Jigsaw puzzle metasurface for multiple functions: polarization conversion, anomalous reflection and diffusion

Yi Zhao; Xiangyu Cao; Jun Gao; Xiao Liu; Sijia Li

doi:10.1364/OE.24.011208

1. Introduction

Electromagnetic (EM) waves can be characterized by some fundamental properties such as polarization state, direction of propagation and amplitude. Due to the capabilities of manipulating EM waves, metasurfaces have obtained great popularity in recent years [1, 2].

A number of implements have been developed aiming at the aforementioned properties through delicate design of sub-wavelength cells and macroscopic layout. For example, polarization manipulation can be achieved by employing anisotropic cells to construct reflective or transmissive polarization conversion metasurface, which can modulate EM wave into cross-polarized state or other forms [3–14]. The propagation direction can be manipulated by introducing gradient phase shift to the interface [15–25]. Based on the generalized Snell’s law, the reflection or refraction can be adjusted at will, which leads to various applications such as anomalous reflector/refractor [15–21], lens [22, 23], beam splitter [24], and propagating wave to surface wave converter [25]. The amplitude manipulation is traditionally based on absorption. Perfect absorbers can achieve nearly 100% absorption of EM wave within limited band so that the amplitude of reflected wave is significantly reduced [26–28]. Recently, an alternative way has attracted much attention in which the incident wave is reflected into numerous directions rather than being absorbed. Hence, the maximum amplitude of reflection could also be attenuated due to energy conservation. This goal has been achieved by metasurfaces with nonuniform phase distributions which are generally realized by sub-wavelength cells of various structures [29–36].

More recently, the concepts of coding metamaterial and digital metamaterial show a new perspective for EM wave manipulation, in which one can manipulate the scattering by designing the coding sequences of “0” and “1”elements [37,38]. Based on this idea, various functionalities have been achieved such as anomalous reflection and diffusion. Terahertz and multi-bit coding metasurfaces have also been investigated [35–37]. Though the coding concept offers a simple way to design metasurface with multiple functions, the polarization conversion has not been included so far. Moreover, it is difficult to switch between functions in practice since the coding sequence is fixed once the metasurface is fabricated. A reconfigurable coding metasurface, namely programmable metamaterial, has been realized by switchable components and field programmable gate array hardware [37]. The switch is controlled by changing the biased direct current voltage of the diode on each cell, resulting in relatively high complexity and cost.

In this article, we propose a simple reconfigurable metasurface with multiple functions. An anisotropic tile is developed as the fundamental element. The tile shows opposite reflection phases under x- and y-polarized normal incidence in specific frequency band which can be appointed as “0” and “1” based on the coding concept. Then, the tiles are arranged together in a certain sequence to construct a two-dimensional metasurface which is like a jigsaw puzzle. Since each of the tiles can be adjusted independently, the whole metasurface can easily achieve diverse functions by using different layouts. For demonstration purposes, we realize polarization conversion, anomalous reflection and diffusion by a jigsaw puzzle metasurface with 6 × 6 pieces of anisotropic tiles. Both simulations and measurements prove that our method offers a simple, flexible and effective strategy for metasurface design.

2. Design of the jigsaw puzzle metasurface

2.1 Design concept and the anisotropic tile

It is known that the non-absorptive metasurface manipulates EM wave by introducing phase variation into the interface. Hence, the cell structure and the macroscopic layout share the equal importance that determines the total performance of the metasurface. The coding metamaterial concept provides a convenient methodology to combine the two factors together. In this article, we propose a novel reconfigurable metasurface based on this concept.

As shown in Fig. 1(a), the metasurface is implemented by joining anisotropic tiles in a certain layout. As the tiles are independent bodies, the sequence can be adjusted at will which is like a jigsaw puzzle. Figure 1(b) illustrates the details of an anisotropic tile. Due to the asymmetrical geometry, the structure is sensitive to the polarization of normally incident EM wave. Figure 1(c) illustrates the reflection properties of the tile obtained by commercial software ANSYS HFSS. According to the coordinate in the inset of Fig. 1(c), the incidence can be classified as x-polarization (E-field is parallel to the long side of the patches) and y-polarization (E-field is perpendicular to the long side of the patches). Due to full metallic ground on the back and low loss substrate, the tile is perfectly reflective for incident waves of both polarizations. However, the reflection phases are of apparent difference. The zero reflection phase under x- and y-polarized incidence appears around 4.5GHz and 7GHz, respectively. Thus, a phase difference around 180°can be satisfied in a wide frequency range. A similar conclusion can be obtained by rotating the tile structure when the incident wave is fixed. Therefore, based on the concept of coding metamaterial, the tile which the long side of the patch parallel to the E-field is defined as “0” element and its counterpart (90°rotation around its center) is defined as “1” element. It is noted that the rectangular patch geometry is chosen just as an example to briefly show our design method. It can be replaced by other asymmetric structures as long as the 180° phase difference can be guaranteed.

Fig. 1 The jigsaw puzzle metasurface and the anisotropic tile. (a) The jigsaw puzzle metasurface is composed of 6 × 6 pieces of anisotropic tiles. Different functions can be realized by different layouts of the tiles. (b) The anisotropic tile. An array of 4 × 4 rectangular metallic patches is attached on the top of a 40mm × 40mm(equal to 0.8λ × 0.8λ at 6GHz) substrate with full metallic ground(a = 10mm, l = 9.4mm, w = 7.5mm, h = 3mm). The substrate is a dielectric board with dielectric constant of 2.65 and loss tangent of 0.001. (c) Reflection properties of the anisotropic tile for both x- and y-polarized incidence and their phase difference.

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Once the “jigsaw puzzle piece” has been prepared, different “patterns” can be constructed. In this article, we investigate three representative layouts: uniform layout, regular layout and irregular layout (see Fig. 2), which can achieve polarization conversion, anomalous refection and diffusion, respectively.

Fig. 2 Three representative layouts constructed by the jigsaw puzzle metasurface. (a) Uniform layout in which all the tiles are “0” or “1” (b) Regular layout in which the “0” and “1” are periodically arranged. (c) Irregular layout in which the “0” and “1” are arranged in specified or random sequence.

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2.2. Uniform layout for polarization conversion

We start with the simplest layout where all the tiles follow the same orientation, namely uniform layout, as shown in Fig. 2(a). Owing to the anisotropy of tiles, the whole metasurface shows anisotropic property as well.

We assume a linear-polarized plane wave normally impinges on the surface and the E-field vector is 45°with respect to the x-axis, as shown in Fig. 3(a). The mechanism can be understood by decomposing the E_i into two components E_x and E_y. E_x represents the component along x-axis and E_y represents the component along y-axis. Then the electric field vector at z = 0 plane can be expressed as

{\overset{⇀}{E}}_{i} = E_{x} \cdot \overset{⇀}{x} + E_{y} \cdot \overset{⇀}{y}

where

\overset{⇀}{x}

and

\overset{⇀}{y}

are the unit vectors in x and y directions. After reflection from the anisotropic metasurface, the electric field vector of reflection wave is

{\overset{⇀}{E}}_{r} = r_{x} E_{x} \cdot \overset{⇀}{x} + r_{y} E_{y} \cdot \overset{⇀}{y}

where

r_{x}

and

r_{y}

are the reflected coefficients along x- and y-axis, respectively. According to the reflection properties of the tile demonstrated in Fig. 1(c),

| r_{x} E_{x} | \approx | r_{y} E_{y} |

and there is a phase difference of 180° between

r_{x}

and

r_{y}

. Consequently, the polarization direction of the synthetic reflection wave is

- \overset{⇀}{x} + \overset{⇀}{y}

, which is orthogonal to that of the incident wave, as shown in Fig. 3(b). In other word, a cross polarization wave is obtained by the reflection of the metasurface. To verify this analysis, we define the co- and cross-polarization reflection coefficient as R_co and R_cross, respectively. The polarization conversion ratio is defined as

P C R = {| R_{c r o s s} |}^{2} / ({| R_{c r o s s} |}^{2} + {| R_{c o} |}^{2})

. Figure 3(c) shows the magnitude of reflection coefficients of the tile. R_co is reduced by more than 15dB from 5.36GHz to 6.66GHz while R_cross approaches 0dB. Therefore, the PCR is higher than 95% in this frequency band as shown in Fig. 3(d), suggesting nearly perfect polarization conversion.

Fig. 3 Polarization conversion of the tile a) Decomposition of electric vectors of incident waves. b) Intuitive scheme of polarization conversion. c) Simulated results of the co- and cross-polarization reflections. d) Calculated polarization conversion ratio.

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2.3. Regular layout for anomalous reflection

The regular layout means that “0” and “1” tiles are regularly or periodically arranged. Patterns fall into this category when “0” and “1” tiles are deposited in alternate rows/columns or interlaced like a chessboard. In this article, the metasurface composed by “0” and “1” tiles in rows (see Fig. 2(b)) is chosen as an example to demonstrate the capability of manipulating reflected beam directions. This phenomenon is attributed to the discontinuous phase shift on the interface and can be explained by the generalized Snell’s law [16]. For reflection the law is written as

\sin (θ_{r}) - \sin (θ_{i}) = \frac{1}{k_{0}} (\frac{Δ φ}{d x})

where k₀ is the wave vector in free space,

Δ φ / d x

is the phase gradient on the surface. Thus, for normal incidence(

θ_{i} = 0

), the anomalous reflection angle as a function of frequency can be predicted by

θ_{r} = arc \sin (\frac{c}{2 π f} (\frac{Δ φ}{d x}))

where c is the velocity of light. In this article, considering the phase difference of adjacent two rows and their dimensions, the phase gradient is

π / 4 a

.

In order to validate the analysis above, both full wave simulation and mathematical calculation are carried out. The scattering field versus frequency is demonstrated in Fig. 4(a). It can be observed that the normally incident beam is mostly reflected to two symmetrical directions within the frequency band from about 5GHz to 6.5GHz. The reflected angle decreases along with the frequency increase. Good agreement can be obtained between the simulated result and the calculated one by Eq. (4). This phenomenon can be further verified by the near- and far-field patterns at 5.8GHz, in which two beams at angle of ± 40.2°in the xoz plane can be observed, as shown in Figs. 4(b) and 4(c). The surface current distribution in Fig. 4(d) reveals the operating mechanism of the metasurface. It can be observed the “0” rows resonate fiercely while the “1” rows keep almost unexcited. The discrepant resonance yields the necessary discontinuous phase shift and finally results in anomalous reflection.

Fig. 4 Anomalous reflection of regular layout (a) Scattering ﬁeld spectrum versus frequency. The dash lines represent the calculated result by Eq. (4). (b) Near-E-field distribution on the xoz plane at 5.8GHz. (c) The corresponding 3D far-field pattern. (d) Surface current distribution on the metasurface.

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2.4. Irregular layout for diffusion

In contrast to the regular layout, the irregular one has geometry that “0” and “1” tiles are arranged in aperiodic or random distribution. To obtain a diffusion pattern, the layout has many variations and can be optimized by algorithms. For the normally incident case, array theory offers an efficient way to fast predict the scattering field of the metasurface. The function can be expressed as

E_{t o t a l} = E F \cdot A F

where EF represents the pattern function of a tile. In our model, we assume that all the tiles share the same pattern function which approximates to

\cos θ

, and

θ

is the elevation angle. Thus, the total field of a M × N array is determined by the array factor AF which can be described as

A F = \sum_{m = 1}^{M} \sum_{n = 1}^{N} e^{j [(m - 1 / 2) (k d \sin θ \cos φ) + (n - 1 / 2) (k d \sin θ \sin φ) + ϕ (m, n)]}

where d is the distance between the structural centers of two adjacent tiles,

φ

is the azimuth angle.

ϕ (m, n)

is the phase compensation after the reflection from tile_m,n. In our model, the

ϕ (m, n)

of “0” and “1” tiles are 0°and 180°, respectively.

In order to show the feasibility of the jigsaw puzzle metaurface, we adopt the optimized code 001011 presented in [37] as an example. The layout is demonstrated in Fig. 2(c) in which the 1-D code has been extended into a 2-D form. The results of a same–sized full metal board are also presented for comparison. Figure 5(a) shows the radar cross section versus frequency of both objects. Obvious magnitude suppression can be obtained in wide band ranging from 4GHz to 8GHz. The maximum reduction value of 13.7dB appears at 6.1GHz, which agrees well with the calculated result in [37]. Figures 5(d) and 5(e) depict the scattering patterns obtained by full wave simulations. The scattering field of the metasurface splits into 16 small beams, so that the amplitude of each beam is significantly suppressed due to energy conservation. The results agree well with the ones by mathematical calculation as shown in Figs. 5(b) and 5(c). Figures 5(f) and 5(g) give more visual illustration of reflected magnitude versus angles. The metasurface has even reflected energy distribution in the upper half space which can be deemed as diffusion. In contrast to the results of regular layout as shown in Figs. 4(b) and 4(d), the near-E-field of the irregular one is directionless, as shown in Fig. 5(h), owing to the disordered distribution of resonant cells on the metasurface(see Fig. 5(i)). The above results sufficiently prove the viability of jigsaw puzzle metasurface for reflection magnitude reduction. It is worth mentioning that the far field can be further modified for better diffusion behavior by optimizing the layout. Array theory combined with optimization algorithms could offer an efficient way for this purpose [34].

Fig. 5 Diffusion properties of irregular layout (a) Radar cross section versus frequency compared with a same-sized metal board. b,c) Scattering patterns calculated by Eq. (5): (b) metasurface and c) metal board. (d,e) Scattering patterns obtained by full wave simulations at 6.1GHz. (f,g) Scattering spectrum in the backward space (h) The near-E-field distributions. (i) Surface current distribution.

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3. Fabrication and measurement

To validate the performance mentioned above, a jigsaw puzzle metasurface sample has been fabricated and tested. As shown in Fig. 6(a), the sample is composed of 36 identical tiles. Each tile is manufactured by printed circuit board processing technology. F4B board is selected as the dielectric substrate. The metal patches and ground are made of 0.036mm-thick copper layers. The tiles are carried in a rigid foam frame and fixed by double-side tap. The frame has a dielectric constant which is close to 1 and thus it brings negligible impact to the measurement. Since the tiles are copied individuals, they can be substituted for each other and assembled for arbitrary layout. Figures 6(b)-6(d) are the completed states of the jigsaw puzzle metasurface corresponding to the numerical models in Fig. 2.

Fig. 6 Fabricated jigsaw puzzle metasurface and the basic measurement setup. (a) The partially done jigsaw puzzle metasurface which is composed of 36 pieces of identical tiles and a rigid foam frame. (b-d) The totally done states: (b) uniform layout (c) regular layout and (d) irregular layout. (e) The basic measurement setup.

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The basic setup is shown in Fig. 6(e). The sample is measured in an anechoic chamber. Two identical horn antennas are utilized as transmitting and receiving devices, respectively. Both of the antennas are initially set as horizontal polarization(x-polarization, referring to the coordinate axes in Fig. 6(e)). A piece of absorbing material is set between the antennas to reduce undesired coupling. The height of the sample is kept the same with the antennas and the distance is far enough to satisfy the far field measurement requirement. Then, the scattering performance is evaluated by the transmission coefficients obtained by vector network analyzer (VNA) Agilent N5230C. Gate-reflect-line calibration in time-domain analysis kit of VNA is employed to further eliminate the noise in the environment.

Due to the different properties of the three layouts, the measurement setup is slightly adjusted in each case. In the uniform layout measurement, the polarization of transmitting antenna is rotated to 45° with respect to the x-axis, while the polarization of receiving antenna is set as ± 45° to obtain the co- and cross-polarized signals, respectively. In the regular layout measurement, the transmitting antenna normally illuminates the metasurface, while the receiving antenna is placed at the angle of 40° with respect to the normal direction of the metasurface to detect the anomalous reflection. In the irregular layout measurement, the basic setup is not changed but a same-sized metal board is measured additionally to help evaluate the reflection reduction effect of the metasurface.

The measured results are demonstrated in Fig. 7 along with their corresponding simulated curves. Figure 7(a) shows that the uniform layout presents good polarization conversion performance around 6GHz. The anomalous reflection performance of regular layout is shown in Fig. 7(b). It can be seen that along with the frequency variation, the reflected signal appear a wave crest at about 6GHz, implying that energy is redirected to the observation direction at this frequency. Figure 7(c) demonstrates the wide band reflection reduction property of the irregular layout compared with the full metal board, 6dB reduction is observed from 4GHz to7.3GHz while the maximum value 15.5dB appears at 6.2GHz. The measured results agree well with the simulated ones. The deviations can be attributed to imprecise placement of measurement devices, fabrication and splicing errors. The above results confirm that the jigsaw puzzle metasurface provides an effective method to manipulate reflected waves.

Fig. 7 Measured and simulated results. (a) The normalized reflections of the uniform layout. co., co-polarized reflection; cross., cross-polarized reflection; meas., measurement; sim., simulation. (b) The normalized reflection of the regular layout at the observing angle of 40deg. (c) The reflection reduction magnitude of the irregular layout compared to full metal board.

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4. Conclusion

We have proposed a concept of jigsaw puzzle metasurface. The metasurface offers a reconfigurable and low-cost approach to realize multiple functions. Mechanical control and electronic control can be further developed based on this idea. Great application value can be expected in beam reconfigurable antennas, target stealth and so on. The performance can be further improved by seeking novel anisotropic tiles and expanding the scale. This concept could also be applied in other frequency ranges.

Acknowledgments

Yi Zhao and Xiangyu Cao contributed equally to this work. This work is supported by the National Natural Science Foundation of China (Grant No.61271100, No.61471389 and No.61501494), the Doctoral Foundation of Air Force Engineering University under Grant (No. KGD08091502).

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Jigsaw puzzle metasurface for multiple functions: polarization conversion, anomalous reflection and diffusion

Abstract

1. Introduction

2. Design of the jigsaw puzzle metasurface

2.1 Design concept and the anisotropic tile

2.2. Uniform layout for polarization conversion

2.3. Regular layout for anomalous reflection

2.4. Irregular layout for diffusion

3. Fabrication and measurement

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (7)

Equations (6)

Optics Express