Abstract
Metamaterials with tailored electromagnetic properties hold great promise for the manipulation of electromagnetic waves. Here, we propose an intriguing off-resonance meta-device to control the polarization states and dispersive features of the electromagnetic waves simultaneously. The proposed meta-device is composed of stacks of bilayer gear-like metallic patterns, which exhibit significant anisotropy due to the geometric asymmetry. The results show that the considered meta-device operates in a transmission mode and can achieve broadband and nondispersive cross-polarization transmission with a high polarization conversion ratio nearly 100% for both of the normal incident linear and circular polarization waves. Moreover, the broadband and efficient polarization conversion behavior of the meta-device can be maintained regardless of the incident angle for the circular polarization waves. These fascinating performances enable the meta-device to act as an excellent half-wave plate being greatly beneficial for polarization manipulation.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
As one of the most important features of electromagnetic waves, polarization plays a key role in many physical effects. Manipulation of the polarization states of electromagnetic waves enables a wide variety of important applications, which have brought tremendous influences to our daily life. The traditional methods to control the polarization states of electromagnetic waves are usually using the birefringence effect of anisotropic materials or optical activity effect of chiral materials, which leads to the phase retardation between the two orthogonal polarization components [1–3]. However, due to the inherent drawbacks (for instance, weak anisotropy or chirality of natural materials), the conventional polarization controllers made of naturally available materials generally suffer from quite bulky configurations, narrow bandwidths, or high losses, which extremely restrict the integration of polarization controllers into compact devices and hinder the potential applications.
Metamaterials with the tailored electromagnetic properties open a new opportunity to efficiently manipulate the electromagnetic waves [4–8]. Recent progress in metamaterials has demonstrated that metamaterials can flexibly control the transmission/reflection amplitudes [9–12], propagation directions [4,6,13,14], dispersive features [15–17], and even the polarization states [18–23] of the electromagnetic waves. Utilizing strong resonant responses, metamaterials can achieve giant anisotropy or chirality which is about five orders of magnitude larger than that of the natural substances [24–27], thereby enabling the thicknesses of metamaterial-based polarization controllers to be reduced down to subwavelength scale. Although various ultra-thin polarization controllers have been proposed on the basis of the strong anisotropy or chirality, limited by the resonant responses, most of these polarization controllers operate in narrow bandwidths [24,25,28–31]. To extend the operating bandwidths, the helical structures [32–34], multilayer structures [35,36], and cavity mechanism [37,38] have been used to design metamaterial polarization controllers. However, the fabrication difficulty of three-dimension structures is still a challenge in the optical frequency region even using the current state-of-the-art technology. Recently, the two-dimension anisotropic metasurfaces with the advantages of low-profile and high energy conversion efficiency have also been demonstrated to manipulate the polarization states of electromagnetic waves in broad frequency bandwidths [39–44]. Nevertheless, the transmission or reflective spectra of these metasurface-based polarization controllers are generally dispersive. More recently, although some progress has been made in designing nondispersive polarization controllers [17,45–47], the existing issues such as high losses and fabrication difficulty remain impediments to practical applications. Thus, there is still a growing interest in designing broadband, high-efficiency, and nondispersive polarization controllers.
In this paper, we have proposed a transmissive-type anisotropic meta-device consisting of bilayer gear-shaped metallic patterns to manipulate the polarization states of electromagnetic waves. As the proposed meta-device operates in the off-resonance region, the high losses resulting from strong resonances can be effectively avoided. The numerical and experimental results show that the designed anisotropic meta-device can achieve nondispersive cross-polarization conversion for both linearly and circularly polarized incident waves in a broadband frequency region simultaneously. At the same time, the transmission spectra of the linearly and circularly polarized incident waves are the same because of the special structure design. Furthermore, the performance is basically not affected by the incident angle. With the intriguing manifestations, the considered anisotropic meta-device can function as an excellent multi-function half-wave plate, which may find important applications in areas such as telecommunications, microwave devices, and so on.
2. Simulation and experimental results
The schematic view of the unit cell of the proposed meta-device is shown in Fig. 1(a). The unit cell is composed of bilayer gear-like metallic patterns which are mirror symmetry and connected by a metallization hole with the diameter of 0.6 mm. Obviously, the unit cell possesses significantly anisotropic feature for the linear polarization waves due to the geometric asymmetry along the u- and v-axis directions. Thus, when an electromagnetic wave passes through the proposed meta-device, if the phase difference between the u- and v-polarization components is π, the meta-device will work as a half-wave plate, which can realize cross-polarization conversion for the linearly and circularly polarized waves [1,31]. The structural parameters of the unit cell are as follows: a = 13 mm, b = 18.5 mm, c = 5 mm, r = 6.4 mm, w = 0.6 mm, t = 3 mm, and θ = 10°. The metal cladding is copper with the thickness of 0.035 mm and conductivity of σ = 5.8 × 107 S/m. The relative permittivity of the dielectric substrate is 2.65 with a loss tangent of 0.003. Figure 1(b) shows the photograph of the assembled meta-device, of which the overall effective dimension of the experimental sample is 195 × 200 × 18.5 mm3.
Numerical simulations and experiments were both carried out to study the electromagnetic behaviors of the meta-device. The simulations were accomplished via the commercial finite element software CST Microwave Studio. In simulations, the periodic boundary conditions were employed, and the electromagnetic waves propagated along z-axis with the polarization direction along the x- or y-axis. The transmission spectra were measured by using an AV 3629 network analyzer with broadband linearly and circularly polarized horn antennas in an anechoic chamber.
Figure 2 shows the simulated and experimental results of the proposed meta-device in the case of x- and y-polarization incidence. The numerical and measured linearly co-polarized and cross-polarized transmission coefficients, () and (), are plotted in Figs. 2(a) and 2(b), respectively. It is seen in Fig. 2(a) that, there are two resonances occur around 8.4 and 12.4 GHz, respectively, and the simulated co-polarization/cross-polarization transmission spectra for the x-polarization and y-polarization incident waves are the same in the whole frequency region, i.e., , . This phenomenon is attributed to that the unit cells are mirror symmetric with respect to the plane x - y = 0 (uow plane) [31]. In the off-resonance region, the cross-polarization transmission coefficients, and , are larger than 0.90 from 9.0 GHz to 11.9 GHz, whereas the co-polarization transmission coefficients, and , are less than 0.15. That is to say, when the x(y)-polarization waves pass through the meta-device, the transmitted waves are mainly transformed into y(x)-polarization waves in this region. Particularly, it is worth noting that the cross-polarization transmission spectra become flat between 9.4 GHz and 11.5 GHz without changing with the frequency, which implies a remarkably nondispersive cross-polarization transmission effect. In the experiments, the results of and in Fig. 2(b) are measured to be over about 0.90 between 9.2 GHz and 12.3 GHz, while the values of and are less than 0.23. It is obvious that the experimental results are in good qualitative agreement with the simulation data except for the slight discrepancies resulting from the fabrication imperfections and measurement errors.
The polarization conversion ratio (PCR), which is defined as , is used to describe the polarization conversion property of the meta-device. Numerical results in Fig. 2(d) show that the PCR of the proposed meta-device is over 0.95 within 8.8 ~12.0 GHz. And a PCR larger than 0.95 is obtained in the frequency range of 9.0 ~12.3 GHz experimentally [see Fig. 2(e)]. Obviously, both of the numerical and experimental results confirm that the meta-device can accomplish highly efficient cross-polarization conversion. In Figs. 2(g) and 2(h), we illustrate the differentials of cross-polarization transmission coefficients to frequencies, dT/df, which characterize the dispersion feature of the cross-polarization transmission spectra of the designed meta-device. It is of significance that the values of the differentials of cross-polarization transmission coefficients to frequencies are nearly zero from 9.4 GHz to 11.5 GHz, further indicating that the cross-polarization transmission spectra are nondispersive in this region. The aforementioned results reveal that the proposed meta-device can realize broadband, high-efficiency, and nondispersive cross-polarization conversion for the x- or y-polarized waves.
It is well known that, when an electromagnetic wave passes through a dispersive optical system, the circular polarization transmission coefficients can be obtained via the linear ones by the following equation:
Here, and are the co-polarized transmission coefficients of the right-handed circularly polarized (RCP) and left-handed circularly polarized (LCP) waves, respectively. And and stand for the cross-polarized transmission coefficients of the RCP and LCP waves, separately. However, in order to exactly reflect the polarization conversion performances of the meta-device for an actual circularly polarized wave source, we carried out further simulations and experimental measurements.For the presented meta-device, owing to , the Eq. (1) can be simplified as:
Thus, we can further obtain that, From Eqs. (3) and (4), it is found that the anisotropic meta-device will realize the same transmission for the circularly and linearly polarized waves. Hence, the numerical results for the circular polarization waves are completely the same as those in Figs. 2(a), 2(d), and 2(g). Figure 2(c) portrays the experimental circular co-polarization and cross-polarization transmission spectra, from which we can see that the measured and are larger than 0.90 in the 9.2 GHz to 12.2 GHz range, meanwhile with the and being less than 0.26. The corresponding PCR is given in Fig. 2(f). It is evident that a really high PCR (>0.95) is obtained over a wide frequency range from 9.2 GHz to 12.0 GHz, which indicates an efficient and broadband circular cross-polarization conversion effect. In Fig. 2(i), the values of the differentials of circular cross-polarization transmission coefficients to frequencies based on the experimental data are also close to zero within 9.4 GHz to 11.5 GHz, which together with the numerical results in Fig. 2(g) confirm the phenomena of broadband and nondispersive cross-polarization transmission.To characterize the circular polarization properties of the transmitted waves, we calculate the degree of circular polarization (DOCP), as shown in Fig. 3. Here, DOCP is defined as [39], where the and represent the intensities of the RCP ( and ) and LCP ( and ) components in the transmitted waves, respectively. It is seen in Fig. 3(a) that the simulated DOCP of the transmitted waves is nearly close to 1 (>0.95) in the frequency range of 8.9 ~12.0 GHz. This fact reveals that the transmitted waves remain circularly polarized with high purity, i.e., the LCP (RCP) incident waves will be perfectly transformed into RCP (LCP) waves after penetrating the meta-device. Figure 3(b) portrays the experimentally measured DOCP. Compared with the numerical results, in spite of the existing deviations, the measured values of DOCP are still sufficiently close to unity between 9.4 GHz and 11.5 GHz. The results mentioned above indicate that the intriguing meta-device can be a good candidate to function as a high-performance broadband half-wave plate.
Figure 4 shows the electromagnetic properties of the meta-device for the circularly polarized waves at oblique incidence. The incident angle is increasingly tuned by a step of 5°. It is seen in Fig. 4(a) that, in the frequency range of 9.0 ~11.6 GHz, although the values of the cross-polarization transmission spectra gradually reduce as the incident angle increases, the transmission coefficients are still larger than 0.9 even the incident angle rising up to 45°. The corresponding transmission energy conversion ratio is shown in Fig. 4(b), from which it can be found that the meta-device can still maintain a high energy conversion ratio over 0.8 between 9.0 GHz and 11.6 GHz when the incident angle is 45°. These facts indicate that this intriguing meta-device can realize efficient and broadband cross-polarization conversion independent of the incident angles for the circularly polarized waves.
Additionally, further simulations were carried out to study the effects of the structural parameters on the cross-polarization transmission spectra of the proposed meta-device, as shown in Fig. 5. It is seen in Fig. 5(a) that, as the angle θ decreases (the number of teeth of the gear-like structure will increase), the operating frequencies of the cross-polarization transmission spectrum generate significant blue shift and the operating bandwidth of the meta-device gradually increases. Moreover, the cross-polarization transmission spectrum becomes flatter in the operating frequency region. Figure 5(b) exhibits that the operating frequencies of the cross-polarization transmission spectrum significantly shift to the lower frequencies with the radius of the gear-like structure increasing, simultaneously accompanied by the increment of the cross-polarization transmission coefficients. The effect of line-width on the cross-polarization transmission property of the designed meta-device is shown in Fig. 5(c). Obviously, when the line-width of the gear-like structure increases, the operating frequencies of the cross-polarization transmission spectrum exhibit significant blue shift and the operating bandwidth of the meta-device increases. Nevertheless, the cross-polarization transmission coefficients of our design increase first and then decrease. On the basis of the aforementioned results, we can therefore obtain the best cross-polarization conversion property via the optimal structural parameters.
3. Discussions
To illustrate the efficient cross-polarization conversion effect of the meta-device, further simulations as well as experiments were performed. According to the special structure design, we can find that the two principal axis of the anisotropic meta-device are, respectively, along the directions of u- and v-axis [see Fig. 1(a)]. Figure 6 shows the results of the proposed meta-device as the linearly polarized incident waves are u- and v-polarizations. It is seen in Figs. 6(a) and 6(b) that the co-polarization transmission curves, and , are close to each other in the off-resonance frequency region from 9.0 GHz to 11.9 GHz, simultaneously accompanied by a high transmission. Figures 6(c) and 6(d) plot the simulated and experimental transmission phases of u- and v-polarizations and the relative phase difference, respectively. It is of significance that the transmission phase of the u-polarization is ahead of that of the v-polarization in the frequency range of 9.0 ~11.9 GHz, implying the u- and v-axis being the fast and slow axis, respectively. Moreover, the phase difference ∆φ between the u- and v-polarizations is roughly kept about ± π, which therefore enables the anisotropic meta-device to function as an excellent half-wave plate in a broadband frequency region.
4. Summary
In summary, we have numerically and experimentally demonstrated a kind of anisotropic meta-device, which is constructed by stacking gear-shaped geometrical structures and operates in the off-resonance frequency region. The results show that, because of the strong anisotropy, this fascinating meta-device can achieve broadband, efficient, and nondispersive cross-polarization conversion for the linearly and circularly polarized waves simultaneously. Especially, in the case of circularly polarization wave incidence, the considered meta-device can operate in a wide incident angle range meanwhile maintaining a high energy conversion ratio, which implies more application flexibility. With the excellent properties, the interesting meta-device can work as a high-performance half-wave plate, which holds great promises for manipulating the polarization states of the electromagnetic waves.
Funding
National Natural Science Foundation of China (NSFC) (61601375, 11674267); Natural Science Basic Research Plan in Shaanxi Province of China (2018JQ1036, 2017JM1009); Fundamental Research Funds for the Central Universities (3102016ZY029, 3102017jghk02004, 3102017zy015, 3102017OQD076); National Aerospace Science Foundation of China (2016ZF53061); Alfred P. Sloan Research Fellow (grant BR2013-123); KRISS (grant GP2018-0023).
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