regime is set with [40]

ε_{Z n S} = 8.393 + \frac{0.14383}{λ^{2} - {0.2421}^{2}} + \frac{4430.99}{λ^{2} - {36.71}^{2}}

The permittivity of gold in the infrared regime can be expressed with a Drude model:

ε_{A u} = 1 - \frac{ω_{p}^{2}}{ω (ω + i ω_{c})}

where

ω

is the angular frequency of the light,

ω_{p} = 1.32 \times 10^{16} r a d / s

, and

ω_{c} = 1.2 \times 10^{14} r a d / s

. The thicknesses of ZnS and Au are

t_{z}^{k}

and

t_{a}^{k}

where k (k = 1, 2, …, m) is the index of Au-ZnS film pair. The value of k increases from 1 to m along z direction in this paper. The grating period and width are described with

p

and

w

, respectively. The thickness of a pair of Au-ZnS films maintains

0.030 μ m

, in other words,

t = t_{a}^{k} + t_{z}^{k} = 0.030 μ m

. The thickness of Au film increases with the increasing k. However, the thicknesses of ZnS film decreases with the increasing k. A TM-polarization plane electromagnetic wave is incident upon the proposed structure at an angle of

θ

(

90^{0} > θ \geq 0 {}^{0}

). The absorption spectrum and field distribution will be calculated with the rigorous coupled-wave analysis (RCWA) [41]. Figure 1(c) shows the absorption spectrum of the multilayer grating structure with the red curve. With the increasing k, the thickness of Au film increases from

0.010 μ m

to

0.025 μ m

, and the thickness of ZnS film decreases from

0.020 μ m

to

0.005 μ m

. The other optimized parameters are

p = 1.000 μ m

, m = 16,

w = 0.800 μ m

, and

θ = 0^{o}

. From Fig. 1(c), we can see broadband absorption in the wavelength range from

5.65 μ m

to

8.05 μ m

with the minimal absorption rate lager than 0.95. Compared with the broadband absorbers with tapering structures [30–39], the distinguishing feature is that our absorber has the uniform-sized grating widths which will facilitate the process of patterning the multilayer grating structure.

Fig. 1 (a) Schematic of the multilayer grating structure. (b) One unit cell in the x-z plane. (c) Absorption spectrum of the multilayer grating structure.

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To understand the broadband absorption mechanism, we firstly consider the periodic Au-ZnS films. The thicknesses of ZnS and Au are $t_{z}$ and $t_{a}^{}$ , respectively. If the wavelength of the incident light is much larger than the thickness of the Au-ZnS pair, the periodic Au-ZnS films can be treated as a homogeneous medium with effective anisotropic permittivity. According to the effective medium theory (EMT) [42,43], the effective permittivity of components $ε_{x}$ , $ε_{y}$ and $ε_{z}$ can be described with

ε_{x} = ε_{y} = f ε_{A u} + (1 - f) ε_{Z n S}

ε_{z} = \frac{ε_{A u} ε_{Z n S}}{f ε_{Z n S} + (1 - f) ε_{A u}}

where

f = t_{a}^{} / (t_{a}^{} + t_{z}^{})

is the filling ratio of the Au film. Figure 2 shows the wavelength-dependent effective permittivity of the periodic Au-ZnS films with different filling ratios. From Fig. 2, we can see that the absolute values of the real and imaginary parts of the effective permittivity increase with the increase of filling ratio. Furthermore, from Figs. 2(a) and 2(c), we can see

Re (ε_{x}) < 0

and

Re (ε_{z}) > 0

which mean that the periodic Au-ZnS films behave as hyperbolic metamaterials (HMM) in the wavelength range from

3.0 μ m

to

12.0 μ m

.

Fig. 2 Effective permittivity of the periodic Au-ZnS films as a function of wavelength; (a) real part of $ε_{x}$ , (b) imaginary part of $ε_{x}$ , (c) real part of $ε_{z}$ , (d) imaginary part of $ε_{z}$ .

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According to the structure parameters used in Fig. 1(c), each pair of Au-ZnS films has a different filling ratio. For example, the filling ratios of the top and bottom Au-ZnS pairs in our absorber are $\frac{1}{3}$ and $\frac{5}{6}$ , respectively. To show the filling ratios used in Fig. 1(c), the relation between the filling ratio f and the index of Au-ZnS pair k has been plotted in Fig. 3(a). Furthermore, according to Fig. 2, different filling ratios have different effective permittivity for the same wavelength. Thus, we can regard these 16 pairs of Au-ZnS films in one unit cell as 16 layers of hyperbolic metamaterials films with different effective permittivity. The blue curve in Fig. 3(b) is the absorption spectrum calculated with effective permittivity based on Eqs. (3) and (4). To compare the absorption characteristics, we re-plot the absorption spectrum of the multilayer grating structure by using RCWA with red curve in Fig. 3(b). As seen in Fig. 3(b), the blue and red curves agree well. Therefore, the effective medium theory works well for this kind of structure shown in Fig. 1(a).

Fig. 3 (a) Filling ratio as a function of the Au-ZnS pair index. (b) Absorption spectra calculated with EMT and RCWA.

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Next, we consider an air/HMM/air waveguide whose core width is $w$ shown in Fig. 4(a). According to the discussion in Ref [30], the slow-light modes can be excited in this air/HMM/air waveguide. To concisely describe the influence on the slow-light resonance wavelength in the air/HMM/air waveguide, we only focus on the fundamental slow-light mode excitation. The resonance wavelength of fundamental mode can be approximately described with [30]

λ_{s} \approx 2 w \sqrt{ε_{z}}

From Eq. (5), we can see that the resonance wavelength is related with the core width and z-component of effective permittivity. Furthermore, Eq. (5) indicates that, for a certain core width in the air/HMM/air waveguide, the wavelength of the exciting slow-light modes increases linearly when

\sqrt{ε_{z}}

increases. Figure 4(b) shows the relation between the slow-light resonance wavelength and z-component of effective permittivity according to Eq. (5). The value of the core width

w

is set as

0.800 μ m

. It can be seen that the air/HMM/air waveguides with different z-component of effective permittivity have the different resonance wavelengths. According to Eqs. (3) and (4), our proposed structure used in Fig. 1(c) can be regarded as 16 layers films with different z-component of effective permittivity, so that the different resonance wavelengths can be simultaneously excited in our proposed structure based on Eq. (5) or Fig. 4(b) to form the broadband absorption spectrum which has shown in Fig. 1(c).

Fig. 4 (a) Diagram of the air/AMM/air waveguide. (b) Resonance wavelength as a function real part of $ε_{z}$ .

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To further understand the broadband absorption mechanism, we plot the distributions of the magnetic field $| H_{y} |$ in the x-z plane at the incident wavelengths of $5.7 μ m$ , $6.4 μ m$ , $7.1 μ m$ , and $7.8 μ m$ in Fig. 5. In the simulation process, all parameters are the same with those used in Fig. 1(c) if it is not specified in the next part of this paper. From Fig. 5, we can see great magnetic-field enhancement in different parts of the multilayer grating structure. Furthermore, it can be seen that the incident light with the shorter wavelengths is located in the upper parts which have smaller real part of effective z-component permittivity according to Eq. (4) or Fig. 2(c). For example, the incident light at the wavelength of $5.7 μ m$ concentrates in the top part of the multilayer grating structure, while the incident light at the wavelength of $7.8 μ m$ locates in the bottom part. The phenomenon of resonance magnetic field in Fig. 5 agrees well with the discussion of the fundamental mode excitation based on Eq. (5).

Fig. 5 Magnetic field distribution in the x-z plane at different incident wavelengths; (a) $λ = 5.7 μ m$ (b) $λ = 6.4 μ m$ , (c) $λ = 7.1 μ m$ , (d) $λ = 7.8 μ m$ .

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According to the discussion of the broadband absorption mechanism, one can broaden or shrink the absorption spectrum by adding or reducing Au-ZnS pairs. In the simulation process, the Au-ZnS pairs are added or reduced on the base of structure with 16 pairs of Au-ZnS films used in Fig. 1(c). First, the adding or reducing Au-ZnS pairs are located in the bottom part of the multilayer structure used in Fig. 1(c). We plot the absorption spectrum with blue curve in Fig. 6(a) by using 18 pairs of Au-ZnS films where the thickness of Au film increases from $0.010 μ m$ to $0.027 μ m$ and the thickness of ZnS film decreases from $0.020 μ m$ to $0.003 μ m$ with k increasing from 1 to 18. As seen in Fig. 6(a), the absorption rate is more than 0.95 in the wavelength range of $5.65 ~ 8.31 μ m$ which is broader than that shown with red curve with 16 pairs of Au-ZnS films. To compare the influence on the change of the absorption bandwidth, we plot the absorption spectrum with black curve with 14 pairs of Au-ZnS films where $t_{a}^{k}$ increases from $0.010 μ m$ to $0.023 μ m$ and $t_{z}^{k}$ decreases from $0.020 μ m$ to $0.007 μ m$ with k increasing from 1 to 14. From the black curve, we can see that the absorption rate is higher than 0.95 in the waveband $5.65 ~ 7.4 μ m$ which is narrower than that with 18 pairs of Au-ZnS films. Next, the adding or reducing Au-ZnS pairs are located in the top part of the multilayer structure used in Fig. 1(c). The blue curve in Fig. 6(b) shows the absorption spectrum of the 18 pairs of Au-ZnS multilayer structure. In the simulation, $t_{a}^{k}$ increases from $0.008 μ m$ to $0.025 μ m$ and $t_{z}^{k}$ decreases from $0.022 μ m$ to $0.005 μ m$ when k increases from 1 to 18. The black curve in Fig. 6(b) represents the absorption spectrum of the 14 pairs of Au-ZnS multilayer structure where $t_{a}^{k}$ increases from $0.012 μ m$ to $0.025 μ m$ and $t_{z}^{k}$ decreases from $0.018 μ m$ to $0.005 μ m$ with k increasing from 1 to 14. As seen in Fig. 6(b), we can see that the absorption bandwidth for absorption rate larger than 0.9 with more pairs of Au-ZnS films will be broader. Thus, the absorption bandwidth can be engineered by adding or reducing Au-ZnS pairs. On the other hand, we can also conclude that the total thickness of Au-ZnS films can be reduced by reducing the pairs of Au-ZnS films if the absorption bandwidth required is not very wide.

Fig. 6 Absorption spectra with different Au-ZnS pairs; (a) adding or reducing pairs located in the bottom parts, (b) adding or reducing pairs located in the top parts.

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Next, we investigate the influence of the Au and ZnS thicknesses on the absorption characteristics. In the simulation process, the Au and ZnS thicknesses are added or reduced on the base of the optimized structure parameters used in Fig. 1(c). Figure 7(a) shows the absorption spectra with adding and reducing Au film thicknesses. For example, the black curve in Fig. 7(a) represents the absorption spectrum of the multilayer grating structure where each Au film thickness is reduced by 2nm compared with the parameters used in Fig. 1(c) and the thickness of each pair of Au-ZnS film is reduced to $0.028 μ m$ . The red curve in Fig. 7(a) shows the absorption spectrum without adding or reducing the Au film thickness. As shown in Fig. 7(a), the broadband absorption can be maintained when adding or reducing the Au film thickness, and the broadband absorption peaks shift to longer wavelength when the Au film thickness is added. Figure 7(b) shows the absorption spectra with adding and reducing ZnS film thicknesses. Similarly, the black curve in Fig. 7(b) represents the absorption spectrum of the multilayer structure where each ZnS film thickness is reduced by 2nm compared with the parameters used in Fig. 1(c). As seen in Fig. 7(b), the broadband absorption spectra can be achieved when the ZnS film thickness is reduced or added. Thus, from Fig. 7, we can conclude that the multilayer grating structure can still have nearly perfect absorption in a broad bandwidth even when the Au or ZnS thicknesses have some deviation from the optimized parameters.

Fig. 7 (a) Absorption spectra with adding and reducing Au film thicknesses. (b) Absorption spectra with adding and reducing ZnS film thicknesses.

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According to Eq. (5), we can shift the resonance absorption wavelengths by changing the grating width $w$ . To verify this effect, the absorption spectra with the different grating width are shown in Fig. 8(a). As seen in Fig. 8(a), the broadband absorption peaks will shift to longer wavelengths with near-perfect absorption if $w$ increases. The red-shift phenomenon agrees well with Eq. (5). In addition, the Au-ZnS pairs with smaller filling ratios are located in the upper parts in our designing structure in Fig. 1(c) to decrease the reflection of the absorber. To demonstrate such antireflection function, we reverse the order of Au-ZnS pairs used in Fig. 1(c), and its absorption spectrum is shown in Fig. 8(b) with blue curve. In the reversed-order configuration, the thickness of Au film changes from $0.025 μ m$ to $0.010 μ m$ and the thickness of ZnS film changes from $0.005 μ m$ to $0.020 μ m$ when k increases from 1 to 16. As seen in Fig. 8(b), the maximum absorption rate is less than 0.7 which means that the antireflection effect in our designing structure shown in Fig. 1(c) plays an active role in broadband absorption. In order to easily compare influence of the antireflection effect on absorption characteristics, the absorption spectrum of the structure used in Fig. 1(c) is also plotted in Fig. 8(b) with red curve.

Fig. 8 (a) Absorption spectra with different grating widths. (b) Absorption spectra with normal or reversed order of Au-ZnS pairs.

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We simulate the absorption spectra with different incident angles in Fig. 9 to investigate the angle dependence of this broadband absorber. From Fig. 9, we can see that the broadband absorption spectra maintain their broadband profile, and the minimal absorption rate from $5.65 μ m$ to $8.05 μ m$ is larger than 0.9 for angles up to $50 º$ . For angles larger than $50 º$ , although the absorption magnitudes decrease, the broadband absorption spectra are still obvious. Thus, the broadband absorption of our absorber can retain well in wide angles.

Fig. 9 Absorption as functions of wavelengths and incident angles.

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We believe the proposed structure with broadband absorption can be experimentally realized by current fabricating technology. First, the multilayer Au-ZnS films can be deposited by atomic layer deposition (ALD) technique. Then FIB milling can be used to pattern the grating structure. Compared with the fabrication of the tapered structures in Ref [30–39], the unique advantage of our broadband absorption scheme is that we do not need to adjust the etching condition during the FIB milling process.

3. Conclusion

A broadband absorber in the infrared regime is reported by using uniform-sized hyperbolic metamaterial composed of the multilayer metal-dielectric gratings with different filling ratios. The broadband absorption mechanism is attributed to the multiple slow-wave modes. We can engineer the absorption bandwidth by adding or reducing metal-dielectric pairs. The absorption performance of the proposed absorber retains well for angles up to $50 º$ . The unique advantage of our broadband absorber in fabrication is that we do not need to adjust the etching condition during the FIB milling process. This broadband absorber is a good candidate for potential applications such as detection and phase imaging.

Funding

Provincial Natural Science Foundation of Anhui Higher Education Institution of China (Grant No. KJ2018A0175 and KJ2017A342); Anhui Provincial Natural Science Foundation (No. 1608085MA10 and 1508085MF136); National Natural Science Foundation of China (No. 11604343).

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Wide-angle broadband absorber based on uniform-sized hyperbolic metamaterial

Abstract

1. Introduction

2. Results and discussion

3. Conclusion

Funding

References and links

Cited By

Figures (9)

Equations (5)

Optical Materials Express