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In this paper, we propose to achieve high-efficiency polarization conversion based on spatial dispersion modulation of spoof surface plasmon polaritons (SSPP). Different k is firstly designed in the two transverse directions by aligning an SSPP-supporting fishbone structure in y direction while maintaining free space in x direction. The orthogonal phase difference is introduced by larger k of SSPP waves for y-polarized component of incident waves. Meanwhile, to achieve high efficiency, gradient k in z-direction is designed so that the y-polarized component of incident waves can be coupled perfectly as SSPP waves. By rotating the fishbone structure with respect to the polarization direction of incident waves, different polarization states for transmitted waves can be realized. As an example, a polarization converter prototype with the central working frequency f = 8GHz was designed, fabricated, and measured. Both the simulation and experiment demonstrate the high-efficiency linear-to-circular (LTC) polarization conversion in 6.9-9.6GHz.
© 2016 Optical Society of America
1. Introduction
Polarization is one of the fundamental properties of electromagnetic waves [1,2]. It is of great significance to have the capability of freely controlling polarization of EM waves and researchers have devoted great interests into the realization of polarization manipulation. Polarization conversion is the first step, including polarization rotation, linear-to circular and circular-to-linear polarization conversions. In the visible spectrum, polarization conversions have always realized using wave-plates made of birefringent materials such as crystalline solids and liquid crystals [3,4]. Bulky configuration and narrow working bandwidth prevent such wave-plates from being integrated into micro-optical systems. In the microwave regime, polarization conversions have usually resorted to ferrite phase shifter and multi-layered gating polarizers. With the rapid development of electromagnetic metamaterials, polarization manipulations can also be achieved using anisotropic or chiral metamaterials [5,6], yet still with thickness limitations for broadband or wideband use. In recent years, metasurfaces, the 2D version of metamaterials, provide another way of polarization manipulation. By metasurfaces, the concept of phase “discontinuities” was proposed, and the phase shift necessary for polarization conversion can be easily achieved. The ultra-thin thickness and lower loss of metasurface-based polarization converters [7–14] have attracted great interests from researchers. However, wideband polarization conversion efficiency of metasurfaces is not so satisfactory especially for transmitted waves.
In addition to pure polarization conversion, tunable polarization conversion, frequency-tunable or polarization-tunable [15–21], has gained more and more research interests due to the great application potentials. Many researchers have dedicated to the realization of tunable polarization. For example, a tunable mid-infrared polarization converter composed of asymmetric graphene nanocrosses was devised to dynamically tune the transmitted wavelength and polarization states by varying the Fermi energy of grapheme [15]. A freely tunable broadband polarization rotator for terahertz waves was demonstrated using a three-layer metallic grating structure, which can rotate the polarization of a linearly-polarized terahertz wave to any desired direction with nearly perfect conversion efficiency [16].
In this paper, we proposed to achieve high-efficiency polarization conversion based on spatial dispersion modulation of spoof surface plasmon polaritons (SSPP), a new scheme for polarization conversion. SSPP is the low-frequency counterpart of surface plasmon polaritons at optical frequencies, a hybrid excitation of electron oscillation and electromagnetic oscillation [22–27]. To couple propagating waves efficiently as SSPP mode, metallic fishbone structure is employed as the SSPP-supporting structure. Due to the nearly perfect SSPP coupling of the fishbone structure, y-polarized waves Ey are converted into SSPP mode with larger k while x-polarized waves Ex are kept as propagating mode in free space. Hence, a larger phase accumulation can be obtained for y-polarized EM waves. This leads to a phase difference between the two orthogonal components of incident waves, a necessary condition for polarization conversion. Thanks to the designable k-dispersion of SSPP, a π/2 phase difference between the SSPP and free-space mode in y- and x- direction can be achieved. By rotating the fishbone structure, the amplitudes of the two orthogonal component |Ex| and |Ey| (|Ex|2 + |Ey|2 = |E0|2, where E0 is the amplitude of incident waves) can be tailored to tune the polarization state of transmitted waves. Therefore, considering the near-unity transmissions of both the SSPP and free space mode in y- and x- directions, very high-efficiency tunable polarization conversion can be achieved via rotating the fishbone structure. Compared with other schemes of polarization conversion, this scheme can be potentially thin because of the strong dispersion of the SSPP. Furthermore, it is also believed that the configuration and design of our scheme are simple compared with other schemes.
2. SSPP on the metallic blade structure
The metallic fishbone structure is proposed as the SSPP-supporting structure to couple and guide SSPP. Figure 1 present the dispersion curve of uniform fishbone structures with different h, plus the field maps of the three electric field components along the structure. The inset in Fig. 1(a) displays the front view of the unit cell of the uniform fishbone structure with the blade width w, blade length h, lattice constant p, and the metallic ridge line width w1. We employ the full-wave finite-element method to numerically calculate the dispersion diagrams of the y-polarized waves propagating on the structure. The geometrical parameters for the structure in simulations are: p = 0.4mm, w = 0.2mm, b = 10mm, w1 = 0.3mm, and four values for the blade length h = (2, 4, 6, 8) mm. Figure 1(a) gives the dispersions of the fundamental SSPP mode. The red bold line is the light line. From the f-k relations, we can find that the dispersion curves of the waves on the uniform fishbone structure are below the light line, with larger k at the same frequency than waves in free space. This indicates that this periodic structure is capable of confining electromagnetic waves on the surface. Therefore, waves on this structure can be considered as SSPP at microwave frequencies. In addition, it is observed that the mode properties of the SSPP can be controlled by changing the blade length h. The propagation constant k increases with the blade length h, and the cut-off frequency decreases with the blade length h. To demonstrate the SSPP on the structure, we simulated the distributions of the electric field components Ex, Ey, and Ez of SSPP on the structure with the blade length h = 8mm at the frequency f = 8.0GHz, as shown in Fig. 1(b). 60 blades make up the uniform fishbone structure with a total length 24.0mm. The y-polarized wave is incident from + z direction. The boundary conditions in all directions are set to be open. It is found that SSPP is highly confined on the structure, and the wavelength is significantly reduced compared with that in free space.
Fig. 1 (a) The dispersion diagrams of SSPP on the uniform fishbone structures with different blade length; the inset displays the front view of the blade structure, (b) the distributions of the electric field components Ex, Ey, and Ez of the SSPP on the metallic blade structure at f = 8GHz.
3. Design of the polarization converter based on SSPP coupling
The unit cell of the proposed polarization converter is illustrated in Fig. 2, where Fig. 2(a) gives the perspective view, Fig. 2(b) the x-view, and Fig. 2(c) the front view. The unit cell is composed of three layers. A gradient fishbone structure placed in yoz plane is sandwiched in between two 0.6mm-thick F4B (εr = 2.65, tanδ = 0.001) dielectric substrates. The gradient fishbone structure consists of 30 blades etched on F4B dielectric substrate is used to couple and guide SSPP. The repetition periods in x- and y-directions are a = 5mm and b = 10mm. The total length of the fishbone structure along z-direction l = 12mm. The spatial distribution of the blade length h(z) for the gradient fishbone structure is given in Fig. 2(d). The corresponding spatial distribution of wave-vector of the SSPP kspp(z) is given in Fig. 2(e). The wave-vector linearly grows from the smallest value to the highest value firstly, and then drops back to the smallest value linearly. This specific design is just for the wave vector matching at the air-dielectric and dielectric-air interfaces. This guarantees high conversion efficiency between the SSPP and the free space waves. Thus the transmittivity based on SSPP coupling can be greatly enhanced. During the design process, the linearly spatial distribution of the wave-vector for the coupled SSPP kspp(z) is firstly designed according to the desired phase difference △φ = π/2 for linear-to-circular polarization conversion at the central frequency. Then the spatial distribution of the blade length h(z) for the gradient fishbone structure is obtained according to the dispersion diagrams of the SSPP on the uniform fishbone structures with different blade length.
Fig. 2 (a) Perspective view, (b) x-view, and (c) front view of the unit cell for the designed polarization converter, (d) the spatial distribution of the blade length for the gradient fishbone structure h(z), and (e) the corresponding spatial distribution of the wave vector kspp(z).
As for gradient fishbone structure in Fig. 2, y-polarized component of incident waves is highly transmitted based on the high-efficiency SSPP coupling and decoupling of the fishbone structure. Meanwhile, the x-polarized component of incident waves can also penetrate completely through the structure because the fishbone structure has no effect on x-polarized waves. Therefore, the phase difference between the transmitted x- and y-polarized waves can be expressed as
where f is the working frequency, k(z) the spatial distribution of the wave vector for the SSPP on the fishbone structure, and l the total length of the fishbone structure.Via delicate design, this phase difference can be designed as π/2 at the working frequency. Assuming that the incident electric field is expressed as Ei = E0cos(φ)exp(ikzz) + E0sin(φ)exp(ikzz)ŷ, where φ is the polarization angle of incident waves. The transmitted field can be expressed as Et = txxexp(iφxx)E0cos(φ)exp(ikzz) + tyyexp(iφyy)E0sin(φ)exp(ikzz)ŷ, where txxexp(iφxx) and tyyexp(iφyy) are the co-polarization transmission coefficients of x- and y-polarized waves. According to above analysis, the amplitudes of the transmission coefficients at the two orthogonal directions are approximately 1, and the phase difference at the working frequency is π/2. Therefore, for incident linearly polarized waves, we can conclude: (i) the transmitted wave is left-handed circularly polarized (LCP) if the polarization angle of the incident waves is φ = 45°, and right-handed circularly polarized (RCP) when φ = −45°; (ii) the polarization state is kept for purely x- or y-polarized waves with φ = 0° or 90°; (iii) the transmitted waves are elliptically polarized (EP) for linearly polarized (LP) waves with other polarization angles.
4. Simulation, analysis and experiment verification
The simulated transmission coefficients of the polarization converter under x- and y-polarized waves are given in Fig. 3. It is found that the amplitudes of the transmission coefficients are greater than 0.95 in the entire frequency range 7.0-11.5GHz. The phase φxx is linearly dependent on frequency since x-component waves is the free space wave mode, while the phase φyy changes nonlinearly with the frequency since y-component waves are coupled as SSPP mode. The π/2 phase difference is located at f = 8.4GHz, which slightly deviates from the theoretically designed frequency f = 8.0GHz.
The polarization converter sample fabricated by the printed circuit board (PCB) technology is shown in Fig. 4(a). The metallic fishbone structure array is sandwiched in between two 0.6mm-thick F4B dielectric substrates. The total thickness of the polarization converter is 13.2mm. The experimental measurement setup is illustrated in Fig. 4(b). The sample is vertically fixed between two standard gain horn antennas. The x-, y-, v-, and u-polarized waves can be transmitted or received by placing the short side of the horn antenna in its direction(v- and u-polarized waves are LP waves with the polarization angle φ = 45° and −45°, respectively). Under normally incident v-(u-) polarized waves, the LTC polarization conversion transmissions (PCT) are simulated and the results are given in Fig. 4(c). It is found that the v-(u-) polarized waves are highly transmitted and converted into LCP (RCP) wave with the PCT greater than 0.95 in the frequency regime 6.9-9.6GHz. The relative operation bandwidth is about 33%. Vice versa, in the same frequency range, the LCP (RCP) waves can be highly converted into u-(v-) polarized waves. According to the measured transmission coefficients of the y- and x-polarized transmitted waves under normally incident v-polarized wave, the LTC PCT are derived as given in Fig. 4(d). It is found that the experimental results agree well with the simulated results. Both the experimental results and the simulated results demonstrate the excellent linear-to-circular (LTC) conversion performance of the polarization converter. In addition, the incidence angle dependence of the PCT is given in Fig. 5, in which the polarization conversion transmission spectrums tLv(f, θi), tRu(f, θi), tuL(f, θi), and tvR(f, θi) are given separately. It is observed that the PCT are kept above 0.95 in frequency ranging from 7.2 to 9.4GHz for incidence angle less than 30°.
Fig. 4 (a) Fabricated prototype of the polarization converter, (b) the experimental measurement setup, (c) the simulated LTC PCT for v- and u-polarized waves normal incidence, (d) the experimental LTC PCT for v-polarized wave normal incidence.
Fig. 5 Simulated polarization conversion transmission spectrums for LP and CP incident waves with different incident angles.
According to the above analysis, we know that the polarization of transmitted waves can be manipulated by changing the polarization angle φ of incident LP waves. That is to say, the polarization of transmitted wave can be tuned by rotating the fishbone structure. The full-polarization states on the zero longitude line of the poincaré sphere can be achieved by changing the polarization angle of the incidence wave. The PCT can be kept above 95% while the polarization angle of the incident wave is changed. To discuss the polarization state of transmitted waves under normally incident LP waves with different polarization angle φ at the frequency f = 8.4GHz, four Stokes parameters are introduced as below.
where tvv(uv) and φvv(uv) are amplitudes and phases of the co-(cross-)polarization transmissions, and φdiff = φuv-φvv is the phase difference between the cross- and co-polarization transmissions. The simulated amplitudes and phases of the co- and cross-polarization transmission coefficients versus the polarization angle of LP incident waves are given in Fig. 6(a), in which the left axis denotes the amplitudes and the right axis denotes the phases. Define A = tuv/tvv. If the phase difference φdiff = 0 or π, the transmitted wave is LP; when A = 1 and φdiff = π/2 are simultaneously satisfied, the transmitted wave is CP; otherwise, the transmitted wave is EP. In addition, when the phase difference meets 0<φdiff<π, the transmitted waves are left-handed polarized, and are right-handed polarized for π<φdiff<2π (or -π<φdiff<0). The polarization ellipse of the transmitted waves is defined by the polarization azimuth angle α and ellipticity angle β, as shown in Fig. 6(b), where the polarization azimuth angle α describes the principal axis direction of ellipse, and ellipticity angle β describes the shape of the ellipse. α and β can be obtained by tan2α = U/Q and tan2β = V/I, respectively. Figure 6(c) gives α and β for 0°≤φ≤180°.The ellipticity angle 2β are in close proximity to π/2 for φ = 45° and 135°, and about zero for φ = 0°, 90°, and 180°. Accordingly, the transmitted waves are CP for φ = 45° and 135°, and LP for φ = 0°, 90°, and 180°. Besides, the axis ratio of the transmitted wave calculated using r = 10log10(tan(β)) is given in Fig. 6(d). It is found that the axis ratio is about zero for φ = 45° and 135°, and up to 38dB for φ = 0°, 90°, and 180°. This is in good agreement with the above analysis.Fig. 6 (a) The simulated amplitudes and phases of the co- and cross-polarization transmission coefficients versus the polarization angle of incident LP waves at f = 8.4GHz, (b) the schematic description of the polarization ellipse, (c) the polarization azimuth angle α and ellipticity angle 2β of the transmitted waves, (d) axis ratio of the transmitted waves.
The polarization ellipses of the transmitted waves for LP incident wave with different polarization angles (0°, 22.5°, 45°, 67.5°, 90°, 112.5°, 135°, 157.5°, and 180°) are presented in Fig. 7. We can find that the transmitted waves are y-polarized for φ = 0° and 180°, x-polarized for φ = 90°, LCP for φ = 45°, RCP for φ = 135°, LEP for φ = 22.5° and 67.5°, and REP for φ = 112.5° and 157.5°. The principal axis directions of these polarization ellipses are determined by the azimuth angle α given in Fig. 6(c).
Fig. 7 The polarization ellipses of the transmitted waves under LP incident waves with different polarization angles at f = 8.4GHz.
5. Conclusion
In summary, we propose to achieve polarization conversion based on SSPP. High-efficiency transmissions can be achieved in two orthogonal directions independently, where the transmission in one direction is based on high-efficiency SSPP coupling, and the propagation in its orthogonal direction is in free space. A phase difference between the transmissions in the two orthogonal directions can be realized by the different phase accumulation of the SSPP and free-space waves. Via accurate design, a π/2 phase difference can be achieved. The polarization of the transmitted waves can be tuned by rotating the fishbone structure. Both the experimental results and the simulated results demonstrated the high-efficiency LTC polarization transmission in frequency regime 6.9-9.6GHz. This polarization converter may have potential applications in wireless communication, electronic countermeasure, etc.
Funding
National Natural Science Foundation of China (NSFC) (Nos. 61331005, 11304393, 61302023, 61501503).
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