A metasurface is a planar optical device that controls the phase, amplitude, and polarization of light through subwavelength-scale unit elements, called meta-atom. The tunability of plasmonic vortex lens (PVL) which generates surface plasmon polaritons (SPPs) carrying orbital angular momentum can be improved by using meta-atom. However, conventional PVLs exhibit nonuniform field profiles according to the incident polarization states owing to the spin-orbital interaction (SOI) effect observed during SPP excitation. This paper describes a method of compensating for SOI of PVL by using the geometric phase of distributed nanoslits in a gold film. By designing the orientation angles of slit pairs, the anti-phase of the SOI effect can be generated for compensatory effect. In addition, polarization-independent PVLs are designed by applying a detour phase based on the position of the slit pairs. PVLs for center-, off-center-, and multiple-focus cases are demonstrated and measured via a near-field scanning microscope.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
A metasurface is an artificially designed planar optical device consisting of subwavelength-scale unit cells called meta-atoms. Metasurfaces have been widely used to control a waveform of transmitted or reflected light by delaying the spatial phase of incident light via the geometric phase formed by the shape of the unit-cells [1–3]. Their compactness and simple design principle mean that metasurfaces have been applied across a range of fields, including digital holograms [4–7], perfect light absorbers [8–11], ultrathin lenses [12–14], and orbital angular momentum (OAM) generators [15–17]. Moreover, metasurfaces exhibit different performance according to the anisotropy of their meta-atoms. For example, rectangular, v-shaped, and c-shaped meta-atoms have been widely used in applications that require strong polarization sensitivity, such as dual-polarity metalenses , waveplates , multiplexing optical vortices , and multiplexing holograms [21,22]. In contrast, when isotropic meta-atoms are used, it was reported that metasurfaces can easily achieve polarization-independent characteristics. Square [23,24] and cylinder-shaped  meta-atoms are most frequently used for applications that require polarization independence.
Plasmonic lenses (PLs) or plasmonic vortex lenses (PVLs) are often used to make a focus or vortex in the near field by guiding surface plasmon polaritons (SPPs) . The plasmonic vortex, which has a ring-shaped profile and helical wavefront, has generated significant interested because of its compactness and the tunability of optical torque generation. As PVLs can generate strong SPP fields at the interface between a dielectric and a metal, numerous applications such as optical tweezers  and miniature polarization analyzers [28,29] have been proposed. Conventional PVLs, consisting of several continuous slits (e.g., spiral slits [30–32], concentric slits [33–36], and diffractive slit patterns ) or nanohole array , have been used to generate various sizes of vortices. In conventional PVLs, the topological charge () of the vortex can be expressed by combining the OAM charge affected by spin-orbital interactions () and the radial shift of the slit pattern ().
Recently, a method was introduced that allows the plasmonic focus to be multiplexed through circular polarized states with the Pancharatnam–Berry phase [39,40]. The focus can be designed by tilting the angle or shifting the position of rectangular nano-apertures, corresponding to polarization-dependent and -independent phases, respectively. Another study has reported that, instead of using continuous slits, distributed nanoslits along contour-like double rings generate a high-order plasmonic vortex if the nanoslit orientations are suitably controlled . The net topological charge of the vortex generated by this device was expressed by , where n is the total number of rotations of the nanoslits’ self-orientation over one cycle of revolution. Furthermore, combining distributed nanoslit configuration with a radial shift in the slit pattern has been also published .
Although conventional PVLs have the advantage of switching the topological charge by changing the polarization of incident light, their use as practical devices is often limited by their polarization sensitivity. Research that removes the linear polarization-dependence of PVL has been reported, but the fixed length and width of nanoslit, as well as the thickness of the metal, restrict the freedom of tuning of PVL . However, it is difficult to completely get rid of the polarization-dependence of PVLs because PVLs must have some spin-orbit interaction (SOI), which is the interaction between the photon’s orbit and its intrinsic spin state . As SPPs must be excited in the direction perpendicular to the long axis of the nanoslits, they will have different phase excitation characteristics depending on the polarization of the incident light . Therefore, PVLs are inevitably accompanied by SOI, which means that the different plasmonic field profiles depend on the photon’s spin state. For this reason, it is quite difficult to generate a plasmonic focus or vortex for incident light of arbitrary polarization state without any field distortion.
In this article, we propose a method that eliminates the polarization dependence of conventional PVLs by perfectly compensating the SOI with the geometric phase of distributed nanoslits. Figure 1 shows a conceptual schematic of the proposed structure. To remove the polarization dependency, we controlled the orientation of the distributed nanoslits of the PVLs. To provide an experimental demonstration, we deposited thin gold film with a thickness of 150 nm on SiO2 and fabricated a nanoslit pattern using a focused ion beam (FIB). By measuring the intensity profile using a near-field scanning optical microscope (NSOM), it has been demonstrated that manufactured PVLs exhibit identical field profiles for circular polarized, linear polarized, and even arbitrarily polarized incident light. Although the polarization of the incident light changed, the intensity profile maintained the form of the same-order Bessel function of the first kind, with the exception of the unique polarization state when the SPP field profiles perfectly disappeared inside the PVL. Through experiments and simulations based on dipole modeling methods , we show that the proposed technique can be applied to various continuous-slit PVLs designed for center-, off-center-, and multiple-focus vortex generations .
2. Basic theory and design principle
In previous research, distributed nanoslits located along the double-lined ring generated a high-order plasmonic vortex . Thus, we used a similar design for our PVLs under the following conditions. Figure 1(b) illustrates the geometric parameters of the nanoslit pairs.
The size of nanoslit and period of nanoslit pair were carefully designed considering the SPP transmittance and phase uniformity. Reducing the size and period of nanoslit will improve phase continuity, but exponentially decrease the transmittance and degrade aspect ratio of nanoslit due to fabrication limits. On the other hand, increasing period results to the nonuniform SPP generation, it has been known that the distance between adjacent cells should be shorter than an effective wavelength of SPP in order to avoid in-plane diffraction. For these reasons, we chose the length (L) and width (W) of the nanoslit to 300 nm and 60 nm, respectively. The period of the meta-atoms in the azimuthal direction (P) is 1.5 times of the slit length. A pair of nanoslits is considered to be a unit meta-atom; the difference in radius and orientation angle between the inner and outer slits is and , respectively, where is the effective wavelength of the SPP mode at the metal–air interface (nm in our simulations and experiments). To minimize the interference of the SPPs excited by the inner slits and outer slits, the azimuthal locations of the inner and outer slits are shifted by P/2 with respect to each other .
In designing a PVL with meta-atoms, let us consider the position of the inner-line nanoslits, as the position of the outer-line nanoslits can then be automatically determined. To calculate the distributed slit patterns, we assume a virtual source of diverging SPPs at the origin. Next, we define a virtual concentric band with an inner radius of and an outer radius of . The nanoslit locations N are set along the contours that satisfy the following condition:Equation (2) indicates that faster self-rotation of the nanoslits generates a higher-order vortex. As the polarized states of the incident light strongly affect the topological charge, due to the property that SPP is always excited perpendicular to the slits, cannot avoid the effect of the spin angular momentum (SAM) when n is not equal to 0.5. In other words, SAM does not affect when we set n to be 0.5, as then becomes zero. If we substitute n = 0.5 into Eq. (2), we obtainFig. 2(a). When LCP light illuminates the sample (left side of Fig. 2(a)), SOI may occur in the counterclockwise direction, whereas the geometric phase occurs in the clockwise direction along the contour of the PVL. In contrast, for the case of RCP light illumination, the SOI phase and geometric phase change their direction of rotation, as shown on the right of Fig. 2(a). As the geometric phase has the opposite direction of the phase resulting from SOI, the phase of the excited SPP fields at every position inside the PVL are unchanged for two circular polarization states, and they are proportional to the 0th-order Bessel function of the first kind.
One can simply infer that any linear combination of and will have the same field profile, given by
The proposed design method can be adapted to any kind of detour phase that is independent of the geometric phase of the distributed nanoslits . For example, a polarization-independent PVL (PI-PVL) can be designed by adding angular orbital momentum to the detour phase . Similar to Eq. (1), by setting the nanoslit positions to satisfy and , the field generated by the PI-PVL can be written asEq. (2), is proportional to the -order Bessel function of the first kind, rather than the 0th-order function.
Furthermore, the SPP vortex at an arbitrary location can be designed to have polarization independence by applying a diffractive detour phase at the position of the nanoslit pairs. To represent this phase simply, we use Cartesian coordinates in this case. To extract the SPP phase distributions, we assume there is a virtual source generating spiral SPPs located at . The diverging phase of the z-directional electric field from the virtual SPP focus can then be expressed as
3. Simulation method and experimental setup
To calculate the phase and intensity profiles inside the PVLs, dipole modeling based on a dyadic Green’s function was used . The wavelength of the incident light was set to 980 nm. When is small, the optical vortex may be distorted under the rough phase discretization caused by the large phase difference between the nearby nanoslits. If is too large, the entire shape of the PVL cannot be measured through NSOM, which has a maximum scanning range of μm. Hence, we set μm for the 0th-order PL and higher-order PVLs. Therefore, the total size of the PI-PVL for generating a 4th-order vortex was approximately μm, as shown in Fig. 2(b). For the case of multiple-foci PVL, the minimal and maximal radii of the PVL for left-side focus at (−2 μm, 0 μm) were designed to be (7.750 μm) and (9.688 μm), whereas those for the right-side focus at (2 μm, 0 μm) were designed to be (7.750 μm) and (8.719 μm), respectively. The numbers of nanoslits for the PVL without SOI, center-focusing PI-PVL, off-center focus PI-PVL, and multiple-foci PVL were set to 224, 232, 234, and 488, respectively.
To manufacture the proposed structure, thin gold film of 150-nm thickness was deposited on a SiO2 substrate using a thermal evaporator (MHS-1800). The nanoslits were patterned by FIB (FEI Company, Versa3D LoVac) under 30 kV and 1.5 pA. As shown in Fig. 2(c), a 980-nm-wavelength laser source passed through the half-wave and quarter-wave plates to control the polarized states of the incident light before illuminating the backside of the sample, and the polarization state was precisely measured by a polarimeter module (Thorlabs, PAX5710IR-T). The SPP field profiles after being transmitted through the distributed nanoslits were measured by NSOM (Nanonics, Multiview 4000).
4. Results and discussion
First of all, we simulated two simple structures to exhibit polarization-dependence of conventional PVLs [33,38]. The continuous slit PVL generates different order vortices of at the origin for two circular polarizations due to SOI effect, as shown in Figs. 3(b) and 3(c). The polarization-dependence appears more clearly when the linear polarized light is incident, as shown in Figs. 3(d) and 3(e). The discontinuous type PVL consisting of 112 nano-holes array also shows the same polarization dependent characteristics as the continuous slit PVL as shown in Figs. 3(g)–3(j).
To show the proposed SOI compensation characteristics, we compared two nanoslit-distributed PLs having different rotation factors of n = 1 (Figs. 4(a)–4(e)) and n = 0.5 (Figs. 4(f)–4(j)). For n = 1, the electric field intensity profiles exhibit an SOI-affected distribution, as shown in Figs. 4(b)–4(e); this is the same response as given by the conventional PVL. The SPP intensity profiles of LCP (Fig. 4(b)) and RCP (Fig. 4(c)) are difficult to distinguish, but small dark spots can be clearly seen, especially in Fig. 4(b), which is a 1st-order Bessel function. In Fig. 4(b), measured radius of the dark spot with 350 nm has been obtained, and the shape of the measured intensity profile greatly well-matched to 1st-order Bessel function. The small imperfection of azimuthal symmetry in experimental results may be caused by various degradation issues such as anisotropic NSOM tip shape, anisotropic scanning route, and imperfect slit fabrication. Polarization-dependence for the case of n = 1 is revealed more clearly in the intensity profiles of 135° (Fig. 4(d)) and 45° (Fig. 4(e)) linear polarizations, because SPPs are only excited along the direction of the incident linear polarization.
However, when the SOI compensation is applied (n = 0.5), the field intensity profiles exhibit almost the same optical responses for LCP, RCP, and even for the two linearly polarized incident lights, as shown in Figs. 4(g)–4(j). For every case of incident polarization, the intensity profile has the same form as the 0th-order Bessel function, although the intensity varies. By observing the simulation results near the focus, which is depicted in the inset of each figure, it is apparent that the phases of the focus did not change with the polarization state. Therefore, we have shown that the SOI can be perfectly compensated by using the appropriate geometric phase of the distributed nanoslits.
Similar to the case of 0th-order PVLs, those for higher-order plasmonic vortices can also be designed to be polarization-independent. Figures 5(b)–5(e) show NSOM images for center-located 4th-order PI-PVLs under various polarization states. Figures 5(g)–5(j) show images for off-center 4th-order PI-PVL. As shown in Figs. 5(b)–5(d), for the three representative polarizations of LCP, RCP, and x-polarization, the same vortex order can be maintained. The vortex order of off-center-focus PI-PVLs is also the same for LCP, RCP, and x-polarization, although the location of the vortex is shifted, as shown in Figs. 5(g)–5(i). Interestingly, destructive interference occurs for both types of PVLs when y-polarized light illuminates the sample, as shown in Figs. 5(e) and 5(j). To explain the phenomenon whereby the near-field patterns perfectly disappear, we use the Jones matrix. The Jones matrix of the y-polarization state can be described by . The intensity becomes zero when the magnitude and phase of the SPPs generated by LCP and RCP are equal. As predicted in the simulations, the overall intensity values may vary as the polarization changes, but the shape of the vortex will not change. The intensity of the PVL can perfectly vanish under y-polarization, although the order of the plasmonic vortex will be maintained, as shown in the numerically calculated phase profiles (insets of Figs. 5(e) and 5(j)).
Based on the proposed concept, we can simultaneously design polarization-independent and -dependent plasmonic vortices in multiple-foci PVL; the results of numerical calculations are shown in Fig. 6. We combined one PVL with SOI and another PVL without SOI. The method for determining the position of the nanoslits followed previously reported research . The plasmonic vortex without SOI at (−2 μm, 0 μm) was found to have an invariant topological charge for arbitrary polarized light. In contrast, the plasmonic vortex with SOI at (−2 μm, 0 μm) had topological charges of and under incident LCP (Fig. 6(a)) and RCP (Fig. 6(b)), respectively. The plasmonic vortex without SOI exhibits an invariant phase and amplitude profile, except for y-polarization, and the vortex may vanish in the y-polarization state. As shown in Fig. 6(d), the field profiles vanish in the SOI-compensated case when specific polarization illuminates the sample, although the SPPs generated from conventional PVLs are maintained. We expect these characteristics of the proposed PVLs to be applied to the selective switching of plasmonic vortices.
In summary, we have proposed a method for generating polarization-independent plasmonic vortices by compensating for SOI using the geometric phase of nanoslits. Theoretically, we have shown that the meta-atom consisting of a nanoslit pair can perfectly compensate the SOI. By tilting the orientation angle of the meta-atoms, the geometric phase can be controlled to be exactly the opposite of the SOI effect. PVLs without SOI were shown to generate plasmonic vortices with an identical topological charge for LCP, RCP, linear polarization, and even for any arbitrary polarization. Moreover, the proposed method can be applied to conventional circular PVLs such as ring-type, center-focus, and off-center-focus. To demonstrate this, we designed a PI-PVL that can focus plasmonic vortices at the designed position through distributed nano-apertures. Through simulations and experiments, we demonstrated that the intensity profiles of the plasmonic vortices were matched to same-order Bessel functions for LCP, RCP, and x-polarized incident light. Interestingly, a singularity occurred in the case of y-polarization because LCP and RCP light excites identical SPP amplitude and phase profiles. In addition, we simulated a multiple-foci PVL that simultaneously generates plasmonic vortices with and without SOI at different locations. We believe that this method could be used in various novel applications such as super-resolution microscopy, optical tweezers, ultra-compact OAM generators, and nanoscale optical polarization analyzers.
National Research Foundation of Korea (NRF) Korea government Ministry of Science and ICT (No. 2017R1C1B2003585 and 2017R1A4A1015565).
The authors thank Mr. Yohan Lee, Seok Woo Park for fabricating sample, Young-Gyu Bae, Woo-Young Choi for simulation and experiments, and the two anonymous reviewers for the constructive comments and suggestions.
1. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011). [CrossRef] [PubMed]
2. N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nat. Photonics 8(12), 889–898 (2014). [CrossRef]
4. X. Ni, A. V. Kildishev, and V. M. Shalaev, “Metasurface holograms for visible light,” Nat. Commun. 4(1), 2807 (2013). [CrossRef]
5. L. Huang, X. Chen, H. Muhlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4(1), 2808 (2013). [CrossRef]
7. G.-Y. Lee, G. Yoon, S.-Y. Lee, H. Yun, J. Cho, K. Lee, H. Kim, J. Rho, and B. Lee, “Complete amplitude and phase control of light using broadband holographic metasurfaces,” Nanoscale 10(9), 4237–4245 (2018). [CrossRef] [PubMed]
8. H. Zhu, F. Yi, and E. Cubukcu, “Plasmonic metamaterial absorber for broadband manipulation of mechanical resonances,” Nat. Photonics 10(11), 709–714 (2016). [CrossRef]
9. Y. Yao, R. Shankar, M. A. Kats, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators,” Nano Lett. 14(11), 6526–6532 (2014). [CrossRef] [PubMed]
10. M. Kang, F. Liu, T.-F. Li, Q.-H. Guo, J. Li, and J. Chen, “Polarization-independent coherent perfect absorption by a dipole-like metasurface,” Opt. Lett. 38(16), 3086–3088 (2013). [CrossRef] [PubMed]
11. Y. Cheng, R. Gong, and Z. Cheng, “A photoexcited broadband switchable metamaterial absorber with polarization-insensitive and wide-angle absorption for terahertz waves,” Opt. Commun. 361, 41–46 (2016). [CrossRef]
13. M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016). [CrossRef] [PubMed]
15. Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric Meta-Reflectarray for Broadband Linear Polarization Conversion and Optical Vortex Generation,” Nano Lett. 14(3), 1394–1399 (2014). [CrossRef] [PubMed]
16. P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultrathin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012). [CrossRef]
17. N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nat. Photonics 8(12), 889–898 (2014). [CrossRef]
18. X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3(1), 1198 (2012). [CrossRef] [PubMed]
19. N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A Broadband, Background-Free Quarter-Wave Plate Based on Plasmonic Metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012). [CrossRef] [PubMed]
20. M. Q. Mehmood, S. Mei, S. Hussain, K. Huang, S. Y. Siew, L. Zhang, T. Zhang, X. Ling, H. Liu, J. Teng, A. Danner, S. Zhang, and C.-W. Qiu, “Visible-Frequency Metasurface for Structuring and Spatially Multiplexing Optical Vortices,” Adv. Mater. 28(13), 2533–2539 (2016). [CrossRef] [PubMed]
21. W. Ye, F. Zeuner, X. Li, B. Reineke, S. He, C.-W. Qiu, J. Liu, Y. Wang, S. Zhang, and T. Zentgraf, “Spin and wavelength multiplexed nonlinear metasurface holography,” Nat. Commun. 7(1), 11930 (2016). [CrossRef] [PubMed]
23. Y. Yang, L. Jing, B. Zheng, R. Hao, W. Yin, E. Li, C. M. Soukoulis, and H. Chen, “Full-polarization 3D metasurface cloak with preserved amplitude and phase,” Adv. Mater. 28(32), 6866–6871 (2016). [CrossRef] [PubMed]
25. Y. F. Yu, A. Y. Zhu, R. Paniagua-Domínguez, Y. H. Fu, B. Luk’yanchuk, and A. I. Kuznetsov, “High-transmission dielectric metasurface with 2π phase control at visible wavelengths,” Laser Photonics Rev. 9(4), 412–418 (2015). [CrossRef]
27. W.-Y. Tsai, J.-S. Huang, and C.-B. Huang, “Selective trapping or rotation of isotropic dielectric microparticles by optical near field in a plasmonic archimedes spiral,” Nano Lett. 14(2), 547–552 (2014). [CrossRef] [PubMed]
31. W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Experimental confirmation of miniature spiral plasmonic lens as a circular polarization analyzer,” Nano Lett. 10(6), 2075–2079 (2010). [CrossRef] [PubMed]
32. 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]
40. G.-Y. Lee, S.-Y. Lee, H. Yun, H. Park, J. Kim, K. Lee, and B. Lee, “Near-field focus steering along arbitrary trajectory via multi-lined distributed nanoslits,” Sci. Rep. 6(1), 33317 (2016). [CrossRef] [PubMed]
41. S.-Y. Lee, S.-J. Kim, H. Kwon, and B. Lee, “Spin-Direction Control of High-Order Plasmonic Vortex With Double-Ring Distributed Nanoslits,” IEEE Photonics Technol. Lett. 27(7), 705–708 (2015). [CrossRef]
42. Q. Tan, Q. Guo, H. Liu, X. Huang, and S. Zhang, “Controlling the plasmonic orbital angular momentum by combining the geometric and dynamic phases,” Nanoscale 9(15), 4944–4949 (2017). [CrossRef] [PubMed]
43. H. Wang, L. Liu, C. Liu, X. Li, S. Wang, Q. Xu, and S. Teng, “Plasmonic vortex generator without polarization dependence,” New J. Phys. 20(3), 033024 (2018). [CrossRef]
44. K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015). [CrossRef]
45. J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X.-C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013). [CrossRef] [PubMed]
46. S.-Y. Lee, K. Kim, S.-J. Kim, H. Park, K.-Y. Kim, and B. Lee, “Plasmonic meta-slit: shaping and controlling near-field focus,” Optica 2(1), 6–13 (2015). [CrossRef]
47. 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). [CrossRef]