Mechanically Tunable Terahertz Circular Polarizer with Versatile Functions

Circular polarizers that selectively transmit only one handedness of circular polarization are useful for imaging and wireless communications. Conventional circular polarizers involve 3D chiral structures, which impose fabrication challenges, while typically introducing chirality within a limited bandwidth. To overcome the limitations associated with conventional non‐planar designs, a three‐layer metasurface‐based planar circular polarizer exhibiting strong and broadband chirality is presented here. Its superiority over existing multilayer designs is derived from a systematic design procedure. Measurement results reveal that the proposed structure maintains a 15‐dB extinction ratio from 251 to 293 GHz for the preferred handedness of circular polarization, leading to a fractional bandwidth of 15.4% with a transmission efficiency above 92.7%. Furthermore, the proposed structure is mechanically tunable to alter its functionality or operation bandwidth. Specifically, through simply rotating the top or bottom metallic layer by 90°, the structure can function as a transmissive quasi‐half‐wave plate that reverses the sense of circular polarization. Moreover, the presented structure can operate at nearby frequency ranges for the aforementioned functionalities by mechanically adjusting the air gap spacings between the metallic layers. Further calculations based on the measured results of each layer suggest that the proposed structure is robust to deviations in the air gap spacings.


Introduction
In nature, a myriad of biological molecules such as glucose, amino acids, and enzymes provide unique signatures in response to different handednesses of incident circularly polarized waves at terahertz frequencies. The differential responses are induced by chirality -an intrinsic property of chiral molecules, which do not exhibit internal mirror symmetry in their structures. [1] Chirality can be divided into circular dichroism and optical activity. Circular dichroism refers to a difference in material absorption between left-handed (LHCP) and right-handed circularly polarized (RHCP) waves, [2] while optical activity indicates the polarization plane rotation of linearly polarized waves. [3] Inspired by the functionality of chiral molecules, artificial three-dimensional chiral structures such as helices, [4,5] metafoils, [6] and microcoils [7] have been employed to introduce chirality for various functions, including negative index refraction, [8,9] polarization-dependent absorption, [10] optically induced torque, [11] and polarization conversion. [12] Among those chiral devices, circular polarizers, also known as circular-polarization-selective surfaces, are utilized to filter the circular polarization of one handedness and are highly demanded in spectroscopy, [13] biological imaging, [14] chiral structure characterization, [15] space applications, [16] color display, [17] microscopy and photography. [18] At microwave frequencies, three-dimensional Pierrot cells consisting of two orthogonal metallic arms connected by a quarter-wave metal via were designed to act as circular polarizers. [19][20][21] In optics, circular polarizers can be realized by implementing cholesteric liquid crystals that utilize Bragg reflection, [22] and helical arrays that exhibit inherent chirality as a result of their three-dimensional curled structures. [23,24] These three-dimensional structures lead to substantial thicknesses and high fabrication complexity. Moreover, they typically feature limited 15-dB extinction ratio fractional bandwidths, where the extinction ratio is defined as a difference in transmission between the two handednesses. Stacking multiple circular polarizers is beneficial to bandwidth enhancement, but at the expense of a high transmission loss and fabrication complexity. [25,26] www.advancedsciencenews.com www.lpr-journal.org As alternatives to non-planar chiral structures, it was shown that planar multilayer structures, such as metasurfaces, are viable for realizing designable chirality with a low profile and reduced fabrication complexity. Planar metasurfaces are formed by periodic arrays of subwavelength metallic [27][28][29][30] or dielectric resonators. [31][32][33] Each resonator interacts locally with the incident waves to impose a scattering response, so that the wavefront or polarization state of the outgoing waves can be manipulated at will. Owing to their planar structures, metasurfaces can be readily fabricated by employing existing standard lithography techniques in typically stacked configurations, which facilitate their integrability. However, despite the fact that diverse resonators such as propeller-shaped resonators, [34] stacked nanorods, [35] and L-shaped traces [36] were developed for metasurface-based circular polarizers, their operation bandwidth and efficiency remain to be further improved.
To maintain the desired chirality property over a wide bandwidth, various metasurfaces involving systematic design approaches were presented across the electromagnetic spectrum. In the microwave engineering community, an analytical model was presented to synthesize a circular polarizer design made of bianisotropic particles, [37] which delivered the required polarizabilities for predefined reflection and transmission coefficients. However, the resultant circular polarizer designed in standard circuit board technologies exhibited a relatively low polarization purity for transmitted waves and a simulated transmission efficiency of ≈ 20% over a narrow bandwidth. Aside from that, a frequency-selective surface consisting of patches and strips was designed with equivalent circuit models for realizing circular polarization selectivity. [38] The structure maintained a simulated 15-dB extinction ratio relative bandwidth of only 2.0%. Moreover, it employed fourteen metallic layers and ten substrates, resulting in significant fabrication challenges. In the millimeter-wave domain, a tri-layer metasurface-based circular polarizer was designed using a systematic approach, [39] and it exhibited a simulated 15-dB extinction ratio fractional bandwidth of 8.8%. In the optics region, a broadband bianisotropic response was obtained by stacking nanorod arrays with a tailored rotational twist. [40] This twisted optical structure involved a generalized Bloch analysis in combination with transmission-line theory to determine appropriate metallic layer rotation angles, while its transmission efficiency and 15-dB extinction ratio fractional bandwidth demanded further enhancement. To reduce ohmic losses introduced by metallic layers at optical frequencies, an all-dielectric metasurface was presented to function as a circular polarizer. [41] The metasurface design involved a systematic approach incorporating transmission-line theory and an optimization algorithm to maximize transmission efficiency. However, the employed optimization algorithm was based on the gradient descent method that is susceptible to trapping in local optima, thus leaving room for further performance enhancement.
In order to overcome some of the limitations associated with the existing designs, we propose a metasurface-based circular polarizer with superior performance including large bandwidth, frequency tunability, and versatile functionalities. The presented circular polarizer is developed with the aid from a broadband semi-analytical approach, [42] and it achieves a wideband bianisotropic response without involving complicated fabrication processes. Specifically, the broadband approach determines Schematic of a tri-layer transmissive metasurface unit cell. The metasurface consists of three metallic layers each on a dielectric substrate, and they are separated by two air gaps. The 2 × 2 admittance tensor of an i th metallic layer in response to x-and y-polarizations is denoted as Y si . The three dielectric substrates share the same thickness of t, while the two air gaps have identical spacings of d 1 and d 2 .
frequency-independent optimal circuit parameters for the circular polarizer, so as to achieve pre-specified complex transmission coefficients over a broad bandwidth. Thereafter, physical realizations of each metallic layer are performed separately to reproduce the responses of those optimal circuit parameters. Measured results reveal that the structure enables an extinction ratio higher than 15 dB from 251 to 293 GHz, equivalent to a relative bandwidth of 15.4% with RHCP waves transmission efficiency above 92.7%. The measured relative bandwidth is increased significantly compared to the largest-bandwidth planar circular polarizer to date, which achieved a relative bandwidth of 10.0%. [43] Through rotating the middle layer by 90 • , the orthogonal circular polarization can be transmitted instead. In addition, through rotating the top or bottom metallic layer by 90 • , the proposed structure can act as a transmissive quasi-half-wave plate (also known as circular polarization converter [44] ) that reverses circular polarization from one handedness to the other. The versatile operation modalities provided by the structure make it different from its existing counterparts that were typically designed for a fixed functionality at a given frequency. Importantly, a broadband frequency tunability that is not achievable for conventional passive devices can be realized by mechanically adjusting the air gap spacings between the metallic layers. The mechanical frequency tunability evaluated based on measured results of each layer suggests that the tunable range can cover the entire WR-3.4 waveguide frequency band from 220 to 330 GHz, [45] which is foreseen for point-to-point wireless terahertz communications. [46]

Design
As illustrated in Figure 1, we consider a transmissive metasurface composed of three metallic layers on three subwavelength dielectric substrates that are separated by two air gaps. The ensemble of three metallic layers enables a full control of the electric, magnetic, and magneto-electric responses to incident waves, leading www.advancedsciencenews.com www.lpr-journal.org to a large transmission phase coverage and a high transmission efficiency. [47,48] A broadband semi-analytical approach involving network analysis and genetic algorithm is implemented to expedite the metasurface synthesis and optimization. [42] The network analysis investigates the scattering characteristics of the multilayer metasurface based on its circuit parameters, while the genetic algorithm facilitates the search for frequency-independent optimal circuit parameters that collectively achieve a prescribed performance in a wide frequency range. To start with, we choose a particular category of anisotropic pattern for each metallic layer, whose pattern-equivalent circuits are distinctive for the x-and ypolarized incident waves. The possible equivalent circuits for one specific polarization include a purely inductive or capacitive circuit, or a parallel or series mixture of them. Metals are assumed to be lossless to simplify the synthesis. To build the admittance tensor of an i th metallic layer, we assume that it can be modelled as a purely inductive circuit with an inductance of L xi for the xpolarization and a purely capacitive circuit with a capacitance of C yi for the y-polarization. Thus, the admittance tensor of the i th metallic layer can be expressed as where denotes the angular frequency. A chosen metallic pattern should have mirror symmetry to avoid introducing undesired cross-polarization. Hence, the off-diagonal terms of Y xy si and Y yx si equal zero. Each metallic layer can be rotated around the zaxis to introduce magneto-electric coupling, while the rotation angle is restricted to an integer multiple of 45 • so as to maintain pattern connectivity with their neighboring unit cells. [49] In accordance with transmission-line theory, the dielectric substrates and air gaps can be represented by transmission line sections along the wave travelling direction. Ultra-low loss cyclic olefin copolymer (COC) is utilized for dielectric substrates so as to minimize the material loss. COC has a relative permittivity of r = 2.33 and loss tangent of tan δ = 0.0005 over the frequency band of interest from 220 to 330 GHz. [50,51] At this stage, each component of the structure presented in Figure 1 can be described by an ABCD matrix. As such, the scattering characteristics of the whole transmissive metasurface in response to circularly polarized incident waves under normal incidence can be readily evaluated at different frequencies by using the transfer matrix method (see Section A, Supporting Information). In order to optimize the metasurface design, the broadband semi-analytical approach employs a genetic algorithm [52] to find the optimal frequency-independent circuit parameters that collectively maintain the desired S-parameters over a wide bandwidth. The circuit parameters to be optimized are (L xi , C yi ) for the i th metallic layer, d 1 and d 2 for the air gaps, and t for the dielectric substrates.
As an objective for the optimal circuit parameters search, the metasurface-based circular polarizer is designed to transmit RHCP waves but reject LHCP waves with an extinction ratio Table 1. Calculated optimal circuit parameters provided by the broadband semi-analytical approach.

Top layer
Middle layer Bottom layer The optimal equivalent inductance and capacitance of the i th metallic layer along the x-and y-polarizations are denoted as L xi and C yi , respectively. The i th metallic layer pattern is rotated anti-clockwise by an angle of i around the z-axis, and the rotation angle is viewed from the +z-axis. The units for inductances and capacitances are pH and fF, respectively.
higher than 15 dB over a wide bandwidth. Here, the extinction ratio is defined as where the subscripts R and L denote RHCP and LHCP, respectively. It is noted that when using this expression, the polarization conversion from LHCP to RHCP is anticipated to be suppressed, so that the circular polarizer can be potentially applied in wireless communications where cross-talk between orthogonally polarized channels is undesired. An extinction ratio of 15 dB is implemented as a criterion for evaluating polarization purity of transmitted circularly polarized waves, and it is equivalent to an axial ratio of ≈3 dB. [42] In addition to achieving a 15-dB extinction ratio, the circular polarizer is expected to maintain a transmission coefficient with magnitude above −1 dB or 89.1% over the entire frequency band of operation. As design constraints, the achievable equivalent inductance and capacitance ranges of diverse patterns are explored by 3D full-wave simulations within a unit cell of fixed size. It is noted that the unit cell size is typically determined by in-band operation remaining free from higher-order diffraction effects. Moreover, in order to take the fabrication feasibility into consideration, the dielectric substrate thickness t is specified in a range from 20 to 200 μm, while identical air gap spacings of d 1 and d 2 ranging from 100 to 500 μm are adopted. Subsequently, the broadband semi-analytical approach is employed to determine the optimal frequency-independent circuit parameters for the circular polarizer. Calculations reveal that a pattern providing purely inductive and capacitive responses for the two orthogonal polarizations accompanied with a pattern rotation around the z-axis is preferred for each metallic layer to realize the desired performance. The calculated optimal circuit parameters are detailed in Table 1.
To realize the optimal circuit parameters, physical realizations for each metallic layer are performed separately (see Section B, Supporting Information). Electromagnetic simulations are conducted with the commercial software ANSYS HFSS. In the HFSS simulations, periodic boundary conditions are employed in the planes transverse to a unit cell to model an infinite uniform planar array, while Floquet ports are applied as a wave source to emit plane waves and collect scattered waves. To minimize the metal loss, gold is employed for each metallic layer, and its surface impedance at terahertz frequencies is detailed by a Drude model. [53] A subwavelength unit cell size of a = 400 μm, corresponding to 0.44 0 at 330 GHz, is chosen to avoid Top / bottom metallic layer Middle metallic layer  diffraction. Figure 2 shows the physically realized unit cell geometry of the circular polarizer, and Table 2 presents its detailed physical dimensions. The top and bottom metallic layers share an identical pattern, but the bottom layer is rotated by 90 • around the z-axis with respect to the top layer, as suggested by its optimal rotation angle of 3 = 90 • . Thinner metal strips result in larger equivalent inductances, while smaller separations between metal patches lead to higher equivalent capacitances. [48] Moreover, metallic patterns with equivalent inductive or capacitive circuits in parallel exhibit a reduced total inductance or increased total capacitance, respectively. By applying these design strategies with the help of simulations, a thin metallic strip oriented along the x-axis is employed for the top metallic layer to achieve a relatively high equivalent inductance. On the other hand, the I-shaped patches are in parallel along the y-axis to form a relatively high equivalent capacitance but a very limited inductance, so as to provide a predominately capacitive response for the y-polarization. A similar methodology is adopted for the middle metallic layer to achieve the desired reactances for the two orthogonal polarizations. The middle layer is rotated anti-clockwise by an angle of 2 = 45 • around the z-axis to yield the magneto-electric coupling, so that a bianisotropic response can be introduced. Figure 3 shows the transmission magnitude and extinction ratio provided by the broadband semi-analytical approach and the 3D full-wave simulation. An excellent agreement between the calculated and simulated results is achieved. The slight  deviation between them can be attributed to the difference between the equivalent reactances of the physically realized structure and the optimal circuit parameters. It can be inferred from Figure 3a that the proposed circular polarizer only allows RHCP incident waves to be transmitted, while LCHP transmission is largely suppressed. Importantly, circular polarization conversion from one handedness to its orthogonal counterpart is well below −15 dB at ≈275 GHz, making the proposed structure applicable for wireless communications, in which a low cross-talk between orthogonally polarized channels is desired. In Figure 3b, a simulated extinction ratio higher than 15 dB can be maintained from 251 to 298 GHz, leading to a fractional bandwidth of 17.1%. Moreover, a RHCP transmission magnitude above −0.45 dB, equivalent to a minimum transmission efficiency of 90.2%, can be sustained over the entire simulated 15-dB extinction ratio operation bandwidth.
The operation mechanism of the proposed circular polarizer involves multiple reflections, but for understanding, it can be simplified to a sequence of circular-to-linear and linear-tocircular polarization transformations. In general, the tri-layer structure can be considered as a combination of two quarterwave plates sandwiching one linear polarizer. Further simulations reveal that the top and middle metallic layers collectively form a quarter-wave plate, which realizes circular-to-linear polarization conversion. Thus, RHCP incident waves can be effectively transformed into linearly polarized waves after interacting with the top and middle layers, and their electric field is oriented in a direction perpendicular to the middle layer metallic strips as shown in Figure 4a. Consequently, the middle layer transmits these linearly polarized waves with low attenuation. In contrast, LHCP incident waves are converted to linearly polarized waves with an electric field aligned in a direction parallel to the middle layer metallic strips, and as a consequence they are completely reflected as illustrated in Figure 4b. Similarly, simulations suggest that the middle and bottom layers in combination function as a second quarter-wave plate, which realizes linear-to-circular polarization conversion. Linearly polarized waves converted from RHCP incident waves can be decomposed into two orthogonal electric field components that align with the x-and y-axes, respectively. Moreover, a phase difference of around −90 • between the  . Operation principle of the circular polarizer. a) Transmission of RHCP waves. The top and middle metallic layers collectively transform RHCP incident waves into linearly polarized waves, whose electric field is oriented in a direction perpendicular to the metallic strips in the middle layer. Subsequently, the middle and bottom layers jointly convert linearly polarized waves back into RHCP transmitted waves. b) Reflection of LHCP waves. The top and middle metallic layers transform LHCP incident waves into linearly polarized waves, with their electric field aligned with the middle layer metallic strips, and they are all reflected. Incident waves propagate along the −z-axis.
x-and y-directed field components can be obtained after passing through the second quarter-wave plate. As a result, linearly polarized waves converted from RHCP incident waves are eventually transformed back into RHCP transmitted waves. It is noted that a similar concept that combined quarter-wave plates and linear polarizers was utilized to design a microwave circular polarizer employing fourteen metallic layers, [38] which exhibited a simulated 15-dB extinction ratio relative bandwidth of 2.0% and would www.advancedsciencenews.com www.lpr-journal.org  . Simulated and measured performances of the proposed circular polarizer that selectively transmits RHCP waves. a) Transmission magnitude, b) extinction ratio, c) transmission efficiency, and d) axial ratio. The extinction ratio is defined as |T RR | 2 ∕(|T RL | 2 + |T LR | 2 + |T LL | 2 ), where R and L denote RHCP and LHCP, respectively. The transmission efficiency is calculated as |T RR | 2 . The shaded area marks the measured 15-dB extinction ratio bandwidth from 251 to 293 GHz. Error bands indicate the standard deviations of measured data. Moving average filter is applied to smoothen the measured results.
be practically very difficult to be scaled for fabrication at terahertz and optical frequencies. In contrast, the systematically designed three-layer structure relies on multiple reflections in between the metallic layers, making its operation principle fundamentally different from that of multilayer devices merely cascading Jones matrices.

Results and Discussion
Images of the fabricated sample are given in Figure 5, and the fabrication details are available in our previous publications. [27,42] In order to validate its performance, the fabricated structure is experimentally characterized from 220 to 330 GHz, and the measurement setup is detailed in the Experimental Section. A holder achieving the desired air gap spacings with sufficient accuracy has not been available to the authors, due to limitations of accessi-ble fabrication facility. However, further calculations and simulations reveal that near-field couplings between the metallic layers are negligible with an air gap spacing of d 1 = d 2 = 136 μm, which is equivalent to an electrical spacing of 0.10 0 at 220 GHz. As such, the air gaps can be analytically represented by transmission lines. Consequently, the measurements are conducted on each layer separately and the cumulative responses of the whole structure are then re-constructed numerically (see Section C, Supporting Information). Figure 6 reveals that a reasonable agreement between the simulated and measured results is obtained, while the deviation between them can be attributed to unavoidable fabrication tolerances and experimental misalignment. It can be inferred from Figure 6 that the manufactured structure enables a measured 15-dB extinction ratio from 251 to 293 GHz, corresponding to a fractional bandwidth of 15.4% with a RHCP waves transmission efficiency higher than 92.7%. Moreover, Figure 6d  suggests that a measured axial ratio of less than 2.6 dB can be sustained over the entire 15-dB extinction ratio operation bandwidth, equivalent to an output wave ellipticity of −0.96, where an ellipticity of −1 denotes a perfect RHCP waves (see Section D, Supporting Information for transformation between axial ratio and Stokes parameters). Further evaluations reveal that the circular polarizer is robust to air gap spacings deviations, but accompanied with a frequency shift of the operation bandwidth (see Section E, Supporting Information). Specifically, the circular polarizer is capable of maintaining a measured 15-dB extinction ratio for d 1 with a spacing deviation of −75 μm (−35.7%) or +60 μm (+28.6%) from the designed value of 210 μm, while corresponding tolerances for d 2 are −50 μm (−23.8%) or +90 μm (+42.9%). In addition, decreasing the air gap spacing of d 1 or d 2 results in a blue shift of the 15-dB extinction ratio operation bandwidth and peak transmission efficiency.
In addition to the aforementioned measured operation frequency range from 251 to 293 GHz, the proposed circular polarizer is also able to operate at nearby frequency ranges by mechanically adjusting the air gap spacings as evidenced in Figure 7. It can be seen that the proposed circular polarizer is capable of covering the entire WR-3.4 waveguide bandwidth from 220 to 330 GHz with a measured extinction ratio higher than 15 dB by varying the air gap spacings. It is noted that the non-linear relationship in Figure 7 results from the interference of multiple reflections between the metallic layers.

Reconfigurability
The operation principle of the circular polarizer suggests that the proposed structure can be configured to selectively transmit LHCP incident waves. This is realized by simply rotating the middle metallic layer by 90 • around the z-axis. As depicted in Figure 8b, LHCP waves transmission of the configured structure can be explained by the linear polarization filtering of the middle layer. A 90 • rotation of the middle layer makes the metallic strips perpendicular to the electric field of linearly polarized waves converted from LHCP incident waves, but parallel to that trans-formed from RHCP incident waves. Linearly polarized waves converted from LHCP incident waves are then transformed back into LHCP transmitted waves after propagating through the second quarter-wave plate. Consequently, the configured structure will correspondingly transmit LHCP incident waves with the identical measured 15-dB extinction ratio relative bandwidth, transmission efficiency, and axial ratio as that of the structure transmitting RHCP waves. The only difference is the polarization exchange between RHCP and LHCP. Hence, the definitions of extinction ratio and transmission efficiency are re-defined accordingly for the LHCP transmission scenario.
Apart from working as circular polarizers, the proposed structure can also function as a transmissive quasi-half-wave plate to reverse circular polarization from one handedness to the other. This can be configured by a 90 • rotation of the top or bottom metallic layer around the z-axis. A quasi-half-wave plate is useful for polarization diversity in communications at microwave and terahertz frequencies, [54,55] or for magnetic recording and target detection at optical frequencies. [56,57] We choose the bottom metallic layer rotation as an example as illustrated in Figure 8d. A 90 • rotation of the bottom layer results in a phase difference of around 90 • between the x-and y-polarized transmitted waves. Thus, linearly polarized waves converted from RHCP incident waves are then transformed into LHCP transmitted waves after propagating through the second quarter-wave plate. The proposed structure with a 90 • rotation of the top metallic layer works in a similar manner, but it transforms LHCP incident waves into RHCP transmitted waves. Further evaluations reveal that the tailored configurations exhibit the same 15-dB extinction ratio fractional bandwidth, transmission efficiency, and axial ratio as the structure functioning as circular polarizers. The achievable functionalities of the structure by a 90 • rotation of a single metallic layer are summarized in Figure 8. Importantly, the operation bandwidths of the device working in different states can be tuned to nearby frequency ranges by mechanically adjusting the air gap spacings between the metallic layers. The tunable operation bandwidths allow the device to fit various practical applications and maximize the extinction ratio and efficiency at a particular frequency. Table 3 shows a performance comparison of the proposed structure with representative existing planar designs from the literature. For a fair comparison, the list excludes optical realizations due to vastly different fabrication technologies and much higher metallic losses. It can be seen that the largest-bandwidth circular polarizer design to date presented a measured 15-dB extinction ratio fractional bandwidth of 10.0% and a transmission efficiency above 16.6%. [43] However, the proposed circular polarizer provides a relative bandwidth that is increased by a factor of more than 1.5 to 15.4%, accompanied with a high transmission efficiency of higher than 92.7%. Notably, the proposed structure exhibits frequency tunability and reconfigurability. These features are not commonly available in passive terahertz devices. At terahertz frequencies, mechanically reconfigurable chiral metamaterials were developed based on stretchable substrates. [34,58] Their frequency tunability was obtained by mechanically tailoring the morphology of the structure through stretching or releasing the substrates. However, both structures achieved an extinction ratio of less than 15 dB and remained at the conceptual level without fabrication. The characteristics The term "quasi-half-wave plate" denotes that the configuration can invert circular polarization from one handedness to the other, but cannot rotate linear polarization by 90 • . All functionalities presented here share the same measured 15-dB extinction ratio fractional bandwidth of 15.4%, transmission efficiency of more than 92.7%, and axial ratio of less than 2.6 dB (corresponding to an ellipticity of ±0.96, where the sign is dependent on the circular polarization handedness). The extinction ratio and transmission efficiency definitions are adapted to the different scenarios. of large bandwidth, frequency tunability, and reconfigurability demonstrate that the systematically designed circular polarizer achieves significant performance improvement compared to most existing multilayer passive devices. The achieved large fractional bandwidth together with a high efficiency of the proposed structure can be attributed to the design method employing the broadband semi-analytical approach. The broadband approach provides optimal circuit parameters so as to achieve desired performance over a large bandwidth. Its frequency tunability results from the involvement of air gaps that can be mechanically adjusted, while the reconfigurability is introduced by the constituent layers that can be rotated to invert the phase difference between x-and y-polarizations or selectively transmit one linear polarization. Essentially, the proposed design exploits interference of multiple reflections between metallic layers, leading to a small number of metallic layers. In addition, the proposed structure does not rely on near-field couplings between metallic layers, thus relaxing the alignment requirements during fabrication.

Conclusion
This paper has presented a metasurface-based circular polarizer exhibiting a measured 15-dB extinction ratio fractional bandwidth of 15.4% from 251 to 293 GHz. The circular polarizer can filter circular polarization of the preferred handedness with a transmission efficiency higher than 92.7% over the bandwidth of operation. Relying on the interference of multiple reflections in between the metallic layers, the proposed structure achieves bianisotropic responses with a planar and subwavelength profile. Calculations based on the measured results of each layer confirm that the proposed structure exhibits robustness to deviations of air gap spacings. Furthermore, the proposed structure can also function as a transmissive quasi-half-wave plate through simply  rotating a single metallic layer by 90 • . Importantly, the proposed structure presents mechanical frequency tunability, thus allowing to maximize the extinction ratio at a particular frequency. The large bandwidth, versatile functionalities, and frequency tunability of the structure present a great leap from the reported designs. Its bandwidth performance can be further improved by involving more metallic layers. [59] Spectroscopic detection of chiral molecules in biology and polarization-division multiplexing in communications can benefit from the proposed design.

Experimental Section
As illustrated in Figure 9, a Keysight Precision Network Analyzer (PNA) together with VDI WR-3.4 extension modules are employed to investigate the scattering performance of the manufactured circular polarizer from 220 to 330 GHz. The PNA sends a microwave signal that passes through the VDI extension module. The microwave signal is thus converted into a terahertz signal in a frequency range from 220 to 330 GHz and transmitted by a linearly polarized horn antenna. It is noted that a terahertz source producing broadband circularly polarized waves is not available to the authors. As an alternative, linearly polarized horn antennas can be employed for experimental characterization of terahertz devices, and their scattering responses under circularly polarized waves can be directly converted from linear basis to circular basis (see Section A, Supporting Information). Four lenses are used to collimate and focus the terahertz beam. The focused beam illuminating the sample is vertically polarized with a focal spot of ≈1 mm in diameter. The Rayleigh range of the focused beam at 220 GHz is 0.58 mm, which can cover the whole structure that is of 0.48-mm thickness in total, thus normally incident plane waves can be assumed. The reflected and transmitted waves from the sample are then collected by the horn antennas. No polarizers are involved in the experiment, as horizontally polarized waves experience a significant attenuation in the waveguide feeds of the horns. The extension modules are shielded by absorbers to eliminate spurious reflections.
Due to limitations of the available facility to the authors, a holder maintaining desired air gap spacings with high accuracy cannot be obtained. As such, each layer comprising a metallic layer and a supporting dielectric substrate is measured separately. In order to ensure data reliability, five sets of measurement are conducted for each layer at five different regions of its surface. Each set of measurement acquires the complex copolarization responses of each individual layer, that is, S xx 11 , S yy 11 , S xx 21 , S yy 21 , S xx 22 , and S yy 22 . It is noted that the performance under x-or y-polarization is measured by rotating the sample by 90 • or 0 • around the wave propagation direction. To simplify the experiment and reduce errors introduced by misalignments, no cross-polarization measurements are conducted, but they are obtained analytically based on the measured complex copolarization terms (see Section C, Supporting Information). Moreover, only the top and middle layers are measured since the top and bottom layers share an identical pattern. For reference measurements in reflection, the sample is replaced with a gold-coated mirror, while those in transmission are taken without the presence of the sample. More details including the measured data processing are provided in Section C, Supporting Information.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.