Polarization manipulation based on electromagnetically induced transparency-like (EIT-like) effect Lei Zhu,1,2 Fan-Yi Meng,1,3 Liang Dong,2 Jia-Hui Fu,1 Fang Zhang,1 and Qun Wu1,* 2
1 Department of Microwave Engineering, Harbin Institute of Technology, Harbin, 150001, China Communication and Electronics Engineering Institute, Qiqihar University, Qiqihar, 161006, China 3 [email protected] * [email protected]
Abstract: We proposed, designed and fabricated a high transparency of metasurface-based polarization controller at microwave frequencies, which consists of orthogonal two pairs of cut wires. The high transmission and the strong dispersion properties governed by electromagnetically induced transparency-like (EIT-like) effects for both incident polarizations make our device efficiently manipulating the polarization of EM waves. In particular, the proposed polarization device is ultrathin (~0.017λ), as opposed to bulky polarization devices. Microwave experiments are performed to successfully demonstrate our ideas, and measured results are in reasonable agreement with numerical simulations. ©2013 Optical Society of America OCIS codes: (160.3918) Metamaterials; (350.4010) Microwaves; (260.2110) Electromagnetic optics.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
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#198925 - $15.00 USD Received 4 Oct 2013; revised 7 Dec 2013; accepted 10 Dec 2013; published 18 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032099 | OPTICS EXPRESS 32099
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#198925 - $15.00 USD Received 4 Oct 2013; revised 7 Dec 2013; accepted 10 Dec 2013; published 18 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032099 | OPTICS EXPRESS 32100
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1. Introduction Manipulating the polarization state of electromagnetic (EM) waves is of great importance for many practical applications [1]. Over the last few decades, various methods for controlling the polarization of EM waves have been proposed, such as Faraday effect [2], twisted nematic liquid crystals, birefringence effects, etc [3, 4]. These methods generally lead to thicknesses of devices comparable to the operation wavelength, which is extremely inconvenient for low frequency applications [5, 6]. Recently, metamaterials as artificial composite microstructures have received increasing attention because their EM properties can be controlled at will by adjusting geometry parameters for structure cells, which opens a new way to manipulate the polarization of EM waves [6]. As a consequence, a large amount of metamaterial-based polarization devices have been proposed [1, 7–24]. Although the thicknesses of these devices are ultra-thin compared with the operation wavelength, the systems are typically not high transparent for EM waves, which results in that the energy losses are very large [5, 6]. Sun et. al. designed an anisotropic transparency metamaterial to manipulate the polarization of EM waves in transmission geometry based on the tunneling effect and extraordinary optical transmission (EOT) [6]. This system does not suffer large energy losses due to almost perfect transmission. However, this transparent polarization control requires three layers of metasurfaces. Single-layer frequency selective surface (FSS) has also been proposed for polarization conversion [15,18–20]. Polarization converter based on plasmonic metamaterial in visible light has also been recently reported [24]. However, few reports can be found for polarization converters or rotators based on electromagnetically induced transparency-like (EIT-like) metamaterials [25–37]. Very recently, metamaterials are engineered to mimic some quantum phenomena, such as EIT effect and Fano resonance [25–37]. A Fano resonance can be regarded as the classical analogue of EIT phenomenon under certain conditions that are the small frequency detuning and different resonance linewidth of two coupled resonance modes. Generally, when the coupling between two resonance modes occurs, the destructive interference can suppress the resonance absorption and thus lead to the classical transparency effect [35,36]. This transparency effect usually accompanies with the strong dispersion, which brings many important applications in slow light, sensor, polarization control, nonlinear and switching areas [14, 31–33]. Therefore, this paper proposes an EIT-like metasurface to manipulate the polarization of EM waves. In contrast to Ref [14], where the polarization conversion results from the EITlike effect in single one polarization direction and this system is not high transparency (T = 40%), we employ EIT-like effects in two orthogonal polarizations to manipulate polarization of EM waves. The proposed metasurface’s thickness is much thinner than wavelength (~0.017λ), and our device is high transparency for EM waves. Another prominent advantage of the proposed scheme is that our structure is more convenient for fabrication, and the high transparent polarization conversion can be easily achieved by just adjusting the lengths of the four wires, which would be particular important for structures realized for the THz regime. 2. Metasurface design The basic building block of the proposed EIT-like metasurface is shown in Fig. 1(a), where the unit cell of structure is composed of orthogonal two pairs of cut wires. The cut wires are constructed from the copper with a thickness of 35 μm, and are fabricated on substrate with a relative dielectric constant of 3.2, a loss tangent of 0.001 and a thickness of 0.5mm. The
#198925 - $15.00 USD Received 4 Oct 2013; revised 7 Dec 2013; accepted 10 Dec 2013; published 18 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032099 | OPTICS EXPRESS 32101
geometry parameters of unit cell displayed in Fig. 1 are l1 = 14.9 mm, l2 = 10.8 mm, l3 = 12.3 mm, and l4 = 9 mm, respectively. The period of arrays for cut wires is 20mm. Figure 1(b) shows the two-dimensional metasurface sample which consists of 15 × 15 unit cells with a total square area of 300mm × 300mm. The resonant transmission behavior of the metasurface sample was measured by employing the free-space test method. Our experiments were carried out in an anechoic chamber using two standard horn antennas operating at the frequency band of 7~12 GHz with the sample placed in between and an Agilent 8510B vector network analyzer (VNA). For each measurement, a reference measurement was performed to minimize influences of noise and inference in the absence of the sample. The transmission spectra and the associated resonant modes are simulated using the commercial software of CST Microwave Studio based on the finite-integration time-domain (FITD) method [35].
Fig. 1. (a) Unit cell configuration of the EIT-like metasurface (b) Photograph of the fabricated sample
From Fig. 1, it can be seen that the wires I, II parallel to the y-axis and the wires III, IV parallel to the x-axis. Moreover, the lengths of wires I and II (wires III and IV) along y (x) direction are different. For y-polarized incident wave, the alone wire I strongly couples with the incident waves and produces a low quality (Q) factor resonance (Q~2), and thus it is designated as the bright element. While the alone wire II weakly couples with the incident waves and its resonance has a relatively high Q factor (Q~4), and thus it is considered as the quasidark element. When the wires I and II are assembled the structure as shown in Fig. 1(a), a pronounced transparency window appears in transmission spectrum [Fig. 2(a)] due to the destructive interference between scattered EM fields of wires I and II [27–30]. In this case, the coupling between the wires mainly depends on the length difference between the wires I and II and slightly depends on the separation between the wires [26–29,31,32,34]. In addition, the transmission behaviors of the designed metasurface for y-polarization incident light are almost not affected by dropping the wire-pair III, IV because the wires III and IV are normal to the wires I and II (the correspondingly simulated results are not given). We note that the resonant behaviors of wires III and IV under x-polarized incident wave are similar to those of wires I and II for y-polarized incident wave. Hence, the EIT-like effect can also be excited for x-polarization incident wave using the destructive interference between scattering EM fields of wires III and IV [Fig. 2(b)]. In this case, the wire III is regarded as the bright element, and the wire IV is designated as the quasi-dark element. It is exactly because the wires I and II are perpendicular to the wires III and IV, we can obtain two independent transparency windows with high transmittances for x- and y-polarization incident waves, respectively. By judiciously adjusting the sizes of each wire pair, we can find a frequency where the transmission window for x-polarization incidence coincides with the transparency window for y-polarization incidence. If the transmission coefficients of our
#198925 - $15.00 USD Received 4 Oct 2013; revised 7 Dec 2013; accepted 10 Dec 2013; published 18 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032099 | OPTICS EXPRESS 32102
system for two incident polarizations at a common frequency meeting the following criteria [15]: tx
2
2
= ty ,
arg(t x ) − arg(t y ) = 90.
(1)
(2)
then the linear-to-circular polarization conversion can be realized, where t x and t y are complex transmission coefficients of our metasurface for x- and y-polarization input waves, respectively. It needs to be especially pointed out that the lengths of the wires I and II (the wires III and IV) are set to be different for controlling the coupling between wires I and II (wires III and IV), and thus manipulating the transmission amplitude and resonance width of the transparency window for y-polarization (x-polarization) incidence. The sizes for each wire pair are set to be different for obtaining two transparency windows with different center frequencies for two incident polarizations, and thus achieving the desired phase difference. In the following, we demonstrate that a high transparency and ultra-thin polarization manipulation originates from EIT-like effects for two incident polarizations. 3. The EIT-like effect and electromagnetically induced polarization manipulation
We start our analysis by discussing resonance behaviors of metasurface for y-polarized incident wave. The transmission response of the metasurface to normally incident linearly ypolarized wave is simulated and plotted in Fig. 2(a). Due to the different length of wires I and II along y-axis, the coupling between wires is introduced, which results in a high transparency of transmission window appearing at the frequency of 8.49 GHz with the maximum amplitude of 0.98. The reason for this transparency window emergence is attributed to the fact that the bright element is excited by two different pathways: one is the direct excitation by the incident wave, and the other is the indirect excitation by the EM fields for the quasidark element [35,36]. The destructive interference between both pathways greatly suppresses the excitation of the bright element and thereafter induces the classical EIT-like phenomenon [35, 36]. To illustrate this phenomenon, the distribution of E-field for the metasurface at the EITlike peak frequency is shown in Fig. 3(a). It can be seen that the anti-symmetric E-field appears on the wires I and II, which leads to the destructive interference between scattering EM fields of wires I and II and thus induces the classical EIT-like effect [36, 38]. In this case, the EM energy is mainly trapped in high Q factor of the quasidark element [36, 38]. It can also be observed from Fig. 3(a) that the E-field on wires III and IV is extremely weak, which means that the wires III and IV are almost not excited by y-polarized incident wave. This interesting phenomenon can also be well interpreted using the method of plasmon hybridization [39, 40]. When the lengths of wires I and II are different, the coupling between wires leads to the formation of two plasmon modes: the antisymmetric and the symmetric plasmon modes. The antisymmetric and symmetric modes correspond to the currents on wires I and II, flowing in the opposite direction and in the same direction, respectively [38], as shown in Figs. 3(b) and 3(c). The frequency difference of two modes can be understood as follows: for the symmetric (antisymmetric) mode, the charges at the ends of two wires repel (attract) each other. It leads to an increased (reduced) restoring force of the charge oscillation inside the wires and thus results in a higher (lower) resonant frequency [38]. Specially, the spectral overlap of the antisymmetric mode and the symmetric mode induces a pronounced transparency window [41]. Worth noting that, in above process, the coupling between the wires mainly depends on the length difference between wires I and II and slightly depends on the separation distance between the wires [26–29,31,32,34]. As a consequence, by adjusting
#198925 - $15.00 USD Received 4 Oct 2013; revised 7 Dec 2013; accepted 10 Dec 2013; published 18 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032099 | OPTICS EXPRESS 32103
the length difference between wires I and II, we can manipulate the transmission amplitude and resonance width of the transparency window for y-polarization incidence. The spectral behavior of the transparent window can be fine-tuned by adjusting the separation distance between the wires. The above analysis is helpful in understanding the physical mechanism of EIT-like effect, which allows us freely and independently to manipulate the transparent window. The linear polarization is rotated to the x-axis and the complex transmission coefficient t x can be obtained. Similar to the case of y-polarized incidence, a high transparency of transmission window also appears in spectrum for x-polarization incident wave [Fig. 2(b)]. In this case, the wire III is considered as the bright element, and the wire IV is regarded as the quasi-dark element. The excited principle of transparency window for x-polarized incident wave is similar to that of y-polarized incident wave [Figs. 3(d)–3(f)]. Therefore, we don’t repeat it again.
Fig. 2. Transmission amplitudes and phases of the metasurface for (a) y-polarization incident wave and (b) x-polarization incident wave. The pink (blue) parts indicate the areas of the phase advance (phase retard). The elements enclosed by dashed line in the inset of panel (a)/(b) can control the excitation of EIT-like effect for y-/x- polarization incident wave.
#198925 - $15.00 USD Received 4 Oct 2013; revised 7 Dec 2013; accepted 10 Dec 2013; published 18 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032099 | OPTICS EXPRESS 32104
Max
Max
Ey
Ey
(b)
-Max (a) Max
Ex -Max
Ey
(d)
(c)
Ex
Ex (e)
0 Max
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Fig. 3. (a) The E-field plots of the designed metasurface at a frequency of 8.49 GHz for ypolarization incident wave, as indicated by the blue circular in Fig. 2(a). Surface current distributions of the designed metasurface at the frequencies of (b) 7.6 GHz and (c) 9.7 GHz for y-polarization incident wave, as shown two transmission dips in Fig. 2(a). (d) The E-field plots of the designed metasurface at a frequency of 9.65 GHz for x-polarization incident wave, as indicated by the blue circular in Fig. 2(b). Surface current distributions of the designed metasurface at the frequencies of (e) 8.9 GHz and (f) 10.8 GHz for x-polarization incident wave, as shown two transmission dips in Fig. 2(b).
Because the wires I and II are normal to the wires III and IV, two independent EIT-like windows for x- and y-polarized incident waves can be obtained, respectively. By judiciously adjusting the sizes of each wire pair, we can find a frequency where the transmission window for x-polarization incidence coincides with the transparency window for y-polarization incidence. The simulated transmission amplitudes and transmission phase differences through the optimized system are displayed in Fig. 4 as solid lines for two incident polarizations. It can be seen that the EIT-like metasurface is high transparency (T~0.7) for both incident polarizations at the frequency of 9.2 GHz. Moreover, the transmission phase difference between two incident polarizations is about 90° . Such a big phase difference originates from the fact that the EIT-like effect accompanies with the strong phase dispersion [35, 36, 42]. As shown in Figs. 2(a) and 2(b), in transparency window, the phase quickly varies with the frequency. Moreover, the left (right) parts of the transparency peak correspond to areas of phase advance (retard), as shown the pink (blue) areas in Figs. 2(a) and 2(b). As a result, to obtain the 90° phase difference, the center frequencies of two transparency windows for two incident polarizations must be different [Fig. 2]. Accordingly, the sizes of each wire pair must also be different. By properly selecting the sizes of each wire pair, we can make that the left parts of transmission window for x-polarized incidence coincide with the right parts of transparency window for y-polarized incidence [see Fig. 2], and thus obtain the desired phase difference [Fig. 4(b)]. To illustrate the physical mechanism of linear-to-circular polarization conversion, the surface currents of metasurface at 9.2 GHz for two incident polarizations are shown in Figs. 5(a) and 5(b). Obviously, the antiparallel currents distribute on each pair of wires, which means that the EIT-like effects are effectively excited along two orthogonal directions. In other words, the excitations of EIT-like effects for two incident polarizations play key roles in the process of linear-to-circular polarization conversion.
#198925 - $15.00 USD Received 4 Oct 2013; revised 7 Dec 2013; accepted 10 Dec 2013; published 18 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032099 | OPTICS EXPRESS 32105
Sim-y Sim-x
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The measured transmission amplitudes and transmission phase differences are also displayed as dash lines in Fig. 4 for two incident polarizations. We note that the general variational trace of measurement results follows closely to that of simulation results. Especially, measurement results also demonstrate that the high transparency transmission is realized for both incident polarizations at about 9.2 GHz with phase difference of 90° . This means that the high transparence of linear-to-circular polarization conversion can be achieved in our system. 150
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Fig. 4. Simulated (solid curves) and measured (dashed curves) (a) transmission amplitudes and (b) transmission phase differences for two incident polarizations. The blue dotted lines indicate the spectral location of the polarization conversion occurrence.
Fig. 5. Surface current distributions of the designed metasurface at a frequency of 9.2 GHz for (a) y-polarization incident wave and (b) x-polarization incident wave.
Worth noting that the thickness of our system is only 0.017λ, while the thickness of material of ordinary polarization modulation is comparative to wavelength [43]. Moreover, our system can realize highly transparent polarization conversion due to low loss nature of EIT-like effect. In the connected case, another different configuration has been studied by Sun et al., where although the metamaterial can also achieve the transparency polarization conversion [6], its thickness is about 4 times thicker than that of our system. Moreover, our polarization conversion is based on the EIT-like effects, and its physical mechanism is different from the case of the literature [6]. Our design is essentially similar to the FSS polarizer. However, the introduction of the EIT concept provides a new method for construction of the linear-to-circular polarization converter. Specially, this method provides more conveniences for controlling the phase behavior of device compared with the cases of Refs [18–23]. In other words, by adjusting the asymmetric degree of the metasurface in each direction, we can more easily obtain the desired phase difference and thus achieve the circular polarization state in a more simple way. Contrasting with the schemes in Refs [21–23], our proposed structure is more convenient for fabrication and the high transparent polarization conversion can be easily achieved by just adjusting the lengths of the four wires, which would
#198925 - $15.00 USD Received 4 Oct 2013; revised 7 Dec 2013; accepted 10 Dec 2013; published 18 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032099 | OPTICS EXPRESS 32106
be particular important for structures realized for the THz regime, in which many important functionalities, such as polarization conversion, beam steering and wave front shaping, have been extremely challenging to accomplish. Although the structures proposed by Refs [21,22]. are ultrathin and can also realize the polarization conversions, their structures are complex, involving to the alignments of circular and double-layered structures, which brings fabrication challenges for THz frequencies. Once the fabrication tolerance becomes large, the device performance is substantially degraded, and even the device can’t achieve the polarization conversion. Moreover, our device achieves the polarization conversion in transmission geometry, which avoids the interference problem of structure based on reflection geometry in Ref [23]. To further verify the polarization property of EM waves transmitted through the metasurface, the axial ratio (AR) is calculated [21], and is shown in Fig. 6(a). Here, the AR is defined as the ratio of the minor to major axes of the polarization ellipse [15]. It can be observed that the simulated AR value is greater than 0.9 from 9.09 to 9.38 GHz and a measured AR value of over 0.9 from 9.09 to 9.41 GHz. The measured results are in excellent agreement with the simulated results. The circular polarization characteristic of the designed metasurface is also investigated for oblique incidence. Figure 6(b) shows the simulated AR of the polarization device with different incident angle θ . We notice that when the incident angle varies from 0° to 20° , the center frequency where the maximum of AR occurs shifts. However, the value of AR is still more than 0.9 from 9.27~9.33 GHz when the incidence angle varies between 0° and 20° . 1.0
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9.7
Fig. 6. (a) Measured and simulated AR results, (b) Simulated AR results with different incidence angle θ . The incident angle θ is the angle separation between a linearly polarized input wave and the z-axis.
The transmission loss of the designed metasurface with different incident angle θ is also computed and displayed in Fig. 7. The transmission loss value can be obtained directly from the simulated S parameters as [44]: 2
s loss (dB / mm) = −10 log10 ( 21 2 ) / d slab . (3) 1 − s11 It is found that the transmission loss becomes large when the incident angle varies from 0° to 20° However, the maximum value of transmission loss is about 1.3 dB/mm from
9.27~9.33 GHz when the incidence angle varies between 0° and 20° (in this case, the AR value is still more than 0.9). Because the thickness of our designed metasurface is ultrathin (~0.017λ), its loss is very low (~0.67 dB).
#198925 - $15.00 USD Received 4 Oct 2013; revised 7 Dec 2013; accepted 10 Dec 2013; published 18 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032099 | OPTICS EXPRESS 32107
Transmission loss
10 8
0o 10o 20o
6 4 2 0 9.15 9.20 9.25 9.30 9.35 9.40 9.45 Frequency (GHz)
Fig. 7. Transmission loss of metasurface for different incident angle θ . The incident angle θ is the angle separation between a linearly polarized input wave and the z-axis.
To better quantification of the polarization state for the transmitted wave, Stokes parameters [1, 15] are introduced as: 2
2
2
2
S0 = t x cos α in + t y sin α in , S1 = t x cos α in − t y sin α in , S 2 = 2 t x cos α in t y sin α in cos ϕdiff ,
(4)
S3 = 2 t x cos α in t y sin α in sin ϕdiff ,
where the α in is the angle separation between a linearly polarized wave at the input port and the x-axis (i.e. the polarization angle at the input port), and the phase difference ϕ diff equals to arg(t y ) − arg(t x ) . According to formula (4), the polarization azimuth α out and the ellipticity angle χ are derived as: tan 2α out = sin 2 χ =
S2 , S1
S3 , S0
(5) (6)
Where χ = 0 corresponds to linear polarized wave whereas χ = ±45° corresponds to circular polarization wave. The α out is the angle separation between the principle axis of polarization ellipse at the output port and the x-axis (i.e. the polarization angle at the output port). The angles associated with Stoke’s parameters are plotted in Fig. 8. The incident angle θ is the angle separation between a linearly polarized input wave and the z-axis, which is the same with angle θ in Figs. 6 and 7. The θ = 0 indicates the normal incidence. According to [Eqs. (4)–(6)], when α in = 45° , the corresponding polarization azimuth and ellipticity angles are computed as α out = 33.6° and χ = −43.9° at 9.2 GHz. Since sin 2 χ = −0.999 , this indicates that the linearly polarized incident wave is highefficiently converted to circularly polarized wave, as shown the green solid line in Fig. 9(a). Our system can also realize the linear-to-elliptical polarization conversion, as revealed in
#198925 - $15.00 USD Received 4 Oct 2013; revised 7 Dec 2013; accepted 10 Dec 2013; published 18 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032099 | OPTICS EXPRESS 32108
Fig. 9(b). When α in = 60° , α out = 178.2° and χ = −29.7° . This means that the linearly polarized wave becomes an elliptically polarized wave with the principal axis azimuth of 178.2° and the ellipticity of sin 2 χ = −0.861 . Similarly, according to the measured transmission amplitudes and phases of the fabricated sample for two incident polarizations as well as [Eqs. (4)–(6)], we can obtain the polarization azimuth of α out and the ellipticity of sin 2 χ . Hence, we can confirm the angle separation between the principal axis of the polarization ellipse and the x-axis, as well as the circular polarization degree. Using these two parameters, we can plot the measured polarization ellipse at the output port, as shown the dots in Fig. 9. Obviously, the experiment and simulation results are quite good agreement. As a consequence, our structure can realize the different polarization conversion at the different polarization incident angle.
k θ
E
α in
H
Fig. 8. The angles associated with the stoke’s parameters.
αin = 45
αin = 60
sim mea
1.0 0.5
αout = 33.6
0.5
0.0
0.0
-0.5
-0.5
-1.0
sim mea
1.0
αout = 178 .2
-1.0 -1.0 -0.5
0.0
0.5
1.0
-1.0 -0.5
0.0
0.5
1.0
Fig. 9. (a) The simulated (solid curves) and measured (dots) polarization ellipses at 9.2 GHz for a 45° linearly polarized input wave, representing 99.9% circular polarization (linear-tocircular conversion), and (b) the simulated (solid curves) and measured (dots) polarization ellipses at 9.2 GHz for a 60° linearly polarized wave, representing 86.1% circular polarization (linear-to-elliptical conversion). The axes represent the magnitude of the normalized electric field along the x and y axes after passing through the metasurface. The top panels indicate the polarization states at the input port. The bottom panels indicate the polarization states at the output port.
#198925 - $15.00 USD Received 4 Oct 2013; revised 7 Dec 2013; accepted 10 Dec 2013; published 18 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032099 | OPTICS EXPRESS 32109
4. Conclusion
In this paper, we have achieved the polarization control of EM waves based on the EIT-like metasurface. It has numerically and experimentally demonstrated that the high transparency of polarization manipulations (linear-to-circular and linear-to-elliptical polarization conversions) can be realized in the designed system formed by orthogonal two pairs of cut wires. The high transmissions and the significant phase difference governed by EIT-like effects for two incident polarizations make the proposed structure being an excellent polarization controller. Moreover, our structure is more convenient for fabrication, and the high transparent polarization conversion can be easily achieved by just adjusting the lengths of the four wires, which would be particular important for structures realized for the THz regime. In addition, the thickness of the proposed polarization device is much thinner than wavelength (0.017λ), as opposed to bulky polarization devices. With the presented results, many applications can be envisaged, such as miniaturized and light weight quarter wave plates. The proposed approach offers a new way for manipulating the polarization of EM waves. By scaling down the designed metasurface, our scheme could also be utilized at other frequency regimes, such as millimeter wave, and terahertz. Acknowledgments
This work is supported by the National Natural Science Foundation of China (Grant Nos. 61371044 and 60971064), and the Education Department of Heilongjiang Province (Grant No. 12531775).
#198925 - $15.00 USD Received 4 Oct 2013; revised 7 Dec 2013; accepted 10 Dec 2013; published 18 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032099 | OPTICS EXPRESS 32110
1 Department of Microwave Engineering, Harbin Institute of Technology, Harbin, 150001, China Communication and Electronics Engineering Institute, Qiqihar University, Qiqihar, 161006, China 3 [email protected] * [email protected]
Abstract: We proposed, designed and fabricated a high transparency of metasurface-based polarization controller at microwave frequencies, which consists of orthogonal two pairs of cut wires. The high transmission and the strong dispersion properties governed by electromagnetically induced transparency-like (EIT-like) effects for both incident polarizations make our device efficiently manipulating the polarization of EM waves. In particular, the proposed polarization device is ultrathin (~0.017λ), as opposed to bulky polarization devices. Microwave experiments are performed to successfully demonstrate our ideas, and measured results are in reasonable agreement with numerical simulations. ©2013 Optical Society of America OCIS codes: (160.3918) Metamaterials; (350.4010) Microwaves; (260.2110) Electromagnetic optics.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
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#198925 - $15.00 USD Received 4 Oct 2013; revised 7 Dec 2013; accepted 10 Dec 2013; published 18 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032099 | OPTICS EXPRESS 32099
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#198925 - $15.00 USD Received 4 Oct 2013; revised 7 Dec 2013; accepted 10 Dec 2013; published 18 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032099 | OPTICS EXPRESS 32100
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1. Introduction Manipulating the polarization state of electromagnetic (EM) waves is of great importance for many practical applications [1]. Over the last few decades, various methods for controlling the polarization of EM waves have been proposed, such as Faraday effect [2], twisted nematic liquid crystals, birefringence effects, etc [3, 4]. These methods generally lead to thicknesses of devices comparable to the operation wavelength, which is extremely inconvenient for low frequency applications [5, 6]. Recently, metamaterials as artificial composite microstructures have received increasing attention because their EM properties can be controlled at will by adjusting geometry parameters for structure cells, which opens a new way to manipulate the polarization of EM waves [6]. As a consequence, a large amount of metamaterial-based polarization devices have been proposed [1, 7–24]. Although the thicknesses of these devices are ultra-thin compared with the operation wavelength, the systems are typically not high transparent for EM waves, which results in that the energy losses are very large [5, 6]. Sun et. al. designed an anisotropic transparency metamaterial to manipulate the polarization of EM waves in transmission geometry based on the tunneling effect and extraordinary optical transmission (EOT) [6]. This system does not suffer large energy losses due to almost perfect transmission. However, this transparent polarization control requires three layers of metasurfaces. Single-layer frequency selective surface (FSS) has also been proposed for polarization conversion [15,18–20]. Polarization converter based on plasmonic metamaterial in visible light has also been recently reported [24]. However, few reports can be found for polarization converters or rotators based on electromagnetically induced transparency-like (EIT-like) metamaterials [25–37]. Very recently, metamaterials are engineered to mimic some quantum phenomena, such as EIT effect and Fano resonance [25–37]. A Fano resonance can be regarded as the classical analogue of EIT phenomenon under certain conditions that are the small frequency detuning and different resonance linewidth of two coupled resonance modes. Generally, when the coupling between two resonance modes occurs, the destructive interference can suppress the resonance absorption and thus lead to the classical transparency effect [35,36]. This transparency effect usually accompanies with the strong dispersion, which brings many important applications in slow light, sensor, polarization control, nonlinear and switching areas [14, 31–33]. Therefore, this paper proposes an EIT-like metasurface to manipulate the polarization of EM waves. In contrast to Ref [14], where the polarization conversion results from the EITlike effect in single one polarization direction and this system is not high transparency (T = 40%), we employ EIT-like effects in two orthogonal polarizations to manipulate polarization of EM waves. The proposed metasurface’s thickness is much thinner than wavelength (~0.017λ), and our device is high transparency for EM waves. Another prominent advantage of the proposed scheme is that our structure is more convenient for fabrication, and the high transparent polarization conversion can be easily achieved by just adjusting the lengths of the four wires, which would be particular important for structures realized for the THz regime. 2. Metasurface design The basic building block of the proposed EIT-like metasurface is shown in Fig. 1(a), where the unit cell of structure is composed of orthogonal two pairs of cut wires. The cut wires are constructed from the copper with a thickness of 35 μm, and are fabricated on substrate with a relative dielectric constant of 3.2, a loss tangent of 0.001 and a thickness of 0.5mm. The
#198925 - $15.00 USD Received 4 Oct 2013; revised 7 Dec 2013; accepted 10 Dec 2013; published 18 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032099 | OPTICS EXPRESS 32101
geometry parameters of unit cell displayed in Fig. 1 are l1 = 14.9 mm, l2 = 10.8 mm, l3 = 12.3 mm, and l4 = 9 mm, respectively. The period of arrays for cut wires is 20mm. Figure 1(b) shows the two-dimensional metasurface sample which consists of 15 × 15 unit cells with a total square area of 300mm × 300mm. The resonant transmission behavior of the metasurface sample was measured by employing the free-space test method. Our experiments were carried out in an anechoic chamber using two standard horn antennas operating at the frequency band of 7~12 GHz with the sample placed in between and an Agilent 8510B vector network analyzer (VNA). For each measurement, a reference measurement was performed to minimize influences of noise and inference in the absence of the sample. The transmission spectra and the associated resonant modes are simulated using the commercial software of CST Microwave Studio based on the finite-integration time-domain (FITD) method [35].
Fig. 1. (a) Unit cell configuration of the EIT-like metasurface (b) Photograph of the fabricated sample
From Fig. 1, it can be seen that the wires I, II parallel to the y-axis and the wires III, IV parallel to the x-axis. Moreover, the lengths of wires I and II (wires III and IV) along y (x) direction are different. For y-polarized incident wave, the alone wire I strongly couples with the incident waves and produces a low quality (Q) factor resonance (Q~2), and thus it is designated as the bright element. While the alone wire II weakly couples with the incident waves and its resonance has a relatively high Q factor (Q~4), and thus it is considered as the quasidark element. When the wires I and II are assembled the structure as shown in Fig. 1(a), a pronounced transparency window appears in transmission spectrum [Fig. 2(a)] due to the destructive interference between scattered EM fields of wires I and II [27–30]. In this case, the coupling between the wires mainly depends on the length difference between the wires I and II and slightly depends on the separation between the wires [26–29,31,32,34]. In addition, the transmission behaviors of the designed metasurface for y-polarization incident light are almost not affected by dropping the wire-pair III, IV because the wires III and IV are normal to the wires I and II (the correspondingly simulated results are not given). We note that the resonant behaviors of wires III and IV under x-polarized incident wave are similar to those of wires I and II for y-polarized incident wave. Hence, the EIT-like effect can also be excited for x-polarization incident wave using the destructive interference between scattering EM fields of wires III and IV [Fig. 2(b)]. In this case, the wire III is regarded as the bright element, and the wire IV is designated as the quasi-dark element. It is exactly because the wires I and II are perpendicular to the wires III and IV, we can obtain two independent transparency windows with high transmittances for x- and y-polarization incident waves, respectively. By judiciously adjusting the sizes of each wire pair, we can find a frequency where the transmission window for x-polarization incidence coincides with the transparency window for y-polarization incidence. If the transmission coefficients of our
#198925 - $15.00 USD Received 4 Oct 2013; revised 7 Dec 2013; accepted 10 Dec 2013; published 18 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032099 | OPTICS EXPRESS 32102
system for two incident polarizations at a common frequency meeting the following criteria [15]: tx
2
2
= ty ,
arg(t x ) − arg(t y ) = 90.
(1)
(2)
then the linear-to-circular polarization conversion can be realized, where t x and t y are complex transmission coefficients of our metasurface for x- and y-polarization input waves, respectively. It needs to be especially pointed out that the lengths of the wires I and II (the wires III and IV) are set to be different for controlling the coupling between wires I and II (wires III and IV), and thus manipulating the transmission amplitude and resonance width of the transparency window for y-polarization (x-polarization) incidence. The sizes for each wire pair are set to be different for obtaining two transparency windows with different center frequencies for two incident polarizations, and thus achieving the desired phase difference. In the following, we demonstrate that a high transparency and ultra-thin polarization manipulation originates from EIT-like effects for two incident polarizations. 3. The EIT-like effect and electromagnetically induced polarization manipulation
We start our analysis by discussing resonance behaviors of metasurface for y-polarized incident wave. The transmission response of the metasurface to normally incident linearly ypolarized wave is simulated and plotted in Fig. 2(a). Due to the different length of wires I and II along y-axis, the coupling between wires is introduced, which results in a high transparency of transmission window appearing at the frequency of 8.49 GHz with the maximum amplitude of 0.98. The reason for this transparency window emergence is attributed to the fact that the bright element is excited by two different pathways: one is the direct excitation by the incident wave, and the other is the indirect excitation by the EM fields for the quasidark element [35,36]. The destructive interference between both pathways greatly suppresses the excitation of the bright element and thereafter induces the classical EIT-like phenomenon [35, 36]. To illustrate this phenomenon, the distribution of E-field for the metasurface at the EITlike peak frequency is shown in Fig. 3(a). It can be seen that the anti-symmetric E-field appears on the wires I and II, which leads to the destructive interference between scattering EM fields of wires I and II and thus induces the classical EIT-like effect [36, 38]. In this case, the EM energy is mainly trapped in high Q factor of the quasidark element [36, 38]. It can also be observed from Fig. 3(a) that the E-field on wires III and IV is extremely weak, which means that the wires III and IV are almost not excited by y-polarized incident wave. This interesting phenomenon can also be well interpreted using the method of plasmon hybridization [39, 40]. When the lengths of wires I and II are different, the coupling between wires leads to the formation of two plasmon modes: the antisymmetric and the symmetric plasmon modes. The antisymmetric and symmetric modes correspond to the currents on wires I and II, flowing in the opposite direction and in the same direction, respectively [38], as shown in Figs. 3(b) and 3(c). The frequency difference of two modes can be understood as follows: for the symmetric (antisymmetric) mode, the charges at the ends of two wires repel (attract) each other. It leads to an increased (reduced) restoring force of the charge oscillation inside the wires and thus results in a higher (lower) resonant frequency [38]. Specially, the spectral overlap of the antisymmetric mode and the symmetric mode induces a pronounced transparency window [41]. Worth noting that, in above process, the coupling between the wires mainly depends on the length difference between wires I and II and slightly depends on the separation distance between the wires [26–29,31,32,34]. As a consequence, by adjusting
#198925 - $15.00 USD Received 4 Oct 2013; revised 7 Dec 2013; accepted 10 Dec 2013; published 18 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032099 | OPTICS EXPRESS 32103
the length difference between wires I and II, we can manipulate the transmission amplitude and resonance width of the transparency window for y-polarization incidence. The spectral behavior of the transparent window can be fine-tuned by adjusting the separation distance between the wires. The above analysis is helpful in understanding the physical mechanism of EIT-like effect, which allows us freely and independently to manipulate the transparent window. The linear polarization is rotated to the x-axis and the complex transmission coefficient t x can be obtained. Similar to the case of y-polarized incidence, a high transparency of transmission window also appears in spectrum for x-polarization incident wave [Fig. 2(b)]. In this case, the wire III is considered as the bright element, and the wire IV is regarded as the quasi-dark element. The excited principle of transparency window for x-polarized incident wave is similar to that of y-polarized incident wave [Figs. 3(d)–3(f)]. Therefore, we don’t repeat it again.
Fig. 2. Transmission amplitudes and phases of the metasurface for (a) y-polarization incident wave and (b) x-polarization incident wave. The pink (blue) parts indicate the areas of the phase advance (phase retard). The elements enclosed by dashed line in the inset of panel (a)/(b) can control the excitation of EIT-like effect for y-/x- polarization incident wave.
#198925 - $15.00 USD Received 4 Oct 2013; revised 7 Dec 2013; accepted 10 Dec 2013; published 18 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032099 | OPTICS EXPRESS 32104
Max
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(f)
0
Fig. 3. (a) The E-field plots of the designed metasurface at a frequency of 8.49 GHz for ypolarization incident wave, as indicated by the blue circular in Fig. 2(a). Surface current distributions of the designed metasurface at the frequencies of (b) 7.6 GHz and (c) 9.7 GHz for y-polarization incident wave, as shown two transmission dips in Fig. 2(a). (d) The E-field plots of the designed metasurface at a frequency of 9.65 GHz for x-polarization incident wave, as indicated by the blue circular in Fig. 2(b). Surface current distributions of the designed metasurface at the frequencies of (e) 8.9 GHz and (f) 10.8 GHz for x-polarization incident wave, as shown two transmission dips in Fig. 2(b).
Because the wires I and II are normal to the wires III and IV, two independent EIT-like windows for x- and y-polarized incident waves can be obtained, respectively. By judiciously adjusting the sizes of each wire pair, we can find a frequency where the transmission window for x-polarization incidence coincides with the transparency window for y-polarization incidence. The simulated transmission amplitudes and transmission phase differences through the optimized system are displayed in Fig. 4 as solid lines for two incident polarizations. It can be seen that the EIT-like metasurface is high transparency (T~0.7) for both incident polarizations at the frequency of 9.2 GHz. Moreover, the transmission phase difference between two incident polarizations is about 90° . Such a big phase difference originates from the fact that the EIT-like effect accompanies with the strong phase dispersion [35, 36, 42]. As shown in Figs. 2(a) and 2(b), in transparency window, the phase quickly varies with the frequency. Moreover, the left (right) parts of the transparency peak correspond to areas of phase advance (retard), as shown the pink (blue) areas in Figs. 2(a) and 2(b). As a result, to obtain the 90° phase difference, the center frequencies of two transparency windows for two incident polarizations must be different [Fig. 2]. Accordingly, the sizes of each wire pair must also be different. By properly selecting the sizes of each wire pair, we can make that the left parts of transmission window for x-polarized incidence coincide with the right parts of transparency window for y-polarized incidence [see Fig. 2], and thus obtain the desired phase difference [Fig. 4(b)]. To illustrate the physical mechanism of linear-to-circular polarization conversion, the surface currents of metasurface at 9.2 GHz for two incident polarizations are shown in Figs. 5(a) and 5(b). Obviously, the antiparallel currents distribute on each pair of wires, which means that the EIT-like effects are effectively excited along two orthogonal directions. In other words, the excitations of EIT-like effects for two incident polarizations play key roles in the process of linear-to-circular polarization conversion.
#198925 - $15.00 USD Received 4 Oct 2013; revised 7 Dec 2013; accepted 10 Dec 2013; published 18 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032099 | OPTICS EXPRESS 32105
Sim-y Sim-x
Transmission amplitude
1.0
Mea-y Mea-x
0.8 0.6 0.4 0.2 0.0
Transmission phase difference
The measured transmission amplitudes and transmission phase differences are also displayed as dash lines in Fig. 4 for two incident polarizations. We note that the general variational trace of measurement results follows closely to that of simulation results. Especially, measurement results also demonstrate that the high transparency transmission is realized for both incident polarizations at about 9.2 GHz with phase difference of 90° . This means that the high transparence of linear-to-circular polarization conversion can be achieved in our system. 150
Sim Mea
100 50 0 -50
-100
7
8
9 10 Frequency (GHz)
11
-150
7
8
9 10 Frequency (GHz)
11
Fig. 4. Simulated (solid curves) and measured (dashed curves) (a) transmission amplitudes and (b) transmission phase differences for two incident polarizations. The blue dotted lines indicate the spectral location of the polarization conversion occurrence.
Fig. 5. Surface current distributions of the designed metasurface at a frequency of 9.2 GHz for (a) y-polarization incident wave and (b) x-polarization incident wave.
Worth noting that the thickness of our system is only 0.017λ, while the thickness of material of ordinary polarization modulation is comparative to wavelength [43]. Moreover, our system can realize highly transparent polarization conversion due to low loss nature of EIT-like effect. In the connected case, another different configuration has been studied by Sun et al., where although the metamaterial can also achieve the transparency polarization conversion [6], its thickness is about 4 times thicker than that of our system. Moreover, our polarization conversion is based on the EIT-like effects, and its physical mechanism is different from the case of the literature [6]. Our design is essentially similar to the FSS polarizer. However, the introduction of the EIT concept provides a new method for construction of the linear-to-circular polarization converter. Specially, this method provides more conveniences for controlling the phase behavior of device compared with the cases of Refs [18–23]. In other words, by adjusting the asymmetric degree of the metasurface in each direction, we can more easily obtain the desired phase difference and thus achieve the circular polarization state in a more simple way. Contrasting with the schemes in Refs [21–23], our proposed structure is more convenient for fabrication and the high transparent polarization conversion can be easily achieved by just adjusting the lengths of the four wires, which would
#198925 - $15.00 USD Received 4 Oct 2013; revised 7 Dec 2013; accepted 10 Dec 2013; published 18 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032099 | OPTICS EXPRESS 32106
be particular important for structures realized for the THz regime, in which many important functionalities, such as polarization conversion, beam steering and wave front shaping, have been extremely challenging to accomplish. Although the structures proposed by Refs [21,22]. are ultrathin and can also realize the polarization conversions, their structures are complex, involving to the alignments of circular and double-layered structures, which brings fabrication challenges for THz frequencies. Once the fabrication tolerance becomes large, the device performance is substantially degraded, and even the device can’t achieve the polarization conversion. Moreover, our device achieves the polarization conversion in transmission geometry, which avoids the interference problem of structure based on reflection geometry in Ref [23]. To further verify the polarization property of EM waves transmitted through the metasurface, the axial ratio (AR) is calculated [21], and is shown in Fig. 6(a). Here, the AR is defined as the ratio of the minor to major axes of the polarization ellipse [15]. It can be observed that the simulated AR value is greater than 0.9 from 9.09 to 9.38 GHz and a measured AR value of over 0.9 from 9.09 to 9.41 GHz. The measured results are in excellent agreement with the simulated results. The circular polarization characteristic of the designed metasurface is also investigated for oblique incidence. Figure 6(b) shows the simulated AR of the polarization device with different incident angle θ . We notice that when the incident angle varies from 0° to 20° , the center frequency where the maximum of AR occurs shifts. However, the value of AR is still more than 0.9 from 9.27~9.33 GHz when the incidence angle varies between 0° and 20° . 1.0
Sim Mea
0.9
Axial Ratio
Axial Ratio
1.0
0.8 0.7 8.7
0.9
0o 10o o 20
0.8 0.7
8.9
9.1 9.3 9.5 Frequency (GHz)
9.7 8.7
8.9
9.1 9.3 9.5 Frequency (GHz)
9.7
Fig. 6. (a) Measured and simulated AR results, (b) Simulated AR results with different incidence angle θ . The incident angle θ is the angle separation between a linearly polarized input wave and the z-axis.
The transmission loss of the designed metasurface with different incident angle θ is also computed and displayed in Fig. 7. The transmission loss value can be obtained directly from the simulated S parameters as [44]: 2
s loss (dB / mm) = −10 log10 ( 21 2 ) / d slab . (3) 1 − s11 It is found that the transmission loss becomes large when the incident angle varies from 0° to 20° However, the maximum value of transmission loss is about 1.3 dB/mm from
9.27~9.33 GHz when the incidence angle varies between 0° and 20° (in this case, the AR value is still more than 0.9). Because the thickness of our designed metasurface is ultrathin (~0.017λ), its loss is very low (~0.67 dB).
#198925 - $15.00 USD Received 4 Oct 2013; revised 7 Dec 2013; accepted 10 Dec 2013; published 18 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032099 | OPTICS EXPRESS 32107
Transmission loss
10 8
0o 10o 20o
6 4 2 0 9.15 9.20 9.25 9.30 9.35 9.40 9.45 Frequency (GHz)
Fig. 7. Transmission loss of metasurface for different incident angle θ . The incident angle θ is the angle separation between a linearly polarized input wave and the z-axis.
To better quantification of the polarization state for the transmitted wave, Stokes parameters [1, 15] are introduced as: 2
2
2
2
S0 = t x cos α in + t y sin α in , S1 = t x cos α in − t y sin α in , S 2 = 2 t x cos α in t y sin α in cos ϕdiff ,
(4)
S3 = 2 t x cos α in t y sin α in sin ϕdiff ,
where the α in is the angle separation between a linearly polarized wave at the input port and the x-axis (i.e. the polarization angle at the input port), and the phase difference ϕ diff equals to arg(t y ) − arg(t x ) . According to formula (4), the polarization azimuth α out and the ellipticity angle χ are derived as: tan 2α out = sin 2 χ =
S2 , S1
S3 , S0
(5) (6)
Where χ = 0 corresponds to linear polarized wave whereas χ = ±45° corresponds to circular polarization wave. The α out is the angle separation between the principle axis of polarization ellipse at the output port and the x-axis (i.e. the polarization angle at the output port). The angles associated with Stoke’s parameters are plotted in Fig. 8. The incident angle θ is the angle separation between a linearly polarized input wave and the z-axis, which is the same with angle θ in Figs. 6 and 7. The θ = 0 indicates the normal incidence. According to [Eqs. (4)–(6)], when α in = 45° , the corresponding polarization azimuth and ellipticity angles are computed as α out = 33.6° and χ = −43.9° at 9.2 GHz. Since sin 2 χ = −0.999 , this indicates that the linearly polarized incident wave is highefficiently converted to circularly polarized wave, as shown the green solid line in Fig. 9(a). Our system can also realize the linear-to-elliptical polarization conversion, as revealed in
#198925 - $15.00 USD Received 4 Oct 2013; revised 7 Dec 2013; accepted 10 Dec 2013; published 18 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032099 | OPTICS EXPRESS 32108
Fig. 9(b). When α in = 60° , α out = 178.2° and χ = −29.7° . This means that the linearly polarized wave becomes an elliptically polarized wave with the principal axis azimuth of 178.2° and the ellipticity of sin 2 χ = −0.861 . Similarly, according to the measured transmission amplitudes and phases of the fabricated sample for two incident polarizations as well as [Eqs. (4)–(6)], we can obtain the polarization azimuth of α out and the ellipticity of sin 2 χ . Hence, we can confirm the angle separation between the principal axis of the polarization ellipse and the x-axis, as well as the circular polarization degree. Using these two parameters, we can plot the measured polarization ellipse at the output port, as shown the dots in Fig. 9. Obviously, the experiment and simulation results are quite good agreement. As a consequence, our structure can realize the different polarization conversion at the different polarization incident angle.
k θ
E
α in
H
Fig. 8. The angles associated with the stoke’s parameters.
αin = 45
αin = 60
sim mea
1.0 0.5
αout = 33.6
0.5
0.0
0.0
-0.5
-0.5
-1.0
sim mea
1.0
αout = 178 .2
-1.0 -1.0 -0.5
0.0
0.5
1.0
-1.0 -0.5
0.0
0.5
1.0
Fig. 9. (a) The simulated (solid curves) and measured (dots) polarization ellipses at 9.2 GHz for a 45° linearly polarized input wave, representing 99.9% circular polarization (linear-tocircular conversion), and (b) the simulated (solid curves) and measured (dots) polarization ellipses at 9.2 GHz for a 60° linearly polarized wave, representing 86.1% circular polarization (linear-to-elliptical conversion). The axes represent the magnitude of the normalized electric field along the x and y axes after passing through the metasurface. The top panels indicate the polarization states at the input port. The bottom panels indicate the polarization states at the output port.
#198925 - $15.00 USD Received 4 Oct 2013; revised 7 Dec 2013; accepted 10 Dec 2013; published 18 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032099 | OPTICS EXPRESS 32109
4. Conclusion
In this paper, we have achieved the polarization control of EM waves based on the EIT-like metasurface. It has numerically and experimentally demonstrated that the high transparency of polarization manipulations (linear-to-circular and linear-to-elliptical polarization conversions) can be realized in the designed system formed by orthogonal two pairs of cut wires. The high transmissions and the significant phase difference governed by EIT-like effects for two incident polarizations make the proposed structure being an excellent polarization controller. Moreover, our structure is more convenient for fabrication, and the high transparent polarization conversion can be easily achieved by just adjusting the lengths of the four wires, which would be particular important for structures realized for the THz regime. In addition, the thickness of the proposed polarization device is much thinner than wavelength (0.017λ), as opposed to bulky polarization devices. With the presented results, many applications can be envisaged, such as miniaturized and light weight quarter wave plates. The proposed approach offers a new way for manipulating the polarization of EM waves. By scaling down the designed metasurface, our scheme could also be utilized at other frequency regimes, such as millimeter wave, and terahertz. Acknowledgments
This work is supported by the National Natural Science Foundation of China (Grant Nos. 61371044 and 60971064), and the Education Department of Heilongjiang Province (Grant No. 12531775).
#198925 - $15.00 USD Received 4 Oct 2013; revised 7 Dec 2013; accepted 10 Dec 2013; published 18 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032099 | OPTICS EXPRESS 32110
