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Abstract
A high efficient broadband polarization converter is an important component in integrated miniaturized optical systems, but its performances is often restricted by the material structures, metallic metasurfaces for polarization control in transmission mode never achieved efficiency above 0.5. Herein, we theoretically demonstrate that metallic metasurfaces constructed by thick cross-shaped particles can realize a high efficient polarization transformation over a broadband. We investigated the resonant properties of designed matesurfaces and found that the interaction between double FP cavity resonances and double bulk magnetic resonances is the main reason to generate a high transmissivity over a broadband. In addition, through using four resonances effect and tuning the anisotropic optical response, we realized a high efficient (> 0.85) quarter-wave plate at the wavelength range from 1175nm to 1310nm and a high efficient (> 0.9) half-wave plate at the wavelength range from 1130nm to 1230nm. The proposed polarization converters may have many potential applications in integrated polarization conversion devices and optical data storage systems.
© 2017 Optical Society of America
1. Introduction
Polarization states, one of the most important properties of light source that cannot be detected by human eyes, have drawn widespread attention. By controlling the polarization states, light source can be widely used in various applications [1–4], including photography, optical metrology, biosensing and communication. The conventional method of modulating the polarization states of light is based on the birefringence properties of optical components. However, the practical application require the compact optical systems to generate controllable polarized light, and traditional optical components suffered from narrow bandwidths and bulky footprints, restricting the miniaturization and integration of optical systems.
Many works have been reported that metamaterials (i.e. dielectric metasurfaces and plasmonic metasurfaces) provide a promising pathway towards the realizing of polarization conversion. The artificial structure and tunable spectral response make metamaterials a much better candidate over traditional devices in various applications. Compared to plasmonic metasurfaces, polarization rotations based on dielectric metasurfaces have been realized in fantastic performances [5–7]. And Huygens’ surfaces build with dielectric materials can realize excellent phase control with ultra-high efficiency during the broad bandwidth [7–10]. However, most of dielectric Huygens’ surfaces are built with Si, which is lossy above 300THz. Dielectric phase control metasurfaces at visible wavelengths are realized with materials with wider band gap like TiO2 [8, 11]. But a wider band gap usually means a lower refractive index. The fabrication of the TiO2 nanoparticles with high aspect ratio is rather challenging. Thus, exploring the practical limitations of plasmonic metasurfaces is still of great theoretical and practical significance.
Recently, a series of new-type polarization converters have been realized by use of plasmonic metasurfaces from reflection and transmission [12–33]. Various possible polarization conversions have also been realized in compact metamaterials, such as V-shaped particle arrays [12], an elliptical bull’s eye structure [13], L-shaped periodic arrays [14, 15], and anisotropic metasurfaces [16, 17]. In some very recent studies, an ultrathin 90° polarization rotator has been realized by metal-dielectric composite structure and L-shaped antenna arrays, expressing relative high-efficiency and broad bandwidth [18, 19]. Specially, the high performance of a quarter-wave plate also can be achieved by use of metal-dielectric composite structure [18]. However, the tunable high efficiency and bandwidth of these converters only for reflection, the efficiency of many transmitted polarization rotators are lower than 0.5 [16, 20–24]. What is more, they cannot achieve good performances with high efficiency and broadband of operation, simultaneously.
In this paper, we demonstrate that metallic metasurfaces constructed by thick cross-shaped particles can realize a high efficient polarization transformation over a broadband. The high efficient broadband performance is illustrated by the interaction of four-resonance modes, which consist of double FP cavity resonances (FPCR) and double bulk magnetic resonances (BMR). In addition, through tailoring the structure parameter, the polarization characteristics of the transmitted wave can be manipulated. A high efficiency (> 0.85) and broadband (135nm) quarter-wave plate can be realized in the wavelength range from 1175nm to 1310nm. Moreover, A high efficiency (> 0.9) and broadband (100nm) half-wave plate is also generated in the wavelength range from 1130nm to 1230nm. The results of the proposed polarization converters may have many potential applications in integrated polarization conversion devices and optical data storage systems.
2. Structure and methods
Figures 1(a) and 1(b) schematically illustrate the designed plasmonic structure and geometrical parameters of the unit cell, respectively. The matesurface composed of cross-shaped Ag nanoparticle arrays, the optical constants of Ag are taken from ref [34]. Whole structure is surrounded by the medium of silica, whose refractive index is 1.48. Simulations are performed using the finite element method. A linearly polarized plane wave, with its electric field vector at 45° to the x-axis, is perpendicularly incident to the matesurface. Periodic boundary conditions are used in the x and y directions of a unit cell, waveguide ports boundary conditions and perfectly matched layers are applied along z direction. S-parameters of x-polarized and y-polarized transmitted filed are extracted and used to calculate the corresponding amplitude and phase.
Fig. 1 (a) Schematic diagram of the plasmonic metasurfaces, which composed of cross-shaped Ag particle arrays embedded in silica. The thickness of Ag antenna is h = 380nm. The lattice constant of the antenna arrays is 600nm. (b) Top view of the unit cell of cross-shaped Ag nanoparticles. The geometric parameters are w = 100nm, Ly = 430nm, Lx = 345nm, respectively.
Figure 2(a) shows the spectral response of Cross-shaped antenna arrays. Obviously, it can be found that the transmissivity T is higher than 0.85 from 1170nm to 1500nm. When the polarization of the incident field is 45° to the x-axis, the fields in both arms of the cross-shaped particles are excited simultaneously and resonate largely independently. Hence, there exist two resonance peaks corresponding to the excitation of the resonance in each arm [29]. Two different resonance peaks are located at 1200nm and 1410nm, respectively. Obviously, the broadband response of metasurface is caused by the interaction between these two different resonances. In order to find out the physical mechanism of designed high efficient plasmonic metasurfaces, we investigate the electromagnetic response of these two resonance peaks. Owing to the anisotropy of cross-shaped Ag particles, the transmitted electric field can be decomposed into two orthogonal electric components along the x-axis and y-axis, which defined as Ex and Ey, respectively. The electric field distribution Ex for left peak is shown in Figs. 2(b) and 2(c). It can be clearly seen that this is a FP cavity resonance (FPCR) supported in the cavity formed by parallel sidewalls of adjacent thick nanoparticles. Figures 2(d) and 2(e) show electric current distribution of the structure for right peak. As can be seen, strong surface current elements are mainly located at the sidewalls of the each thick nano-cuboid particles. Each current element represents a dipolar electric resonance. The two dipolar resonances on parallel sidewalls are antiparallel. Therefore, they form a bulk magnetic resonance (BMR) together. Additionally, according to the corresponding electric field distribution Ex, as shown in Figs. 2(f) and 2(g), we infer that the BMR is also a localized surface plasmon resonance. The above two kinds of resonance mechanisms have been detailedly discussed by use of thick nano-cuboid particles, and the results here are coincident with our previous works [35]. Under the action of these two resonances, there exhibit a high efficient transmission within a broadband spectrum.
Fig. 2 Spectral response, field and currentdistributions of the metasurface. (a) Transmittance of the metasurface. (b)-(c) Electric field component Ex distribution at 1200 nm. (d)-(e) Electric current distribution of the structure. (f)-(g) Magnetic field component Hx, and electric field component Ex distributions at 1430 nm, respectively.
The same analyses are taken to Ey. The corresponding electromagnetic properties are shown in Figs. 3(a)-3(d). Apparently, the high efficient broadband spectral responses are also caused by the interaction between FPCR and BMR. Considering the designed whole structure, therefore, the high efficient broadband performance can be illustrated by the interaction of four-resonance modes, which consist of double-FPCR and double-BMR. It is worth noting that the spectral positions of FPCR peak and BMR peak are related to the structure parameters. Specifically, Fig. 3(e) shows the transmission spectrum as a function of the thickness of the cross-shaped particles. As the thickness h decreases, the positions of double-FPCR peak and double-BMR peak are gradually close to each other. When h = 350nm, the four formants are overlapped and merged into a smooth resonance curve, which results a high efficiency over a broadband. Hence, we can modulate the polarization conversion by using merged four resonance modes within a high efficient broad bandwidth.
Fig. 3 Field and spectral response of the metasurface. (a)-(b) Electric field component Ey distribution at 1200 nm. (c)-(d) Magnetic field component Hy, and electric field component Ey distributions at 1430 nm, respectively.(e) The transmission spectrum as a function of structure parameter h.
3. Results and discussions
3.1 Broadband and high efficiency quarter-wave plate
The theory of tuning polarization rotation can be illustrated by considering two perpendicular noninteracting electric dipolar resonators centered at the origin of the coordinate system with electric dipole moments in the x- and y-direction, respectively. Detuned electrical dipoles can readily be implemented in asymmetric cross-shaped Ag antennas whose resonances can be adjusted by tuning their aspect ratio [36], and the plasmonic quarter-wave plate can be constructed by tuning the slightly displacing two resonators along the respective propagation direction. For an ideal circularly polarized beam, the phase difference Δφ between electric field components Ex and Ey should be equal nπ/2, where n represents an odd number. Nevertheless, when a tolerable range of phase difference is ± 10°, the performance as a quarter–wave plate is still acceptable. And another essential transmissivity condition is Tx = Ty. For purpose of these conditions, we optimize the structure parameter as h = 350nm.
The linear transmissivities Tx - Ty, Tx + Ty and Δφ are calculated and depicted in Fig. 4(a). It is seen that, as predicted, the transmitted component Tx is equal to Ty at the wavelength rang from 1175nm to 1310nm. And the efficiency of polarization converter is higher than 0.85, which far above previous work [16]. However, we obtain a 270° ± 10° phase difference and a −90° ± 10° phase difference respectively located at wavelength range from 1175nm to 1200nm and from 1200nm to 1310nm. Both of the phase differences are meet the phase condition of a quarter wave plate, but the rotation direction of the generated circularly polarized light is opposite. Furthermore, the ellipticity angle ζ and ellipticity χ are calculated by the results of Eq. (1) and Eq. (2) as:
From Fig. 4(b), it can be seen that the ζ is near 45° at the wavelength range from 1175nm to 1310nm, indicating that the transmitted wave is circularly polarized light. And the calculate χ is more than 0.9 around whole wavelength range. These results further demonstrate that the linearly polarized light has been converted to circularly polarized light after being transmitted by the designed metasurface.Fig. 4 (a) The linear transmissivities Tx - Ty and Tx + Ty, the phase difference between electric field components Ex and Ey for the designed quarter-wave plat. (b) The calculated ellipticity angle ζ and ellipticity χ.
3.2 Broadband and high efficiency half-wave plate
Under the condition of Tx = Ty, the Δφ = mπ is an essential condition for realizing a half-wave plate, where m represents an odd number. For this purpose, we make use of anisotropic optical resonance mode of cross-shaped antennas, and optimize the geometrical parameter as h = 350nm and Lx = 285nm, respectively. In this situation, the transmissivities Tx - Ty, Tx + Ty and Δφ are also calculated and shown in Fig. 5(a). It can be found that the tansmissivity Tx is equal to Ty at the wavelength range from 1130nm to 1230nm, and the Δφ is nearly equal −180° at this whole wavelength range. Relating to the incident linearly polarized beam, that is to say, the transmitted linear polarized light has been rotated 90°, whose electric field vector at −45° to the x-axis. Fascinatingly, the efficiency of designed half-wave plate is always above 0.9 in the wavelength range from 1130nm to 1230nm. For more preciseness, the polarization rotation angle (PRA) Ψ and degree of linear polarization (DoLP) η are calculated by the results of Eqs. (3) and (4):
A light with a DoLP value above 0.9 can be regarded as a perfect linear polarized light. From Fig. 5(b), we can know that the η value of transmitted light is higher than 0.9 at the wavelength range from 1130nm to 1230nm, which indicates that the transmitted light is always the linearly polarized light. What is more, the Ψ denotes the angle between the major axis of polarization plane and x-axis. It can be clearly seen that Ψ is nearly −45° around the wavelength range. Thus, the major axis of polarization plane has been rotated to 90° direction respect to the incident direction in this broadband. These results indicate that the designed half-wave plasmonic plate has been obtained with high transmitted intensity 0.9 around the above wavelength range.Fig. 5 (a) The linear transmissivities Tx - Ty and Tx + Ty, the phase difference between electric field components Ex and Ey for the designed half-wave plat. (b) The calculated PRA Ψ and DoLP η.
It is worth noting that the wavelength range of designed half-wave plat is narrower than quarter-wave plate, which is mainly caused by the different length of Lx. In our previous works, the spectral position of BMR peak is sensitive to the structure parameter Lx, and the decreased length of Lx will causes the blue shift of BMR peak [35]. Even though FPCR peak is insensitive to Lx, the decreased Lx still causes the slightly red shift of FPCR peak. Therefore, relative to proposed quarter-wave plate, the wavelength range of designed half-wave plat is narrower and more focus on lower wavelength range. What is more, the shorter length of Lx reduces the ohmic loss in metallic components. Thus, the transmitted efficiency of the half-wave plate is higher than the quarter-wave plate.
Conclusion
In conclusion, the high efficient broadband quarter-wave plate and half-wave plate have been realized by using thick cross-shaped particle arrays. The interaction of four-resonance modes, which consist of double-FPCR and double-BMR, decided the designed metasurafaces have a high efficient polarization rotation performance over a broad bandwidth. Through tailoring the structure parameters, the polarization characteristics of the transmitted wave can be manipulated. A quarter-wave plate with an efficiency of 0.85 and bandwidth of 135nm has been generated in the wavelength range from 1175nm to 1310nm. In addition, a high efficiency (0.9) and broadband (100nm) half-wave plate is also generated in the wavelength range from 1130nm to 1230nm. The ellipticity property and polarization rotation have been investigated to further demonstrate the designed wave plates have good performances. The results of the proposed polarization converters may have many potential applications in integrated polarization conversion devices and optical data storage systems.
Funding
National Basic Research Program of China (973 Program) (2015CB932402, 2015CB351902); Key Research Program of Frontier Sciences, the Chinese Academy of Sciences (QYZDY-SSWJSC004); National Key R&D Program of China (2016YFB0402400, 2016YFB0400601); National Nature Science Foundation of China (U143231); Beijing Science and Technology Projects (Z151100001615042).
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