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Interleaved coding Janus metasurface with independent transmission and reflection phase modulation

Guanyu Shang, Guoyu Li, Weisong Zhao, Kuang Zhang, Qun Wu, Jianxing Liu, Shah Nawaz Burokur, Haoyu Li, and Xumin Ding

Open Access Open Access

Abstract

An interleaved coding Janus metasurface is proposed, which can generate bidirectional functionalities with full phase control of the reflected and transmitted waves. By introducing rotation and geometric parameter changes into the meta-atoms, the reflection and transmission channels with required energy distribution and foci are realized. More remarkably, our approach is based on a single metasurface design that arranges two types of unidirectional propagating unit structures with simultaneous desired reflection and transmission properties into a checkerboard configuration to obtain four different holograms. The results verify the excellent performances of the multifunctional metasurface, laying a foundation for manipulation of EM waves with more degree of freedom, and promoting its applications in the entire frequency spectrum.

© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Metasurfaces, have attracted broad attention and become a rapidly developing research field thanks to their unique capacity for arbitrarily modulate the phase, amplitude, and polarization of EM waves with a compact footprint and powerful versatility in producing various special optical effects, such as anomalous refraction and reflection [1–4], polarization controls [5–7], focusing lenses [8–10] holograms [11–13] and so on. More recently, due to the concept of digital coding metasurfaces [14] that has been proposed in 2014 and rapidly evolved, the design and optimization procedures have been greatly simplified. Subsequently, time-modulated metasurfaces were thoroughly explored for coding applications [15–17]. By judiciously arranging the coding sequences, some efforts have been devoted to engineer the metasurfaces, providing a new way for the design of multifunctional systems [18–25]. For instance, currently available hologram metasurfaces operate in either reflection channel or transmission channel, leading the other semi-space uncontrollable.

With the growing of miniaturization technology and highly integrated system, it is meaningful to explore metasurface designs that can simultaneously manipulate transmission and reflection EM waves operating at different frequencies [26,27]. In addition, by adjusting the bias voltage of the loaded tunable electronic components, reconfigurable meta-devices with EM response characteristics that can be dynamically controlled, which can provide a flexible platform to fully unveil the great potential for the realization of full-space devices [28–30]. For instance, a typical reconfigurable anisotropic digital coding metasurface at microwave frequencies uses PIN diodes to independently control the full space modes of EM waves [30]. However, compared to passive metasurfaces, the design process of reconfigurable metasurfaces is more complex and requires additional bias networks, which inevitably leads to an increase in the system cost and loss. Moreover, anisotropic multilayer metasurfaces have been presented to control the transmitted and reflected wavefronts to realize full-space EM manipulation [31–33]. Essentially, such multifunctional metasurface is realized by utilizing polarization multiplexing, where the transmitted and reflected waves can only operate under two different orthogonal polarizations.

Although great diversity of achievements has been reported for full-space metasurfaces, there is still much room to conceive new and fascinating functions. Directional multiplexing technology occupies an important field in the implementation of multitasking architecture. Recently, the “Janus” features related to the propagation direction of the incident wave have been implemented in ultrathin metasurfaces. The optical Janus metasurface can enable dual-functionalities, amongst focusing lens, beam shifter, fisheye lens, holographic encryptions, and polarization-encrypted data storage [34,35]. Moreover, directional functionalities metasurfaces, known as Janus metasurfaces, have been studied at microwave frequencies [36,37]. For instance, Xu et al. [37] adopted a wavelength-direction-multiplexed metasurface to realize reflection and transmission channels under spin excitation. However, very limited demonstrations are reported for single wavelength and linear-polarized (LP) operation in full-space control of directional multiplexing. In previous work, we exploited the triangular segmented metasurface for bidirectional reflection and transmission [38]. Under forward incidence, one triangular region is effective to play its role and enables functions only in its corresponding area. Similarly, the other triangle provides the reflection and transmission wave manipulations of the corresponding area under backward incidence, which limits the degree of freedom in the control and potential applications of such devices. Recently, we have studied a non-interleaved Janus metasurface to make full use of the reflection and transmission channels [39]. Due to the properties of the unit structure, part of the incident energy is transmitted to the cross-polarized reflection and co-polarized transmission channel, and cannot be adjusted, which leads to energy waste to a certain extent. Therefore, to tackle these problems, the bi-directional multi-functional metasurface with both reflection and transmission for a single wavelength needs to be further studied.

Here, we propose a directional multiplexed transmission-reflection-integrated coding metasurface, which simultaneously projects four separate images at the same frequency. As illustrated in Fig. 1, under the y linearly polarized (LP) forward incidence, the co-polarized (y-LP) reflection channel presents the hologram “L” and the cross-polarized (x-LP) transmission channel emerges the hologram “O”. Interestingly, when the wave is incident from the reverse direction to the metasurface, its corresponding channel produces different holograms “V” and “T”. The key step is to judiciously design a collection of meta-atoms with both specific transmission and reflection characteristics. Having sufficient energy in the desired co-polarized reflection and cross-polarized transmission channels and very low energy in the unwanted cross-polarized reflection and co-polarized transmission channels inevitably enables avoiding the waste of energy. By special arrangement, the metasurface can control the transmission and reflection wavefronts of two incident waves in opposite directions. In addition, the imaging area is not limited, and the energy of each channel can be distributed arbitrarily. The experimental results match well with the theoretical ones, verifying the excellent performances of the Janus metasurface. Manipulating electromagnetic (EM) waves in multiple desired directions with a single planar device, especially in transmission and reflection schemes, is particularly important for equipment miniaturization and system integration. The proposed metasurface broadens the prospect for the development of multifunctional devices regulated in the full space and lays a foundation for the further development of imaging and communication systems.

 figure: Fig. 1.

Fig. 1. Schematic demonstration of the coding Janus metasurface to independently manipulate the co-polarized reflected and cross-polarized transmitted waves under the y linearly polarized wave incidence from both forward and backward directions.

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2. Meta-atom design and operation principle

To achieve our goal, a multilayer meta-atom is designed to simultaneously tailor high-performance reflection and transmission characteristics. Figure 2(a) shows the structure of the multilayer coding element. The coding element consists of three 18 µm thick copper layers, which are marked as #P1, #P2, and #P3, and spaced by two F4B dielectric substrates having relative permittivity εr = 2.65, tangent loss tan δ = 0.001 and thickness h = 3 mm. The center working frequency is set to 15 GHz. #P1 and #P3 are composed of gratings, which are geometrically identical, but orthogonally oriented. The two gratings form a “Fabry-Perot-like” cavity, as schematically illustrated in Fig. 2(b). The period of the coding element is p = 6 mm, and the others parameters are fixed as s = 1.2 mm, w = 0.4 mm and b = 0.6 mm.

 figure: Fig. 2.

Fig. 2. Geometry of the coding meta-atom. (a) Schematic representation of the coding element constructed by alternately stacking three copper layers and two dielectric substrates. (b) Schematics representation of the Fabry-Perot-like resonance occurring in multilayer metasurface. Calculated and simulated characteristics of the unit cell. (c) Forward reflection and transmission amplitudes for varying angle ${\theta}$ with l = 4 mm and d = 0.5 mm. (d) Forward co-polarized reflection and cross-polarized transmission phases for varying angle ${\theta}$ with l = 4 mm and d = 0.5 mm.

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In order to better understand the physical mechanism of the unit structure, we use the transfer matrix method to analyze the reflection and transmission scattering properties. The transfer matrix method is a commonly used mathematical technique that describes how waves are transmitted, reflected, and altered at each interface or layer [40]. It enables the calculation of the overall transmission and reflection properties of the entire layered structure by considering the individual interactions at each interface. Then, the Jones matrix is applied to analyze and manipulate the polarization state of light [41]. For a two port network, the S-parameter matrix can be represented as:

$$S = \left( {\begin{array}{cc} {{S_{11}}}&{{S_{12}}}\\ {{S_{21}}}&{{S_{22}}} \end{array}} \right)$$
where ${S_{11}}$ and ${S_{21}}$ are the reflection and transmission coefficients in the forward direction. ${S_{22}}$ and ${S_{12}}$ are the reflection and transmission coefficients in the backward direction. The reflection and transmission Jones matrix R and T of the arrow-shaped resonator (#P2) under forward incidence can be expressed in the general form given by
$${S_{11}} = R = \left[ {\begin{array}{cc} {{r_{11}}^{xx}}&{{r_{11}}^{xy}}\\ {{r_{11}}^{yx}}&{{r_{11}}^{yy}} \end{array}} \right]$$
$${S_{21}} = T = \left[ {\begin{array}{cc} {{t_{21}}^{xx}}&{{t_{21}}^{xy}}\\ {{t_{21}}^{yx}}&{{t_{21}}^{yy}} \end{array}} \right]$$
where ${r_{11}}^{xx} = |{{r_{11}}^{xx}} |{e^{i\varphi _r^{xx}}}$, ${r_{11}}^{yy} = |{r_{11}^{yy}} |{e^{i\varphi _r^{yy}}}$ and $t_{21}^{xx} = |{t_{21}^{xx}} |{e^{i\varphi _t^{xx}}}$, $t_{21}^{yy} = |{t_{21}^{yy}} |{e^{i\varphi _t^{yy}}}$ represent the diagonal linear reflection and transmission coefficients of the layer, respectively. $r_{11}^{xy} = |{r_{11}^{xy}} |{e^{i\varphi _r^{xy}}}$, $r_{11}^{yx} = |{r_{11}^{yx}} |{e^{i\varphi _r^{yx}}}$ and $t_{21}^{xy} = |{t_{21}^{xy}} |{e^{i\varphi _t^{xy}}}$, $t_{21}^{yx} = |{t_{21}^{yx}} |{e^{i\varphi _t^{yx}}}$ are the off-diagonal linear reflection and transmission coefficients, respectively. θ is the in-plane rotation angle of layer #P2. Additionally, with the parameters g, n, and l fixed, transmission with a large phase range can be achieved by changing the angle θ. Then, the Jones matrices can be formulated as
$$R(\theta ) = A( - \theta ) \cdot R \cdot A(\theta )$$
$$T(\theta ) = A( - \theta ) \cdot T \cdot A(\theta )$$
where $A(\theta ) = \left( {\begin{array}{cc} {\cos \theta }&{\sin \theta }\\ { - \sin \theta }&{\cos \theta } \end{array}} \right)$ represents the rotation matrix. If the meta-atom possesses a symmetry, the components of the R/T matrix must also have a symmetry. When the rotation angle of the unit structure is zero (θ = 0°), the meta-atom is mirror-symmetric with respect to the xoz plane and we have $A(0) = \left( {\begin{array}{cc} 1&0\\ 0&1 \end{array}} \right)$. The R/T matrix for the structure is then identical to the original one (R(0) = R and T(0) = T). So any structure that obeys that symmetry may be obviously described by a diagonal R/T matrix. In this way, the co-polarized reflection and cross-polarized transmission coefficients of the rotating metal sheet become
$$R(0) = \left( {\begin{array}{cc} {r_{11}^{xx}{{\cos }^2}\theta + r_{11}^{yy}{{\sin }^2}\theta }&{(r_{11}^{xx} - r_{11}^{yy})\sin 2\theta /2}\\ {(r_{11}^{xx} - r_{11}^{yy})\sin 2\theta /2}&{r_{11}^{yy}{{\cos }^2}\theta + r_{11}^{xx}{{\sin }^2}\theta } \end{array}} \right) = \left( {\begin{array}{cc} {r_{11}^{xx}}&0\\ 0&{r_{11}^{yy}} \end{array}} \right)$$
$$T(0) = \left( {\begin{array}{cc} {t_{21}^{xx}{{\cos }^2}\theta + t_{21}^{yy}{{\sin }^2}\theta }&{(t_{21}^{xx} - t_{21}^{yy})\sin 2\theta /2}\\ {(t_{21}^{xx} - t_{21}^{yy})\sin 2\theta /2}&{t_{21}^{yy}{{\cos }^2}\theta + t_{21}^{xx}{{\sin }^2}\theta } \end{array}} \right) = \left( {\begin{array}{cc} {t_{21}^{xx}}&0\\ 0&{t_{21}^{yy}} \end{array}} \right)$$

When the rotation angle of the unit structure is not zero ($\theta \ne 0$), under y-LP wave incidence, the cross-polarized conversion for the transmission channel is directly proportional to the sine of the rotation angle of the meta-atom for a certain $t_{21}^{xx}$ and $t_{21}^{yy}$, which leads to the relationship $t_{21}^{xy}(\theta ) \propto \sin 2\theta$. The co-polarized reflection channel is symmetric with respect to θ, i.e. $r_{11}^{yy}(\theta ) = r_{11}^{yy}( - \theta )$. In addition, the introduction of the Fabry-Perot-like cavity is indeed a general method to enhance the cross-polarized transmission and the co-polarized reflection efficiencies. Therefore, we analyze the transmission matrix of each layer. When an incident wave is transmitted through the metasurface, a 4 × 4 transfer matrix Mmn is exploited to illustrate the relationship between the forward and backward propagating fields [42]

$$\left( {\begin{array}{c} {E_{mx}^f}\\ {E_{my}^f}\\ {E_{mx}^b}\\ {E_{my}^b} \end{array}} \right) = {M_{mn}}\left( {\begin{array}{c} {E_{nx}^f}\\ {E_{ny}^f}\\ {E_{nx}^b}\\ {E_{ny}^b} \end{array}} \right)$$
where f and b indicate forward and backward propagating directions. Mmn is then given as
$${M_{mn}}\textrm{ = }{\left( {\begin{array}{cccc} 1&0&{ - {r_{mx,mx}}}&{ - {r_{mx,my}}}\\ 0&1&{ - {r_{my,mx}}}&{ - {r_{my,my}}}\\ 0&0&{{t_{nx,mx}}}&{{t_{nx,my}}}\\ 0&0&{{t_{ny,mx}}}&{{t_{ny,my}}} \end{array}} \right)^{ - 1}} \times \left( {\begin{array}{cccc} {{t_{mx,nx}}}&{{t_{mx,ny}}}&0&0\\ {{t_{my,nx}}}&{{t_{my,ny}}}&0&0\\ { - {r_{nx,nx}}}&{ - {r_{nx,ny}}}&1&0\\ { - {r_{ny,nx}}}&{ - {r_{ny,ny}}}&0&1 \end{array}} \right)$$
where r and t are the reflection and transmission coefficients, and the subscripts mi, ni denote that wave propagates from the medium m to n with polarization i (i = x,y). As such, we can get the transfer matrix M32 of the layer #P2. In addition, for the given homogeneous medium $\zeta $ with a refractive index ${\eta _\zeta }(\varpi )$, the propagation matrix is given by ${P_\zeta } = diag({e^{i{k_0}{n_\zeta }h}},{e^{i{k_0}{n_\zeta }h}},{e^{ - i{k_0}{n_\zeta }h}},{e^{ - i{k_0}{n_\zeta }h}})$, where k0 is the wave number in free space. Finally, as shown in Fig. 2(b), the overall M-matrix can be written as [42]
$$M = {M_{43}}{P_\zeta }{M_{32}}{P_\zeta }{M_{21}}$$

Because of the two orthogonally oriented gratings of the meta-atom and the power conservation, we can clearly see that reflection and transmission amplitudes of the meta-atom present continuous tuning when changing the orientation angle θ under y-LP wave incidence, as illustrated in Fig. 2(c). Given the relationship between reflection and transmission amplitudes, the characteristics shown in Fig. 2(c) can be summarized as:

$$\left\{ {\begin{array}{c} {|{{r_{yy}}} |is\textrm{ min},\textrm{ }|{t_{xy}^{}} |is\textrm{ max},\textrm{ when }\theta \textrm{ = } \pm {{45}^ \circ }}\\ {|{r_{yy}^{}} |is\textrm{ max},\textrm{ }|{t_{xy}^{}} |\textrm{ is min},\textrm{ when }\theta \textrm{ = }{\textrm{0}^ \circ }}\\ {0 < |{r_{yy}^{}} |< 1,\mathrm{\ 0\ < }|{t_{xy}^{}} |< 1,\textrm{ when }\theta \ne \textrm{ }{\textrm{0}^ \circ }} \end{array}} \right.$$

It can be seen that the meta-atom has an influence on the co-polarized reflection and cross-polarized transmission channels. The energy can be arbitrarily distributed in two channels through the orientation angle θ. In the cross-polarized reflection and co-polarized transmission channels, there is almost no energy, which is also an important factor to improve the efficiency of each channel. In addition, Fig. 2(d) clearly reveals that the transmission phase always experiences a phase shift of π as θ changes from the range [−π/2, 0] to [0, π/2] (e.g. ${\varphi _t}^{xy}(\theta ) = {\varphi _t}^{xy}( - \theta ) \pm \pi $), which is consistent with (6). The reflection phase also always experiences a symmetry shift as θ changes from the range [−π/2, 0] to [0, π/2] such that ${\varphi _r}^{yy}(\theta ) = {\varphi _r}^{yy}( - \theta )$. So, the proposed meta-atom has the capability to modulate the phase of the reflection and transmission channels independently and simultaneously, which provides a powerful method for full-space wave manipulation.

3. Unidirectional reflection and transmission energy distribution regulation

To investigate the energy relationship between the transmission and reflection characteristics of the metasurface, CST Microwave Studio software is used to simulate the meta-atoms under y-polarized incidence and we design a metasurface to verify the equal energy allocation and phase control in the full space. The variation of the multiple parameters g, n, l and θ provides further possibilities for the ultimate simultaneous reflection and transmission. As illustrated in Table 1, “0” and “1” represent the calculated discrete phase value of 0 and π, respectively. Before and after the “+” represent the phase state of the reflected and transmitted channels respectively, which indicates that the meta-atom shows the properties of π phase change of the reflection component and also π phase change of the transmission component.

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Table 1. The detailed parameters of the 1-bit meta-atoms

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The 1-bit coding level is adopted here as a good trade-off between design complexity and discretization losses. The reflection and transmission intensity spectra of the properly designed coding elements are exhibited in Figs. 3(a) and 3(c). It can be clearly seen that the intensity of the four coding elements is around 0.5 at 15 GHz, which signifies that half of the incident energy is reflected and the other part is transmitted. Therefore, the relationship between co-polarized reflection and cross-polarized transmission keeps the ratio of 1. Figure 3(b) presents the phase of the unit cells “0 + 0” and “1 + 0” (or “0 + 1” and “1 + 1”) undergoing an abrupt π change for the reflected y-LP channel. Meanwhile, the phase of π difference can be easily introduced for “0 + 0” and “0 + 1” (or “1 + 0” and “1 + 1”) for the transmitted x-LP component as illustrated in Fig. 3(d), such intriguing characters provide a flexible degree of freedom to have an independent phase state in each component sharing the same aperture.

 figure: Fig. 3.

Fig. 3. (a) and (b) Reflection intensity and phase response of all four coding elements for the y-LP component, respectively. (c) and (d) Transmission intensity and phase response of all four coding elements for the x-LP component, respectively.

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Based on the advantages of the proposed meta-atom, an improved weighted Gerchberg-Saxton (GSW) retrieval algorithm [43,44] is used to derive the optimal phase distributions under unidirectional y-LP incidence. In order to have the field intensity of each focus uniformly distributed in each image, we introduce a weighting factor wm to reduce the intensity difference between the N focal points. The following phase distribution ${\phi _m}$ is further obtained by iteration:

$$\phi _m^p = \arg (\sum\limits_{n = 1}^N {\frac{{{e^{ikr_m^n}}}}{{r_m^n}}} \frac{{w_n^pE_n^{p - 1}}}{{|{E_n^{p - 1}} |}})$$
where $r_m^n$ is the distance between the mth coding meta-atom and the nth focal point, k is the phase constant, wn presents the intensity ratio of nth focus to the first one, and the superscript p represents the pth iteration. $|{E_n^{p - 1}} |$ denotes the electric field intensity of the nth focal point in the (p-1)th iterative step. The reconstructed electromagnetic field at each focal position can be expressed as:
$$E_n^p = \sum\limits_{m = 1}^M {\frac{{{e^{ - ikr_m^n + i\phi _m^p}}}}{{r_m^n}}} $$

By adjusting the weight factor wn, given as

$$w_n^p = w_n^{p - 1}\frac{{\sum\limits_{n = 1}^N {|{E_n^{p - 1}} |} }}{{N|{E_n^{p - 1}} |}}, $$
we can eliminate the deviations of $|{{E_n}} |$ from the desired intensity. The initial condition is set as:
$$w_n^0 = 1, \phi _m^0 = \frac{{2\pi m}}{M}$$

To verify the proposed full-space focusing, a coding metasurface is properly designed, which shows reflected “square” and transmitted “rhombus” images under y-LP incidence. In the Figs. 4(c) and 4(f), the coding maps of the multiplexed metasurface are constructed by the coding rule of Table 1. The simulated results of the Ey-field and Ex-field distributions in the xoy imaging plane are shown in Figs. 4(d) and 4(g). To demonstrate the performance of the proposed unidirectional metasurface, a sample composed of 41 × 41 units with the size of 246 mm × 246 mm is fabricated using classical printed circuit board (PCB) technology, as shown in Fig. 4(b). A near-field scanning system is used for the experimental measurement, as schematically illustrated in Fig. 4(a). The feeding antenna is placed far enough away from the metasurface to guarantee a quasi-planar incident wave. The electric field distribution in the reflection and transmission spaces is measured by using a purely dielectric fiber-optic active antenna as the field-sensing probe, which is moved in a small step size of 4 mm in the xoy plane. The feeding horn antenna and the field sensor probe are both connected to a vector network analyzer (VNA) to measure both the amplitude and phase of the reflection and transmission coefficients. Figures 4(e) and 4(h) show the measured holographic images of the y-LP reflection and x-LP transmission at the same distance of 80 mm from the metasurface under the y-LP incidence at 15 GHz. Four hot spots with uniform intensity are obtained, and the ratio of the sum of the energy of the four focuses of reflection and transmission is close to 1:1, which is match well with the theoretical prediction and simulation results.

 figure: Fig. 4.

Fig. 4. (a) Measurement setup used to scan the electric field distribution. (b) Photograph of the fabricated sample. (c) and (f) Phase maps of the 1-bit coding metasurface designed for equal energy distribution in reflection and transmission spaces. (d) and (g) Simulation results in the reflection and transmission channels. (e) and (h) Measured holographic images in the reflection and transmission channels.

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Moreover, in order to further realize different energy distributions in the reflection and transmission channels, we adopt the method of parameter adjustment to have a π phase-change of the reflection channel, and also a π phase-change of the transmission channel. The parameters of the relevant cell structures are shown in Table 2. The reflection and transmission intensity spectra of the elements are indicated in Figs. 5(a) and 5(c), showing that the ratio of reflection and transmission intensities of the four coding elements is 1:3 at 15 GHz. Figures 5(b) and 5(d) show that the phase difference is π for the reflection x-LP and transmission y-LP components. Based on these meta-atoms, a 1-bit coding meta-hologram is devised, which projects reflected “square” and transmitted “rhombus” images with unequal energy distribution. A coding metasurface composed of 41 × 41 elements with the size of 246 mm × 246 mm, which contains two coding patterns to realize the desired distribution of reflected and transmitted energy at the same frequency. Figures 6(a) and 6(d) show the phase distribution required for the images. Figures 6(b), 6(e) and Fig. 6(c) and 6(f) present the simulated and corresponding experimental results. As expected, four good hotspots with uniform intensity are obtained in each semi-space, and the ratio of the sum of reflected and transmitted energy is close to 1:3, which is match well with the theoretical prediction and simulation results. From the above examples, it is shown that the reflected and transmitted energy can further realize arbitrary energy distribution between the two channels by adjusting the amplitude relationship through the parameters of the unit structure. In addition, the proposed strategy can be readily applied to higher frequencies through appropriate scaling.

 figure: Fig. 5.

Fig. 5. (a) and (b) Reflection intensity and phase response of all four coding elements for the y-LP component, respectively. (c) and (d) Transmission intensity and phase response of all four coding elements for the x-LP component, respectively.

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 figure: Fig. 6.

Fig. 6. (a) and (d) Coding maps and electric field intensity distributions obtained from the 1-bit coding metasurface designed for unequal (ratio 1:3) energy distribution in reflection and transmission spaces. (b),(c) y-LP reflection showing the image of a “square”. (e),(f) x-LP transmission showing the image of a “rhombus”.

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Table 2. The detailed parameters of the 1-bit meta-atoms

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4. Reflection and transmission multiplexing for bidirectional holographic imaging

Finally, we demonstrate more advanced functionalities of coding metasurfaces, multiplexed for different propagation directions. Specifically, the metasurface for such purpose is composed of meta-atoms shown in Table 1, which maintains similar energy in both channels. It is worth noting that the key idea is to combine two meta-atoms, rotated by 180° around the z-axis with respect to each other and combined into a 2 × 2 “checkerboard” configuration array as a supercell as shown in Figs. 7(a) and 7(b), to form a metasurface. The yellow elements have the ability to simultaneously control reflection and transmission channels for the forward y-LP incidence, which can inhibit the backward y-LP incidence. Meanwhile, the working mechanism is similar to EM waves imposing on the opposite side of the metasurface. When the wave illuminates from the back layer of the metasurface, the red elements will also be able to reflect and transmit at the same time, providing the necessary phase profile. Finally, four spatial phase contours used to reconstruct the target image are mapped to the coding metasurface, and these four spatial phase contours are interpreted by the two different meta-atoms in the supercell. Therefore, the coding metasurface can alternate directional waves and reconstruct four required images in two opposite directions.

 figure: Fig. 7.

Fig. 7. Schematic of the design principle for a bidirectional interleaved metasurface. Schematic of the first layer of the metasurface when it is seen along (a) the forward direction, and (b) the backward direction. The red element is formed by rotating the yellow element 180° along the z axis.

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For an experimental proof-of-concept demonstration, we exploit a single coding metasurface to produce four different holograms: the forward wave produces the reflected letter “L” and the transmitted letter “O” and the backward wave produces the reflected letter “V” and the transmitted letter “T”. The distance between the imaging planes and the metasurface is 80 mm in all cases. A photograph of the fabricated sample is shown in Fig. 8. As shown in Figs. 9(a)-9(d), the phase distributions required for the reconstruction of the different images are optimized by the GSW algorithm, and the designed metasurface is composed of a total of 21 × 21 supercells. The supercells at odd positions have the ability to simultaneously control reflection and transmission channels under the forward y-LP incidence and can take either the “0” or “1” phase state, while the even positions are invalid and marked as ‘Null’, as shown in Figs. 9(a)-(b). Similarly, under the y-LP backward incidence, the supercells at even positions can take the “0” or “1” phase state as shown in Figs. 9(c)-(d), while the odd regions are marked as ‘Null’. It is important to note that the ‘Null’ regions are complementary for the forward and backward incidences. The simulation results of Figs. 9(e)–9(h) shows that the metasurface can fully project the different images when illuminated by forward and backward plane waves. In addition, the crosstalk between the images in the opposite region is negligible, suggesting that the metasurface can achieve arbitrary independent holographic images. The measured results for different observation planes are shown in Figs. 9(i)–9(l), which agree well with the numerical simulations.

 figure: Fig. 8.

Fig. 8. Photograph of the fabricated sample. (a) Front view. (b) Back view.

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 figure: Fig. 9.

Fig. 9. (a)-(d) Phase maps of the reflection and transmission channels under the y-LP forward and backward incidences. (e)-(h) Simulation results showing the different reflected and transmitted images. (i)-(l) Experimental holographic images in the four channels.

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Two parameters are further introduced to evaluate the quantification of each channel. The reflection (transmission) efficiency is defined as the ratio of the total intensity of the wave reflected (transmitted) by the metasurface to the incident intensity on the surface [45,46]. Under y-LP forward wave incidence, the reflection/transmission efficiency is measured to be 29.2%/22.4% for the images of “L” and “O”, and the total energy utilization of the incident wave is 51.6%. For the backward incident wave, the reflection/transmission efficiency is calculated as 27.57%/21.1%, and the total energy utilization is 48.67%. The imaging efficiency, defined as the ratio of the power received in the focus to the total energy in the reflection or transmission imaging plane [47], has also been calculated. The imaging efficiency of the letter “L”, “O”, “V” and “T” is calculated as 60.9%, 60.5%, 64.6% and 56.1%. Losses are mainly due to the fact that part of the energy is reflected in the cross-polarized channel and transmitted in the co-polarization channel. In addition, part of the energy loss is also due to dielectric losses in the dielectric substrates. To further demonstrate the advantages of our strategy, a comparison with previously reported directional multiplexed metasurfaces is presented in Table 3. The proposed coding metasurface increases the number of regulated channels compared with the work in [36] and achieves a higher incident wave utilization efficiency in each incident direction at a single frequency compared with the study in [39]. The multifunctional design is conducive to system integration and device miniaturization and can be used as high-efficiency directional electromagnetic screens and antenna radomes.

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Table 3. The comparison of the Janus metasurface

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5. Conclusion

In conclusion, we explore the energy distribution relationship between reflection and transmission channels of coding metasurfaces. We validate a directional multiplexed coding meta-hologram in the microwave domain, which is obtained from an interleaved array of meta-atoms achieving simultaneous control of reflection and transmission characteristics. By changing the direction of the incident wave, four different holograms are further obtained, and the total utilization of EM wave under unidirectional incidences is 51.6% and 48.67%. Both numerical and experimental results show that the four predicted functions have fine independent character enabling additional degrees of freedom for the control of EM waves. In addition, our proposed concept can be extended to higher frequencies and even in optics to meet a variety of exciting applications. In general, we believe that arbitrary functions can be integrated into metasurface applications in a direction-dependent manner, which has profound implications from the perspective of information science.

Funding

Natural Science Foundation of Heilongjiang Province (YQ2021F004); National Natural Science Foundation of China (62171153, 62275063); State Key Laboratory of Millimeter Waves (K202309); State Key Laboratory of Robotics and System (SKLRS-2022-KF-04).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (9)
Fig. 1.
Fig. 1. Schematic demonstration of the coding Janus metasurface to independently manipulate the co-polarized reflected and cross-polarized transmitted waves under the y linearly polarized wave incidence from both forward and backward directions.

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Fig. 2.
Fig. 2. Geometry of the coding meta-atom. (a) Schematic representation of the coding element constructed by alternately stacking three copper layers and two dielectric substrates. (b) Schematics representation of the Fabry-Perot-like resonance occurring in multilayer metasurface. Calculated and simulated characteristics of the unit cell. (c) Forward reflection and transmission amplitudes for varying angle ${\theta}$ with l = 4 mm and d = 0.5 mm. (d) Forward co-polarized reflection and cross-polarized transmission phases for varying angle ${\theta}$ with l = 4 mm and d = 0.5 mm.

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Fig. 3.
Fig. 3. (a) and (b) Reflection intensity and phase response of all four coding elements for the y-LP component, respectively. (c) and (d) Transmission intensity and phase response of all four coding elements for the x-LP component, respectively.

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Fig. 4.
Fig. 4. (a) Measurement setup used to scan the electric field distribution. (b) Photograph of the fabricated sample. (c) and (f) Phase maps of the 1-bit coding metasurface designed for equal energy distribution in reflection and transmission spaces. (d) and (g) Simulation results in the reflection and transmission channels. (e) and (h) Measured holographic images in the reflection and transmission channels.

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Fig. 5.
Fig. 5. (a) and (b) Reflection intensity and phase response of all four coding elements for the y-LP component, respectively. (c) and (d) Transmission intensity and phase response of all four coding elements for the x-LP component, respectively.

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Fig. 6.
Fig. 6. (a) and (d) Coding maps and electric field intensity distributions obtained from the 1-bit coding metasurface designed for unequal (ratio 1:3) energy distribution in reflection and transmission spaces. (b),(c) y-LP reflection showing the image of a “square”. (e),(f) x-LP transmission showing the image of a “rhombus”.

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Fig. 7.
Fig. 7. Schematic of the design principle for a bidirectional interleaved metasurface. Schematic of the first layer of the metasurface when it is seen along (a) the forward direction, and (b) the backward direction. The red element is formed by rotating the yellow element 180° along the z axis.

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Fig. 8.
Fig. 8. Photograph of the fabricated sample. (a) Front view. (b) Back view.

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Fig. 9.
Fig. 9. (a)-(d) Phase maps of the reflection and transmission channels under the y-LP forward and backward incidences. (e)-(h) Simulation results showing the different reflected and transmitted images. (i)-(l) Experimental holographic images in the four channels.

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Tables (3)

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Table 1. The detailed parameters of the 1-bit meta-atoms

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Table 2. The detailed parameters of the 1-bit meta-atoms

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Table 3. The comparison of the Janus metasurface

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Equations (15)

Equations on this page are rendered with MathJax. Learn more.

S = ( S 11 S 12 S 21 S 22 )
S 11 = R = [ r 11 x x r 11 x y r 11 y x r 11 y y ]
S 21 = T = [ t 21 x x t 21 x y t 21 y x t 21 y y ]
R ( θ ) = A ( − θ ) ⋅ R ⋅ A ( θ )
T ( θ ) = A ( − θ ) ⋅ T ⋅ A ( θ )
R ( 0 ) = ( r 11 x x cos 2 θ + r 11 y y sin 2 θ ( r 11 x x − r 11 y y ) sin ⁡ 2 θ / 2 ( r 11 x x − r 11 y y ) sin ⁡ 2 θ / 2 r 11 y y cos 2 θ + r 11 x x sin 2 θ ) = ( r 11 x x 0 0 r 11 y y )
T ( 0 ) = ( t 21 x x cos 2 θ + t 21 y y sin 2 θ ( t 21 x x − t 21 y y ) sin ⁡ 2 θ / 2 ( t 21 x x − t 21 y y ) sin ⁡ 2 θ / 2 t 21 y y cos 2 θ + t 21 x x sin 2 θ ) = ( t 21 x x 0 0 t 21 y y )
( E m x f E m y f E m x b E m y b ) = M m n ( E n x f E n y f E n x b E n y b )
M m n  =  ( 1 0 − r m x , m x − r m x , m y 0 1 − r m y , m x − r m y , m y 0 0 t n x , m x t n x , m y 0 0 t n y , m x t n y , m y ) − 1 × ( t m x , n x t m x , n y 0 0 t m y , n x t m y , n y 0 0 − r n x , n x − r n x , n y 1 0 − r n y , n x − r n y , n y 0 1 )
M = M 43 P ζ M 32 P ζ M 21
{ | r y y | i s  min ,   | t x y | i s  max ,  when  θ  =  ± 45 ∘ | r y y | i s  max ,   | t x y |  is min ,  when  θ  =  0 ∘ 0 < | r y y | < 1 ,   0   < | t x y | < 1 ,  when  θ ≠   0 ∘
ϕ m p = arg ⁡ ( ∑ n = 1 N e i k r m n r m n w n p E n p − 1 | E n p − 1 | )
E n p = ∑ m = 1 M e − i k r m n + i ϕ m p r m n
w n p = w n p − 1 ∑ n = 1 N | E n p − 1 | N | E n p − 1 | ,
w n 0 = 1 , ϕ m 0 = 2 π m M
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