Abstract
We propose a new family of impedancematched chiral metasurfaces that offer arbitrary polarization control at two different frequencies. To this end, two main problems are addressed: (1) determination of the required surface impedances for a certain userdefined chiral functionality at two frequencies and (2) their physical realization at microwaves. The first milestone is achieved through a proposed synthesis method that combines a semianalytical method and a nonlinear optimization technique. In particular, the impedances are computed such that the devised chiral metasurface is also impedancematched to a terminating medium. The chiral metasurfaces are then physically realized at microwaves by cascading layers of rotated arrays of multiple concentric rectangular copper rings. We establish that these proposed unit cells offer distinct dualresonances that can be arbitrarily and independently tuned for two orthogonal linear polarizations at each of the two operating frequencies. This allows simultaneous physical mapping of the required surface impedances at two frequencies. The versatility and generality of the proposed numerical and physical solutions are demonstrated through two design examples: A dualband circular polarization selective surface (CPSS) and a dualband polarization rotator (PR). The dualband CPSS is further confirmed experimentally at 20 GHz and 30 GHz based on a freespace quasioptical system.
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Introduction
The idea of using artificial surfaces, or metasurfaces to control various aspects of scattered electromagnetic (EM) waves has gained much interest due to their exotic beam manipulation capabilities within a low profile. These surfaces consist of arrays of subwavelengthsized scatterers, or unit cells that locally interact with electric, magnetic, or both components of an incident field to manipulate the state of the scattered EM waves^{1,2,3,4,5,6,7,8}. Various metasurfaces have been demonstrated in which the main goal has been to manipulate the wavefront of scattered EM waves such that an incident beam is custom reflected/refracted^{2,3,4,6,8}, focused^{5}, or reshaped^{7}. The unit cells in these surfaces are adjusted to encode certain phase/amplitude profiles across the surface to engineer the scattered wavefront. While these phase/amplitude metasurfaces have been extensively investigated, another important aspect to consider is the ability to arbitrarily control the polarization state of the scattered waves. This is of particular importance in many applications both in the microwave and optical regimes. In this regard, microwave and optical birefringent metasurfaces have been proposed^{7,9,10,11}. These birefringent metasurfaces are similar to the phase/amplitude metasurfaces except that they utilize anisotropic unit cells which scatter an incident field with two different reflection/transmission phases for two orthogonal linear polarizations. Despite their successful demonstration as quarter or half waveplates, they do not offer complete polarization control of EM waves. This is because they fail to control the flow (e.g., phase velocity) of different circular polarizations (CPs). Such a functionality, however, can be realized with chirality, which allows controlling the flow of both lefthanded circular polarization (LHCP) and righthanded circular polarization (RHCP). Therefore, it is possible to realize a circular polarization selective surface (CPSS) with such chiral metasurfaces, which transmit one handedness of CP, while reflecting the opposite handedness. Such a CPSS is of particular interest in satellite communications as it would allow reducing the number of main reflectors required for generating multiple beam patterns^{12}. Another useful chiral metasurface application includes a polarization rotator (PR), which allows rotating an incoming linearly polarized wave by any angle of choice regardless of the incident polarization plane.
Motivated from such applications that require chirality, chiral metasurfaces or metasurfaces that mimic chirality have been previously demonstrated both in the microwave and optical regimes. It should be noted that we use the term ‘chiral metasurfaces’ for those devices that control the flow of a RHCP and a LHCP field in the sense that the eigenmodes of a chiral medium are circularly polarized. For example, a linear polarizer sandwiched between two circular polarizers has been demonstrated to function as a CPSS^{13} in the microwave regime. Nonetheless, these require many layers and only operate in a single frequency band. On the other hand, a CPSS^{14} and a PR^{15} have been demonstrated in the optical regime by cascading identical unit cells that are progressively rotated along the propagating direction of an incident field. The operation of these socalled ‘twistedmetamaterials’ is akin to mimicking a helical structure which is a known geometry for chiral molecules found in nature^{16}. However, because they rely on a rotated lattice effect such that the chirality becomes realizable in a simple way, the corresponding structures are not necessarily optimal, in the sense that they are not always impedancematched, which results to degraded efficiency from undesired reflections^{14,15}. Likewise, microwave chiral metasurfaces comprising arrays of Pierrot unit cells^{12} and multiple layers of progressively rotated meander lines^{17} have been proposed. While the meander lines are progressively rotated, their dimensions from layer to layer are not identical and they are optimized to satisfy the impedancematching condition. However, they are singlebanded while many antenna applications require metasurfaces that can operate at two different frequency bands^{18,19}. For example, certain communication satellites have two operating frequency bands for uplink and downlink that are centered around 20 GHz and 30 GHz. In these applications, CP is preferred, because alignment between transmitting and receiving antennas is then not needed. Therefore, it naturally draws interest in developing a dualband chiral metasurface configured as a dualband CPSS. Very recently, multiple layers of progressively rotated meander lines have been further investigated numerically for such a purpose^{19}. Nevertheless, their dualband chiral functionality is fixed to CP selectivity. In other words, it is not feasible to realize a dualband chiral functionality other than dualband CP selectivity (e.g., a dualband PR). It should further be mentioned that their CP selectivity is also not general in the sense that the handedness of the reflected CP waves is fixed. Specifically, if a LHCP field is reflected at one of the operating frequencies, then a RHCP field is reflected at the other frequency and vice versa. Therefore, such a method does not allow a dualband CPSS that only reflects a LHCP field at its two operating frequencies. Furthermore, they require many layers and their two operating frequencies also depend on the number of layers used. On the other hand, Selvanayagam et al., Kim et al., and Pfeiffer et al. have recently demonstrated general impedancematched chiral metasurfaces based on multiple layers of tensor impedance surfaces in the microwave and optical regimes^{20,21,22,23}. While their chiral functionality and operating frequency can be userdefined, they are singlebanded which limits their applications.
In departure from the aforementioned works, this paper proposes general dualband chiral metasurfaces that are also impedancematched. Preliminary numerical results for an impedancematched dualband CPSS have been reported in^{24}. Here, we further demonstrate the versatility and generality of our approach by presenting the detailed design of two examples: A dualband CPSS and a dualband PR that are impedancematched and operate at 20 GHz and 30 GHz. Experimental results for the impedancematched dualband CPSS are also presented here. These devices are based on only four cascaded layers of tensor impedance surfaces. Each of these layers consists of arrays of multiple concentric rectangular metallic (copper) rings and each layer is rotated with respect to one another. However, they are not progressively rotated and only a few layers are used, unlike the aforementioned previous works^{13,14,15,19}. Instead, we shall show that the hereby proposed unit cell geometries and their interlayer rotation angles are precisely determined such that they encode specific surface impedance values for a certain userdefined dualband chiral functionality with maximum efficiency. By maximum efficiency, we specifically mean that the devised dualband chiral metasurface is also impedance matched such that unwanted reflections are minimized.
Results
Synthesis of impedancematched dualband chiral metasurfaces: Dualband CPSS and dualband PR
To demonstrate a general dualband chiral metasurface that is also impedancematched, we first begin by discussing its synthesis method based on a design example of a dualband CPSS operating at f_{1} = 20 GHz and f_{2} = 30 GHz. As we shall show, the synthesis method can be applied to other dualband chiral functionalities and combines both semianalytical and nonlinear optimization methods. For an impedancematched dualband CPSS, we utilize four tensor impedance surfaces that are separated by 3 mm as shown in Fig. 1a. Different number of layers can be considered. However, one cannot employ less than three layers for realizing a CPSS as theoretically explained in^{20}. In other words, even for a single band of operation, at least three cascaded layers are required^{20}. Here, an additional layer is inserted to increase the degrees of freedom. The goal now is to determine the required impedances in each layer at f_{1} and f_{2} such that the cascaded layers operate as an impedancematched CPSS at the two frequencies. There are two main steps for achieving this goal: (1) determination of the surface impedances at f_{1} and the rotation angle of each layer that make the cascaded layers an impedancematched CPSS at f_{1} and (2) determination of the surface impedances at f_{2} that make the cascaded layers an impedancematched CPSS at f_{2} with the same rotation angles found in the previous step.
Following these two main steps, we first analyze the fourlayered system at f_{1}. To this end, we refer to the analysis outlined in^{20} from where the key steps are summarized here. Specifically, an equivalent circuit model based on the multiconductor transmission line (MTL) theory is used to describe the system as shown in Fig. 1b. Here, each tensor impedance layer is modeled as a shunt network, while the air gaps between the layers are modeled as fourwired transmissionlines having the intrinsic characteristic impedance. The circuit physically consists of one input and one output port, yet two orthogonal linear polarizations (linearlypolarized fields along the x and ydirections) at each port are treated separately. Hence, the whole circuit is regarded as a fourport system. As such, the input and output relationship is expressed in terms of the scattering matrices (Smatrices) in a linear polarization basis as,
where the superscripts “in” and “out” respectively denote whether a field is an input or an output. The subscripts x and y respectively represent the polarization direction of the fields. The subscript number (1 and 2) denotes the port number. The 4 × 4 Smatrix, S, describes the equivalent MTL circuit and it is in the form given by,
where
The scattering parameters are defined as S (outputport m, output mode i, input port n, input mode j) where m, n, i, and j are either 1 or 2. We note that mode 1 and mode 2 refer to the fields that are polarized along the x and ydirections respectively. For example, S (2111) indicates S(outputport 2, outputmode 1, inputport 1, inputmode1) and defines the field ratio between mode 1 at port 2 to mode 1 at port 1, assuming that it is the only input. On the other hand, more compact 2 × 2 impedance and admittance matrices (Z and Y) can be defined to describe each tensor impedance layer, which is in a form given by,
where \({{\rm{Z}}}_{ij}^{{\rm{sh}}}\) represents the shunt impedance of the n^{th} layer in which i and j are again either 1 or 2 for representing mode 1 or 2. R is a rotational matrix and θ_{ n } is the angle for which the n^{th} layer is rotated by. In other words, R is a square matrix whose columns are the linearly independent eigenvectors of one of Z and Y. Moreover, the form given in (4) can also be used to define the input impedance and admittance anywhere along the equivalent circuit shown in Fig. 1b for which it is related to Γ_{A} as
where Z_{ref} is a diagonal matrix having the intrinsic characteristic impedance of Z_{o} as its nonzero component and \({{\bf{Y}}}_{{\rm{ref}}}={{\bf{Z}}}_{{\rm{ref}}}^{1}\).
In this first part of the analysis at f_{1}, it is first assumed that the surface impedances for the first and last layers are known. The rest of the unknown impedance values for the middle two layers are solved for such that the net Smatrix of the cascaded layers matches to that of an ideal CPSS (S_{CPSS}) which is given by,
where ϕ is an arbitrary phase constant. From (6), it is seen that the transmission of a LHCP field is identically 1 (i.e., impedancematched and lossless), while that of a RHCP field is identically 0 (i.e., perfect reflection). Furthermore, the axial ratio for the transmitted LHCP field and the reflected RHCP field ideally remain unity, which implies that a LHCP field is transmitted into a pure LHCP field, while a RHCP field is reflected as a pure RHCP field.
To determine the unknown impedances of the middle two layers, we first note that (6) represents the desired Smatrix of the overall system. Therefore, the desired copolarized and crosspolarized input reflection coefficients at point “a” (refer to Fig. 1b) is the first quadrant of (6) (i.e., Γ_{A} of S_{CPSS}). The input admittance at point a, Y_{a}, can then be solved via (5). Furthermore, because the admittance of the first layer, Y_{1}, is assumed to be known, the input admittance at point b, Y_{b}, is given as,
Similarly, the input admittance at point g, Y_{g}, can be found because the admittance of the last layer, Y_{4}, and the input admittance at point h are known (Y_{h} = Y_{ref}). On the other hand, Y_{b} and Y_{g} are respectively related to the input admittance at points c (Y_{c}) and f (Y_{f}) via the phase shift of the air gaps^{20}. For example,
Once Y_{c} and Y_{f} are obtained, the input admittance at point e, Y_{e}, is solved via the algebraic Ricatti equation given as^{20},
where t is the separation length between the tensor impedance layers, which is fixed to 3 mm, and β is the freespace wavenumber. Re() and Im() respectively imply the real and imaginary parts of the admittance matrices and I is an identity matrix. The Ricatti equation in (9) assumes that each layer is lossless. However, such an assumption is valid in the microwave regime because the complexvalued surface impedances are dominated by their imaginary components. The Ricatti equation has a wellknown analytical method to solve with^{25} and allows identifying the unknown impedances of the middle two layers. Specifically, Y_{3} can be obtained by subtracting Y_{f} from Y_{e} and Y_{2} can be solved by subtracting Y_{c} by Y_{d} which is related to Y_{e} via an equation similar to (8). However, we note that these impedances are not necessarily guaranteed to be the correct solution, because the impedances of the first and last layers are arbitrarily assumed. To ensure that they are indeed the correct solution, they must be cascaded and compared with the desired final Smatrix (i.e., S_{CPSS}). To cascade all tensor impedance layers, the Zmatrix of the n^{th} layer is first expanded to a 4 × 4 Zmatrix, \({{\bf{Z}}}_{{\rm{n}}}^{{\rm{sh}}}\), in a form given by,
which is related to its corresponding Smatrix through the conversion given by,
where G_{ref} is a diagonal matrix having \(1\sqrt{{{\rm{Z}}}_{{\rm{o}}}}\) as as the diagonal entries. On the other hand, the air gaps are represented as transmissionline Smatrices, S_{TL}, given by^{26},
With the Smatrices in (11) and (12) that describe each module, the net Smatrix of the cascaded system (S_{net}) can be analytically computed through the generalized scattering matrix method^{26}. The S_{net} can then be repeatedly compared with S_{CPSS} based on different values of surface impedances in each layer. However, the number of combinations in such a case is impractical. To avoid this, we invoke the symmetry condition of the structure. Specifically, the eigenvalues of the first and last layers, and the second and third layers are set to be the same (i.e., the unrotated Zmatrices of the first and last layers and the second and third layers are the same). This allows the required rotation angles in the third and last layers to be immediately determined from the symmetry, because the rotation angle of the third layer (or the last layer) must be the negative angle of the second layer (or the first layer) in order to comply with the symmetry condition. Therefore, the necessary surface impedances for the third and last layers are completely deduced from the first and second layers. As such, S_{net} can be repeatedly compared with S_{CPSS} only by varying the eigenvalues of the first and second layers, and their rotation angles. In this regard, although the first part of the analysis at f_{1} is semianalytical, the proposed method significantly reduces the solution space by (a) only considering the solutions with the desired input reflection coefficient (i.e., Γ_{A} of S_{CPSS})^{20} and (b) utilizing the symmetry condition of the structure. Table 1 summarizes a solution based on the proposed method from which it is seen that the first and last layers are identical to each other except that the first layer is rotated by 20°, while the last layer is rotated by −20°. Similarly, the second and third layers are the same except that the second layer is rotated by 30°, while the third layer is rotated by −30°. These rotation angles are obtained by substituting the impedance parameters in Table 1 to (4). It should also be noted that displacements of the layers in the xy plane do not affect S_{net}. This is because each layer is modularized and it is characterized by its own scattering matrix which assumes that the layer infinitely extends in the xy plane. As such, S_{net} is insensitive to the displacements of layers in the xy plane.
Once \({{\bf{Z}}}_{{\rm{n}}}^{{\rm{sh}}}\) and θ_{ n } are determined at f_{1}, the system is now solved at f_{2}. For this second step, we must use the same rotation angles, θ_{ n }, found in the first step to ensure the same physical structure at f_{2}. To this end, we employ the nonlinear numerical optimization process as outlined in^{21,24}. Specifically, we first construct a cost function by utilizing the MTL theory again to model the overall structure. In particular, the cost function is defined as
where S_{goal} is the desired final Smatrix, which in this case is S_{CPSS}, and Max() returns the maximum value out of 16 parameters. In obtaining S_{net}, the rotation matrices for all layers are fixed to R(θ_{ n }) found in the previous step at f_{1}, while the eigenvalues of Z are varied within ±j800 Ω. We note that a greater range of impedances can be considered. However, this will increase the Ohmic loss and reduce the bandwidth of operation. Similarly to the first part of the analysis, the net Smatrix is then constructed by employing the generalized scattering matrix method^{26}.
To minimize the cost function, MATLAB’s builtin optimizer, fmincon, is employed. The fmincon function is based on the gradient descent method that finds a local minimum, rather than the global minimum, of a scalar function of several variables starting with an initial estimate. Although it finds a local minimum, we have determined that the optimizer typically converges in less than 100 iterations with the given range of shunt impedances of ±j800 Ω. Table 2 summarizes the solution found with the proposed nonlinear optimization method at f_{2} for which the cost function is evaluated to be 0.05. We note that if the solution at f_{1} is substituted to (13), then it results to 0.08, which again is a small value as desired.
As discussed above, the required impedances at f_{1} and f_{2} are respectively obtained via the semianalytical and nonlinear optimization methods. However, it should be noted that it is possible to avoid solving (9) at f_{1} and employ only the nonlinear optimization method to simultaneously minimize (13) at f_{1} and f_{2}. However, the solution space in such a case is large and takes much computational effort. On the contrary, what we have proposed here dramatically minimizes the solution space by (a) only considering the solutions with the desired reflection coefficient (Γ_{A} of S_{CPSS}) at f_{1}, (b) forcing the eigenvalues of the first and last layers and the second and third layers to be the same at f_{1}, and (c) only varying the eigenvalues of the first and second layers with fixed eigenvectors at f_{2} in the nonlinear optimization step. Therefore, both the first and second analyses at f_{1} and f_{2} effectively minimize the solution space and significantly reduce the computational effort.
To further demonstrate the generality and versatility of the proposed synthesis method, we aim to realize a dualband PR which rotates a linearlypolarized wave by 90 ° at f_{1} and f_{2}. For it to rotate any linearlypolarized wave regardless of its incidence polarization plane with the highest possible efficiency, it must satisfy the following three conditions:

Maximize the crosspolarized transmission

Minimize the copolarized reflection (i.e., impedancematching)

Achieve 180° phase difference between the crosspolarized transmitted fields
It is noted that the first two conditions guarantee the corresponding system to behave as a PR only for the incident fields that are polarized along the principal axes, while the last condition ensures polarization rotation regardless of the incident polarization plane^{20}. The three conditions can be compactly represented as the ideal Smatrix for a PR given by,
For the demonstration of dualband PR, we assume six cascaded layers of tensor impedance surfaces. Similar to a CPSS, a PR must consist of at least four layers even for a singleband operation^{20}. Here, the number of layers has been chosen to increase the number of degrees of freedom such that the cost function can be better minimized at f_{2}. However, it is possible to reduce the number of layers at the cost of a degraded performance as long as it is greater than four. To obtain the required surface impedances at f_{1} and f_{2}, we follow the same synthesis method as before, which is summarized below:

1.
Define a chiral operation (e.g., polarization rotation and CP selection) and its ideal Smatrix.

2.
Assume that the only unknowns are the middle two layers at f_{1}.

3.
Based on the desired Smatrix and the known impedance values, obtain the unknowns by solving (9) at f_{1}.

4.
Repeat steps #2 and #3 with different initial assumptions, until the actual net Smatrix matches to that of a desired Smatrix at f_{1}.

5.
Extract eigenvectors for all tensor impedance layers (i.e., their rotation angles) at f_{1}.

6.
Use the same eigenvectors for all tensor impedance layers at f_{2} and utilize the nonlinear optimization method to minimize (13).
Based on the synthesis methodology listed above, the 6 layers are solved to function as a PR at f_{1} and f_{2} and the results are summarized in Table 3. The values of the cost function at f_{1} and f_{2} with the impedance values listed in Table 3 result to 0.145 and 0.04 respectively.
Physical realization at microwaves
With the required surface impedances determined at f_{1} and f_{2} via the proposed synthesis method, a unit cell is designed to physically encode the required impedances. The required eigenvalues of each Zmatrix for the dualband CPSS and dualband PR are either capacitive or inductive. Therefore, to physically encode these impedances, a unit cell must (a) possess two resonances for accessing both capacitive and inductive values near f_{1} and f_{2} and (b) the two resonant frequencies should be arbitrarily and independently tunable for the two orthogonal linearlypolarized waves (mode 1 and mode 2). To realize such a unit cell, we propose multiple concentric rectangular copper rings as shown in Fig. 2. It has been previously reported that an array of double concentric rectangular rings possesses dualresonances^{27}. However, with only two concentric rings, we find that the unit cell periodicity needs to be large to resonate which results in higherorder Floquet modes. This is not desirable, since our analysis assumes only the fundamental mode propagating. Here, however, we show that having more rectangular rings allows dualresonances with electrically small unit cell sizes. Specifically, the proposed unit cell periodicity is 4 mm (2.5 times smaller than the smallest operating wavelength) and Fig. 3a shows the variation in surface reactance for different physical geometries. The dotted curves show the variation in case of concentric square rings in which a field that is polarized along the xdirection (mode 1) and another field that is polarized along the ydirection (mode 2) experience the same physical structure. From Fig. 3a, it can be noted that there exists clear dualresonances for which their resonant frequencies can be tuned. This specific example demonstrates tuning of the two resonant frequencies from 19 GHz and 27 GHz to 18 GHz and 33 GHz. On the other hand, the blue and red curves respectively show the variation for modes 1 and 2 in case of concentric rectangular rings from which it is seen that the resonant frequencies for the two modes can also be independently tuned. Therefore, the proposed unit cell can simultaneously implement any impedance value at 20 GHz and 30 GHz and the required impedances shown in Tables 1 and 2 can be physically mapped. The details of their geometrical values are found in the caption of Fig. 2.
To evaluate its performance as a dualband CPSS, the net Smatrix of the cascaded layers with the proposed unit cells is numerically computed. To this end, it is desirable to simulate the whole structure, however this is not feasible because each layer is rotated with respect to one another and the corresponding global periodicity is too large to simulate. Instead, we have simulated a single layer at a time with ANSYS High Frequency Electromagnetic Field Simulation (HFSS) (see Methods) and analytically cascaded all layers through the generalized scattering matrix method^{26}. Such an approach does not capture the coupling between the layers. Nonetheless, provided that higher order Floquet modes are sufficiently small, the effect of coupling can be minimized. The result is shown in Fig. 3b in which it is seen that the transmitted LHCP and the reflected RHCP are maximized near 20 GHz and 30 GHz. The transmission coefficients of a LHCP wave at 20 GHz and 30 GHz are respectively −1.1 dB and −0.56 dB, whereas the reflection coefficients for a RHCP wave at 20 GHz and 30 GHz are −0.52 dB and −0.22 dB respectively. Furthermore, the axial ratio shown in Fig. 3c is well below 5 dB near 20 GHz and 30 GHz which confirms that what gets transmitted and reflected remains circularly polarized. Hence, the stack of the proposed unit cells indeed functions as an impedancematched dualband CPSS.
A similar approach has been taken to numerically verify the performance of the proposed dualband PR. Figure 4a shows that the crosspolarized transmission of a linearly polarized wave is maximized at 20 GHz and 30 GHz, while the copolarized transmission and reflection coefficients are well below −10 dB at these frequencies as shown in Fig. 4b and c. Specifically, the crosspolarized transmission coefficients of a xpolarized wave (T_{ xy }) at 20 GHz and 30 GHz are −2.11 dB and −1.72 dB respectively. For the crosspolarized transmission coefficients of a ypolarized wave (T_{ yx }), the maximum values at 20 GHz and 30 GHz are −3.56 dB and −1.72 dB respectively. Furthermore, Fig. 4d shows that the phase difference between the two crosspolarized transmitted fields are nearly 180° as desired (190° at 20 GHz and −185° at 30 GHz).
Experimental Verification of the Dualband CPSS
To further verify the proposed dualband chiral metasurfaces and their synthesis method, the previously designed dualband CPSS has been fabricated and measured. The metalization has been deposited on a 0.127 mm thick Rogers 5880 substrate for all layers and each layer has been cascaded onto each other with 3mm thick foam boards to create the necessary air gaps. Figure 5a shows the constructed dualband CPSS. To measure its scattering properties, we have employed the freespace quasioptical system shown in 5b. The system consists of transmitting (Tx) and receiving (Rx) horn antennas with two lenses in between. The dualband CPSS (DUT) is placed between the two lenses as shown in the figure. The output of each horn antenna is modeled as a Gaussian beam to determine the optimal distance between the horn antennas and lenses^{28} which are computed to be 130 mm and 480 mm at 20 GHz and 30 GHz respectively. Each port of the antennas is connected to a 4port vector network analyzer (Agilent Technologies E8361C connected to the Sparameter test set, N4421B). Hence the set up is fully vectorial and a 4 × 4 Smatrix can be measured in a single pass provided that the Tx and Rx antennas are dualpolarized. For the measurement near 20 GHz, we have actually utilized dualpolarized horn antennas. However, singlepolarized horn antennas have been used at 30 GHz due to lack of dualpolarized horns. Nonetheless, by rotating either the Tx or the Rx antenna by 90°, the complete transmission properties can be measured.
Based on the calibrated set up (see Methods), the timegated copolarized and crosspolarized reflection and transmission coefficients are first measured near 20 GHz. The measured Sparameters are then converted in terms of the CP basis and Fig. 6a,b,c summarize the results. Figure 6a shows that the copolarized transmission of LHCP (T_{lhcp}) and reflection of RHCP (R_{rhcp}) are maximized near 20 GHz (T_{lhcp} = −4.8 dB and R_{rhcp} = −3.5 dB at 20 GHz), while the copolarized reflection of LHCP (R_{lhcp}) and transmission of RHCP (T_{rhcp}) are all below −10 dB. Furthermore, the crosspolarized reflection and transmission coefficients are also well below −10 dB near 20 GHz as shown in Fig. 6b. These results indicate that the devised surface is wellmatched to its terminating medium. Figure 6c further confirms that the measured axial ratio of the transmitted LHCP and reflected RHCP are in general agreement between the simulated values, and are 3.55 dB and 2.95 dB respectively at 20 GHz.
The same quasioptical set up has been used to measure the dualband CPSS near 30 GHz, but with singlepolarized horn antennas. Since the horn antennas are singlepolarized, it is not feasible to measure the crosspolarized reflection coefficients. Nonetheless, full transmission properties can still be obtained from two measurements in which the Tx and Rx antennas are aligned in the first measurement whereas the Rx antenna is rotated by 90° in the second measurement. Figure 7a and b respectively show the copolarized and crosspolarized transmission coefficients in the CP basis, while Fig. 7c shows the axial ratio of the transmitted LHCP wave. Again, the copolarized transmission of LHCP is maximized near 30 GHz (T_{lhcp} = −2.2 dB at 30 GHz), while the other transmission coefficients are minimized and are all below −10 dB. However, the measured axial ratio at 30 GHz (4.8 dB) deviates further from the corresponding simulated value (0.21 dB) compared to the deviation at 20 GHz. In what follows, the discrepancy between the measured and simulated values is discussed in detail.
The measurements at 20 GHz and 30 GHz show that the fabricated surface indeed functions as an impedancematched dualband CPSS. However, it is not perfect as there are some discrepancies between the measured and simulated values. In particular, at 20 GHz, the measured transmission of the LHCP wave is −4.8 dB, whereas the corresponding simulated value is −1.1 dB. Furthermore, the simulated minimum of the crosspolarized transmission coefficient at 20 GHz is not observed in the measurements despite the fact that the measured value is still small (−16.8 dB or 0.145 in the linear scale). On the other hand, at 30 GHz, the measured axial ratio of the transmitted LHCP wave is 4.6 dB, while the corresponding simulated value is 0.21 dB. Moreover, the measured crosspolarized transmission coefficient is maximized at 30 GHz in the measurement window (29 GHz–31 GHz) although the corresponding simulated value is minimized at 30 GHz. The Supplemental Information analyzes two main sources of these discrepancies: fabrication imperfections and Ohmic losses. The fabrication imperfections include a physical variation in the actual unit cell geometries and an increase in the separation length between each layer due to the finite thickness of the doublesided tapes used between layers. These variations alter the spectral responses rather significantly and affect the overall performance of the device (see Supplemental Information). Moreover, the metallic Ohmic loss pertaining to the device sensitivity also affects the overall device performance. In particular, it predominantly affects the discrepancies in the copolarized transmission of the LHCP waves. This is also seen from Figs 6 and 7 because the crosspolarized transmission and reflection between LHCP and RHCP and the copolarized reflection of the RHCP waves are all small (below −10 dB). It should be noted that the discrepancy in the copolarized transmission coefficient of the LHCP wave is greater at 20 GHz compared to the discrepancy at 30 GHz. This is because the unit cells are operating closer to their first resonance at 20 GHz and they are electromagnetically smaller compared to the ones at 30 GHz. Therefore, any small physical deviation in the fabricated sample makes the unit cells to operate even closer to their first resonance at 20 GHz, thereby resulting to a higher overall loss and consequently higher discrepancy. Furthermore, surface roughness effectively reduces the conductivity of copper that also results to a higher overall loss in the measurements. Once the aforementioned variations are taken into account, the measured values at 20 GHz and 30 GHz approach closer to the simulated ones (see Supplemental Information). Lastly, a measurement error can also occur during the calibration process if a metal plate has been misplaced even by 1 mm when defining the reflect standard or if a quarterwavelength line has not been consistent during the calibration process. A physical misplacement of 1 mm translates to 36° of artificial phase difference at 30 GHz. As a result, the error in the axial ratio is amplified because it is very sensitive to the relative phase between the two orthogonal linearlypolarized waves. All these factors contributed to the mismatch between the measured and simulated values and are areas of further investigation in manufacturing these surfaces.
Discussion
We have introduced a new family of general impedancematched dualband chiral metasurfaces. The proposed numerical design process combines semianalytical and nonlinear optimization methods and allows solving for the required surface impedances in each layer at two userdefined operating frequencies. These layers are cascaded together to form the desired dualband chiral metasurface. To physically encode the required surface impedances, multiple concentric rectangular rings have been proposed as the unit cell comprising the surface. We have shown that these physical surfaces exhibit distinct dualband resonances. Furthermore, it has been shown that these resonant frequencies can also be independently and arbitrarily tuned for two orthogonal linearlypolarized waves. To demonstrate the versatility and generality of our approach, two design examples of an impedancematched dualband CPSS and PR operating at 20 GHz and 30 GHz have been demonstrated numerically. The impedancematched dualband CPSS has been further confirmed experimentally with freespace quasioptical measurements. Good agreement between the experimental and simulation results has been achieved.
Methods
Simulation of the unit cell
Fullwave electromagnetic simulations are performed using the Ansoft High Frequency Structure Simulator (HFSS) commercial software. The conductivity of 5.8 × 10^{7} Siemens/m is set for the copper. A single unit cell is simulated in a three dimensional environment by assigning Floquet ports on its top and bottom surfaces for a normally incident planewave excitation and terminating its sides by periodic boundary conditions to simulate an infinite array. The shunt impedances of an infinite array of the unit cells are directly related to the Zparameters that HFSS computes as,
Calibration of the quasioptical measurement set up
The standard fourport and twoport TRL calibrations are respectively performed for the measurements near 20 GHz and 30 GHz. A metal plate is used as the reflect standard and the reference planes of the sample are defined as thru. The horn antennas, lenses, and the DUT are all placed on micrometer translation stages such that the freespace quarterwavelength line can be accurately defined as the line standard. Furthermore, to filter out the unwanted reflection from the lenses and horn antennas, time gating has been applied for all Sparameter measurements^{20}. We note that care must be taken when positioning the metal plate to define the reflect standard for Tx and Rx antennas especially at high frequencies. Similarly, one must ensure using a consistent line standard (the freespace quarterwavelength line) for all ports. This is because any slight deviation translates to large artificial reflection and transmission phases which have strong influence on the measured values especially on the axial ratio measurements.
References
Semchenko, I. V., Khakhomov, S. A. & Samofalov, A. L. Helices of optimal shape for nonreflecting covering. Eur. Phys. J. Appl. Phys. 49, 33002, https://doi.org/10.1051/epjap/2009149 (2010).
Yu, N. et al. Light propagation with phase discontinuities: generalized laws of reflection and refraction. Science 334, 333–337 (2011).
Selvanayagam, M. & Eleftheriades, G. V. Discontinuous electromagnetic fields using orthogonal electric and magnetic currents for wavefront manipulation. Opt. Express 21, 14409–14429 (2013).
Yu, N. et al. Flat optics: Controlling wavefronts with optical antenna metasurfaces. IEEE Journal of Selected Topics in Quantum Electronics 19, 4700423 (2013).
Monticone, F., Estakhri, N. M. & Alù, A. Full control of nanoscale optical transmission with a composite metascreen. Phys. Rev. Lett. 110, 203903 (2013).
Kim, M., Wong, A. M. H. & Eleftheriades, G. V. Optical Huygens’ metasurfaces with independent control of the magnitude and phase of the local reflection coefficients. Phys. Rev. X 4, 041042, https://doi.org/10.1103/PhysRevX.4.041042 (2014).
Lin, D., Fan, P., Hasman, E. & Brongersma, M. L. Dielectric gradient metasurface optical elements. Science 345, 298–302 (2014).
Wong, J. P. S., Epstein, A. & Eleftheriades, G. V. Reflectionless wideangle refracting metasurfaces. IEEE Antennas and Wireless Propagation Letters 15, 1293–1296, https://doi.org/10.1109/LAWP.2015.2505629 (2016).
Yu, N. et al. A broadband, backgroundfree quarterwave plate based on plasmonic metasurfaces. Nano Letters 12, 6328–6333 PMID: 23130979 (2012).
Pors, A. & Bozhevolnyi, S. I. Efficient and broadband quarterwave plates by gapplasmon resonators. Opt. Express 21, 2942–2952 (2013).
Wu, X. et al. Anisotropic metasurface with nearunity circular polarization conversion. Applied Physics Letters 108, 183502 (2016).
SanzFernández, J., Saenz, E. & de Maagt, P. A circular polarization selective surface for space applications. IEEE Transactions on Antennas and Propagation 63, 2460–2470, https://doi.org/10.1109/TAP.2015.2414450 (2015).
Mohamad, S., Momeni, A., Abadi, H. & Behdad, N. A broadband, circularpolarization selective surface. Journal of Applied Physics 119, 244901, https://doi.org/10.1063/1.4954319 (2016).
Zhao, Y., Belkin, M. A. & Alù, A. Twisted optical metamaterials for planarized ultrathin broadband circular polarizers. Nat Commun 3, 870 (2012).
Wang, Y.H. et al. Unidirectional cross polarization rotator with enhanced broadband transparency by cascading twisted nanobars. Journal of Optics 18, 055004 (2016).
Gansel, J. K. et al. Gold helix photonic metamaterial as broadband circular polarizer. Science 325, 1513–1515 (2009).
Ericsson, A. & Sjoberg, D. Design and analysis of a multilayer meander line circular polarization selective structure. IEEE Transactions on Antennas and Propagation (In print), https://doi.org/10.1109/TAP.2017.2710207.
Masud, M. M., Ijaz, B., Iftikhar, A., Rafiq, M. N. & Braaten, B. D. A reconfigurable dualband metasurface for EMI shielding of specific electromagnetic wave components. In 2013 IEEE International Symposium on Electromagnetic Compatibility 640–644, https://doi.org/10.1109/ISEMC.2013.6670490 (2013).
Lundgren, J. Dual Band Circular Polarization Selective Structures for Space Applications. Master’s thesis, Lund University (2016).
Selvanayagam, M. & Eleftheriades, G. V. Design and measurement of tensor impedance transmitarrays for chiral polarization control. IEEE Transactions on Microwave Theory and Techniques 64, 414–428, https://doi.org/10.1109/TMTT.2015.2505718 (2016).
Kim, M. & Eleftheriades, G. V. Highly efficient alldielectric optical tensor impedance metasurfaces for chiral polarization control. Opt. Lett. 41, 4831–4834, https://doi.org/10.1364/OL.41.004831 (2016).
Pfeiffer, C., Zhang, C., Ray, V., Guo, L. J. & Grbic, A. High performance bianisotropic metasurfaces: Asymmetric transmission of light. Phys. Rev. Lett. 113, 023902 (2014).
Pfeiffer, C., Zhang, C., Ray, V., Guo, L. J. & Grbic, A. Polarization rotation with ultrathin bianisotropic metasurfaces. Optica 3, 427–432, https://doi.org/10.1364/OPTICA.3.000427 (2016).
Kim, M. & Eleftheriades, G. V. Dualband chiral metasurfaces. In 2017 IEEE International Symposium on Antennas and Propagation USNC/URSI National Radio Science Meeting 1491–1492 (2017).
Potter, J. E. Matrix quadratic solutions. SIAM Journal on Applied Mathematics 14, 496–501, https://doi.org/10.1137/0114044 (1966).
Bhattacharyya, A. K. GSM Approach for Multilayer Array Structures 187–226 (John Wiley & Sons, Inc., 2006).
Ryan, C. G. M. et al. A wideband transmitarray using dualresonant double square rings. IEEE Transactions on Antennas and Propagation 58, 1486–1493, https://doi.org/10.1109/TAP.2010.2044356 (2010).
Goldsmith, P. F. Gaussian Beam Coupling to Radiating Elements, 157–185 (WileyIEEE Press, 1998).
Acknowledgements
We would like to thank M. Chen and T. R. Cameron for their helpful discussions and support in the experiments and Prof. S. V. Hum for his support with equipment.
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The authors jointly conceived the main ideas in this work and developed the theory. M.K. performed theory and numerical calculations and conducted related experiments. G.V.E. provided overall guidance to the project. Both authors contributed to writing and editing the manuscript.
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Kim, M., Eleftheriades, G.V. Design and Demonstration of Impedancematched Dualband Chiral Metasurfaces. Sci Rep 8, 3449 (2018). https://doi.org/10.1038/s41598018200562
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DOI: https://doi.org/10.1038/s41598018200562
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