Highly decorrelated multiplexing metasurface for simultaneous dual-wavelength and dual-polarization continuous phase manipulation

Yu Dang; Yu Dang; Yongheng Mu; Yongheng Mu; Jiaran Qi

doi:10.1364/OE.399430

1. Introduction

Metasurfaces have shown attractive capabilities from the microwave to the optical regions in tailoring the phase, amplitude, and polarization states of electromagnetic waves with a high degree of freedom, and thus enable compact devices with novel functionalities. Among the reported advanced applications, metasurfaces featuring wavelength or polarization multiplexing play a more and more important role in, e.g., vortex beam generation [1], anticounterfeiting images [2], additive color mixing [3], space-bandwidth product optimization [4], reconfigurable antenna, and information encryption [5–8]. Besides, in the emerging 5G mobile communication, frequency and polarization multiplexing will further enhance the channel capacity to meet the demand on ultra-high data transmission rate.

To achieve polarization multiplexing, various methods have been introduced. In terms of linear polarization multiplexing, interleaved metaatoms often comprising multiple elements in one unit cell arranged in two orthogonal directions, such as birefringent nanorods [9–11], nanoslits [12], and paired nanospheres [13], enable independent manipulation on different polarized waves. By independently tuning two geometrical parameters of a few meta-atoms, e.g., the major and the minor axes of an elliptical amorphous silicon post [14,15], or the length and the width of a rectangular patch resonator [16], one can also achieve polarization multiplexing functionality for incoming linearly polarized waves. As for the circular polarization multiplexing, meta-atoms with helicity switchable phase responses were usually adopted. Metasurfaces with interleaved [17,18] or segmented [1] metamolecule have been widely proposed. Besides, recent studies reveal that extraordinary diffractions [19–21] can improve defects of traditional metasurfaces to achieve wide-band high-fidelity polarization multiplexing meta-holograms with extreme angle tolerances in the visible-near-infrared regime [22].

On the other hand, similar to polarization multiplexing, metasurfaces consisting of meta-molecules with multiple aluminum rods, Si blocks [23], and Si pillars [24–27] of different geometrical dimensions have been reported to realize wavelength multiplexing. In particular, a pixelated frequency multiplexing dielectric metasurface with a range of discrete sharp resonances in mid-infrared was proposed to read out at multiple spectral points the molecular absorption signatures, and thus the information is translated into a barcode-like spatial absorption map for imaging [28]. Moreover, recent advances in nonlinear metasurfaces [29–31] pave a new avenue for frequency multiplexing by implementing different phase profiles at the fundamental wavelength and high-order harmonics.

The aforementioned metasurfaces, nevertheless, often suffer from the channel correlation resulting from insufficient independence and deficient interference suppression among different channels. The reported geometrically simple nanostructures with anisotropic responses for plane-wave excitations with orthogonal linear polarization, do simplify the design yet often exhibit deficiency in independent polarization control and incapability of an entire 2π phase coverage for both polarizations. The insufficient phase response coverage can be partly addressed by a digital phase coding sequence at the cost of the overall performance of an imaging system, e.g., imaging quality and efficiency. As for the multi-functional metasurfaces manipulating the incoming electromagnetic wave with a circular polarization, it is still quite challenging to fully unlock the helicity dependency, resulting in hardly achievable polarization decorrelation and typically low efficiency [32]. Moreover, the key point for wavelength multiplexing lies in realization of distinct functionalities without too much cross-talk, which cannot readily be satisfied by the structures aforementioned. For instance, in the holographic application scenarios, conjugate images or dual-images inevitably occur on account of the insufficient wavelength isolation. With regard to the nonlinear metasurfaces, the inherent relation between the generated higher-order harmonics and the fundamental frequency unfortunately limits the design freedom. More importantly, for the lower frequency, Kerr-type materials or superconductors, which are necessary for realizing nonlinear phenomenon, tend to be relatively elusive to implement. Finally, all-dielectric merged Mie-scatters are often large and difficult to fabricate and integrate in the microwave region.

Here, in this work, to overcome the aforementioned restrictions we propose a simultaneous wavelength and polarization multiplexing metasurface platform in the microwave region aiming at realizing high isolation among different four channels. As an intuitive application example, the metasurface platform is customized to realize multiplexing holography. Owing to the complete 2π reflection phase coverage and highly decorrelated channel characteristics, the wavefront of each channel can be completely independently reconstructed by our metasurface platform with low background noises. The proposed dual-wavelength and dual-polarization metamolecule featuring low cross-talk guarantees the low interference between four generated holograms, while its whole 2π phase coverage and high reflection amplitude provide good transmission and imaging efficiencies. Correspondingly, the mechanism behind the satisfactory isolation and the analytical expression of the unit cell resonant frequency is revealed and formulated to facilitate our design. Furthermore, a modified weighted holographic algorithm is proposed to help us determine the phase distribution for different holograms. Then, a series of numerical simulations and experimental verifications are performed in the microwave region, which generates two different holographic images comprising four independently controlled parts without conjugate twin graphs, to demonstrate that the proposed metasurface platform has highly decorrelated and independent multiplexing property. It is noted that our metal-dielectric prototype can be fabricated with the convenient PCB photolithography.

2. Mechanism of the proposed metamolecules

The geometrical details of the proposed reflective metamolecule are illustrated in Fig. 1(a). Two circular microstrip ring patches of different radii for two wavelengths are etched on the upper dielectric substrate (Taconic RF-60A). The second layer, i.e., the slot layer, is composed of two pairs of crossed slots. These two layers are separated by an air gap which is in practice replaced by a rigid polymethcryimide (PMI) foam with a near-unity effective permittivity. The slot layer is placed on one side of the lower substrate playing the role of a relay, which can decompose the coupled electromagnetic wave from the circular ring patch into orthogonal linear polarization components in both frequency bands, respectively. On the other side of the lower substrate, four metallic microstrip delay lines acting as the phase shifter for two polarization states at both bands are properly arranged. To suppress the backward radiation, the reflection plate on the bottom layer is also separated from the lower substrate with an air gap. It should be noted that many factors affect the operational characteristics of the proposed metamolecule, e.g., the relative permittivity of the dielectric substrate, the air gap between adjacent substrates, the matching between the microstrip line and the slot, and the ratio between inner and outer radii of the ring patch. It is thus challenging to realize a completely independent control on the reflection phase responses for the desired four channels corresponding to the four combinations of two polarizations and two frequencies. To greatly simplify the design process, we carefully determine the interval between two frequency bands. On one hand, they have to be well separated to guarantee sufficient spacing between two circular patches sharing a given unit cell dimension. A good inter-band isolation level will then be inherently promised which in turn allows us to independently optimize the configuration of one ring patch and relevant structures without influencing the other. On the other hand, their interval cannot be too large in case the smaller ring patch of the higher band resonates at the higher-order harmonics of the larger ring patch of the lower band, which will deteriorate the inter-band isolation. As a result, a wise choice for the two central operating frequencies is 20.4 GHz and 30.2 GHz, which facilitates the overall optimization and the completely independent reflection phase control of the four channels. Nevertheless, there is no sufficient interspace left for two orthogonal linear polarizations. Fortunately, inspired by the widely applied crossed dipole, crossed slots as the complementary elements to the dipole pair are employed to make a difference. As shown in Fig. 1(b), the magnetic field distribution implies the high decorrelation between the induced orthogonal polarization pair, since it is witnessed that the vertical slot is well excited while the horizontal slot stays terminated, and vice versa. Let us zoom in the slots in the blue circle of Fig. 1(b). It is illustrated that the null locus can be specified along the middle line. The coupled currents from the vertical slot to the horizontal slot are also depicted. It is shown that the coupled currents along the upper and the lower radiating edges of the horizontal slot are of the same amplitude and phase [33], and thus cancel out so that the slots remain decoupled. To demonstrate that the properties of our proposed metamolecule, the reflection amplitude and the reflection phase profiles for the four channels by varying the length of the corresponding microstrip delay line are illustrated in Figs. 1(c) and (d), respectively. It can be observed that the metamolecule provides a complete 2π coverage and high reflection amplitude for all channels. Moreover, the reflection phase is almost linearly proportional to the length the microstrip delay line, which makes the construction of the metamolecule library quite convenient.

Fig. 1. (a) Decomposed topological layouts of the proposed reflective metamolecule where the dielectric substrate and copper are distinguished with different color block. The purple arrows marked with E_i/H_i denote the electric or magnetic fields of the incident wave, while the E_r/H_r denote those of the reflected wave. The two circular rings in the polar coordinates operate in two separated bands—19.6 GHz-21.2 GHz and 29.4 GHz-31 GHz, respectively, as well as the two crossed slots and two pairs of delay lines (b) Magnetic field distributions of the slot layers when only one of the slots is excited, and the magnetic field distribution of the vertical slot in 30 GHz band is shown in the insert. The blue dotted line stands for the null locus and the blue arrows represent the coupled currents. (c) The simulated reflection amplitude profiles versus the variation of the microstrip line length at 20.4 GHz and 30.2 GHz for the horizontal and the vertical polarizations, respectively. (d) The simulated reflection phase responses versus the variation of the microstrip line length at 20.4 GHz and 30.2 GHz for the horizontal and the vertical polarizations, respectively.

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To further demonstrate the excellent inter-band and polarization isolations of our metamolecule, we implement four virtual waveguide ports at the end terminal of every microstrip delay line etched on the bottom substrate as shown in Fig. 2(a). These waveguide ports function as the perfect absorbing boundary condition to collect with no reflection the electromagnetic energy coupled into the corresponding delay lines. We can thus better distinguish the electromagnetic energy flow for our geometrically complicated metamolecule, compared with only analyzing the general reflection coefficient. Figure 2(b) clearly indicates the definitions of the transmission coefficients between the energy input port (denoted as PW_X-Pol or PW_Y-Pol) and the implemented waveguide ports (labelled as from 1 to 4), where all solid lines represent the co-polarization transmission coefficients, while all dotted lines denote the cross-polarization ones. Figure 2(b) also serves as the legend for Fig. 2(c). It can then be observed in Fig. 2(c) that the 3 dB bandwidths of our metamolecule range from 19.6 GHz to 21.2 GHz and from 29.4 GHz to 31 GHz, highlighted with the purple and the yellow blocks, respectively. The maximal inter-band coupling and cross polarizations levels are –16 dB and –41 dB marked in the black dotted rectangles, sufficiently good to guarantee the following synthetization of our simultaneously wavelength and polarization multiplexing metasurface.

Fig. 2. (a) Schematic demonstration of the x-polarized (X-Pol) and y-polarized (Y-Pol) incident wave propagating in the metamolecule, where four purple dashes denote the waveguide ports further implemented in CST and labeled as from 1 to 4. (b) The matchups among energy input port (PW_X-Pol and PW_Y-Pol) and four waveguide ports (from Port 1 to Port 4), where the solid lines indicate the desired co-polarization transmission coefficients while the dotted lines denote the undesired cross-polarization ones. (c) The simulated frequency dependent transmission coefficients which characterize to which extent the incident X-Pol or Y-Pol plane wave can be effectively coupled into different microstrip delay lines. The purple and the yellow blocks point out two 3 dB operational frequency bands. Two frequencies in red are the calculated results with the cavity modal theory. PW is short for plane wave.

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Moreover, we apply the cavity modal theory to predict the central operational frequencies of our metamolecule. When an incident plane wave illuminates the proposed metamolecules, currents are induced on the circular rings. By solving the wave equation in cylindrical coordinates, the radial component of the surface current is given as [34]

(1)$${J_\rho } = \frac{{ - jk{E_0}}}{{\omega \mu }}[{{J_n}^\prime ({k\rho } ){Y_n}^\prime ({ka} )- {J_n}^\prime ({ka} ){Y_n}^\prime ({k\rho } )} ]\cos n\varphi$$

where J_n (-) and Y_n (-) are the nth-order Bessel functions of the first and the second kinds, respectively. It is noted that the radial component of the surface current must vanish along the edges of circular ring at inner radius ρ=a and outer radius ρ=b to satisfy the magnetic wall boundary conditions, which reads,

(2)$${J_\rho }({\rho = a} )= {H_\varphi }({\rho = b} )= 0$$

Therefore, with the aid of the boundary conditions, resonant modes can be derived from the well-known characteristic equation,

(3)$${J_n}^{\prime }({kd} ){Y_n}^{\prime }(k )- {J_n}^{\prime }(k ){Y_n}^{\prime }({kd} )= 0$$

For the given values of inner radius a and outer radius b, d denotes the ratio of b to a, and the order n can be varied, thus the roots of Eq. (3), denoted by K_nma for the resonant mode TM_nm, are determined. To the zeroth-order approximation, the resonant frequency is obtained by

(4)$${f_{nm}} = {k_{nn}}ac/\left( {2\pi a\sqrt {{\varepsilon_r}} } \right)$$

where c is the velocity of light in free space and ε_r denotes the relative permittivity of the dielectric substrate. Equations (3) and (4) work for the majority of resonant patch antennas with reasonable accuracy. However, taking our unusual two-layer coupled structure into consideration, no analytical models are available with satisfactory accuracy. Hence, we here modify the theory to extend its precision in our case to facilitate the further design.

Therefore, a combination of the inverted microstrip line model as depicted in Fig. 3(a) and the parallel plate model as illustrated in Fig. 3(b) are employed. With the parallel plate model which takes the effect of fringing fields into account, the microstrip ring is replaced by an equivalent parallel plate ring resonator with the modified radius of a_e and b_e, the ratio of the modified inner and outer radius reads [34]

(5)$${d_e} = ({b + 3h/4} )/({a - 3h/4} )$$

where h is the height of the substrate. Since the substrate here composes of two layers, effective dielectric constant based on the inverted microstrip line model takes the form as follows, which reads [31]

(6)$$\sqrt {{\varepsilon _{re}}} = 1 + \frac{h}{H}\left( {\bar{a} - \bar{b}\ln \frac{W}{H}} \right)\left( {\sqrt {{\varepsilon_r}} - 1} \right)$$

(7)$$\bar{a} = {\{{0.5173 - 0.1515\ln [{h/({H - h} )} ]} \}^2}$$

(8)$$\bar{b} = {\{{0.3092 - 0.1047\ln [{h/({H - h} )} ]} \}^2}$$

where H denotes the height of the air layer. By replacing d in Eq. (3) and ε_r in Eq. (4) with d_e and ε_re, respectively, Eq. (3) and Eq. (4) are solved and the resonant frequency for our metamolecule is thus determined. As marked in Fig. 2(c) in red, the calculated resonant frequencies are 21.74 GHz and 30.76 GHz for two bands, which are well consistent with the simulated harmonic peaks. Finally, Fig. 3(c) illustrates the surface current distribution on the larger and the smaller ring patches at 20.4 GHz and 30.2 GHz, respectively. It is shown that only the dominant mode TM₁₁ exists in both bands. For any given frequency, it is known that compared to higher-order modes, the dominant one (i.e., the TM₁₁ mode) has the minimum requirement on the mean radius of the ring. Such a phenomenon indicates that at both bands only the dominant mode is excited due to the wise selection of the frequency-band interval as well as the overall optimization of the metamolecule. It further guarantees the inter-band isolation since coupling due to high-order harmonics and multipole responses are eliminated by the single mode excitation.

Fig. 3. (a) The inverted microstrip line model, where h=0.254 mm, H=1 mm, ring width w=0.6 mm for lower band, w=0.4 mm for higher band, and ε_r=6.15.(b) The parallel plate model, where a=1.22, b=1.82 mm for lower band, a=0.72 mm, b=1.12 mm for higher band. (c) The simulated surface current distribution on the circular rings at 20.4 GHz and 30.2 GHz. (d) Sum-square error (SSE), varying with the iteration steps.

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3. Modified GSW algorithm

Well studied since Francesca Ianni, weighted Gerchberg-Saxton (GSW) algorithm has been widely adopted for computer-generated holograms. For phase-only holograms, it is the extraordinary efficiencies and robustness make the GSW prevailed [35,36]. Considering a hologram composing of N elements while M ones for the target plane, we can derive the pixel phase on the hologram when substituting the surface integral in the calculation of Fraunhofer diffraction with the summation:

(9)$${\phi _n} = \arg \left[ {\sum\limits_{m = 1}^M {\frac{{{e^{jk{r_{mn}}}}}}{{{r_{mn}}}}} \frac{{{w_m}{E_m}}}{{|{{E_m}} |}}} \right]$$

where r_nm, w_m and E_m denote the distance between the Nth points on the metasurface to the Mth points on the target plane, weight factor, and electric field components on target plane, respectively. Obviously, the above formula expresses ϕ_n in an implicit form, containing also the unknown weights w_m. Thus, starting from a random guess for ϕ_n and setting w_m as 1, the iteration proceeds as follows:

(10)$$\begin{array}{ll} 0th\;\textrm{step}\; & w_m^0{\kern 1pt} = 1,{\kern 1pt} {\kern 1pt} {\kern 1pt} \phi _n^0 = {\kern 1pt} Random(\phi )\end{array}$$

(11)$$\begin{array}{ll} kth\;\textrm{step }\; & w_m^k{\kern 1pt} = w_m^{k - 1}\frac{{\left\langle {|{E_m^{k - 1}} |} \right\rangle }}{{|{E_m^{k - 1}} |}}{\kern 1pt} ,{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \phi _n^k = \arg \left[ {\sum\limits_{m = 1}^M {\frac{{{e^{jk{r_{mn}}}}}}{{{r_{mn}}}}} \frac{{w_m^k{\kern 1pt} E_m^{k - 1}}}{{|{E_m^{k - 1}} |}}} \right]{\kern 1pt}\end{array}$$

where $\left\langle {|{E_m^{k - 1}} |} \right\rangle$ denotes the system average, which reads,

(12)$$\left\langle {|{E_m^{k - 1}} |} \right\rangle \textrm{ = }{\textrm{s}_m}{{\sum\limits_{m = 1}^M {|{E_m^{k - 1}} |} } / {\sum\limits_{m = 1}^M {{\textrm{s}_m}} }}$$

where s_m is the preset intensity ratio of the mth focal point. Particularly, s_m equals to 1 for imaging with uniform intensity distribution. In other words, at each step we adjust the weight w_m in such a way to reduce $E_m^{k - 1}$ deviations from the average $\left\langle {|{E_m^{k - 1}} |} \right\rangle$. The disparity can be quantitatively expressed in the sum-square error (SSE) equation as follows,

(13)$$SSE = {{\sum {{{\left( {|{{E_m}} |- \left\langle {{E_m}} \right\rangle } \right)}^2}} } / {\sum {{{|{{E_m}} |}^2}} }}$$

By depicting the SSE versus iteration steps, the convergence speed is revealed. However, some hidden difficulties reduce the robustness of the aforementioned weighting criteria, and make them inflexible to apply, resulting in divergence or local convergence. For instance, the initial pixel phase matrix especially for a problem involving a large metasurface composed of hundreds of metaatoms. In addition, since the iteration process is determined after designating starting value in conventional GSW, and there are no other adjustable parameters, the design of freedom is very limited. Therefore, we here introduce a relaxation factor P to the weighting factor to improve the robustness and convergence speed of the GSW, which reads,

(14)$$w_m^k{\kern 1pt} = w_m^{k - 1}{\kern 1pt} {\left[ {{{\left\langle {|{E_m^{k - 1}} |} \right\rangle } / {|{E_m^{k - 1}} |}}} \right]^P}$$

Equation (14) is reduced to the GS algorithm as we set P=0 since the weight factor vanishes, and to the GSW when setting P=1. Figure 3(d) clearly demonstrates the effect of the introduced relaxation factor P. Starting with the same initial value, P=0.5 leads to a gentle and stable convergence, P=1.2 shows us an extremely oscillating iteration process, and P=1 provides a good convergence after 17 steps yet regresses to intensive swing after 23 steps.

4. Design of the holographic metasurfaces

Based on our proposed metamolecule which effectively restrains the channel crosstalk to better tailor the subwavelength features, it is now possible to generate the highly decorrelated multiplexing holographic metasurfaces by modulating the phase response of the reflected wave with the modified GSW. The proposed metasurface is sketched in Fig. 4(a) where different materials are distinguished by colors.

Fig. 4. (a) Schematic demonstration of the proposed metasurface which can independently manipulate four-channel reflected waves for projecting holographic images. As a case study, two combination of reconstructed pictures are investigated to construct “H” (x-pol @30 GHz), “I” (y-pol @30 GHz), “T” (x-pol @20 GHz), “smile” (y-pol @20 GHz), and a “smile face puzzle”. (b) The Fraunhofer diffraction based theoretical calculation results of the normalized intensity profiles and the simulated results. (c) Simulated asymmetric “smile” whose intensity ratio is set to 1:0.7 in calculation. (d) The simulated intensity ratio in four sampling positions as depicted in (c).

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Obviously, the actual equiphasic surface of the incident quasi-plane wave can be better mapped with a spherically shaped surface. Hence, a roughly circular aperture, rather than the square ones, can help minimize the phase disparity between the fringe and the central elements. Totally, 1232 metamolecules are arrayed within the overlapping region of a circle with 150 mm as the radius and a square with the side length of 285 mm. There are at most 38 unit cells in one row and the periodicity of the elements equals 7.5 mm (0.5λ at 20Ghz and 0.75λ at 30 GHz). The side length of the dielectric substrate (TACONIC RF-60A with relative permittivity ε_r = 6.15, thickness t=0.254 mm, and its dissipation factor DF=0.0028) is set as 300 mm, and thus 7.5mm-width space on each side retains unoccupied to provide protection and a circumambient environment approximate to the infinite period array. In addition, rigid polymethcryimide (PMI) structural foam whose EM parameter is close to air (more specifically, ε_r = 1.11 and DF=0.0039 at 30 GHz) serves as the air gap to separate and prop up different layers.

By using the modified GSW algorithm, the required phase distributions can be retrieved and then converted into the length of the delay lines in each metamolecule, facilitating the design of two sets of holographic images (as shown in Fig. 4(a)) to validate the performance of the proposed multiplexing metasurface.

Firstly, the combination of reconstructed images made up of “H”, “I”, “T” and a smile figure, where each channel possesses specified focal length, pattern, and intensity distribution, exhibits four totally independent functionalities that can be switched by altering the polarization or the wavelength of the incident illumination without conjugate images. To be more specific, the proposed metasurface can on one hand divert the incident energy, which is under the given polarization and frequency state, to holographic images with the preset focal length of f_H = 100 mm, f_I=120 mm, f_T=140 mm, and f_Smile=160 mm, respectively. On the other hand, it can adjust the intensity distribution of the projected picture by modulating the value of S_m in Eq. (12), as illustrated by the smiling face with asymmetric energy distributions in Fig. 4(a). In our demonstrations, X-pol, Y-pol at 30 Ghz and X-pol, Y-pol at 20 Ghz are utilized to project the H, I, T, and smile images, separately, and the intensity ratio is set to 1:0.7 for left and right parts of the smiling face. As depicted in Fig. 4(b), the Fraunhofer diffraction based theoretical calculation results (first row of Fig. 4(b)) and the simulated ones (second row of Fig. 4(b)) which are implemented in commercial full-wave software CST Microwave Studio, are in good accordance with each other. To characterize the simulated ratio of intensity distribution, the normalized intensity profiles in horizontal cuts at different positions as indicated in Fig. 4(c) are provided in Fig. 4(d), where a set of acceptable simulated intensity ratios are observed to be 1:0.68, 1:0.65, 1:0.61, and 1:0.62 for different cut lines, respectively.

To further explore the independence and mutual interference among four channels, the second set of holographic images with the uniform intensity distribution and same focal length is carried out to make up a smile face puzzle, where each channel retains impassive to any illumination signals excluding the incident wave with the only triggering combination of polarization and wavelength, resulting in a clear puzzle without conjugate images as displayed in the right side of Fig. 5(a).

Fig. 5. (a) Schematic diagram of the projected “smile face puzzle”. (b) The panorama of the experiment setup. The insets show the corrugated horn and the rigid coaxial cable probe. (c) Calculated, simulated and measured “smile face puzzle” (second row, f=145 mm at center frequency), measured results when shifting the detection plane from 140 mm to150 mm (first row, at center frequency), and the measured results when tuning the frequency (third row, f=145 mm). (d) The four intact holographic images (f=145 mm at center frequency), of which the “smile face puzzle” at center frequency and theoretical position is composed and the corresponding imaging efficiency.

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Here, for the sake of demonstration, a metasurface for projecting the “smile face puzzle"(as plotted in Fig. 5(a)) is fabricated and measured in an anechoic chamber with the corresponding near-field experiment setup depicted as the panorama in Fig. 5(b). With the help of a specially customized cross-pol restrained dual-frequency corrugated horn, which launches the required dual polarizations incident wave at two operating bands, as demonstrated in the left zoom-in inset in Fig. 5(b), and a rigid coaxial cable with inner core exposed on one end serving as a near-field probe, as illustrated in the right inset, the holographic puzzle is thus detected on the target plane. On the premise of guaranteeing the sufficient received power with a power amplifier, the distance between the feed horn and the metasurface under test is maximized to 4 m, so as to make the equiphasic plane of the incident quasi-plane wave as flat as possible.

In the middle row of Fig. 5(c) from left to right the calculated, simulated, and measured reconstructed images, which are captured at the center frequency on the designated target plane (f=145 mm) are depicted orderly. Good agreements among one another can be observed. A pair of orthogonal polarizations at λ=15 mm contribute to the left and right eyes of the smile, while another pair of polarizations at λ=10 mm reconstruct two half mouths. Attributed to the high isolation feature of the proposed metamolecule and the continuous phase manipulation across the surface at each wavelength, all the four parts of the puzzle delineate the image profile distinctly without squints.

Two projected images with tuned measuring frequency, as displayed in the third row of Fig. 5(c) manifest that the working frequency band of proposed metasurface can span from 19.6 to 21.2 GHz and 29.6 to 31.2 GHz for two separated bands, respectively, ensuring a reasonable manipulation range of frequency. Moreover, when shifting the detection plane from 140 mm to 150 mm, the holographic pictures given in the first row of Fig. 5(b) can still show clear contour, which indicates that the proposed metasurface possesses strong robustness and relative tolerance against the measuring distance. The four intact reconstructed images, of which the smile puzzle at the center frequency and the theoretical position is composed, are shown in Fig. 5(d) to reveal the detail of low-level background noise, which results in a superior measured imaging efficiency of 73.2%, 68.8%, 63.4%, and 58% for left eye, right eye, left mouth, and right mouth, respectively.

5. Conclusion

To summarize, a dual-wavelength and dual-polarization multiplexing metasurface platform is proposed, and theoretical and numerical investigations are carried out at both the metamolecule and hologram algorithm levels. Accordingly, with the presented metasurface, two paradigms to design highly decorrelated multiplexing hologram are performed to demonstrate the capability of independent manipulation and the cross-talk repression of four different channels provided by our metasurface platform.

The proof-of-concept experimental prototype which projects the smile face puzzle validates our design since the calculated, full-wave simulated, and measured results at microwave regime are well congruous with one another. The constructed holographic image involving four independently controlled parts without conjugate twin images demonstrate the decorrelated and independent multiplexing property of our proposed metasurface platform. Furthermore, our metadevices show satisfactory measured imaging efficiency for all the channels, which promisingly provides an enhanced alternative platform for the storage, transmission, and expression of the information encoded in the optical or microwave carrier wave.

Funding

National Natural Science Foundation of China (61671178, 61301013).

Disclosures

The authors declare no conflicts of interest.

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Highly decorrelated multiplexing metasurface for simultaneous dual-wavelength and dual-polarization continuous phase manipulation

Abstract

1. Introduction

2. Mechanism of the proposed metamolecules

3. Modified GSW algorithm

4. Design of the holographic metasurfaces

5. Conclusion

Funding

Disclosures

References

Cited By

Figures (5)

Equations (14)

Optics Express