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Broadband circular and linear polarization conversions have been proposed in the paper by using thin birefringent reflective metasurfaces, which are composed of two orthogonal I-shaped structures placed on the top of a printed circuit broad with grounded plane on the bottom. We show that the metasurface manipulates the reflective phases of two orthogonal linearly-polarized waves independently by changing the dimensions of I-shaped structure. Hence, the polarization states of a linearly-polarized incident wave with normal incidence can be manipulated as desired after reflected by the anisotropic metasurface. Two polarization conversions have been presented by using such thin birefringent reflective metasurfaces: from linearly-polarized wave to circularly-polarized wave, and from linearly-polarized wave to cross-polarized wave. The metasurfaces work at microwave frequency, and the axial ratio better than 1dB is achieved within fractional bandwidth of 15% for circular polarization. Numerical and experiment results demonstrate good polarization conversions in a broad frequency band, which have excellent agreements with the theoretical calculations.
© 2014 Optical Society of America
1. Introduction
The polarizations of electromagnetic waves or lights are basically classified into linear polarization, circular polarization, and elliptic polarization, which have wide applications in engineering. Many efforts, including anisotropic metamaterials [1–3], chiral metamaterials [4–6], birefringent metamaterials [7,8], photonic metamaterials [9], quarter-wave plate [10,11], metasurfaces [12,13] and so on [14–22], have been made to manipulate polarization states by using transmissive or reflective polarization converters from microwave to optical frequencies. Most polarization converters are narrow band by using thin metasurface, accompanied with high loss. Some efforts have been made to expand the bandwidth, such as multi-layered anisotropic three-dimensional (3D) metamaterials in microwave [2], gold helix structures in optics [9], planar metamaterial surface at THz frequency [14], and other approaches [3,7,10, 15,18,19,]. Due to the strong anisotropy of reflective metasurface, the thickness of broadband reflective polarization converters [3,14,15] is much smaller than that of transmissive versions [2]. However, most of the reflective metasurfaces are single anisotropic, and only one special polarization can be modulated. On the other hand, the thickness of broadband reflective circular polarization converter is still large [3] compared to the reflective linear polarization converter [14].
In this work, we propose two broadband polarization conversions realized by thin birefringent anisotropic metasurfaces at microwave frequency, which are designed by two orthogonal I-shaped structures placed on the top of a grounded printed circuit board (PCB). Two orthogonal reflection phases of the metasurface can be modulated independently by tuning the dimensions of the I-shaped structure, which provide more agility for controlling different polarization states of reflected waves. Based on above theory, two converters for circular and linear polarization conversions are designed, fabricated, and measured in the microwave frequency to show the advantages of the birefringent anisotropic metasurfaces. In our design, the thickness of two converters is about λ0/10 (λ0 is the wavelength of free space), and the simulation and experiment results illustrate that the bandwidths of circular and linear polarization conversions are about 1.6GHz and 5GHz, respectively, with very good performance. Compared with the circular polarization realized by using one single I-shaped structure [1], which only can work at on single frequency, the bandwidth of circular polarization realized in this paper is much wider with fractional bandwidth is 15%.
2. Simulation results
The proposed birefringent anisotropic metasurface is demonstrated in Fig. 1, in which two orthogonal I-shaped structures are placed on the top of a grounded PCB (F4B) with the relative permittivity 2.65 and tangent loss 0.001. The dimensions of the unit cell are p = 6mm, d = 3mm a = 2mm, w = 0.2mm, ls1 and ls2, in which ls1 and ls2 can be changed independently to obtain different reflection phases for two orthogonal linearly-polarized waves, respectively. Figure 1(b) shows the photograph of a circular polarization converter fabricated on the top of F4B. The magnitude and phase of the S11-parameter of the birefringent anisotropic metasurface are shown in Fig. 2 under the illumination by a normally incident linearly-polarized plane waves, which are simulated by using commercial electromagnetic simulation software CST. We assume that the vertically-polarized incident waves with electric field Ev normally illuminate to the metasurface, which can be decomposed to two orthogonal electric-field vectors of Es1 and Es2, and the angle between Ev and Es2 is φ, as illustrated in Fig. 2(a). The cross unit cell of the metasurface is placed on the condition that the electric-field vectors of Es1 and Es2 are parallel to the I-shaped structure 1 and structure 2, respectively, as shown in Figs. 2(b) and (c). Hence, the reflection responses of Es1 and Es2 can be mainly controlled by such two I-shaped structures independently.
Fig. 1 The birefringent anisotropic metasurface. (a) The schematic and (b) photograph of the birefringent anisotropic metasurface.
Fig. 2 The investigation of electromagnetic responses of the birefringent anisotropic metasurface. (a) v-polarized electric-field vector (E)v) can be decomposed to two orthogonal electric-field vectors of (E)s1 and (E)s2. (b) The unit cell is excited by (E)s1, only the I-shaped structure 1 has response. (c) The unit cell is excited by (E)s2, only the I-shaped structure 2 has response. (d) The S11-parameter magnitudes of the metasurface as a function of frequency and lengths of ls1 (ls2) under the excitation of (E)s1 (E)s2). (e) The S11-parameter phases of the metasurface as a function of frequency and lengths of ls1 (ls2) under the excitation of (E)s1 (E)s2). (f) The reflection phases of unit cell by changing the length of ls2 from 1mm to 5mm with ls1 = 3.6mm under the excitation of (E)s1. (g) The reflection phase differences of (E)s1 and (E)s2 for circular polarization (ls1 = 3.6mm and ls2 = 4.4mm) and linear polarization (ls1 = 1.7mm and ls2 = 4.5mm).
The magnitudes and phases of the S11-parameters of Es1 (or Es2) with different ls1 (or ls2) are demonstrated in Figs. 2(d) and 2(e), respectively. The magnitudes of S11 are all larger than −0.11dB from 3GHz to 15GHz when ls1 (or ls2) varies from 0.5 mm to 5 mm, as shown in Fig. 2(d), which indicates that the incident waves are nearly totally reflected by the metasurface with efficient polarization conversion. The phases of S11 as a function of ls1 (or ls2) and frequency are given in Fig. 2(e). At around 10GHz, a large phase covering about 300° can be achieved by changing the lengths of ls1 (or ls2), which provides the capacity for the birefringent anisotropic metasurface to modulate the reflection phases of waves.
In order to show that the birefringent anisotropic metasurface has independent phase responses for Es1 and Es2, the reflected phases of Es1 are simulated by only changing the length of ls2 with ls1 = 3.6mm, as demonstrated in Fig. 2(f). We notice that the phase curves are nearly the same by varying ls2 from 1mm to 5mm, and hence the dimension of the I-shaped structure 2 (ls2), which is vertical to Es1, will not affect the response of Es1. Similarly, we conclude that the dimension of the I-shaped structure 1 (ls1) will not affect the response of Es2. From above discussions, the metasurface can make total reflections of Es1 and Es2, i. e., |Es1| = |Es2|, but the phases of Es1 and Es2 can be modulated independently by changing the dimensions of ls1 and ls2. Therefore, the polarization state of the reflected wave can be manipulated by varied phase difference between Es1 and Es2, i.e. δθ = arg(Es1)-arg(Es2).
To demonstrate the capacity of the proposed birefringent anisotropic metasurface in manipulating the polarization states of reflected waves, as examples, we design two specific polarization converters: circular and linear polarization converters. The reflection coefficients of Es1 and Es2 are defined as r1 and r2, respectively. Hence the reflected electric fields are written as Ers1 = r1Es1 and Ers2 = r2Es2. Then Es1 and Es2 can be totally reflected by the metasurface with different phase shifts, as shown in Figs. 2(d) and 2(e), implying |r1| = |r2|. We assume that the vertically linearly-polarized incident waves (Ev) normally illuminate to the metasurface, and the angle between Ev and Es2 shown in Fig. 2(a) is set as φ = 45°. Then we have |Es1| = |Es2| and |Ers1| = |Ers2|. We further assume that the phases of Ers1 and Ers2 are defined as θ1 and θ2, and the phase difference between Ers1 and Ers2 is δθ = θ1-θ2. Hence δθ = 90° and 180° are required to convert linearly-polarized incident waves to circularly-polarized and cross-polarized reflected waves, respectively. Thus we choose (ls1 = 3.6mm, ls2 = 4.4mm) and (ls1 = 1.7 mm, ls2 = 4.5mm) to realize the circular polarization and cross linear polarization. The phase differences δθ are simulated and theoretically calculated, as shown in Fig. 2(g), in which the blue solid line and red dashed line are phase differences for realizing the circular polarization and cross linear polarization, respectively. The blue solid line shows that 90° phase difference is achieved from 9.5 to 10.5GHz, which demonstrates that the circularly-polarized reflected waves are obtained. The red dashed line shows that 180° phase difference is achieved from 10.5 to 12.5GHz, implying that the cross- polarized reflected waves are obtained. According to Fig. 2(e), the dimensions of ls1 and ls2 are not unique in designing, on condition that δθ is equal to 90° or 180° for realizing circular polarization or cross linear polarization. However, in order to obtain broadband property, the ls1 and ls2 should be chosen particularly. Take circular polarization for example, the phase difference of δθ should be equal to 90° in a broad frequency band, which can be realized by adjusting the lengths of ls1 and ls2 independently. For ls1 = 3.6mm and ls2 = 4.4mm, the phase difference of δθ = 90° can be achieved from 9.5 to 10.5GHz as the blue solid line shown in Fig. 2(g) with absolute bandwidth of 1GHz for circular polarization.
To verify the performances of the circular and cross polarization conversions, the full-wave simulations are conducted, as shown in Fig. 3. The incident plane wave is assumed to have vertical polarization (Ev) with normal incidence to the metasurface. The reflection coefficients for the vertically polarized incident waves (v polarization) converting to the vertically polarized reflected waves (v polarization) and horizontally polarized reflected waves (h polarization) are defined as Rvv and Rhv, respectively. Then the magnitudes of vertically and horizontally reflected electric fields are written as:
Then the phase difference between Erv and Erh can be calculated as:Hence, |Rvv| = |Rhv| and Arg(Rvv)-Arg(Rhv) = 90° are required for designing the circular polarization conversion; while |Rvv|→0 and |Rhv| = 1 (0dB) are required for designing the cross linear polarization conversion. The dashed lines shown in Fig. 3(a) are the simulated amplitudes of Rvv and Rhv for circular polarization, in which |Rvv|≈|Rhv| is observed from 9.5 to 11GHz, and the phase difference of arg(Rvv)-arg(Rhv) = 90° is obtained as the red dashed line shown in Fig. 3(b). Hence, the linearly v-polarized incident waves are reflected and converted to circularly polarized waves from 9.5 to 11GHz, which has good agreement with the analytical result shown in Fig. 2(g) (blue solid line). The solid lines shown in Fig. 3(a) are the simulated amplitudes of Rvv and Rhv for cross polarization, in which |Rhv| = 0dB and |Rvv|<-15dB from 9.5 to 14.5GHz. Hence, the linearly v-polarized incident waves are reflected and converted to linearly h-polarized waves (cross polarization) from 9.5 to 14.5GHz, which also has good agreement with the theoretical analysis shown in Fig. 2(g) (red dashed line).Fig. 3 The simulated magnitudes and phase differences of Rvv and Rhv, in which Rvv and Rhv are the reflection coefficients of v-polarized and h-polarized reflection waves compared to the v-polarized incident waves. (a) The simulated magnitudes of Rhv and Rvv for both circular and linear polarizations. (b) The phase differences between the Rhv and Rvv for both circular and linear polarizations. (c) The simulated and measured magnitudes of Rhv and Rvv, and magnitude errors between the Rhv and Rvv for circular polarization. (d) The simulated and measured phase differences of Rhv and Rvv for circular polarization.
3. Measurement results
We fabricate and measure the circular polarization converter as shown in Fig. 4(a). Two X-band standard rectangular horns of horn 1 and horn 2 are used as emitter and receiver, respectively. Two horns are connected to the Vector Network Analyzer (VNA, Agilent N5230C) via cables, and the designed metasurface is placed on front of the horns as shown in Fig. 4(a). The horn 1 is fixed with vertical polarization to emit v-polarized incident waves, which will be reflected by the metasurface, and the horn 2 is placed with vertical polarization and horizontal polarization to obtain reflective coefficients Rvv and Rhv, respectively. The measured magnitudes of Rvv and Rhv have good agreements with the simulations as the red and blue lines illustrated in Fig. 4(c), in which |Rvv|≈|Rhv| from 9.5 to 11GHz. The black lines demonstrate the axial ratio (AR) calculated by |Rvv|-|Rhv|, which show that the AR better than 1dB is achieved from 9.5 to 11GHz for simulation and from 9.5 to 10.8GHz for measurement. Hence the absolute bandwidth of the circular polarization with AR better than 1dB is about 1.5GHz from both simulated and measured results, whose fractional bandwidth is 15%. Figure 4(d) shows the phase differences between the measured Rvv and Rhv, which are always equal to 90° from 8 to 12GHz for both simulation and measurement. Thus the measured results also show very good circular polarization conversion modulated by the birefringent anisotropic metasurface.
Fig. 4 The experimental setup and magnitudes and phase differences of Rvv and Rhv. (a) The experimental setup, in which two X-band rectangular standard horns are used as emitter and receiver, respectively. (c) The simulated and measured magnitudes of Rhv and Rvv, and magnitude errors between the Rhv and Rvv for circular polarization. (d) The simulated and measured phase differences of Rhv and Rvv for circular polarization.
4. Theoretical analysis
A multiple reflection and transmission theory is adopted to explain the mechanism of the metasurface, as demonstrated in Fig. 5(a), which is composed of two interfaces and two dielectric layers. The incident waves normally illuminate to the metasurface, which will be partially reflected and transmitted in the interface of the metamaterial structure and be totally reflected in the interface of grounded PEC. If the incident electric field is E0, then the total reflected electric field should be calculated by summing all the reflection and transmission events:
Then the reflection coefficient can be calculated:in which r12, r21, t12 and t21 are the reflection and transmission coefficients in the interface of metastructure (x = 0), which can be calculated by use of CST Microwave Studio, k is the transmission constant in the dielectric of F4B, and d is the distance between two interfaces of metastructure and PEC. The Eq. (5) clearly shows the relationship between reflection coefficient of R and parameters of r12, r21, t12, t21 and d, which will be very helpful for analysing the reflection of such a kind of metasurface with grounded plane. To verify above theoretical analysis, we calculate the reflection phases by use of Eq. (5) to make a comparison with the simulations. Only Es1 with normal incidence is considered, hence the reflection phases of the reflected waves will be only controlled by the dimension of ls1 from the above discussions. The calculated and simulated reflection phases of the unit cell with different ls1 are shown in Fig. 5(b), which show good agreements between the theoretical calculations and numerical simulations. Furthermore, the dispersion curves for ls1 = 3.6mm and 4.4mm show similar variation tendency with phase difference of 90° from 9 to 11GHz, and the dispersion curves for ls1 = 1.7mm and 4.5mm also show similar variation tendency with phase difference of 180° from 9.5 to 15GHz, which provide a good explanation of broadband performance for circular- and cross- polarizations.Fig. 5 The theoretical model of multiple reflections and transmissions for the reflective metasurface and calculated results. (a) The sketch of multiple reflections and transmissions for the reflective metasurface. (b) The calculated and simulated reflection phases of (E)s1 with different ls1.
5. Conclusion
Two broadband polarization conversions have been presented by thin birefringent anisotropic metasurface, which are made of two perpendicular I-shaped structures. The phases of reflected waves can be controlled independently by changing the dimensions of each I-shaped structure. Based on such birefringent anisotropic metasurfaces, two polarization converters have been designed and simulated: the circular polarization and linear polarization converters, which show high efficient conversions in broadband frequencies with thickness of λ0/10. The circular polarization converter is further fabricated and measured, and the measured results show very good agreements with the simulations. Finally, a multiple reflection and transmission theory is used to investigate the phase controlling of the anisotropic metasurface.
Acknowledgments
This work was supported in part by the National Science Foundation of China under Grant Nos. 61138001, 61171024 and 60921063, in part by the National High Tech (863) Projects under Grant Nos. 2011AA010202 and 2012AA030402, and in part by the 111 Project under Grant No. 111-2-05.
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