1. Introduction

Reasonable control of electromagnetic properties has attracted the interest in the past decade. Due to the limitation of natural materials and the larger size of conventional optical devices, the ability to control electromagnetic properties is quite limited. Emergence of Metamaterials (MTMs) has brought the dawn for the research in photonics [1–8]. Unusual capability of light propagation can be realized by MTMs, such as negative and zero refraction [9–11], super imaging [12], light source control [13], and so on. Particularly, a cloak MTMs was proposed to render objects invisible to incident wave, realizing the goal of hiding objects [14–24]. Owing to their unusual electromagnetic properties, MTMs play a significant role in cloaking device design. Generally, transformation optics [25,26] and scattering cancellation [27,28] provide powerful tools to build invisibility cloaks. The design of transformation optics cloaks is through bending light around the concealed regions by coordinate transformation [29]. Scattering cancellation is another method to realize cloaking device by suppressing the dominant multipolar scattering orders. However, the actual function of these cloaks is still far from ideal. Cloaks based on transformation optics are usually anisotropic and inhomogeneous, and they require specific material permittivity and permeability. As for scattering cancellation, in order to meet the number of scattering harmonics, the required number of cloaking layer needs increase according to the size of the object. For some large objects, the design of cloaks is complex. Besides, a quasi-conformal–mapping technique was proposed by restoring the wavefront to design carpet cloak as if light incident on a smooth surface [30]. Unfortunately, there are many disadvantages in the specific cloaks designs. For instance, the realization of cloaks requires complex spatial refractive index distribution and high spatial resolution in three-dimensional fabrication. In addition, the varying index is also related to working environment, leading to it is difficult to realize a cloak in reality.

With the recent development of metasurface, an single layer surface structure consisting of subwavelength meta-atoms, it can provide full control of reflected wavefront, showing great prospects in carpet cloak technique by completely restoring the phase, amplitude, and polarization of reflected light as incident on a flat mirror [31–39]. This novel metasurface cloak relied on local phase compensation, and it has been proposed experimentally. Then, a series of metasurface cloak was realized for millimeter waves, THz waves, and even visible light by similar theoretical. However, metasurface-based carpet cloak still remains narrow band, and the phase value of local compensation strongly depends on specific angle of incidence and frequency. For example, B. Orazbayev proposed a Terahertz carpet cloak based on a ring resonator metasurface, which can only work within 8 GHz and 10° tilt angle [32]. Besides, by designing a complex multi-layer structure to scan parameters or form different resonant units above and below the structure, it can only make cloak work at two fixed frequency points and not have the ability to effectively expand the bandwidth [39]. Therefore, it is important how to implement broadband and wide angle metasurface cloak in metasurface-based cloak. To overcome these challenges, we propose that a high refractive index dielectric layer or “moth-eye-like” structures have a very strong ability to enhance bandwidth and angular response.

Here, we design and demonstrate a novel metasurface-based cloaking with broadband and wide angle based on local phase compensation. The enhancement of bandwidth and angle is based on the idea of adding a high refractive index dielectric layer and antireflective “moth-eye-like” microstructure on metasurface carpet cloaks. This idea is proposed based on Snell law of geometric optics. In general, these cloaks enable wide angle effect of approximately 30° from 0.65 THz to 0.9 THz.

2. Wide spectrum and angle transmission of “moth-eye-like” microstructure

Recently, Bernhard proposed that nanostructures, called as “moth-eye-like” microstructure, can effectively improve the light coupling efficiency [40–43]. When these structures are densely packed together, these sub-wavelength structures are capable of exhibiting a very low effective refractive index. These researches open the way to development of a perfect anti-reflective layer. Meanwhile, the anti-reflective layer has the ability to provide incident electromagnetic waves with effective coupling over a broad spectrum and a wide range of incident angle responses.

As shown in Fig. 1, we calculated the transmission characteristics of a moth-eye-like structure in terahertz range. The period of the structure is kept at 23 $\mu m$ and the height of the cone was maintained at 46 $\mu m$. The material of the structure has a dielectric constant of 11.9 and dielectric loss-tangent of 0.007. The near field and far-field scattering distributions of the reflected light were numerically calculated by finite integral method. When light is incident on the moth-eye-like structure with different angles, the structure has a very high transmittance over a wide spectrum in Fig. 1(a). The inset of Fig. 1(a) shows schematic diagram of moth-eye-like cone type microstructure. The average transmission can be achieved up to 95% above ${45}^{°}$.

 

Fig. 1 The transmission performance of moth-eye-like structure. a) Calculated transmittance of the moth-eye-like from 0.6 THz to 0.9THz; b) The internal electric field distribution of the moth-eye-like structure in the case of incident light at different angles.

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Besides, in order to explore the response of the moth-eye-like structure to a wide angle of incident light, we simulated the internal electric field of the structure in the case of incident light at different angles. As shown in Fig. 1(b), we can see that the incident light wave is greatly deflected after passing through the structure, which conform the ability of the moth-eye-like structure to expand angular response. In other words, by using the moth-eye-like effect, the incident wave with a larger angle will deflect at a small refractive angle. This effect will be explained by the effective graded index of refraction based on Snell law of geometric optic as shown in Fig. 3. Next, we will introduce this moth-eye-like microstructure into metasurface-based carpet cloak to realize broadband and wide angle cloaking.

 

Fig. 2 Schematic view of the metasurface cloak and structure models of three unit cell. a) 3D view of the metasurface cloak composed of an array of rectangle patch. The number 1-6 represents six basic unit cell in each case; b-d) Detail of one unit cell for the typical metasurface, and the metasurface cloaking of case I with dielectric layer, and case II with broadband antireflective moth-eye-like microstructure, respectively. The parameters of three structures as follow: P = 138 $\mu m$, d1 = 0.2 $\mu m$, d2 = 25 $\mu m$, d3 = 0.2 $\mu m$, d4 = 40 $\mu m$, e = 10 $\mu m$, h = 46 $\mu m$, r = 23 $\mu m$.

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Fig. 3 a) Original reflection pattern when light is incident on a plane with an oblique angle; b) The angular response of reflection when adding a dielectric layer with high refractive index; c) The moth-eye-like can be divided into multiple dielectric layers when light is incident on a plane with an oblique angle; d) The working principle of the moth-eye-like microstructure.

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3. Broadband cloaking design

As we all known, when electromagnetic wave is incident on a metal bump with a tilt angle, the metal bump will produce an additional phase to the incident wave. Meanwhile, both the wavefront and far-field scattering will be distorted. Figure 2(a) shows the schematic of the carpet cloak with metasurface. When electromagnetic wave impinges onto this metasurface, the matesurface can introduce an expected phase shift to alter the local reflection phase. Therefore, the wavefront and scattering of reflection will be reconstructed as if the incident wave impinges onto a smooth mirror. The local phase distribution provided by the metasurface cloak satisfies the following relationship as

The important step in designing a metasurface cloak is to obtain the required phase distribution. As shown in Fig. 2(a), six basic unit cell are periodically arranged to form a metasurface, so the phase interval of 60° for each unit cell should be designed. Firstly, we designed a typical three-level metasurface structure as shown in Fig. 2(b). The rectangle metal patch with thickness 0.2 μm is placed on PI(polyimide) layer with thickness of 25 μm, and the bottom layer is foil. The period of unit cell is 138 μm. A terahertz plane wave is incident on the metasuraface at the frequency of f = 0.75 THz. The PI and foil are able to enhance reflection. By changing the length (a1) and width (b1) of rectangle patch, the phase responses of the six unit cell cover 0° to 360°, and the phases of each unit are 0°, 60°, 120°, 180°, 240°, 300°, respectively. Structural parameters are shown in Table 1.

Table 1. The structural parameters, Phase responses of the unit cell of three options ((1), (2), (3) correspond to the typical metasurface, case I, and case II, respectively.)

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Hereafter, for the purpose of realizing broadband and wide angle metasurface cloaking, we will introduce moth-eye-like microstructure on metasurface. In order to compare with the characteristics of moth-eye-like metasurface, we also introduce a high refractive index dielectric layer on metasurface. Based on the idea that the interface of high index material provides a small refractive angle when a plane wave is incident on it with a larger incident angle according to Snell law of geometric optic, we propose that the typical metasurface can be also cladded by a high refractive index dielectric layer to extend the response of reflection angle of metasurface-based cloaks. Thus, we establish two options as shown in Fig. 2(c) (case I) with a high refractive index dielectric layer and Fig. 2(d) (case II) with moth-eye-like microstructure on typical metasurface. In Fig. 2(c) for one unit cell, the dielectric layer has a dielectric constant of 11.9 with a thickness of 40μm. The long side (a2) and wide side (b2) of rectangle patch are variable (case I) to obtain the phase change of 2π.

In addition, we propose the second novel wide-angle and broadband design of cloaking by adding conical antireflective moth-eye-like microstructure on typical metasurface as shown in Fig. 2(d) (case II). The height of the bottom high refractive index medium (ε = 11.9) is 10 μm, the height and diameter of the cone are 46 μm and 23 μm, respectively. And then, we realized the phase change from 0° to 360° through changing the length (a3) and width (b3) of the central rectangle unit cell.

In order to intuitively the enhancement of wide spectrum and wide angle response of case I and case II cloaks, we plotted the schematic diagram of geometric ray method for high refractive index dielectric layer and moth-eye-like structure on the typical metasurface as shown in Fig. 3. In Fig. 3, the “structure” in the schematic diagram indicates the typical metasurface as shown in Fig. 2(b). We assume that the angular response of a unit is θ₁ under original operating conditions in Fig. 3(a), but the angle response range will extend to θ₂ after adding a dielectric material layer with high refractive index in Fig. 3(b). Based on this idea, the unit cell of multi-layered metasurface with high-refractive-index dielectric layer can expand the response to larger angles, that is, it can still reconstruct the reflection field over a wide range of angles. In contrast to case I, we introduce a moth-eye-like microstructure, which is equivalent to multi-layer dielectric layer with a gradual increase of refractive index as shown in Fig. 3(c). According to the characteristics of moth-eye-like microstructure [40–43], moth-eye-like subwavelength microstructure can be equivalent to a graded refractive index layer as shown in Fig. 3(d). The working principle about geometric ray bending to enhance the angle response for the moth-eye-like microstructure is illustrated in Fig. 3(d).

In order to obtain the specific structural parameters of each cell under the condition that the phase distribution is satisfied from Eq. (1), the simulated reflection phases were detailedly calculated by using finite integral method as shown in Table 1. Due to the incident light with angle θ = 45° and tilt angle of cloaking with φ = 20°,the incidence angle at cloaking metasurface are 25° and 65° for left and right side, respectively, as shown in Fig. 2(a). After optimized design, we selected parameters that satisfy the phase gradient distribution in Table 1.

After obtaining the phase distribution of unit cell for proposed metasurface elements, a metasurface cloaking can be realized. The metasurface cloaking with a triangular shape in y-z plane and infinite length in the transverse x direction is demonstrated in Fig. 2(a). The metasurface cloaking is covered on a triangular bump with a tilt angle φ = 20°, an edge length of 2553 μm, and the height of 873 μm. The incident terahertz light has a Gaussian distribution with x-direction polarization. In the calculations, the open boundary condition is applied in y direction while the x direction is set to be periodic boundary.

Figure 4 illustrates the near-field, far-field, and angle scattering distribution for the typical metasurface cloaking without high refractive index layer and moth-eye-like microstructure on metasurface. By unitizing the finite element method [44], the near-field and far-field distribution can be numerically simulated in our calculation. To make a comparison, the spatial distributions for ground plane in Figs. 4(a)-4(d), bare bump without cloaking in Figs. 4(b) and 4(e), and cloaked bump with typical metasurface in Figs. 4 (c) and 4(f) at working frequency f = 0.75THz are shown. As observed, when a Gaussian beam is introduced on the ground plane, the reflected wave is scattered in a direction with an angle equal to the incident angle. When the light hits the bare bump, the scattered field distribution is distorted. Besides, it can be seen that the difference between the far-field radiation patterns of bare bump and the ground plane are also obvious due to the splitting of the near field in Figs. 4(a) and 4(b). After applying a typical metasurface as shown in Fig. 4(c), the near field distribution and the far-field radiation patterns are restored to the same distribution as the plane ground. Meanwhile, there are far-field intensity distributions of the ground plane, bare bump and cloaked bump at different scattering angle as shown in Figs. 4(g), 4(h) and 4(i) respectively. The far-field intensity distribution of cloaked bump is very close to that of the plane ground. It can be certified that the proposed typical metasurface is able to conceal object by using gradient phase to restore the reflected wave. But, it is worth noting that this typical metasurface only performs well when the incident light wave at a tilt angle of about 45°. Broadband and wide angle of cloaking cannot be realized.

 

Fig. 4 a), b), c) Near-field distribution of ground plane, bare bump, cloaked bump, respectively, at 0.75 THz. d), e), f) Far-field intensity distribution corresponding to a),b),c), respectively. g), h), i) Far-field radiation pattern of ground plane, bare bump, cloaked bump at 0.65 THz-0.85 THz.

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To validate two novel design options of the wide angle and broadband metasurface cloaking, we used the unit cell of two cases, such as case I and case II in Figs. 2(c) and 2(d), respectively, to build the metasurface cloaking. The same dimensions as above typical metasurface is given. It should be noted that the phase and the amplitude of unit cell are slightly influenced by the loss of polymide substrate. Then, it can be deduced that the performance of cloaking is slightly affected by the loss of substrate material.

Figure 5 shows the comparison of spatial field distribution at larger incident angle for the typical metasurface cloaking, case I cloaking, and case II cloaking, respectively. In Fig. 5(a), it can be seen that the typical metasurface cloaking cannot restore wavefront when incident wave at an angle of 55°, so it cannot conceal object. As shown in Figs. 5(b) and 5(c), the metasurface cloaking of case I and case II are displayed. It can be found clearly that the case I metasurface cloaking with high refractive index dielectric layer has an ideal scattering distribution, and the wavefront is rebuilt when the incident wave is at an angle of 55°. The case II with antireflective moth-eye-like microstructure also shows a perfect wavefront reestablishment as seen in Fig. 5(c). It can be seen that the metasurface cloaking with antireflective “moth eye like” microstructure in Fig. 5(c) shows a better wavefront reestablishment compared with that from case I. This can be reasonably explained by the physical principle in Fig. 3. When the incident angle is increased to be 55° which is deviated from the designed angle of 45° for the cloaking devices, the incidence angle at cloaking metasurface is 35° for the left section of cloaking device and 75° for the right section of cloaking device. In Fig. 3(c), the moth-eye-like microstructure can be equivalent to multilayer graded refractive index layers in long wavelength limit as shown in inset of Fig. 3(c). Each layer from air to substrate has a gradually increasing equivalent refractive index according to the effective medium theory. The graded refractive index layers reduce the reflection due to a gradual increase of the refractive index, which leads to matching of the optical impedance at the interface and to an adiabatic coupling of incident light into the high refractive index substrate. It has been shown theoretically that a layer with a modified graded refractive index profile has the lowest reflection over a broad spectral and angular range [45–50]. On basis of Snell law, the refractive angle for graded refractive index layers from air to substrate is gradually decreased. According to Figs. 3(b) and 3(d), it can be seen that the “moth eye like” microstructure with an equivalent gradient index property can curve the incident ray in transmission, and the smaller angle is incident on the following metasurface unit cell compared with that by a dielectric layer structure when the incident angle is same in air. This smaller incident angle by using the “moth eye like” microstructure is closer to the design angle, so the wavefront reestablishment for the case II is better than that of the case I in Fig. 5(c).

 

Fig. 5 Scattering field of the wide angle response at 0.75THz. a), b), c)Electric field distribution of the typical cloaking, the metasurface cloak of case I, and case II, respectively, when incident wave at an angle of 55°. d) Far-field radiation pattern of the typical cloaking, the metasurface cloak of case I, and case II, respectively, when incident wave at an angle of 55°. e), f), g) Electric field distribution of the typical cloak, the metasurface cloaking of case I and case II at the incident angle of 60°. h) Far-field radiation pattern of the typical cloaking, the metasurface cloak of case I, and case II, respectively, when incident wave at an angle of 60°.

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Meanwhile, we simulate the far-field intensity distributions of these three cases in Fig. 5(d), which showing the similar results as above. Besides, we continue to numerically analyze the cloaking performance of two options at the incident angle of 60° as shown in Figs. 5(f) and 5(g). As a comparison, we also calculated the near-field distribution of the typical metasurface cloaking in Fig. 5(e), and the far-field intensity distributions of these three cases in Fig. 5(h). These results reveal that the metasurface cloaking of case I and case II still performs well in rebuilding scattering field at larger angles.

Figure 6 shows the bandwidth comparison of the typical metasurface cloaking, case I cloaking, and case II cloaking, respectively. In Fig. 6(a), we show the near-field distribution of the typical metasurface cloaking at 0.65 THz. It can be seen that the near-field produces a little distortion with frequency change. However, case I cloaking and case II cloaking have a stronger capacity to reconstruct wavefront and suppress unexpect scattering than the typical metasurface as shown in Figs. 6(b) and 6(c). The far-field intensity distributions of these three cases at 0.65 THz are plotted in Fig. 6(d). Obviously, the cloaking capacity of case II is better than that of case I. Meanwhile, we calculated the near-field distribution of the typical metasurface cloaking, case I cloaking, and case II cloaking, respectively, at 0.9 THz in Figs. 6(e)-6(g). The far-field intensity distributions of the typical metasurface cloaking, case I cloaking, and case II cloaking, respectively, at 0.9 THz are illustrated in Fig. 6(h). As we expected, the near-field of the typical metasurface also appear distortion with widening frequency. The case I cloaking and case II cloaking are still able to reconstruct the reflected field as a behavior of the ground plane. Generally, these cloaking devices we proposed can expand bandwidth relative to the conventional carpet cloak. Compared to the typical cloaking, the bandwidth of case I and case II is widen from 0.65 THz to 0.9 THz. In order to further demonstrate the broadband invisible function of our designed devices, the far -field radiation pattern of typical, case I and case II, respectively, at broadband range from 0.6THz to 0.9 THz is revealed in Fig. 7. Based on this fact, the near-field distribution and the far-field radiation of the metasurface cloaking verify that our design based on phase gradient compensation can rebuild the reflected wavefront well to implement hiding arbitrary shape objects with a wide angle and bandwidth.

 

Fig. 6 Simulation results of the bandwidth comparison. a), b), c) The near field distribution of the typical cloak, the metasurface cloak of case I, and case II, respectively, at 0.65THz. d) Far-field radiation pattern of the typical cloaking, the metasurface cloak of case I, and case II, respectively, when incident wave at an angle of 0.65THz. e), f), g) The near field distribution of the typical cloak, the metasurface cloaking of case I, and case II, respectively, at 0.9THz. h) Far-field radiation pattern of the typical cloaking, the metasurface cloak of case I, and case II, respectively, when incident wave at an angle of 0.9THz.

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Fig. 7 Far-field radiation pattern of typical, case I and case II at broadband range from 0.6THz to 0.9THz.

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Next, in order to demonstrate the design tolerance of case II with “moth eye like” microstructure, the influence of the height and diameter of microstructure to far-field radiation pattern is shown in Table 2 and Table 3, respectively. The terahertz wave at the frequency of 0.75THz is incident on the metasurface cloaking with “moth eye like” microstructure at 45°. It can be seen that the height and diameter within the range of actual preparation slightly affect the far-field radiation pattern.

Table 2. Far-field radiation pattern of case II with different height of microstructure.

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Table 3. Far-field radiation pattern of case II with different diameter of microstructure.

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4. Summary

To conclude, in this paper we proposed a realization of ultrabroadband metasurface cloaking through high refractive index dielectric layer and antirefletive microstructure. Through the novel design of the metasurface unit, the presented results show that the metasurface-based carpet cloak can suppress the unexpected scattering and reconstruct wavefront by providing local phase compensation from 0.65THz to 0.9THz with a wide range of angles. With the aid of these metasurfaces, we can realize the electromagnetic wave virtual shapes of the ground plane to hide an arbitrary object. Compared to the conventional carpet cloak working at narrow bandwidth, two options we proposed greatly enhance the attributes of the metasurface cloaking in terms of bandwidth and angle. Moreover, the metasurface cloak of case I has better response in bandwidth than the metasurface cloak of case II. Besides, this cloaking principle can be also extended to the optical and microwave domains.