1. Introduction

The concept of metamaterials arises from the artificial material engineering decades ago [1], which enable us to achieve unique electromagnetic (EM) properties which cannot be obtained from natural materials [2,3]. Such extraordinary properties including negative refractive index, negative phase velocity and even the ability of manipulating permittivity and permeability are initially determined by its constituting subwavelength-scale meta-elements, and have led to a set of novel EM devices, such as high-gain low-profile antennas, perfect lenses, transformation optics devices, metasurfaces, and miniaturized filters and polarizers [4,5].

As an important branch of metamaterials, recent years we witness the rapid development of metasurfaces, which are regarded as 2D metamaterials [6,7]. They possess the abilities to fully manipulating propagation behavior of EM waves, including phase, amplitude, polarization and linear/angular momentum upon transmission or reflection with subwavelength dimension along wave propagation direction. Many intriguing functionalities are achieved on the basis of abrupt phase discontinuities at the surface [8], such as anomalous beam bending [8–10], beam forming [11,12], vortex beam generation [8,13,14] and holography [15,16]. The essential technology to realize above functionalities is to control the transmitted or reflected phase of each subwavelength meta-element. To date, 2π phase control has been realized and reported for different incident polarizations through different approaches in several frequency bands [8,13,16–19].

The stealth technology is always an important domain for metamaterials applications [20,21], where reduction of RCS is one of the major challenges. By covering with metamaterials absorbers, the RCS of the targets can be greatly reduced. However, the absorbed EM energy goes to heat [21–23]. The cloaking designs based on transformation optics (TO) are able to conceal the target from affecting the exterior fields [24–26], which behavior similarly as the scattering cancelation or non-reflection designs [27]. They also achieve RCS reduction of the hidden objects. Nevertheless, most of these previous designs are difficult to break through the intrinsic limitation in bandwidth. The arbitrary reflection phase control ability of metasurfaces provide new solutions to achieve RCS reduction. By randomly distributing reflective meta-elements with different reflection phases along the surface, the metasurface can mimic a diffuse reflection surface, which could redistribute the scattered energy from the hidden metallic object to the dispersive reflection directions, hence the backward reflection energy in the direction of incoming waves will be significantly reduced. To realize different reflection phases, one choice is to use same shaped reflective elements of variable sizes, which can be date back to early investigations on reflect-array antenna to obtain broader working bandwidth [28–31]. Recently researchers have used similar method combining with optimization approach to obtain broadband RCS reduction metasurfaces [33,34]. However, to date, most of the reported designs are still lack of flexible consideration, especially in microwave regime, which we think could gain more application potential especially in non-planar shape stealth coating.

In this paper, we propose a flexible low-scattering metasurface. The metasurface is composed of two layers, one polyimide film layer printed with metallic elements over one flexible polyimide substrate layer, which leads to a totally flexible layout. The printed metallic elements layer consists of randomly distributed subwavelength elements of different dimensions. The layout is designed through an optimization process. Such flexible metasurface can be coated to metallic objects with either flat or curved shapes. The obvious backward RCS reduction property of the proposed metasurface has been verified through Full-wave simulations and experimental measurements in the microwave regime.

2. Theoretical design and analysis

The Lambertian surface is regarded as an ideal diffusely reflecting surface in optical domain. Its apparent brightness is regardless of the observation angle, and the luminous intensity obeys Lambert's cosine law. The Lambertian reflectance usually originates from the roughness or material distribution of the surface, which results in a random distribution of the reflection phases along the surface. Inspired by the concept of lambertian surface and diffuse optical phenomenon, we design a kind of random metasurface which is composed of randomly distributed subwavelength reflective elements possessing variable reflection phases. The proposed metasurface can diffuse the incident EM wave within a considerable bandwidth.

In the layout design, we utilize a “#” shaped element as the basic reflective phasing element of the proposed metasurface which is shown in Fig. 1. Comparing with previous reported designs, the proposed element is an achiral rotationally asymmetric structure which is insensitive to the incident polarizations. By placing it over a metallic plate sandwiched with the substrate layer, such meta-element exhibits a large reflection phase variation range within a broad frequency band. From the schematic view, we can see that the proposed “#” shaped element is formed by four intersecting paralleled metallic strips with a complementary “#” shaped slot etched in the center of the strips. Thus, the whole structure can also be regarded as a “#” shaped outer ring with a square ring inserted. The double ring design introduces two resonant frequencies into the structure. When the incident EM wave interacts with the element, there occurs parasitic inductance in the inner and outer rings, respectively. There also occurs parasitic and coupling conductance in the inner and outer ring, respectively. Besides there also occurs conductance between the ground and the inner and outer rings. The resonant frequencies of the inner and outer rings are independent with each other on the basis of their distinct structures. The existence of the two resonant frequencies will increase the total phasing range of the reflective element. To ensure the broadband property, the resonant modes should have lower quality factor to obtain a smaller slope of the reflection phase characteristic. Therefore, a proper thickness of the dielectric layer is designed to further lower the quality factor and improve the reflection phase linearity.

 

Fig. 1 (a) The schematic of the scatter element and (b) the layout of the random metasurface (c) the schematic of coating the random metasurface to a metallic cylinder.

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To enable the flexibility of the whole structure, polyimide film is chosen as the substrate. The metallic elements are printed on a polyimide film through flexible printed circuit (FPC) technology. Utilizing the same element shape as shown in Fig. 1(a) with different dimensions, a group of elements was generated whose phasing ranges cover 360° over the whole X-band with almost linearly reflection phase response. Eleven elements are selected among them with nearly equal phase varying intervals. The simulated reflection phase response curves are plotted in Fig. 2(a) where the parameters are d = 0.6mm g = 0.2mm h = 4mm P_x = P_y = 15mm. The eleven elements correspond to the parameter L varying from 0.5 to 2.2. As shown in the figure, the flat curves validate the broadband reflection phase varying property. The nearly equal phase varying intervals among the curves ensures the functionality of the approximated random reflection phase distribution over the whole X-band when randomly distributing the reflective elements on the surface.

 

Fig. 2 (a) Reflection phase response curves of meta-elements of variable dimensions; (b) Simulated far-field RCS results for metal and one optimized sample at different frequencies from 8GHz to 12GHz.

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Based on the FPC technology, the dimension of the whole metasurface is designed to be 240mm × 240mm, which is composed of 16 × 16 meta-elements. In the single meta-element reflection simulations, the unit-cell boundary is applied. However, in the random distribution design, the coupling between the unit-cells nearby is different. To reduce the above coupling influence, We further take 2 × 2 unit-elements as a basic element to form the surface layout. To realize the random reflection phase distribution based on the chosen elements, we use the random number generation function in the Visual Basic to generate 2-D 8 × 8 random arrays containing integral numbers from 1 to 11. Each number corresponds to one reflective element with specific dimension. Several layouts are made based on the generated arrays. Based on the full-wave simulation results, three layouts among them are selected which exhibit well backward RCS reduction property over the X-band. The simulated results of far field RCS distributions of one sample comparing with one bare metallic plate are shown in Fig. 2(b), where the sub-figures correspond to different working frequencies from 8GHz to 12GHz separately. From the plots, we can see that the sample achieve 10dB RCS reduction over the X-band by coating it to bare metallic plates.

We then coat the samples to the metallic cylinders to check that if such metasurface can be applied in non-planar environments. The schematic is shown in Fig. 1(c). To investigate the RCS reduction performance upon curve surfaces of different radians, we choose two metallic cylinders with radius of 40mm and 80mm. The simulated far-field radiation patterns of the coated cylinders at different frequencies are demonstrated in Fig. 3. As we can see from the figures, comparing with the far-field scattering pattern of the metallic cylinder, the far-field patterns of the coated cylinders firstly have more dispersive distributions along the axial section of the cylinder. Besides, the scattering distributions along the radial section are also not as uniform as the bare metallic case. The coating of the flexible metasurface enables the dispersive scattering property of the whole coated structure, which can redistribute the scattered energy from the metallic cylinder to the more dispersive reflection directions, as we predicted in the theoretic design. Such dispersive scattering leads to a total low scattering layout. Through optimizations, we also can design a randomly distributed metasurface, which can obtain RCS reduction for the specific backward direction. The Simulation results show that both cylinders coated with the selected sample achieve well backward RCS reduction effect over the X-band.

 

Fig. 3 Comparison of the simulated far-field scattering patterns of the bare metallic cylinder and the coated cases at different frequencies with the radius of 80mm.

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3. Fabrication and measurement

In order to verify the theoretic analysis above, the flexible metasurface samples are fabricated following the theoretical design. The top layer is a very thin polyimide film printed with metallic elements through FPC technology. The film is 0.02mm thick with a relative permittivity of 3.88. The printed copper layer is of 0.017mm thick. The fabricated sample reaches a total dimension of 240mm × 240mm which is same as the layout in simulation. The flexible substrate material utilized in the fabrication is polyimide which has the permittivity of 3.88 with loss tangent of 0.001. Polyimide exhibits well dielectric property in room temperature with cheap price. We obtain the none-metal-backed metasurface by attaching the top film layer to the polyimide substrate layer. The total structure exhibits the designed flexibility. The composite layout also offers us the potential to introduce tunability into the metasurface. By choosing different substrate layer thicknesses, we can easily tune the thickness of whole metasurface. Simultaneously the reflection property also can be tuned in the same way.

By coating the metasurface to a bare metallic plate, we measure the reflection coefficients of the three fabricated samples. The measurement setup is shown in Fig. 4(a). It is composed of two horn antennas fixed on an arch truss. Both of the antennas are connected to an Agilent vector network analyzer. The measured far-field reduction results for orthogonal incident polarizations are shown in Fig. 5. When the substrate layer thickness is 4mm, all the samples achieve nearly 10db backward RCS reduction from 8 GHz to 12.5GHz. Because the “#” shaped element is achiral and rotational symmetric, the flexible metasurface exhibits insensitive to the incident polarizations. If we replace the 4mm substrate layer with a 3mm thick one, the maximum RCS reduction value is reduced near the designed central frequency, however the RCS reduction bandwidth has been broadened to higher frequency band, it achieves almost 10dB RCS reduction from 8.2GHz to 15.2GHz. This is because that thinner substrate keeps the reflective elements retaining more equal reflected phase varying intervals comparing with 4mm case in higher frequency band, which makes the reflected phase distribution in higher frequency band still satisfying the designed phase distribution requirements. However, it cannot obtain as well performance as the 4mm case in the designed central frequency.

 

Fig. 4 The measurement setup for (a) coating the metasurface on a metallic plate (b) coating the metasurface to a metallic cylinder.

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Fig. 5 The measured Far-field RCS reduction results of the coated metallic plate with different thick substrates (a) 4mm PVC (b) 3mm PVC for both incident polarizations.

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In order to validate the RCS reduction effect on curved surface, we also measure the backward RCS of cylinders coated with our proposed metasurface. Based on optimizations, one specific layout is picked up, which exhibit backward RCS reduction property. The RCS measurement is carried out in a microwave chamber and the measurement setup in shown in Fig. 4(b). In the measurement, the large radius cylinder is coated with two fabricated flexible metasurface samples.

After some mathematic process, the simulated and measured RCS reduction results are shown in Fig. 6. Comparing with the results of the flat coated metallic plate, the whole RCS reduction is not as large as the planar cases. Because for the metallic cylinder, it possesses a intrinsic uniform far-field scattering pattern in the radial section. The scattering reduction mainly comes from the scattered energy redistribution in the axial section. Thus the total average reduction is lower. However, if we only focus on the backward RCS reduction, the non-uniform scattered energy distribution of the random metasurface in the racial section can be optimized to obtain a specific design, which has lower scattering in the backward direction. This backward low scattering property is mainly determined by the columns of reflective elements towards the backward direction, which play a dominate role in the backward scattering generation. Thus a further optimization is carried to design the random metasurface for coating with the cylinders. As we can see in the figure, for orthogonal incident polarisations, 10dB backward RCS reduction is obtained from 7.6GHz to 12.1GHz for the cylinder with radius of 40mm. For the cylinders with 80mm radius, the 10dB reduction ranges from 7.7GHz to 12GHz. The measured results coincide with the simulation results, which validate the feasiablity of the theoretic design.

 

Fig. 6 Simulated and measured far-field RCS reduction results (a) coated cylinder with radius of 40mm (b) coated cylinder with radius of 80mm.

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4. Conclusion

We present here a total flexible metasurface which is composed of randomly distributed meta-elements of variable dimensions. The proposed flexible metasurface can obtain 10dB backward RCS reduction by coating it to either the metallic plate or metallic cylinders with the thickness of only 1/8 working wavelength. We think that such metasurface can find application in stealth technology for curved surfaces especially in microwave regime.