Open Access
Add to BibSonomy
Abstract
Vector beams (VBs) that possess nonuniform polarization distributions in space have various applications. In view of the utilization of the circularly polarized light in generating VBs based on the metallic structures, this paper proposes an approach to generate VBs using metallic nanoslits with linearly polarized light illumination. These nanoslits are located on two concentric circular orbits, and the nanoslits on the inner circle are perpendicular to the ones in the outer circle. The linearly polarized light is effectively changed into the rotational symmetric VBs by rotating these orthogonal nanoslits, and the polarization order of the VBs can be adjusted by changing the rotation angles of nanoslits. The detailed theoretical analysis provides the basis for the conversion from the linearly polarized light to the VBs. Numerical simulations and experimental measurement demonstrate the performance of VB generators. This paper’s proposed method has advantages that include ultrathin and compact structure, convenient operation and immediate conversion from linear polarization to VBs, and easier expansion of VB applications.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Polarization is an important nature property for light beam. With comparison to the spatially homogeneous polarization beams, such as linearly, circularly and elliptically polarized light, the polarization distribution of vector beams (VBs) is spatially variable. And VBs posses the polarization singularities at the center of light beams, and the intensity distributions of VBs are annular [1]. These particular properties make VBs have many unique advantages like tight focus [2–6] and high-resolution image [7,8]. VBs have been applied in many fields including optical manipulation [9–11], data storage [12] and optical communication [13,14]. The generation of VBs from homogeneous polarization beams has attracted lots of research interest, and several approaches are proposed to generate VBs. The common approaches include q-plate [15,16], optical fibers [17,18] and spatial light modulator [19]. However, the volumes of optical elements used in these methods are large, and the light paths are usually complex, so these methods are difficult to realize the optical integration. The VB generator with compact structure, ease to operate and high performance conversion must expand the applications of VBs in optical micro manipulation and optical integration.
Metallic structures consisting of nanometer units have the ability for manipulating light in nano- and micro-meter scale, and many optical devices based on metallic structures have been designed in recent years, such as plasmonic filter [20,21], plasmonic lens [22,23], quarter wave plate [24,25], polarization state analyzer [26–29] and vortex beams generator [30–32]. Meanwhile, some VB generators based on the metallic structures have been also put forward [33–36]. Yu et al. used the rectangular nanoapertures to form plasmonic metasurfaces and generated VBs under the circularly polarized light illumination [33]. Yue et al. designed a metasurface consisting of rectangular blocks to obtain the VBs with circularly polarized light illumination [34]. We also etched the rectangular holes in sliver film to get the radially and azimuthally polarized light, and the illuminating source is still chosen as the circularly polarized light [36]. With respect to the homogeneous circularly polarized light, the linearly polarized light is spatially asymmetric. And it is not easy to realize the conversion of the linearly polarized light to the VBs. As far as we know, the research about the generation of VBs using linearly polarized light has not been reported.
In this paper, we propose an approach to generate VBs using the metallic structure with linearly polarized light illumination and the polarization order of VBs can be easily changed. This metallic structure is composed by spatially variable nanoslits etched in a silver film, and the polarization order of VBs can be changed by rotating the nanoslits. These nanoslits are arranged along two circular orbits, and the adjacent nanoslits on two orbits are perpendicular to each other. The distance between two orbits equals to a half of surface plasmon wavelength. The proposed metallic structures can realize the conversion of the linearly polarized light to radially and azimuthally polarized beams, and the detail theoretical analysis gives the physical mechanism. The numerical simulations performed according to the finite-difference time domain (FDTD) method show the perfect conversion from the linear polarization to the VBs, and the practical experiment verify the performance of the proposed VB generators.
2. Theoretical analysis
2.1 Geometrical structure of VB generator
Geometrical structure of our proposed VB generator and part of its magnified picture are shown in Fig. 1. This VB generator is composed by nanoslits etched in the silver film, and these nanoslits are arranged in two concentric circles with the radii of r1 and r2. Two adjacent nanoslits at the inner and outer circular orbits are always perpendicular to the each other, and the radius difference between two circles takes d = λspp/2, where λspp is the wavelength of surface plasmon polaritons (SPPs) propagating along the interface of the silver film and the vacuum. Moreover, these nanoslits rotate regularly with respect to their central positions. θ represents the position angle of the nanoslit and α denotes the rotation angle between the short edge of nanoslit and the horizontal direction. l1 and l2 are the length of the short and long edges of the nanoslit. And these geometrical parameters can be seen clearly from the magnified part of VB generator, as shown in Fig. 1.
Fig. 1 Structure diagram of VB generator and its magnified part. Where r1 and r2 are the radii of the inner and outer circular orbits, θ is the position angle of nanoslit, α is the rotation angle between the horizontal direction and the short edge of nanoslit, and l1 and l2 are the lengths of the short and long edges of nanoslit.
For generating the VB with the nth polarization order, we let the rotation angle α and the position angle θ of nanoslit satisfy the following relational expression
where n is an integer, and Δφ is the additional angle of nanoslit. This addition angle equals to π/2 for the nanoslits on the inner circular orbit and 0 for the nanoslits on the outer circular orbit. It needs to be pointed out that the metallic structure shown in Fig. 1 corresponds to the case of n = 1.It’s well known that the nanoslit can be taken as a polarizer with the transmission axis along the short edge when the long edge l2 is much longer than the short edge l1. This is because only the electric field component perpendicular to the long edge of nanoslit can excite SPPs. Figure 2 gives the transmission model of one nanoslit and the numerical simulation results for the transmission fields of the nanoslit with l1 = 50nm and l2 = 200nm according to the finite difference time domain (FDTD) method. Where the thickness of the sliver film deposited on a glass substrate is set at 150nm, the dielectric constant of silver takes ε = −15.92−i1.075 for the incident wavelength of 632.8nm [37], the corresponding SPPs wavelength is λspp = 612.5nm. The simulated range is 2μm × 2μm × 4μm. This rectangular nanoslit limits the transmission polarization along y axis for any polarized light illumination. Figure 2(a) shows the schematic diagram of a nanoslit with 45° linearly polarized light illumination, and Figs. 2(b) and 2(c) are the x and y components of the normalized transmission electric field. It is easy to see that the y component of field is much higher than x component, and this indicates that only the y polarization light can pass the nanoslit. Thus, the transmission polarization of the nanoslit with larger aspect ratio is along its short edge, and the polarization direction of transmission field passing through each nanoslit in VB generator changes with the rotation of nanoslit.
Fig. 2 (a) Transmission model of one nanoslit with 45° linearly polarized light illumination and the simulated transmission fields of (b) x component and (c) y component.
2.2 Transmission of the VB generator
It has been demonstrated that a nanoslit has the same function with a polarizer, so two orthogonal linear polarizations can be obtained by two orthogonal nanoslits with linearly polarized light illumination. When their distance to a point near the center of VB generator is equal to the half of SPPs wavelength, two linear polarizations at this point have a phase delay of π. Thus, the incident linear polarization can be changed into different directions in space by these rotational nanoslits, and the vector beams with nonuniform polarization distributions can be formed with linearly polarized illumination. The detailed theoretical analysis for the vector beam generation is as following.
The nanoslit is equivalent to a polarizer, and it can be expressed by the Jones matrix
where α is the angle between the transmission axis of nanoslit and x axis. Based on the relationship of α and θ given by Eq. (1), the Jones matrices of the nanoslits on the inner and outer circular orbits can be written asandWhen the linearly polarizated light illuminates the VB generator in Fig. 1, SPPs are excited by the nanoslits and transmit toward the center point O of VB generator. For one observation point P(ρ, β) near the center of VB generator, as shown in Fig. 3, the electric field Et superposed by the SPP fields coming from all nanoslits can be expressed in the following integral form
where kspp is the wave vector of SPPs, ρ is the position vector from the center point O to the observation point P, and Ei represents the incident light. Due to the observation point is very close to the center point, the directions of r and d are approximately opposite to kspp. Therefore, the vector products in phase terms can be expanded as kspp·ρ = −ksppρcos(β-θ), kspp·r1 = −ksppr1 and kspp·d = −ksppd, where β is the position angle of the observation point P. For linear polarization illumination, the incident light Ei can be also described by a Jones matrixwhere γ is the polarization angle of incident light with respect to the x axis. Then, Eq. (5) can be rewritten asFig. 3 Schematic diagram for the optical field at the observation point P emitting from one nanoslit on the inner circular orbit
Perform the integration of Eq. (7), the electric field near the center of VB generator can be obtained
From Eq. (8), it can be seen that the electric field conforms to the Bessel function, and the spatial polarization is the function of the position angle. This transmission polarization expression is just the general form of VBs, and the integral n represents the polarization order of the generated VBs.
When the polarization direction of the linearly polarized light is along the x axis, the polarization angle γ takes 0°. Insert this value of γ in Eq. (8) and neglect the constant terms, the transmission field near the center of VB generator can be simplified by:
Similarly, when the incident polarization angle takes γ = 90°, namely the polarization direction of the linearly polarized light is along the y axis, the transmission field near the center of VB generator is:
Equations (9) and (10) represent the VBs with the nth polarization order. While n = 1, Eq. (9) is for the radially polarized light and Eq. (10) represents the azimuthlly polarized light. Obviously, the polarization order of VBs can be adjusted by changing the spin periodicity of the nanoslits. For verifying the performance of the proposed VB generator, we carry out the numerical simulations and the experiment measurement in the following content.
3. Simulations and experiment
3.1 Numerical simulations
We design practically the VB generators according to the above theoretical approach. Firstly, we design the VB generators with n = 1 and 2 and simulate the transmission of these VB generators using the FDTD method. The simulation region takes 14μm × 14μm × 4μm and the perfect matched layer is still chosen as the boundary condition. The monitor plane is set at 3μm above the silver film. Figure 4 shows the geometric structure of the VB generator with n = 1 and the transmission field distributions when linearly polarized light with the polarization directions in x axis and y axis respectively illuminates the VB generator. Where the inner circular orbits radius of VB generator takes 5μm, and the distance between the inner and outer circles is 0.3μm. The magnified structure squared by yellow line shows clearly the spatial distributions of nanoslits on two circular orbits. The transmission distributions include the total intensity |Ex|2 + |Ey|2, x component |Ex|2 and y component |Ey|2. Figures 4(b)-4(d) are the results for the linearly polarized light with the polarization direction along the x axis, and Figs. 4(e)-4(g) are the results with the polarization direction along the y axis.
Fig. 4 Structure of the VB generator with n = 1 (a) and its transmission distributions (b)-(g). Where the results of (b)-(d) corresponds to the linearly polarized light illumination with the polarization direction along the x axis, and the results of (e)-(g) are for the linearly polarized light with the polarization direction along the y axis.
From the intensity distributions with x-polarization illumination, we can see the annular intensity with dark center takes on among the total intensity distribution of Fig. 4(b), and the symmetrical bright fringes appear in the component fields. The fringes for the x component show the left and right symmetry, and the fringes for the y component show the up and down symmetry, as shown in Figs. 4(c) and 4(d). All these characteristics of the intensity distributions are same as those of the radially polarized light. The black arrows drawn in Fig. 4(b) denote the polarization direction of the VB in space. For the intensity distributions with y-polarization light illumination, the annular intensity with dark center also appears in the total intensity distribution of Fig. 4(e) and the symmetrical bright fringes appear the component fields. However, the fringes for the x component show the up and down symmetry, and the fringes for the x component show the left and right symmetry, as shown in Figs. 4(f) and 4(g). All these characteristics of the intensity distributions are consistent with the azimuthally polarized light. The black arrows drawn in Fig. 4(e) denote the polarization direction of this VB in space.
Moreover, we also design the VB generator with n = 2 based on the theoretical analysis. The nanoslits locate on two circular orbits with r1 = 5μm and r2 = 5.3μm and rotate with the spin periodicity taking 1. The structure of the designed VB generator is shown in Fig. 5(a). When this VB generator is illuminated by the linearly polarized light, the transmission intensity distributions are simulated according FDTD method. Figures 5(b)-5(g) are the results for the linearly polarized light illumination with the polarization direction along the x axis and Figs. 5(e)-5(g) are the results with the polarization direction along the y axis. The total intensity distributions of |Ex|2 + |Ey|2 for the VB generators are doughnut-like, and the component intensity distributions show the different symmetric structures. Under the x-polarization light illumination, four bright spots of the x component |Ex|2 appear at two orthogonal coordinate axes, and four bright spots of the y component |Ey|2 appear at four quadrants. Oppositely, under the y polarization light illumination, four bright spots of the x component appear at four quadrants and four bright spots of the y component appear at two orthogonal coordinate axes. All these characteristics of the intensity distributions are consistent with the second order VBs light. The black arrows drawn in Figs. 5(b) and 5(e) denote the polarization directions of VBs in space.
Fig. 5 Structure of the VB generator with n = 2(a) and its transmission distributions (b)-(g). Where the results of (b)-(d) corresponds to the linearly polarized light illumination with the polarization direction along the x axis, and the results of (e)-(g) are for the linearly polarized light with the polarization direction along the y axis.
Similarly, the vector beam with polarization order of n can be generated by changing the rotation angle of the nanoslits according to Eq. (1). Theoretically, the upper limit of polarization order of vector beam is unlimited. However, the practical simulations prove that the spatial uniformity of the intensity distribution of the generated vector beam decreases with increase of the value of n. The number of the nanoslits and the radii of the circular orbits need to increase for the larger n so as to guarantee the quality of the generation vector beam with high polarization order.
3.2 Experiment measurement
In order to verify the performance of the proposed VB generators, we fabricate the samples of VB generators and measure their transmission field. Magnetron sputtering method is used to deposit the silver film with the thickness 150nm on glass substrates, and the focused ion beam etched technique is utilized to etch the nanoslits in the silver film. Put the fabricated sample into the experiment setup shown in Fig. 6(a) and detect its transmission intensity distributions. Where the light beam emitted by He-Ne laser with the wavelength of λ = 632.8nm is chosen as the illumination source, and the polarization direction is in the vertical direction. When it passes through a half wave plate (HWP), the polarization direction of the linearly polarized light changes with the direction of fast axis of the HWP rotating. The linear polarization light with certain polarization direction impinges on the sample (S), the transmission intensity distribution is magnified by a microscopic objective (MO) and then receives by a charge-coupled device (CCD). Two mirrors of M1 and M2 are set in the light path to change the propagating direction of light, and the polarizer P is used to extract the x and y components of transmission field and analyze the polarization characteristics of the transmission field.
Fig. 6 (a) Experimental setup, the scanning electron microscopy (SEM) image of the MS with (b) n = 1 and (i) n = 2, and the measured intensity distributions of (c)-(h) the first-order and (j)-(o) the second-order VBs with different linearly polarized light illumination. Where (c)-(e) and (i)-(l) are the results under x polarization illumination, (f)-(h) and (m)-(o) are the results under y polarization illumination. The inserted arrows in the patterns on the right columns denote the direction of analyzer P.
Figures 6(b) and 6(i) are the scanning electron microscopy (SEM) images of two samples for generating the VBs, where Fig. 6(b) is the VB generator for generating the first polarization order VBs and Fig. 6(i) is for the second order VB generator. The manufacture condition are HV = 5kv, mag = 1600 × , HFW = 16.0μm, WD = 4.1mm, det = ETD and tilt = 0°. The experimental results in Figs. 6(c)–6(h) are the transmission intensity distributions of the first order VB generator and the results in Figs. 6(j)-6(o) are the transmission intensity distributions of the second order VB generator. Figures 6(c)-6(e) and 6(j)-6(l) correspond to the x-polarization light illumination. Figures 6(f)-6(h) and 6(m)-6(o) correspond to the y-polarization light illumination. Figures 6(c), 6(f), 6(j) and 6(m) are the measured total intensity distributions without the polarizer P, and eight pictures on two columns at the right are the results of the polarization analysis, where the polarization directions of the polarizer P are denote by the inserted white arrows. From the total intensity distributions, we can see the annular intensities with dark center. The extracted component intensity distributions take on the same phenomena as the simulation results. For the first order VB generator, the bright fringes for the x polarization illumination appear along the polarization direction of polarizer P, and the bright fringes for the y polarization illumination appear along the direction perpendicular to polarizer P. Therefore, the radial and azimuthal polarization lights really generate using the metasurface structures of Fig. 6(b) with the linear polarization light illumination. For the second order VB generator with the x polarization illumination, four bright spots appear along the directions parallel and perpendicular to the polarization direction of the polarizer P along horizontal direction, but four bright spots appear at four quadrants when the polarization direction of the polarizer P is along vertical direction. The cases for the y-polarization illumination are just opposite. These experiment phenomena are the same as the simulated results and they completely consist with the characteristics of the second order vector polarization light predicted by the theoretical analysis.
4. Conclusions
In conclusion, we propose an approach to obtain VBs from the linearly polarized light. The proposed VB generators consist of nanoslits equivalent to polarizers and they can generate the VBs with any polarization order by controlling the rotation of nanoslits. The theoretical analysis using the Jones matrix of nanoslits and superposition theorem of fields show concisely the design mechanism of VB generators. The numerical simulations on basis of FDTD method effectively testify the reliability of this design. The experiment measurement provides the powerful verification for the performance of the proposed VB generators. From the theoretical design to the sample fabrication and the VB generation, we can find that our proposed approach for generating VBs possesses the advantages of the simple design, the compact structure and the convenient operation. More importantly, it paves a way for the generation of VBs using the linearly polarized light, and this work is benefit for the applications of VBs in optical integration and optical micro-manipulation.
Funding
National Natural Science Foundation of China (Grant No.10874105); Shandong Provincial Natural Science Foundation of China (Grant No. 2015ZRB01864).
References and links
1. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009). [CrossRef]
2. K. Youngworth and T. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000). [CrossRef] [PubMed]
3. Q. Zhan and J. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10(7), 324–331 (2002). [CrossRef] [PubMed]
4. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003). [CrossRef] [PubMed]
5. X. Hao, C. Kuang, T. Wang, and X. Liu, “Phase encoding for sharper focus of the azimuthally polarized beam,” Opt. Lett. 35(23), 3928–3930 (2010). [CrossRef] [PubMed]
6. T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, “Nanointerferometric amplitude and phase reconstruction of tightly focused vector beams,” Nat. Photonics 8(1), 23–27 (2014). [CrossRef]
7. D. P. Biss, K. S. Youngworth, and T. G. Brown, “Dark-field imaging with cylindrical-vector beams,” Appl. Opt. 45(3), 470–479 (2006). [CrossRef] [PubMed]
8. R. Chen, K. Agarwal, C. J. Sheppard, and X. Chen, “Imaging using cylindrical vector beams in a high-numerical-aperture microscopy system,” Opt. Lett. 38(16), 3111–3114 (2013). [CrossRef] [PubMed]
9. K. Huang, P. Shi, G. W. Cao, K. Li, X. B. Zhang, and Y. P. Li, “Vector-vortex Bessel-Gauss beams and their tightly focusing properties,” Opt. Lett. 36(6), 888–890 (2011). [CrossRef] [PubMed]
10. Y. Kozawa and S. Sato, “Optical trapping of micrometer-sized dielectric particles by cylindrical vector beams,” Opt. Express 18(10), 10828–10833 (2010). [CrossRef] [PubMed]
11. C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4(1), 2891 (2013). [CrossRef] [PubMed]
12. V. Parigi, V. D’Ambrosio, C. Arnold, L. Marrucci, F. Sciarrino, and J. Laurat, “Storage and retrieval of vector beams of light in a multiple-degree-of-freedom quantum memory,” Nat. Commun. 6(1), 7706 (2015). [CrossRef] [PubMed]
13. Y. Zhao and J. Wang, “High-base vector beam encoding/decoding for visible-light communications,” Opt. Lett. 40(21), 4843–4846 (2015). [CrossRef] [PubMed]
14. G. Milione, T. A. Nguyen, J. Leach, D. A. Nolan, and R. R. Alfano, “Using the nonseparability of vector beams to encode information for optical communication,” Opt. Lett. 40(21), 4887–4890 (2015). [CrossRef] [PubMed]
15. F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51(10), C1–C6 (2012). [CrossRef] [PubMed]
16. Y. S. Rumala, G. Milione, T. A. Nguyen, S. Pratavieira, Z. Hossain, D. Nolan, S. Slussarenko, E. Karimi, L. Marrucci, and R. R. Alfano, “Tunable supercontinuum light vector vortex beam generator using a q-plate,” Opt. Lett. 38(23), 5083–5086 (2013). [CrossRef] [PubMed]
17. N. K. Viswanathan and V. V. G. K. Inavalli, “Generation of optical vector beams using a two-mode fiber,” Opt. Lett. 34(8), 1189–1191 (2009). [CrossRef] [PubMed]
18. S. Ramachandran, P. Kristensen, and M. F. Yan, “Generation and propagation of radially polarized beams in optical fibers,” Opt. Lett. 34(16), 2525–2527 (2009). [CrossRef] [PubMed]
19. H. Chen, J. Hao, B. F. Zhang, J. Xu, J. Ding, and H. T. Wang, “Generation of vector beam with space-variant distribution of both polarization and phase,” Opt. Lett. 36(16), 3179–3181 (2011). [CrossRef] [PubMed]
20. D. Wu, N. Fang, C. Sun, X. Zhang, W. J. Padilla, D. N. Basov, D. R. Smith, and S. Schultz, “Terahertz plasmonic high pass filter,” Appl. Phys. Lett. 83(1), 201–203 (2003). [CrossRef]
21. Z. Wu, J. W. Haus, Q. Zhan, and R. L. Nelson, “Plasmonic botch filter design based on long-range surface plasmon excitation along metal grating,” Plasmonics 3(2-3), 103–108 (2008). [CrossRef]
22. W. Srituravanich, L. Pan, Y. Wang, C. Sun, D. B. Bogy, and X. Zhang, “Flying plasmonic lens in the near field for high-speed nanolithography,” Nat. Nanotechnol. 3(12), 733–737 (2008). [CrossRef] [PubMed]
23. P. Y. Li, Q. Zhang, Y. Y. Li, H. Wang, L. X. Liu, and S. Y. Teng, “Plasmonic lens based on rectangular holes,” Plasmonics 13(1), 1–5 (2018), doi:. [CrossRef]
24. A. Roberts and L. Lin, “Plasmonic quarter-wave plate,” Opt. Lett. 37(11), 1820–1822 (2012). [CrossRef] [PubMed]
25. Y. Zhao and A. Alù, “Tailoring the dispersion of plasmonic nanorods to realize broadband optical meta-waveplates,” Nano Lett. 13(3), 1086–1091 (2013). [CrossRef] [PubMed]
26. F. Afshinmanesh, J. S. White, W. Cai, and M. L. Brongersma, “Measurement of the polarization state of light using an integrated plasmonic polarimeter,” Nanophotonics 1(2), 125–129 (2012). [CrossRef]
27. Y. B. Xie, Z. Y. Liu, Q. J. Wang, Y. Y. Zhu, and X. J. Zhang, “Miniature polarization analyzer based on surface plasmon polaritons,” Appl. Phys. Lett. 105(10), 101107 (2014). [CrossRef]
28. B. Zhu, G. Ren, M. J. Cryan, C. Wan, Y. Gao, Y. Yang, and S. Jian, “Tunable graphene-coated spiral dielectric lens as a circular polarization analyzer,” Opt. Express 23(7), 8348–8356 (2015). [CrossRef] [PubMed]
29. Q. Zhang, P. Y. Li, Y. Y. Li, X. R. Ren, and S. Y. Teng, “A universal plasmonic polarization state analyzer,” Plasmonics 13(4), 1129–1134 (2018). [CrossRef]
30. H. Kim, J. Park, S. W. Cho, S. Y. Lee, M. Kang, and B. Lee, “Synthesis and dynamic switching of surface plasmon vortices with plasmonic vortex lens,” Nano Lett. 10(2), 529–536 (2010). [CrossRef] [PubMed]
31. H. Zhou, J. Dong, Y. Zhou, J. Zhang, M. Liu, and X. Zhang, “Designing appointed and multiple focuses with plasmonic vortex lenses,” IEEE Photonics J. 7(4), 1–8 (2015).
32. Q. Zhang, P. Y. Li, Y. Y. Li, H. Wang, L. X. Liu, L. L. Zhang, and S. Y. Teng, “Optical vortex generator with linearly polarized light illumination,” J. Nanophotonics 12(1), 016011 (2018). [CrossRef]
33. P. Yu, S. Chen, J. Li, H. Cheng, Z. Li, W. Liu, B. Xie, Z. Liu, and J. Tian, “Generation of vector beams with arbitrary spatial variation of phase and linear polarization using plasmonic metasurfaces,” Opt. Lett. 40(14), 3229–3232 (2015). [CrossRef] [PubMed]
34. F. Yue, D. Wen, J. Xin, B. D. Gerardot, J. Li, and X. Chen, “Vector vortex beam generation with a single plasmonic metasurface,” ACS Photonics 3(9), 1558–1563 (2016). [CrossRef]
35. Y. Zhang, R. Zhang, X. Li, L. Ma, C. Liu, C. He, and C. Cheng, “Radially polarized plasmonic vector vortex generated by a metasurface spiral in gold film,” Opt. Express 25(25), 32150–32160 (2017). [CrossRef] [PubMed]
36. Q. Zhang, P. Y. Li, Y. Y. Li, H. Wang, L. X. Liu, Y. He, and S. Y. Teng, “Vector beam generation based on the nanometer-scale rectangular holes,” Opt. Express 25(26), 33480–33486 (2017). [CrossRef]
37. E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985).
