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Cross-shaped resonator (CSR) in metamaterial usually corresponds to adjust resonant characteristics. In this report, a simple and broadband reflective polarization converter is realized at GHz frequencies by breaking the symmetry of the CSR. The experimental results demonstrate that the polarization conversion ratio (PCR) over 0.8 is achieved from 8.3 GHz to 14.3 GHz for linearly polarized (LP) incident waves under normal incidence. The high polarization conversion efficiency can be sustained when the incident angle increases to 60 degrees. By taking advantage of surface current distribution and the interference theory, the physical mechanisms are elucidated in detail. Finally, the broadband polarization conversion can also be achieved by decreasing the geometrical parameters of the converter in the mid-infrared frequency range.
© 2016 Optical Society of America
1. Introduction
Considerable attention has been drawn to manipulate the polarization of electromagnetic (EM) waves, like quarter-wave plate [1], anomalous reflection [2] and holograms [3]. Achieving full control over EM polarization states is an ever important issue. To realize such control it is highly desirable to have flexible manipulation of phase modulation and amplitude in transmission, reflection and absorption of EM waves [4–8 ]. In conventional polarization control elements such as optical gratings [9] and dichroic crystals [10], a significant propagation distance is needed to acquire disparate phase retardation for different polarizations. And expanding their typically limited bandwidth requires materials with increased complexity.
Metamaterials (MMs) classified as artificial materials have been the subject of hot pursuits in recent years due to their particular properties [11–14 ], possessing many intriguing demonstrations including anomalous refraction [2,15–18 ], quarter and half waveplates [8,19 ] and lensing [20,21 ]. Recently, MMs have been utilized to explore polarization conversion properties of EM waves based on chiral and anisotropic MMs, due to the cross-coupling effect between electric and magnetic fields [22–25 ]. One of the drawbacks of these polarization converters is the narrow operating bandwidth, which may impede their application in practice. Methods and designs have been proposed to extend the polarization conversion bandwidth. Hao et al proposed a reflective polarization converter based on anisotropic MMs, which could generate multiple resonance frequencies [26]. A metamaterial polarizer based on electric-field-coupled resonator for such purpose was proposed in Ref [27,28 ]. He et al presented a multiple-band reflective polarization converter based on deformed F-shaped MMs [29]. Despite its high polarization conversion efficiency, the polarization conversion depends on operating frequency and suffers from narrow bandwidth. In another approach, it was shown that a dielectric meta-reflectarray polarization convertor can achieve over 98% polarization conversion efficiency across a 200 nm bandwidth by utilizing structured silicon cut-wire resonators [6]. Meanwhile, this design avoids complexity by use of low aspect ratio structure with subwavelength thicknesses. The physical mechanism of near-perfect and broadband polarization conversion can be explicated by equivalent media theory and Lorentz-theory approach [26,30,31 ].These intriguing features therefore make it possible for us to design a simple and broadband polarization converter in microwave frequency regime.
In this work, we present a broadband reflective polarization converter based on asymmetric cross-shaped resonator (CSR) MMs, which are capable of converting a linearly polarized (LP) wave into its orthogonal polarization. Our proposed converter exhibits wideband polarization conversion property numerically as well as experimentally. The measured results show that the polarization conversion ratio (PCR) over 0.8 is achieved from 8.3 GHz to 14.3 GHz for linearly polarized (LP) incident waves under normal incidence. Oblique incidence performance of the converter is also given. The physical mechanisms are elucidated by taking advantage of surface current distribution and the interference theory. By decreasing the geometrical parameters of the unit of the converter, the polarization conversion properties are analyzed in mid-infrared frequency range.
2. Design and experiment
The structure to manipulate polarization conversion is usually designed as anisotropic MMs [26–28,32–35 ]. These MMs are mostly constructed of periodic asymmetrical metallic pattern, which can achieve polarization conversion when a prescribed plane wave illuminates the MMs by breaking the symmetry of the pattern [34,36 ]. For these MMs, the back metal plane and the top metallic pattern form a Fabry-Pérot-like cavity [8,37–39 ], where the consequence interference of polarization couplings in the multi-reflection process may enhance or reduce the overall reflected fields with co-and cross-polarizations. This concept can be validated by full-wave numerical simulation and calculated by interference theory (in Section 3.4).
Our simple converter design is composed of a copper-patterned layer at the front and continuous perfect electric conductor (PEC) at the back, separated by a dielectric layer of Teflon. As shown in Fig. 1 , the optimized unit cell is chosen as periodic dimensions of p = 13.0 mm in the x-y plane, and the thickness of dielectric layer is t = 3.0 mm in the propagation of EM wave, z direction. The parameters of the metallic pattern are as follows: l 1 = 8.0 mm, w 1 = 1.0 mm, l 2 = 7.5 mm, w 2 = 1.0 mm, g 1 = 1.5 mm and g 2 = 1.0 mm.
Fig. 1 (a) Schematic diagram of the proposed structure, (b) the front view of one unit cell in simulation.
The aforementioned geometrical parameters have been optimized by the commercial software CST Microwave Studio 2013. In the simulation, the conductivity of copper was σ = 5.8 × 107 S/m, and the Teflon was simulated with a dielectric function of ε = 2.65 × (1 + 0.0002i). The frequency domain solver was carried out with unit cell boundary condition in the x-y directions and the floquet ports in the z-direction to extract S parameters. Owing to the polarized incident EM waves, we assumed that the electric and the magnetic fields were paralleled to y-and x-axis, respectively. Since transmission is eliminated by PEC, all the components of EM wave reflections for different polarizations can be obtained.
To understand the reflective characteristics of the converter, we define ryy = |E yr/E yi| and rxy = |E xr/E yi| to represent the reflectance of y-to-y, and y-to-x polarization conversions, respectively. PCR is defined as PCR = r2xy/(r2xy + r2yy) for linear polarization (rxy = |r xy|, ryy = |r yy|), and η is the angle between converted polarization direction and the incident polarization axis, then η = tan−1(|Exr|/|Eyr|) [32,34 ]. We defined phase difference between the y and x component of the reflected EM wave Δφxy = arg(r xy) - arg(r yy). Δφxy can take arbitrary values within [-180°, 180°] depending on the frequency, indicating that all possible polarization states are realizable for the reflected waves.
The experimental sample is shown in Fig. 2(a) , which has an oversize of 208 mm × 208 mm, containing 16 × 16 unit cells by the conventional printed circuit board (PCB) process with the structural parameter same as the simulated model. The reflectance dependent on frequency was measured by the United States Naval Research Laboratory (NRL) arch method [40] as shown in Fig. 2(b). An Agilent 8720ET vector network analyzer and two broadband horn antennas were connected by a coaxial cable. Two antennas were used to emit and receive EM waves. We can obtain reflectances rxy and ryy by rotating the horn antennas in the arch structure for different incident angle.
Fig. 2 (a) Photography of the fabricated cross-resonator polarization converter and (b) the measured setup.
The measured and simulated results under normal incidence are presented in Fig. 3 . The measured results show good agreement with the simulated ones. From Fig. 3(a), the polarization conversion bandwidth of reflectance rxy over 0.8 can be achieved from 8.1 to 13.8 GHz for simulations and from 8.3 to 14.3 GHz for measurement. Also, we can see from Fig. 3(a) that the simulated reflectance rxy are 0.99 and 1.0 at resonance frequencies of 8.6 GHz and 12.1 GHz, respectively; rxy are 1.0 at both frequencies of 8.9 GHz and 12.2 GHz for experiments. In Fig. 3(b), PCR is all above 0.6 in 8.3-14.0 GHz, and achieves 1.0 at the two resonance frequencies, which means nearly all the energy of y-polarized wave is converted to x-polarized wave. Figure 3(c) employs the polarization azimuth rotation η to describe the angle between the conserved polarization axis and y-axis. We can see that η is 87.3° and 87.7° at the two resonance frequencies, which is more intuitive for pointing out that the reflected waves are converted to x-polarized waves. Otherwise, it is clearly seen from Fig. 3(d) that, at frequencies of 8.0 GHz, rxy = rxy, Δφxy = 87°; at 14.3 GHz, rxy = rxy, Δφxy = 95°, which indicates the circularly polarized (CP) waves in this case.
Fig. 3 Simulated and measured results of LP conversion pattern under y-polarized incident waves. (a) Reflectance of co-and cross-polarization ryy and rxy, (b) PCR, (c) polarization azimuth rotation η and (d) relative phase Δφxy versus frequency between rxy and ryy.
3. Numerical results and discussion
3.1 The effect of thickness on polarization conversion
It is important to investigate the effect of substrate thicknesses on the polarization conversion of the optimized converter. Figure 4(a) and 4(b) depict the simulated reflectances rxy and ryy for different thickness t. It is clearly seen that the thickness has a weak influence on the resonant peaks; the polarization conversion efficiency is near perfect as the thickness is varying. The thickness only affects the polarization conversion bandwidth. And when thickness t = 3.0 mm, the bandwidth over 0.8 can be achieved from 8.1 to 13.8 GHz. Moreover, the converter can convert LP to CP waves in region B with increase of thickness t from Fig. 4(c). In this case, the relative phase Δφxy = 90°, rxy is equal to ryy at some frequencies. The high-resonance peak shifts toward low frequency with increase of t in region A, but smaller offset range. The thickness-independent on resonant peak can be understood by the impedance of the converter shown in Fig. 4(d). The resonance occurs when the imaginary part of the normalized impedance zyy is zero and the real part approaches to unity [41–43 ]. It is found that the imaginary part of zyy is zero in the whole frequency band, and the real part of normalized impedance zyy of the converter is nearly unity with the increase of the thickness at ~8.6 GHz and 12.1 GHz, repectively. When t = 3 mm, the real part of zyy is close to unity between the frequency of 8.6 GHz and 12.1 GHz, meaning a broad polarization bandwidth.
Fig. 4 Simulated results vs. frequency for different thickness t. (a) rxy, (b) ryy, (c) relative phase Δφxy and (d) normalized impedance zyy of the converter.
3.2 Angle independent on the polarization conversion
In this section, the response of our proposed converter for oblique incident performance is examined. To this end, incident angle θ is defined as those formed between the propagation vector of the incident wave and the z-axis over xz-plane. The simulated reflectance varying angle θ is illustrated in Fig. 5 , indicating an almost angle-independent performance up to θ = 60 degree for the resonant peak. Such insensitivity to incident angle provides convenience in practical applications. However, the operating bandwidth decreases resulting from a further reduction of rxy between the two resonance frequencies with increase of θ. When the incident angle θ is 60 degree, rxy = 0.56, ryy = 0.83, which implies that the EM energy is absorbered. The enhanced absorption may originate from an extra resonance between CSR arrays and the PEC in the case of oblique incidence [43,44 ]. Figure 6 gives the simulated and measured results under θ = 30 degree. The measured results show that the resonant peaks are good agreement with the simulations. And the simulated reflectance rxy is 0.99 and 1 at resonance frequencies of 8.5 GHz and 12.0 GHz; rxy achieves 1 at both frequencies of 8.9 GHz and 12.3 GHz for measurement. However, the valley of rxy in measured data between the two resonant peaks is lower than that in simulations. The major factor may be the edge diffraction of the finite unit cells for oblique incident measurement.
3.3 Investigation of the physical mechanism
We use EM field distributions and equivalent circuits to explain how the proposed converter affects the polarization conversion. For convenience in description, the new unit cell is enlarged and shown in Fig. 7(a) and 7(b) with the strip compoments numbered as s1, s2, s3 and s4. Figure 7(c) and 7(e) show the EM field distributions at resonance frequencies of 8.6 GHz and 12.1 GHz, respectively. The impedances Zix and Ziy seen by x and y directions can be written, respectively, as
where the subscript i represents 1 and 2, corresponding to the resonance frequencies of 8.6 GHz and 12.1 GHz, respectively. w is the frequency. Lix, Liy and Cix, Ciy are produced by the E-fields along x- or y-axis direction. Rix and Riy are the resistances of the metallic strips.Fig. 7 (a) Schematic illustration of the proposed converter and (b) two adjacent units of the converter. (c), (e) Electric field distributions and (d), (f) surface current distributions at 8.6 GHz and 12.1 GHz, respectively, for y-polarized wave.
From Fig. 7(c) and 7(d), at frequency of 8.6 GHz, the impedances Z 1 x and Z 1 y seen along x and y directions, respectively, are different. The inductances (L 1 x and L 1 y) formed by the currents flowing on the metallic strips are equal, however, the capacitance C 1 y is less than C1 x formed by the E-fields across the gap between (s1, s3), (s2, s3), and so making Z 1 y less capacitive than Z 1 x. Since Z 1 y is less capacitive than Z 1 x, Ey will lead Ex by arg(Z 1 y - Z 1 x) after going through the converter. If the converter is designed such that arg(Z 1 y - Z 1 x) = 180°, the resultant E-field will be linearly polarized. Similarly, as shown in Figs. 7(e) and 7(f), at frequency of 12.1 GHz, the capacitance C 2 y is less than C 2 x. However, the inductance L 2 y is also less than L 2 x. So if the capacitance and inductance are cancelled out partly, and making arg(z 1 y - z 1 x) be zero, the resultant E-field will also be linear polarization. So if the converter is designed to meet above condition, polarization conversion can be achieved. This analysis can be verified and agrees well with the simulated phase difference depicted in Fig. 3(d). Meanwhile, by the current configuration in Fig. 7, it can also be better understood the physical mechanisms. As shown in Fig. 7(a), the x component E1x of the induced electric field E1 paralleled to the incident magnetic field Hx. Thus, the cross-coupling between the incident magnetic field Hx and E1x leads to a cross-polarization with a y-to-x polarization conversion. The y component E1y of the induced electric field is perpendicular to the incident magnetic field Hx, which cannot excite the cross-polarization due to the same direction of the incident electric field Ey. The similar physical mechanism occurs at resonance frequency of 12.1 GHz as shown in Fig. 7(b). The cross-polarization effect between incident magnetic field Hx and E2x, leads to the y-to-x polarization conversion [45]. Otherwise, Yu et al demonstrated “symmetric” and “antisymmetric” modes supported by V-antennas metasurface, which can also explain the principle of our converter according to the current configurations [2].
3.4 The calculation methods
In order to analyze the reflection characteristics of proposed converter quantitatively, the polarization conversion can be understood by using interference theory [8,35,38,39 ]. Considering the converter as a coupled system, all possible near-field interactions between CSR array and the PEC can be accurately taken into account. As shown in Fig. 8 , the converter is separated into two tuned interfaces, with CSR array and PEC located at the two side of spacer.
As dipicted in Fig. 8, y-polarized waves impinging on the surface of the converter are partially reflected back and partially transmitted into the substrate. Due to the polarization conversion of the converter, the reflected waves are divided into y-to-x and y-to-y components, which corresponds to x-polarized and y-polarized waves, respectively. The transmitted waves also have x- and y-polarized components. Therefore, there are two reflection coefficients rxy 12 and ryy 12, and two transmission coefficients txy 12 and tyy 12. The latter continues to propagate until they reach the ground plane, with a complex propagation phase , where k 0 is the free space wavenumber. After the reflection at the ground plane and additional propagation θ, partial reflection and transmission occur again at the air-spacer interface with CSR with reflection coefficients {r 21} and partially transmitted into free space with transmission coefficients {t 21}. Similarly, y-polarized waves have two reflection coefficients {r 21}, and transmission coefficient {t 21}. The reflection and transmission coefficients corresponding to x-polarized and y-polarized waves, respectively, can be expressed by the following forms.
The overall reflection is then the superposition of the multiple reflections:Therefore, according to Eq. (4) in conjunction with Fig. 8, the reflection coefficients for y-to-y and y-to-x polarized waves are then calculated as follows, respectively.
In above equations, the first term refers to the co-and cross-polarized reflections directly from the CSR array. The other terms are the reflections resulting from superposition of the multiple reflections between the CSR array and PEC. When destructive interference occurs between the first and other terms of the co-polarized reflections, the y-to-y polarized reflection ryy will be very small. And if ryy is nearly zero, the polarization conversion can be achieved.
The reflection coefficients in Eq. (5a) and Eq. (5b) can be obtained through numerically simulating S-parameters of one unit cell containing the CSR located at the interface of semi-infinite air and spacer, i.e, without PEC, as shown in Fig. 9 . By submitting the reflection and transmission coefficients shown in Fig. 10 into above equations, the reflection are calculated and shown in Fig. 11 . We can see that the theoretical calculations based on interference theory are in good agreement with the numerical simulations.
Fig. 10 The reflection and transmission coefficients at the air-metasurface interface obtained by simulations using the unit cell shown in Fig. 9: (a) amplitude and (b) phase.
3.5 Polarization conversion in mid-infrared regime
Further numerical simulation reveals that the polarization conversion of the converter can be occurred in the mid-infrared regimes from 20 μm to 40 μm. Recently, the polarization converter based on graphere sheet in the development of mid-infrared regime has been presented [46,47 ]. In our simulation, the unit in the mid-infrared model is different: dimension changes to μm, and the frequency changes to mid-infrared. Al2O3 was taken as the dielectric substrate with a thickness of 2 μm. The dielectric constant of Al2O3 is 2.18 × (1 + 0.04i). The upper and lower metal is gold with a thickness of 0.5 μm. Its dielectric function is defined by Drude mode with plasmon frequency wp = 2π × 2.18 × 1015 rad/s and damping constant γ = 4.08 × 1013 s−1 [48].
The simulated results under normal incidence are presented in Fig. 12 . From Fig. 12(a), the polarization conversion bandwidth of reflectance rxy over 0.7 can be achieved from 23 μm to 35 μm. Also, rxy are 0.84 and 0.77 at the resonance frequencies of 25 μm and 33 μm, respectively. By the simulated relative phase Δφxy depicted in Fig. 12(b), it is clearly seen that the value of Δφxy is close to ± 180° and zero at these two resonance frequencies, respectively, which means a linearly polarized state. However, the polarization conversion efficiency is lower than that of the converter in microwave regimes due to the high loss in the mid-infrared regimes [49].
Fig. 12 Simulated results of LP conversion pattern under y-polarized incident waves. (a) Reflectance of co-and cross-polarization ryy and rxy, (b) relative phase Δφxy versus wavelength between rxy and ryy.
4. Conclusion
In summary, we have numerically and experimentally demonstrated a polarization converter composed of asymmetric CSR. The proposed converter can accomplish high efficiency and broad bandwidth for linearly polarized waves. The polarization conversion performance of the designed converter can be attributed to the interference effect. The experimental results show that the cross-polarization conversion ratio over 0.8 is achieved from 8.3 GHz to 14.3 GHz for linearly polarized (LP) incident waves under normal incidence. In addition, the high efficient polarization conversion can be sustained as the incident angle is increased to 60 degree. Owing to the simple design, the proposed converter can be a good candidate to fabricate devices in the mid-infrared regimes from 23 μm to 35 μm.
Acknowledgments
The authors are grateful to the supports from the National Natural Science Foundation of China under Grant Nos. 51025208 and 61001026, the Program for Changjiang Scholars and Innovative Research Team in University, the Fundamental Research Funds under Grant Nos. ZYGX2013J029, and the Open Foundation of National Engineering Research Center of Electromagnetic Radiation Control Materials under Grant Nos. ZYGX2013K001-5.
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