A dual-metasurface-based reflective device (“meta-mirror”) has been proposed for broadband polarization manipulation, which is composed of orthogonal metallic cut-wire arrays separated from a grounded plane with different distances. The reflective phases of orthogonally linearly-polarized components can be independently adjusted by changing the dimensions of the cut-wire pairs. Benefiting from the fully released dispersion management ability in both dimensions, achromatic (i.e., ultra-broadband) polarization manipulation can be achieved. The suggested approach has been numerically verified in both microwave and optical band. Moreover, experimental characterization in microwave regime has demonstrated the broadband polarization manipulation ability within 5 – 30 GHz. The underlying physical mechanism of dispersion engineering was explained in general equivalent circuit theory and transmission line model.
© 2015 Optical Society of America
As one of the basic properties of electromagnetic waves, polarization state contains a tremendous amount of information about the materials and topography of the environment . Generally, polarization states can be changed by natural occurring anisotropic media. Nevertheless, conventional polarization devices are cumbersome, which do not lend themselves to photonic system integration. As compelling candidates, metamaterials have been widely employed to realize polarization control in microwave [2–9 ], terahertz [10, 11 ], infrared , and visible band [13, 14 ] during the past decade. Especially, two-dimensional metamaterials (i.e., metasurfaces) will ease the fabrication requirements and provide additional freedom in wavefront manipulation due to the phase abruption along a thin interface [15–18 ]. Both theoretical  and experimental investigations [20–22 ] elucidate that the maximal polarization conversion efficiency through single metasurface can be high up to 100% by introducing a reflective plane behind it (we refer to such a structure as “meta-mirror”). Unfortunately, the resonant nature of subwavelength inclusions causes a narrow operating bandwidth around their design frequency, as a consequence of the general Kramers-Kronig relations.
So far, great efforts have been devoted to overcome the bandwidth limitation of metamaterial based devices. Typically, different resonance modes (i.e., sub-unit cell) are superimposed within a super-unit cell to extend the operation bandwidth, but at a price of expanded unit cell or increased fabrication complexity [23, 24 ]. Moreover, the possible hybridization effects arising from closely stacked unit cells cause substantial change in the effective-media properties and thus pose a challenge to the manipulation . A much better strategy for bandwidth extension is dispersion engineering. By conjugation compensation of the dispersion of metasurface and the frequency-dependent phase shift of the dielectric spacing layer, dispersion-free polarization converters [21, 22, 26, 27 ], perfect absorbers [28–31 ], band-pass filters  and virtual shaping devices  can be realized. Despite of the great progress, there are also several shortcomings unsolved yet. On the one hand, the operational bandwidth is not broad enough. On the other hand, ideal transformer requires the polarization conversion ratio (PCR) changes sharply at the band edge, which cannot be satisfied by most transformers. As a rule of thumb, there is a gradual transition band lying at the boundary of operation band , which wastes the precious bandwidth resource and degrades the validity of converters.
In this letter, we propose a meta-mirror with dual-metasurface configuration for ultra-broadband polarization manipulation, which is constructed by orthogonal metallic cut-wire arrays separated from a grounded plane with different distances. The operation bandwidth of meta-mirrors can be expanded significantly due to the released dispersion management ability in two dimensions. As examples to apply this concept, a broadband polarization converter with operation band spanning from 5 GHz to 30 GHz is designed, fabricated and characterized in the microwave regime. Due to the generality of the concept of dispersion management, the proposal can be applied in developing other broadband devices.
2. Structure and results
As shown in Fig. 1 , the proposed meta-mirror is composed of two metasurfaces separated from a metallic reflection plane by dielectric spacers with different distances (so called dual-metasurface configuration). The metasurfaces consist of metallic cut-wire pair array and share the same period. The metallic cut-wires in each unit cell are orthogonal to each other and thus the reflective phases of orthogonally linearly-polarized components can be independently adjusted by changing the dimensions of the cut-wire pairs. Obviously, the subwavelength inclusions in this paper are simple and highly anisotropic, where u and v representing the principle axis of the proposed dual-metasurface. The dimensions of the unit cell for realization of ultra-broadband half-wave plates are P u = 6.0 mm, P v = 6.4 mm, l 1 = 2.9 mm, w 1 = 0.74 mm, l 2 = 6.3 mm, w 2 = 1.6 mm. The metallic parts are made of copper of a conductivity of 5 × 107 S/m, whose thickness is 0.017 mm. The permittivity of the dielectric spacer is 2.2(1 + 0.001i). In pioneering work made by Zhou et al., the thickness of dielectric spacer was in deep-subwavelength scale (d i < λ/10) . Strong magnetic coupling between the metasurface and the reflection plane caused high dispersion around the resonant frequency, which is believed to be just one of the main reasons of limited bandwidth. In this paper, we set the thickness of the dielectric spacer in the subwavelength scale (d 1 = 2 mm and d 2 = 3 mm, corresponding to the one quarter of wavelengths at 25 GHz and 17 GHz, respectively) to alleviate the frequency-dependent phase shift of the meta-mirrors. Under this circumstance, a low quality factor Fabry-Pérot-like cavity is formed between them and desired polarizations can be enhanced in the reflected fields with appropriate dielectric thickness [11, 12 ].
Circular polarization conversion is investigated by finite element method (FEM) within a unit cell with periodic boundary condition. The handedness of circular polarization is defined from the source plane to keep consists with the commercial simulation software of CST Microwave StudioTM, as shown in Fig. 1. First, we consider the orthogonal metallic cut-wire pairs are center-aligned. Figure 2(a) indicates that most left-handed circular polarization (LCP) is transformed to the right-handed circular polarization RCP after reflection by the meta-mirror. The conversion efficiency is higher than 90% from 5.4 GHz to 32.7 GHz. Especially, six conversion peaks with near 100% conversion efficiency appear at the frequencies of 6.3 GHz, 10.4 GHz, 19.8 GHz, 25.5 GHz, 29.6 GHz and 31.5 GHz. Our converter also exhibits harp roll-off factor at the boundary of the operation band. Then we investigate the situations the cut-wire pairs are misaligned. Three different cases denoted by A, B and C in the inset of Fig. 2(b) represents the horizontal excursion between their centers are (Pu/2, 0), (0, Pv/2) and (Pu/2, Pv/2), respectively. Figure 2(b) reveals that the broadband, high efficiency performance is sustained in all the three cases. Therefore, the proposed structure exhibits high manufacturing tolerance.
As a proof of concept, a sample containing 80 × 80 units has been fabricated and tested, as illustrated in Figs. 3(a) and 3(b) . The geometric parameters are listed in Table 1 . For ease of characterization, we have substituted the circular polarization conversion (LCP-to-RCP) by the linear polarization conversion (x-to-y) in the experiment since they follow the same conversion conditions: |S11,u| = |S11,v| and ΔΦ = |arg(S 11,u) - arg(S 11,v)| = π, where S11,u and S11,v are the reflection coefficients along the two principle axis of the meta-mirror. Two standard linearly polarized horn antennas (the electric field is x polarized) as the transmitter and receiver, respectively, have been connected to a vector network analyzer (R&S ZVA40). As depicted in the Fig. 3(b), we rotate the u axis of the sample with respect to x polarization with an angle of θ = 45° to ensure the magnitudes along the axis are equal so that high efficiency linear polarization conversion can be achieved. The measured results in Fig. 3(c) demonstrate the proposed meta-mirror operate well in the range 5 - 30 GHz, which are in fairly good agreement with the simulated results in Fig. 3(d), with discrepancies possibly arising from different material properties and fabrication errors. We note that the conversion performance in Fig. 3(d) is degenerated compared with that in Fig. 2(a) due to the printed circuit board (PCB) has a higher permittivity (~4.6), which leads to a higher dispersion. Nevertheless, the fundamental principle to achieve broadband polarization manipulation is same.
3. Theoretical analysis
Subsequently, we resort to the transmission line model (TLM) to illustrate the underlying physical mechanism of polarization manipulation, where we take the metasurfaces as thin impedance/conductance sheets whose impedance/conductance can be expressed as:
To make the analysis as general as possible, we first consider isotropic metasurfaces (Ys1, Ys2) and then extend this model to anisotropic metasurfaces (Ys1,u, Ys1,v, Ys2,u, Ys2,v). Assuming a plane wave normally impinges on the meta-mirror, due to reflections occur at the meta-surface and background plane, both the forward and backward going waves exist in the dielectric spacer and surrounding space, as sketched in Fig. 4 . We ignore the harmonic time dependence exp(-iωt) of these waves and denote their electric field amplitudes as An and Bn. Due to the electric field is totally reflected at the metallic plane with a phase change of π, we assume the amplitude of E field of forward (backward) going wave at the reflection plane is 1(−1). According to the boundary conditions of the Maxwell’s equations, we establish the following equations at the boundary of metasurface1:Eq. (5) can be rewritten as:
To verify above analysis, the anisotropic reflection coefficients under orthogonal linear polarization illumination are simulated and calculated, respectively. As indicated in Fig. 5(a) , the anisotropic reflection phases (red and blue lines) share almost the same gradient between 5.4 GHz and 32.7 GHz with the phase difference (black line) fluctuating in the range of (0.81 π, 1.11 π). There are six intersections between it and the ideal phase difference π, which corresponds to the six conversion peaks mentioned above. To verify the TLM above, the circuit parameters are retrieved by fitting the simulated frequency-dependent reflected phases. It is worth to note that when the circuit parameters satisfy (Ls1,u, Cs1,u, Cs1,v) = (7.6 × 10−9 H, 3.7 × 10−15 F, 3 × 10−17 F) and (Cs2,u, Ls2,u, Cs2,v) = (5 × 10−15 F, 5 × 10−10 H, 2 × 10−13 F), the calculated results (red and blue dot lines) agrees well with the simulation results (red and blue solid lines). With these circuit parameters, we further calculate the conversion performance. The results in Fig. 5(b) are consistent with the simulation results in Fig. 2(a).
In order to check the role of each metasurface played in the formation of the ultra-broadband operation bandwidth, single-metasurface configurations (insets of Figs. 6(a) and 6(b) ) are simulated. Figure 6 indicates that metasurface2 and metasurface1 respectively play dominant role in the lower frequency band (5 GHz – 25 GHz) and upper frequency band (28 GHz – 32GHz). However, it cannot be denied that hybrid modes will appear when the two metasurfaces are combined together. To illustrate that the electric field distributions along the principle axis of the meta-mirror (Figs. 7(a) and 7(b) ) are subsequently investigated. From Figs. 7(c)-(h), we can see the resonant modes under the orthogonal linear polarizations illumination vary with the incidence frequencies. When the incidence frequency is 11 GHz, both metasurfaces are resonant with the x- polarization, implying a hybrid mode. While for the y- illumination, the metasurface1 is nearly transparent and only metasurface2 interacts with the incidence. When the incidence frequency is 20 GHz, hybrid modes can be found under both of polarizations. When the incidence frequency is 32 GHz, hybrid mods appear for the TM illumination while the metasurface2 is nearly transparent to the x- incidence.
Finally, we present another design to verify the proposed meta-mirror can also work in the optical band. The dimensions of the unit cell are shown in Table 2 . We replace copper by aluminum as the metal material to avoid the plasmonic effect . The simulated conversion performances shown in Fig. 8 demonstrate the broadband, high efficiency performance maintains well in the optical band. The average conversion efficiency is higher than 70% in a broadband range from 0.4 to 2.4 µm. Note that the decreased efficiency is attribute to the larger absorption of metal at the optical band.
In summary, we demonstrated that the operation bandwidth of meta-mirrors can be improved significantly by dispersion management of dual-metasurface. As an example, an ultra-broadband half-wave plate with operation band spanning from 5 GHz to 30 GHz was demonstrated. In principle, the bandwidth can be further expanded by cascading more metasurfaces or adopting more elaborate design for dispersion engineering. The proposed dispersion management strategy may pave the way for design of broadband metamaterial-based devices..
The work was supported by the National Basic Research Program of China (2013CBA01700), Natural Science Foundation of China (61335005, 61325023) and Research Fund for the Doctoral Program of Higher Education of China (20130184110015).
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