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We propose a more efficient way to obtain much stronger polarization rotatory power by constructing a composite chiral metamaterial (CCMM) which is achieved via the combination of the cut-wire pairs (CWPs) and a purely chiral metamaterial (PCMM) composed of conjugated gammadion resonators. Owing to the strong coupling between the CWPs and PCMM, the polarization rotation in our CCMM is more gigantic than that of the PCMM. Furthermore, the CCMM proposed in this paper can function as a wide-angle 90° polarization rotator for different substrate permittivity without needing to adjust its geometric parameters. Due to the unique properties, the CCMM may greatly benefit potential applications including designing a tunable 90°-polarization rotator, microwave devices, telecommunication, and so on.
©2013 Optical Society of America
1. Introduction
Polarization rotation that refers to the ability of chiral materials to rotate the polarization state of electromagnetic waves plays an important role in optoelectronic devices, biology, as well as analytical chemistry. Recent predictions [1,2] further revealed that strong polarization rotatory power could result in negative refractive index. However, polarization rotatory power in natural materials for instance, quartz, is so weak that the natural materials showing negative refractive indices are therefore not yet identified. Chiral metamaterials (CMMs), which are a subset of metamaterials, have been recently proposed as an alternative route to realize negative refractive index [3–8]. As a matter of fact, besides negative refractive index, CMMs are also extremely appealing for accomplishing strong polarization rotation [9–14], circular dichroism [15–17], and even the prospect of a repulsive Casimir force [18,19]. Due to the outlandish electromagnetic properties, CMMs are of great current interest both for customized functionalities and for potential applications [20,21].
By definition, the unit cell of a CMM cannot be superimposed with its mirror image. Consequently, cross-coupling between the magnetic field and electric field occurs. The strength of cross-coupling is characterized by chirality. So far, some kinds of CMMs have been proposed to get strong chirality [22–27]. Despite the described advantages, there are some non-negligible drawbacks that exist in all of the aforementioned CMMs. For example, polarization rotation of CMMs at some frequencies may change at oblique incidence [22]; or a 90° polarization rotator based on CMM cannot be achieved again if we change the permittivity of the dielectric substrate without adjusting its geometric parameters. As a result, a polarization rotator that is independent of incident angles or can realize a constantly pure polarization rotation for different substrate permittivity still remains as an issue.
In this paper, we propose and experimentally characterize a composite chiral metamaterial (CCMM) that consists of cut-wire pair (CWP) and conjugated gammadion resonators. The considered CCMM exhibits considerably stronger polarization rotatory power than the pure CMM (PCMM) just composed of conjugated gammadion resonators, and it can stably function as a 90° polarization rotator regardless of the incident angles. It is worth noting that the CCMM with certain geometric parameters can perfectly achieve 90° polarization rotation for a linearly polarized incident wave, even if we change the permittivity of the dielectric substrate. This is an unprecedentedly exotic electromagnetic property that has not been obtained by all the CMMs reported previously [9–14,26–28]. Compared to the traditional 90° polarization rotators, which are realized by birefringent half-wave plates with thicknesses comparable to the operation wavelength, our design is much thinner in thickness (about λ / 33.6) due to the giant rotatory power, thereby enabling extensive applications in the low frequency region.
2. Simulations and experiments
Figure 1 shows the schematic view of the considered CCMM in this work. The unit cells are composed of bilayer conjugated gammadion and CWP resonators, which are arranged on the opposite sides of an FR-4 board. The permittivity of the FR-4 board is 4.6 with a dielectric loss tangent of 0.025. The unit cell structure possesses fourfold (C4) symmetry along the z axis. The dimensions of the unit cell are shown in the caption of Fig. 1.
Fig. 1 (a) Schematic view of a unit cell of the CCMM. (b) Photograph of the tested sample. The geometrical parameters are as follows: ax = ay = 10 mm, l1 = 9 mm, l2 = 8 mm, w1 = 1.1 mm, w2 = 0.3 mm and t = 1.5 mm. The thickness of copper is 0.035 mm.
Numerical simulations as well as experiments were performed to investigate the electromagnetic behaviors of the CCMM. The simulations were achieved by the commercial software CST Microwave Studio that implemented a finite integration technique. In the simulations, a linearly polarized electromagnetic wave was incident on the CCMM; the unit cell boundary conditions were applied to the x and y directions and open boundary conditions were applied to the z direction. In practical terms, a CCMM sample composed of 32 × 32 unit cells was fabricated. The transmission coefficients were measured by using an AV 3629 network analyzer with two horn antennas. We measured the four linear copolarization and cross-polarization transmission coefficients, , , , and . The transmission coefficients of circularly polarized waves, that is, , , , and , can be then expressed in terms of the linear measurements using the following equation [4]:
where and are the transmission coefficients of the RCP and LCP waves, respectively. Cross-coupling transmission and can be neglected because they are near zero in C4 symmetry at normal incidence. The transmission-phase difference between the RCP and LCP waves is characterized by the polarization azimuth rotation angle . The circular dichroism of the transmitted wave is revealed by the ellipticity defined as .Firstly, we examine the electromagnetic properties of the PCMM that just consists of conjugated gammadion resonators. The geometric parameters of the PCMM are shown in the caption of Fig. 1. The experimental results are in good qualitative agreement with the simulated values. Figures 2(a) and 2(b) show the simulated and experimental transmission spectrums of the PCMM. It can be seen that there are two resonances in the transmission spectrums. The first one is a narrow peak around f = 5.50 GHz and the other one corresponds to a wide band dip around f = 7.25 GHz. The transmission spectrums of the RCP and LCP waves differ significantly close to the resonances. Figures 2(c)-2(f) illustrate the results of the polarization azimuth rotation angle θ and the ellipticity η. The most interesting property — a pure polarization rotation effect — occurs at η = 0; that is, the transmitted wave remains linearly polarized but with the polarization plane rotated by an angle of θ for a linearly polarized incident wave. At 6.25 GHz, where η = 0, the polarization azimuth rotation angle θ rises to 56.8°, and the corresponding rotation angle per wavelength reaches about 1730° / λ.
Fig. 2 Simulated and experimental results for the PCMM composed of conjugated gammadion resonators. (a) and (b) Transmission spectrums of the RCP and LCP waves. (c), (d), (e), and (f) Polarization azimuth rotation angle θ and ellipticity η of the transmitted wave.
By adding CWPs around the original PCMM, a novel CCMM was fabricated, as shown in Fig. 1. Figure 3 shows the numerical and measured results of the CCMM. In Figs. 3(a) and 3(b), there are also two resonances on the curve of the transmission spectrums. However, compared with Figs. 2(a) and 2(b), the resonant frequencies of the CCMM significantly show red shifts; meanwhile, the second resonance of the CCMM has a significant contraction, and the transmission increases by about 20% at η = 0. Figures 3(c)-3(f) illustrate the results of the polarization azimuth rotation angle θ and the ellipticity η. At f = 5.69 GHz (η = 0), a pure polarization rotation with a rotation angle near 90° is obtained with our CCMM and the corresponding rotation angle per wavelength is as large as 3040° / λ, which is much larger than that of the aforementioned PCMM and the CMMs previously reported [6–12,22]. It is obvious that the polarization rotation of the PCMM is effectively improved by adding the CWPs. This fact implies that the CCMM may be a good candidate to obtain a stronger polarization rotatory power.
Fig. 3 Numerical and experimental results for the CCMM. (a) and (b) Transmission spectrums of the RCP and LCP waves. (c), (d), (e), and (f) Polarization azimuth rotation angle θ and ellipticity η of the transmitted wave.
Before this point, we just consider the case that the electromagnetic wave is normally incident on the CCMM. Here, we further illustrate the performances of the proposed CCMM at oblique incidence. Figure 4 presents the simulation and experimental polarization azimuth rotation angles θ evolving with different incident angles α. The incident angle is tuned with a step of 15°. As shown in Figs. 4(a) and 4(b), at f = 5.69 GHz (η = 0), the polarization azimuth rotation angle θ is kept approximately 90° with the incident angle α increasing from 0° to 75°. The above results reveal that our CCMM can steadily function as a 90° polarization rotator independent of the incident angles.
Fig. 4 (a) Simulated and (b) experimental polarization azimuth rotation angle θ evolve with different incident angle α. (c) and (d) Simulated and experimental transmission spectrum for the RCP and LCP waves at α = 45°. The inset is the schematic of oblique incidence, and the plane normal n forms an angle α with the wave vector k of the incident wave.
Interestingly, a peculiar phenomenon happens around f = 6.50 GHz, where the polarization azimuth rotation angle θ increases instead of converges with increasingly tuned incident angle. This phenomenon can be well interpreted by the transmission spectrum of and in Figs. 4(c) and 4(d), from where, it can be clearly seen that the third resonance occurs around f = 6.50 GHz in addition to the first two resonances around f = 5.3 GHz and f = 6.12 GHz, leading to the transmission spectrum and phases of the RCP and LCP waves significantly different.
To further exploit the interesting electromagnetic behaviors of the present CCMM, additional simulations are carried out to study the influences of permittivity on the polarization rotation of our design. In Fig. 5(a) we show the polarization azimuth rotation angle θ evolving with different dielectric substrates for the CMM in Ref. 28. It is observed that as a result of the increment of permittivity the resonant frequencies have significant red shifts. At 11.9 GHz, 11.24 GHz, 9.21 GHz, and 8.19 GHz, where a pure polarization rotation occurs, the polarization azimuth rotation angle θ are 90°, 83.5°, 60.5°, and 48.8°, respectively. Figure 5(b) shows the polarization azimuth rotation angle θ evolving with different dielectric substrates for the present CCMM. In comparing Fig. 5(b) with Fig. 5(a), although the resonant frequencies of CCMM also significantly undergo red shifts with the increment of permittivity, the two resonances move much closer to each other. It is noteworthy that the most exciting property occurs at 7.43 GHz, 6.97 GHz, 5.69 GHz, and 5.04 GHz, where the polarization azimuth rotation angles θ remain approximately 90°. This result indicates that the proposed CCMM can perfectly rotate the polarization plane of a linearly polarized incident wave by about 90° for different dielectric substrates.
Fig. 5 Polarization azimuth rotation angle θ evolves with different dielectric substrates for (a) the CMM in Ref. [28] and (b) the present CCMM. The geometric parameters of the CMM and CCMM remain always the same in the simulations. The permittivity of Taconic TLY-5, RT5880, FR-4, and Taconic RF-60 are 2.2 + 0.0009i, 2.63 + 0.0009i, 4.60 + 0.025i, and 6.15 + 0.0028i, respectively.
3. Discussions
In order to get physical insight into the mechanism of the enhanced polarization rotation and red shift of the resonances, we now examine the surface current distributions on the front and back metallic patterns for all of the CWPs, PCMM, and CCMM. Figures 6(a) -6(d) show the surface currents for the CWPs driven by a linearly polarized incident wave. Since the CWPs have mirror symmetry in the propagation direction, almost no current distributions could be observed on the top and down sides of the CWPs. The reason is that the cross-polarized conversion is forbidden by the symmetry of the structure as demonstrated previously [28].
Fig. 6 (a), (b), (c), and (d) Surface current distributions on the front and back patterns of the CWPs at f = 9.6 GHz and f = 11.5 GHz. The black (solid) and blue (dot) arrows denote the surface currents of the front and back patterns, respectively.
Figures 7(a) and 7(b) present the surface current distributions for the PCMM driven by the same incident wave. It can be seen that the currents along the H-field direction in the center of front and back gammadions form a current loop, which induces a strong magnetic moment along the E-field direction. This is the origin of the chirality of the PCMM [7,26]. In Figs. 7(c) and 7(d) we show the surface current distributions for the CCMM. Note that, due to the strong coupling effect between the CWPs and PCMM, the surface currents on the top and down sides of the CWPs are also induced. The current loops formed by the pairs of front and back layer of short wires induce magnetic moments along the same direction as the magnetic moment induced in the center of gammadions. Therefore, they induce the magnetic moments along the same direction, which add up and enhance the chirality compared to Figs. 7(a) and 7(b). In addition, the strength of chirality will also increase significantly as the two resonances become closer [26]. Comparing Fig. 3 with Fig. 2, the two resonances have different amount of red shift, which brings the two resonances closer in frequency. As a consequence, the chirality and polarization rotation are enhanced further. The aforementioned red shifts of the two resonances result from the current coupling effects between the basic current loops in the conjugated gammadions and the newly formed current loops indicated by the dash frames. The coupling mechanism here is mainly inductive coupling, which is enhanced via the introduction of CWPs [29]. In the meanwhile, these current coupling effects can also enable the CCMM to function as a 90° polarization rotator for different substrate permittivity.
Fig. 7 (a) and (b) Surface current distributions on the front and back patterns of the PCMM at f = 7.25 GHz. (c) and (d) Surface current distributions on the front and back patterns of the CCMM at f = 6.12 GHz. The black (solid) and blue (dot) arrows denote the surface currents of the front and back patterns, respectively. The thickness of the black and blue arrows approximately represents the relative current intensity.
4. Conclusions
In conclusion, we have numerically and experimentally demonstrated a CCMM which is composed of CWPs and PCMM. Due to the strong coupling between the CWPs and PCMM, the polarization rotatory power in our CCMM is considerably stronger than that of the PCMM, and the origin of the enhanced polarization rotation is physically explained by analyzing the surface current distributions of the CCMM. Thus, the idea of constructing a CCMM may be an efficient approach to obtain much stronger rotatory power. More importantly, because of the current coupling effects, the CCMM proposed in this paper can perfectly function as a wide-angle 90° polarization rotator for different substrate permittivity without altering the geometric parameters. With these intriguing properties, the CCMM are especially suitable for designing a tunable polarization rotator and can also serve for a wide range of applications in areas such as telecommunication, among others.
Acknowledgments
This work was partially supported by the National Natural Science Foundation of China (Grant Nos.50936002, 11174234, 11204241) and the Northwestern Polytechnical University Foundation for Basic Research (Grant No. JC201154).
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