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Abstract
In this study, electromagnetically induced transparency (EIT) effect in all-dielectric metamaterial for dual-band linear-to-circular (LTC) polarization conversion is demonstrated numerically and experimentally. The unit cell is composed of three ceramic blocks with different sizes. Due to the anisotropy of metamaterial and polarization dependence of subsequent EIT effects, transmission spectra for x- and y-polarized incident waves are realized to induce LTC polarization conversion. It is numerically demonstrated that a linearly polarized incident wave is transformed to a nearly perfect circularly polarized wave at around 6.24 and 6.38 GHz. The corresponding ellipticity and transmittivity are about 0.96, 0.6 and 0.94, 0.37, respectively. A metamaterial sample is fabricated and its transmission spectra are measured. The measured results are nearly equal to the simulated results. This LTC polarization convertor, with low loss and ultra thinness, may expand the application of EIT metamaterials, and it can be extended to terahertz up to optical bands. Such a design may find potential applications in microwave wave plates and metamaterial antennas, or other electromagnetic control devices.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
8dongliang@163.com
9These authors contributed equally to this paper
1. Introduction
Polarization is one of the important characteristics of electromagnetic (EM) waves. The manipulation of polarization is essential for antenna, radar communication, sensitive detection and other EM applications [1–3]. To avoid interference effects between the incident and reflected waves, great efforts have been made to design transparent polarization converters [4–10]. Metamaterials have several orders of magnitude greater polarization torsion than natural materials [11], which opens new opportunities to realize desirable polarization conversion of EM waves. In the past few years, different types of polarization converters based on anisotropic and chiral metamaterials have been reported [1–14]. In these reports, most structures are composed of metal-based elements. For example, Silveirinha et. al. designed a long metallic helices structure to realize linear-to-circular (LTC) polarization transformers [12]. Tamayama et al. achieved a LTC polarization converter by using two metallic split-ring resonators [13]. Lin et al. designed and implemented a LTC polarization converter based on a transmissive anisotropic metasurface [14]. However, structures consisting of metallic elements suffer from power handling, oxidation and corrosion problems [15,16]. Lorente-Crespo et al. experimentally demonstrated the availability of all-dielectric LTC polarization converter for avoiding these problems [16].
In this paper, we report the first microwave experimental verification of dual-band LTC polarization converter based on electromagnetically induced transparency (EIT) effect in all-dielectric metamaterial as progressive development of previous report [17]. The unit cell of proposed metamaterial is composed of three ceramic blocks with different sizes. Due to the coupling between three blocks, two dual-band EIT effect with polarization dependence are induced in transmission spectra. On this basis, a dual-band polarization conversion is shaped in our system. To make clear the physics of polarization conversion and evaluate the performance of proposed polarization convertor, electric field (E-field) distributions, polarization azimuth as well as ellipticity are calculated. In addition, metamaterial sample is fabricated and its transmission spectra are measured. Measured results are basically in agreement with the simulated results. Such all-dielectric polarization convertor may have important application in low loss polarization control.
2. Structure design and numerical verification
The unit cell of our structure is shown in Fig. 1. It consists of three dielectric blocks with different sizes. The geometrical dimensions are designed as l1 = 4 mm, l2 = 7 mm, l3 = l4 = l5 = l6 = 5 mm, s1 = 4 mm, s2 = 2 mm, s3 = 3 mm, px = py = 16 mm, and the thickness of three blocks is w = 3 mm. The relative dielectric constant and loss tangent of dielectric blocks are set as εr = 110 and tanδ = 0.0015, and corresponding values of substrate are set as εr = 1 and tanδ = 0, respectively [18]. CST Microwave Studio based on frequency domain solver is employed in our design [19]. In the simulation, the periodic boundary condition is used, and dielectric metamaterial is illuminated by a normally incident EM wave along z-axis with polarized angle αin (the angle between polarization direction of input wave and x-axis) of 45°.
It is apparent that an arbitrarily polarized wave can be regarded as a vector superposition of x- and y-polarized waves [20]. Thus, for ease of simulation, we investigated the transmission response of proposed metamaterial for x- and y-polarized incident waves. Figure 2(a) shows the corresponding transmission amplitudes of proposed metamaterial. It is indicated that the obvious anisotropy in our structure supports resonant effects with polarization dependence [17]. For x-polarized incidence, two sequential EIT effects are excited by destructive interference of scattering EM fields among blocks C, B and A. On the other hand, for y-polarized incidence, blocks A and B couple with block C, and their destructive interference induces two sequential EIT windows. By utilizing strong phase dispersion property of EIT effect, the transmission phase difference between two polarization incidences can be controlled, which provides the possibility for polarization transformation.
Fig. 2 (a) Simulated transmission amplitudes of proposed structure, where Tx and Ty denote the transmission amplitudes for x- and y-polarized incident waves, respectively. (b) Corresponding transmission phase difference.
The transmission amplitudes and phases of structure for x- and y-polarized waves are defined as Tx, Ty, φx and φy, and Δφ = φx-φy represents the transmission phase difference between x- and y-polarized waves. The transmission coefficients of our system for x- and y-polarized incident waves at a common frequency is supposed to meet the following criteria [21]:
Therefore, the LP incident wave will convert into the CP wave [22–25]. Calculated Δφ of x- and y-polarized transmissive waves is displayed in Fig. 2(b). Point A in Figs. 2(a) and 2(b) indicates that Tx = Ty≈0.61 and Δφ is about 90° at around 6.24 GHz. Point B indexes that Tx = Ty≈0.37 as well as Δφ is about 82° at around 6.38GHz. Therefore, two LTC polarization conversion with low loss are obtained in our metamaterial at around 6.24 GHz, and around 6.38 GHz. The reason for this phenomenon appearing is due to EIT effects of dielectric structure for two cross polarization waves as reported earlier [17,21], which can be demonstrated by E-field distributions of dielectric structure at transparent peaks and dips.Figure 3 shows the E-field distributions of transparent peaks and dips of proposed structure for x-polarized in Figs. 3(a)-3(e) and y-polarized in Figs. 3(f)-3(j) of incident waves. As shown in Fig. 3(a), E-field is aggregated in blocks B and C at the first transmission dip for x-polarized incidence, which means that blocks B and C directly coupling with incident wave. However, block A is hardly excited by incident wave. First transparent peak in Fig. 3(b), a violent resonance forms in block A, and block A couples strongly with block B. Due to destructive interference of scattering EM fields among blocks B, C and A, the resonances of blocks B and C are greatly suppressed (especially for block C) and the radiation loss of system is obviously decreased, thus the transmission is enhanced [17,26–29]. Second transmission dip in Fig. 3(c), the resonance of block C appears again and its intensity is larger than that of first transmission dip, which indicates that the destructive interference of scattering EM fields among three blocks are destroyed. With the increase of radiation loss, the high transmission can no longer be maintained. Figures 3(a)-3(c) clearly illustrates that block A acts as the dark mode while blocks B and C serve as the bright modes. For the second EIT window, it can be found by comparing Fig. 3(c) and Fig. 3(d) that the resonance of block A becomes weaker at the second transparent peak, while it is intensified for blocks B and C. The reason for these changes lies in the second destructive interference among three blocks. The destructive interference here is weaker than that of Fig. 3(b), which brings about a lesser EIT window. Even so, similar to the situation in Fig. 3(b), the radiation loss of system is decreased and thus the transmission is enhanced. At the last transmission dip in Fig. 3(e), the resonance of block A is significantly enhanced and its intensity is larger than that of second transmission dip. These signify the destruction of destructive interference, lead to the increase of radiation loss and the disappearance of high transmission. By analyzing the E-field distributions of the second EIT window for x-polarized incidence in Figs. 3(c)-3(e), it appears that block A acts as the bright mode, and block C serves as the dark mode. Meanwhile, block B works as the quasi-dark mode because of its variation trend of E-field distributions is consistent with block C. For y-polarized incidence, there are similar E-field distributions in dielectric structure, as shown in Figs. 3(f)-3(j). A comprehensive analysis of Figs. 3(a)-3(j) indicates that destructive interference in Fig. 3(b) is more intense. Therefore, the EIT effect in first EIT window for x-polarized incident wave is wider and deeper than another three as shown in Fig. 2(a).
Fig. 3 Ez components of structure at (a) 6.19 GHz, (b) 6.30 GHz, (c) 6.37 GHz, (d) 6.41 GHz and (e) 6.46 GHz for x-polarized wave, and Ez components of structure at (f) 6.13 GHz, (g) 6.22 GHz, (h) 6.26 GHz, (i) 6.36 GHz and (j) 6.39 GHz for y-polarized wave.
To evaluate the polarization conversion performance of proposed dielectric metamaterial, four Stokes parameters are introduced [17,21,30,31].
In our scheme, 45° LP incident wave is used, i.e., αin = 45°. According to Eq. (3), the polarization azimuth ψ and ellipticity angle χ are derived [6,17,21,31]:
where χ = 0° corresponds to LP wave, and χ = ± 45° corresponds to CP wave. Then, the ellipticity η is obtained by normalizing χ, that is:The parameters are calculated by using MATLAB, and the results are shown in Fig. 4. The ellipticity in Fig. 4(a) reaches the maximum (~0.96) at the frequency of transmission intersection A. The LP incident wave is supposed to convert to a nearly perfect CP transmitted wave at around 6.24 GHz [6,17]. It also can be found that η ≈ 0.94 and Tx = Ty ≈0.37 in Fig. 2(a) at around 6.38 GHz. However, the loss is relatively large (T<0.4) at higher frequency. Figure 4(b) displays the trend of polarization azimuth ψ in different frequency band, which indicates the angular variation between x-axis and principle axis of polarization ellipse at output port [21]. It is revealed that ψ is approximately equal around 6.24 GHz and 6.38 GHz (their values are about −44° or 136°), which means the polarization angles of transmission waves are rotated about 91° comparing to the polarization angles of incident waves. LTC polarization conversions as shown in numerical analysis originate from the EIT effect with polarization dependence in all-dielectric metamaterial.
To illustrate the physical mechanism of LTC polarization conversion, the E-field distributions of metamaterial at 6.24 GHz and 6.38 GHz for two incident polarizations are displayed in Fig. 5. Figure 5(a) clearly shows that for x-polarized incidence, E-field is mainly concentrated in dark resonator A, and it is very weak in bright resonators B and C at 6.24 GHz. This indicates that bright mode resonances are suppressed and radiation losses are greatly decreased, and thus EIT effect is excited. A similar phenomenon also appears for the case of y-polarized incidence, as shown in Fig. 5(b). Thus, the LTC polarization conversion at 6.24 GHz primarily attributes to the first EIT effects for x- and y-polarized incidences. On the other hand, similar E-field distributions also appear in blocks A, B and C at 6.38GHz, as shown in Figs. 5(c) and 5(d), which means that the LTC polarization conversion at 6.38 GHz principally results from the second EIT effects. As a consequence, the excitations of EIT effects for x- and y-polarized incident waves play key roles in the realization of LTC polarization conversions.
Fig. 5 Ez components of structure at 6.24 GHz for (a) x- and (b) y-polarized wave, and Ez components of structure at 6.38 GHz for (c) x- and (d) y-polarized wave.
3. Experimentation and discussion
In order to verify the LTC polarization conversion validity of proposed all-dielectric metamaterial, 2 unit cells sample was fabricated and placed in a rectangular waveguide, as shown in Fig. 6. The ceramic blocks are made of ZrO2 with εr = 110 and tanδ = 0.0015. A microwave vector network analyzer (Agilent 8510B) was used to measure the magnitudes and phases of transmission coefficients for x- and y-polarized incident waves. Measured results are shown in Fig. 7.
Fig. 7 Measured (a) transmission magnitudes and (b) phase differences of sample for x- and y-polarized incident waves.
As shown in Fig. 7, it is obvious that there are two sequential EIT windows for x- and y-polarized incident waves respectively, and the EIT windows in both directions overlap with each other. Moreover, the magnitude of transmission intersection A' is about 0.69 at around 6.25 GHz, and corresponding transmission phase difference is about 80°. Thus, a low loss LTC polarization conversion is realized. For the second transmission intersection B', the transmission magnitude and corresponding transmission phase difference are about 0.38 and 80° at around 6.37 GHz. Therefore, by using Mie resonance in all-dielectric metamaterial, we experimentally demonstrated a dual-band LTC polarization converter based on two EIT effects in mutually perpendicular directions.
In the following, we analyze the cause of errors between measured and simulated results. First, in simulation, the size of two periodic structures is 32.0mm × 16.0mm, while in measurement, the practical size of waveguide is 34.8 mm × 15.8 mm. Secondly, due to tolerance in cutting ceramic blocks, differences between measured and simulated results occur. Furthermore, the structures in waveguide are put by man-made, then it is no doubt when six blocks of two periodic structures are put together, there must exist some unavoidable position errors compared to the simulation in perfect condition. Thirdly, dielectric constant and loss tangent of the ceramic may show slight difference compared with that of simulation circumstances, which further increases the errors. All of these errors may result in the difference between simulation and measurement data. Nevertheless, the test results are essentially consistent with the simulation results.
In addition, the electrical size α (α = w/λ, where w is thickness of metamaterial and λ is operating wavelength) of proposed structure (~0.06) is smaller than those in references [22] (~0.11) and [32] (~0.2), which means that our structure is more miniaturization, and it is easier to integrate with existing microwave circuits.
4. Conclusion
In summary, by utilizing the strong phase dispersion and high transmission of EIT effect and anisotropy of structure, a dual-band LTC polarization convertor is realized in dielectric metamaterial. The unit cell of our structure consists of three ceramic blocks with different sizes. Numerical simulations have demonstrated that EIT effects for proposed metamaterial result from the destructive interferences of coupling fields between different blocks. Owing to the dual-band EIT effect with polarization dependence, the dual-band polarization conversion is realized in our structure. On the basis of Stokes parameters, the polarization azimuth and ellipticity have been calculated to evaluate the performance of polarization convertor. The polarization azimuth and ellipticity are shown about 44°, 0.96 at around 6.24 GHz and 44°, 0.94 at around 6.38 GHz, respectively. In addition, we have fabricated and measured the sample, and the results are basically in agreement with the simulated results. The function of dual-band polarization conversion is achieved in proposed metamaterial. Finally, we have discussed the source of error. The analysis results show that the errors mainly result from the number of unit cell, the size difference between waveguide and two unit cells, dimension and position errors of dielectric blocks. This low loss and ultra thin LTC polarization convertor is solely composed of all-dielectric material rather than metallic pattern. Thus, application range of EIT metamaterials can be extended to terahertz upto optical bands, which has many potential applications in polarization-controlled devices, such as optical isolators, wave plates and metamaterial antennas.
Funding
National Natural Science Foundation of China (NSFC) (61501275); China Postdoctoral Science Special Foundation (2018T110274); China Postdoctoral Science Foundation (CPSF) (2017M611357); Science Foundation Project of Heilongjiang Province of China (QC2015073); Heilongjiang Provincial Postdoctoral Science Foundation (LBH-Z17045); Young Creative Talents Training Plan of General Universities of Heilongjiang Province of China (UNPYSCT-2017152); Technology Bureau of Qiqihar City of Heilongjiang Province of China (GYGG-201511).
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