Open Access
Add to BibSonomy
Abstract
Bifunctional metalens for generation of pure longitudinal magnetization focal spot with reversible magnetization direction is greatly desired for the miniaturization and integration of all-optical magnetic storage. In this paper, we demonstrate a bifunctional triplex metalens that integrates the functions of an azimuthal polarizer, a helical phase plate, and a focusing lens for all-optical magnetic storage. Constructing the triplex metalens with tetratomic macropixels, the direction of the longitudinal magnetization at the focal spot can be flexibly switched by reversing the handedness of the incident light. Nearly perfect circularly polarized focal spot for left-handed or right-handed incident polarization are experimentally demonstrated, which is well consistent with the numerical simulations. The proposed bifunctional triplex metalens paves the way for the application of metalens in all-optical magnetic storage.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
All-optical helicity-dependent magnetic switching without outside magnetic field has great potentials for high-density magnetic storage [1–4]. Pure longitudinal magnetization at the focal spot is necessary to develop ultra-high-density magnetic storage system [5]. Light induced longitudinal magnetization through the inverse Faraday effect (IFE) [6,7] can be reversed by switching the handness of the incident circularly-polarized optical pulse. Tightly focusing a circularly polarized beam with a high numerical aperture (NA) is a straight choice to realized diffraction-limited light-induce longitudinal magnetization probe. However, the longitudinal electric field at the focal region owing to the depolarization effect under the tightly focusing condition restricts the improvement of the magnetic storage density [8]. Recently, it is theoretically [5,9,10] proposed that a first-order azimuthally polarized vortex (FAPV) beam can generate pure longitudinal magnetization under tightly focusing condition with any high NA. The experimental demonstration [11] of the magnetization reversal in ferromagnetic film with FAPV beam by switching the helicity of optical vortices was carried with a bulky optical setup composed of an azimuthal polarization converter, a helical phase plate and a focusing lens, which is unsuitable for the miniaturization and integration of magnetic storage system.
Optical metasurface is a promising alternative compact optical device for its unprecedent ability to regulate the optical field by the nanoscatters at the subwavelength scale [12–14]. Various functionalities have been demonstrated with metasurface, such as planar lens [15,16], holography [17,18], wave plate [19] and vector beam generation [20,21]. Furthermore, functionalities of multiple traditional optical devices can be integrated onto a single metasurface, and the functions of the metasurface can be switched by regulating the wavelength [22–24], incident angle [25,26] or polarization of the incident light [27–29]. Our previous work [30] has experimentally demonstrated a metalens with triplex optical functionalities of an azimuthal polarizer, a helical phase plate, and a focusing lens, which can take place of the traditional bulky optical devices for all-optical magnetic storage. The helical phase, together with the lens phase, is encoded by the propagation phase of the nanoscatters, which is rigid for a given metasurface. As such, the irreversible handedness of the optical field at the focal spot greatly limits its practical application in all-optical magnetic storage. Actually, it is impossible to encode all the three functionalities independently by utilizing only the propagation phase and geometric phase of the nanopost, which provide two degrees of freedom to manipulate the light. However, in the FAPV scheme, the orientation of the longitudinal magnetization is determined by the handedness of the helical phase implying that helical phase has to be encoded dynamically while the lens phase is static. Therefore, it is necessary to develop the triplex metalens to realize the three different functionalities independently and encode the helical phase dynamically, which is greatly desired in all-optical magnetic storage.
In this letter, we solve the problem by introducing a tetratomic macropixel [31,32] consisting of two pairs of staggered twin-meta-atoms to construct the triplex metalens. The interference within the tetratomic macropixel regulates the Jones matrix of the macropixel with which the helical phase is encoded by the geometric phase and the lens phase by the propagation phase. The handedness of helical phase can be conveniently flipped over by switching the handedness of the incident circularly polarized light owing to the opposite geometric phase induced by left-handed circular polarized (LCP) and right-handed circular polarized (RCP) incident light. Azimuthal polarization is still achieved under the condition of constructive interference for polarization along the short axis (s-polarization) and destructive interference for polarization along long axis (l-polarization) between the two staggered twin-meta-atoms. Both simulation and experimental characterization demonstrated the generation of nearly perfect circularly polarized focal spot for LCP or RCP incidence, implying the generation of pure reversible longitudinal magnetization at the focal spot induced by IFE.
2. Design and simulations
2.1 Property of the bifunctional triplex metalens
As shown in Fig. 1, optical setup to generate focusing FAPV beam for magnetic storage contains at least three conventional devices including an azimuthal polarizer, a helical phase plate and a focusing lens. The bifunctional triplex metalens (right) integrates the functionalities of all these three optical devices together into a single metasurface owing to its ability to manipulate both the polarization and phase distribution of optical wavefront. Binary information is recorded in the ferromagnetic film by the helicity-dependent effective magnetic field of the optical focal spot according to IFE. The up or down magnetization will be switched conveniently with incident light in left-handed or right-handed circular polarization.
Fig. 1. Schematic of the conventional devices (left) for magnetic storage by FAPV beams and the bifunctional triplex metalens (right) which replaces the optical devices including azimuthal polarizer, helical phase plate, and focusing lens and switches the direction of magnetization by changing the handness of the incident circularly polarized light.
According to polarization optics, the functionality of the triplex metalens described by a Jones matrix $J(x,y)$ demands the following relationships for LCP and RCP illumination:
Here, x and y are the coordinates of the metasurface; $\left[ {\begin{array}{c} 1\\ i \end{array}} \right]$ and $\left[ {\begin{array}{c} 1\\ { - i} \end{array}} \right]$ denote the Jones vector of LCP and RCP incident light respectively; $\alpha = \arctan (y/x)$ is the azimuthal angle at point (x,y), thus ${e^{ {\pm} i\alpha }}$ represents the helical phase and $\left[ \begin{array}{c} \sin \alpha \\ - \cos \alpha \end{array} \right]$ denote the azimuthal polarization; the other phase factor ${e^{i\phi }}$ is used to encode the focusing lens phase of $\phi ={-} \frac{{2\mathrm{\pi }}}{\lambda }(\sqrt {{x^2} + {y^2} + {f^2}} - f)$ where $\lambda $ is the wavelength at free space and f is the focal length. It is noted that helical phase depends on the incident polarization and the lens phase is polarization-independent implying two kinds of phase mechanism are necessary to realize the functionalities of the triplex lens. Combing the Eqs. (1) and (2), the Jones matrix $J(x,y)$ of the metalens can be solved as
2.2 Realize bifunctional triplex metalens with tetratomic macropixels
The optical property of the elementary elliptical nanopost can be described by the Jones matrix in the linear polarization base as [14]
Fig. 2. (a) The top view and side view of one tetratomic macropixel consisting of two pairs of twin elliptical silicon nanoposts arranged on silica substrate with dimensions of H = 370 nm and P = 300 nm. The long axis (l) and short axis (s) of the nanopost are defined in the subgraph of top view. (b) The simulated amplitude transmittance (${t_l}$: l-polarization; ${t_s}$: s-polarization) and phase delay (s-polarization) of the sixteen tetratomic macropixels at $\lambda $=633 nm. (c) The state of polarization of the transmitted light with the rotation angle of nanoposts in the 16 tetratomic macropixels from 0° to 180° under LCP (left) and RCP (right) incident light is depicted by blue curve. (d) The phase delay retrieved from the output light in s-polarization for the sixteen macropixels with the rotation angle of nanoposts from 0° to 180° under LCP (left) and RCP (right) incident light.
To circumvent the limitation of the simple metasurface, we turn to the compound metasurface composed of tetratomic macropixels. Figure 2(a) gives the top view and side view of the tetratomic macropixel composed of two pairs of twin elliptical silicon nanoposts arranged on silica substrate. The height of nanopost is 370 nm and the lattice period is 600 nm along both x- and y-direction. The four nanoposts are separately placed in the center of the four quadrants inside the lattice cell and the two nanoposts on each diagonal have the same geometry and orientation. Nanoposts in the second and fourth quadrants are defined as group A and nanoposts in the first and third quadrants are defined as group B. The dimensions of the nanoposts along the long axis and short axis are separately defined as ${D_{Al}}$, ${D_{As}}$, ${D_{Bl}}$ and ${D_{Bs}}$ and the orientation angles ($\theta $) of four nanoposts are all the same. Jones matrix of the nanoposts group A (${J_A}$) and group B (${J_B}$) can both be described by Eq. (4), and the final Jones matrix of the tetratomic macropixel is obtained by the superposition of ${J_A}$ and ${J_B}$
The demand of the bifunctional triplex metalens (Eq. (3)) is met if the following conditions are satisfied:${\varphi _{l(A)}} - {\varphi _{l(B)}} = \mathrm{\pi }$, ${\varphi _{s(A)}} = {\varphi _{s(B)}}$, ${t_{l(A)}} = {t_{l(B)}}$, ${t_{s(A)}} = {t_{s(B)}}$, which implies constructive interference for s-polarization and destructive interference for l-polarization between nanoposts group A and group B;$\theta = \alpha $, which indicates the orientation angle ($\theta $) of four nanoposts in the tetratomic macropixel is equal to its azimuth; ${\varphi _s} = \phi $, which implies the phase delay along the short axis of the nanopost is used to encode the focusing lens phase.
Finite difference time domain (FDTD) simulations are performed to calculate the amplitude transmittance and phase delay of a single elliptical nanopost with the height of 370 nm. Periodic boundary conditions in x and y directions are adopted with the period of 300 nm. The tetratomic macropixel is built by choosing four nanoposts to meet the conditions of ${\varphi _{l(A)}} - {\varphi _{l(B)}} = \mathrm{\pi }$, ${\varphi _{s(A)}} = {\varphi _{s(B)}}$, ${t_{l(A)}} = {t_{l(B)}}$ and ${t_{s(A)}} = {t_{s(B)}}$. Considering the jacent interaction within the tetratomic macropixel [33], FDTD simulation of the tetratomic macropixel has to be performed to check the amplitude transmittance and phase delay.
Figure 2(b) presents the amplitude transmittance of l-polarization and s-polarization for the chosen sixteen tetratomic macropixels, and the phase retardation for light in s-polarization is also plotted. The transmittance of 16 tetratomic macropixels in l-polarization is lower than 13%. The transmittance for s-polarization is higher than 80% and the phase delay along this axis has the coverage of 0-2π, which is used to encode the lens phase in the design of bifunctional triplex metalens. The transmittance for l-polarization is far less than that for s-polarization due to the destructive interference for light in l-polarization. The parameters of the chosen sixteen tetratomic macropixels are listed in Table 1.
Table 1. The parameters of the optimized 16 tetratomic macropixels
The functionality of the azimuthal polarizer is corroborated by simulating the 16 tetratomic macropixels with nanoposts in different rotation angles. The state of polarization of the transmitted light for the 16 tetratomic macropixels with the rotation angle of nanoposts from 0° to 180° under LCP (left) and RCP (right) incident light is depicted by blue curve in Fig. 2(c). It is noted that the light passing through is almost linearly polarized along the short axis of the macropixels for either LCP or RCP incidence, implying azimuthal polarizer function can be realized by rotating the nanopost whatever the handedness of the incident circular polarization is. The phase delay retrieved from the output light in s-polarization for the sixteen macropixels with the rotation angle of nanoposts from 0° to 180° under LCP (left) and RCP (right) incident light are shown in Fig. 2(d). Note that each column in both subgraphs of Fig. 2(d) corresponds to the change in the propagation phase of the sixteen macropixels at a given rotation angle, ranging from 0 to 2π. Each row in both subgraphs of Fig. 2(d) corresponds to the phase change introduced by the rotation of the macropixel based on the geometric phase, and there is opposite phase dependence on the rotation angle under LCP (left) and RCP (right) incident light, which conforms to the theoretical expectation by Eq. (1) and Eq. (2).
2.3 Simulated electric field and magnetization components at the focal plane
Relying on the selected 16 tetratomic macropixels that can control the amplitude and phase delay along the orthogonal direction, we constructed a bifunctional triplex metalens with diameter of 50 µm and focal length of 60 µm. Azimuthal polarization is achieved by the constructive interference for s-polarization and the destructive interference for l-polarization within each tetratomic macropixel. The switchable functionality of the helical phase plate with opposite helicity can be realized by rotating the orientation angle of the nanopost in the tetratomic macropixel to its azimuth ($\theta = \alpha $) due to the fact that opposite phase delay was introduced under LCP and RCP incident light. The functionality of the focusing lens can be realized by arranging the sixteen elemental tetratomic macropixels and encoding the focusing phase profiles $\phi ={-} \frac{{2\mathrm{\pi }}}{\lambda }(\sqrt {{x^2} + {y^2} + {f^2}} - f)$ with phase delay for light in s-polarization (${\varphi _s}$).
FDTD simulation of the bifunctional triplex metalens is conducted to calculate the distribution of electric field components in the xy-plane at the focal region under the LCP and RCP incidence at the wavelength of 633 nm. Figures 3(a) and (b) depict the simulated amplitude and phase distribution of the electric field components at the focal plane upon the LCP and RCP illumination respectively. Compared with the electric field component polarized along x and y-direction (Ex and Ey), the electric field component polarized along the z direction (Ez) is negligible, conforming to the focusing characteristic of the FAPV beam and indicating that there is no transverse magnetization component induced by IFE. It can be clearly seen that Ex and Ey components have equal intensity in the central region, and the phase difference between the two components is uniform at the spot center, with the value of π/2 upon the LCP illumination and –π/2 upon the RCP illumination, which indicate the generation of perfect LCP focal spot and RCP focal spot respectively.
Fig. 3. Simulated amplitude and phase distribution of the electric field components at the focal plane upon the LCP (a) and RCP (b) illumination respectively.
According to the expression of the magnetization components induced by IFE (M = iγE×E*) [34], the calculated distribution of magnetization components (normalized to Mz) at the focal plane under the LCP (top line) and RCP (bottom line) incidence are presented in Fig. 4. It is noted that the transverse magnetization components (Mx and My) is negligible compared with the longitudinal magnetization component (Mz), which is consistent with our goal of reducing the transverse magnetization components.
Fig. 4. Distribution of the magnetization components induced by IFE at the focal plane under the LCP (top) and RCP (bottom) incident light respectively. The scale bar is 1 µm.
3. Experimental characterization
The designed bifunctional triplex metalens was manufactured on 500µm-thick fused silica substrate. First, the substrate was cleaned with acetone, isopropyl alcohol and deionized water in order. Second, 370nm-thick amorphous silicon films were deposited on fused silica substrate by plasma-enhanced chemical vapor deposition (PECVD). Third, the sample was spin coated a layer of hydrogen silsesquioxane (HSQ) and a charge-dissipation layer for electron beam lithography patterning. After the exposure, the sample was first rinsed in deionized water to remove the charge-dissipation layer and then developed in the developer solution. Finally, the sample was etched by inductively coupled plasma-reactive ion etching technology. The diameter of the fabricated metalens is 50 µm. The scanning electron microscopy (SEM) images of the fabricated metalens from the top view and side view are shown in Fig. 5(a) indicating the high quality of the fabrication.
Fig. 5. (a) The SEM images of the fabricated metalens from the top view (left and middle) and side view (right). The four nanoposts circled by the white dotted line in the middle and right subgraphs represent a tetratomic macropixel. (b) Schematic of the experimental setup for the optical characterization of the focal field of the metalens. CL: collimating lens; LP: linear polarizer; QWP: quarter-wave plate.
The polarization distributions at the focal spot of the metalens are characterized by the optical setup depicted in Fig. 5(b). The 633 nm laser after collimation passed through the linear polarizer and the quarter-wave plate to generate the required LCP and RCP light, and then it was focused on the metalens through a long focal length lens ensuring the incident spot can cover the sample. The transmitted field after the metalens was recorded by an imaging system consisting of 40×/0.6 objective lens, tube lens and CCD camera. The combination of a quarter-wave plate and a linear polarizer are applied between the objective lens and the tube lens to obtain a series of intensity diagrams in different polarizations (${I_x}$, ${I_{{{45}^ \circ }}}$, ${I_y}$, ${I_{{{135}^ \circ }}}$, ${I_{\textrm{RCP}}}$, ${I_{\textrm{LCP}}}$). The state of polarization (SOP) of the transmitted field are then retrieved based on the Stokes parameters, which is generally expressed as ${s_1} = {I_x} - {I_y}$, ${s_2} = {I_{{{45}^ \circ }}} - {I_{{{135}^ \circ }}}$ and ${s_3} = {I_{\textrm{LCP}}} - {I_{\textrm{RCP}}}$.
Figure 6 depicts the simulated and measured intensity profiles at the focal plane, from the left to right are the six polarization components (${I_x}$, ${I_{{{45}^ \circ }}}$, ${I_y}$, ${I_{{{135}^ \circ }}}$, ${I_{\textrm{RCP}}}$, ${I_{\textrm{LCP}}}$), the total intensity and the SOP in the central region depicted by white arrows. The experimental results agree well with the simulated ones. The four linear polarization components are nearly equal in intensity. The LCP component in the sixth column is a solid spot and the RCP component in the fifth column is a dim ring under the LCP incidence. The LCP and RCP components are just reversed under the RCP incidence. Almost perfect circularly polarized focal spots are generated at the focal plane in experiment. It is noted some depolarization is induced in the experimental results due to the imperfection of the fabrication. Fortunately, the elliptical polarization in the focal spot can also introduce pure longitudinal magnetization by IFE.
Fig. 6. Simulated and measured intensity distribution corresponding to six polarization components (${I_x}$, ${I_{{{45}^ \circ }}}$, ${I_y}$, ${I_{{{135}^ \circ }}}$, ${I_{\textrm{RCP}}}$, ${I_{\textrm{LCP}}}$), the total intensity and the SOP in the center region depicted by white arrows.
Moreover, the longitudinal magnetization component at the xy-plane is calculated and depicted in Fig. 7(a) according to M = iγE×E*, which is consistent with the simulated results in Fig. 4. The conversion efficiency of the metalens is defined as the ratio of the optical power focused to the desired spot to the input power. The measured efficiency is 13.7% and 13% under the LCP and RCP incidence respectively. Besides demonstrating the field distribution at the xy-plane, the intensity profiles in the xz-plane are also characterized by scanning confocal microscopy shown in Fig. 7(b), and the corresponding simulated intensity distribution in the xz-plane are also depicted for comparison. The focal length of the metalens in experiment is about 56 µm, close to the simulated focal length of 60 µm.
Fig. 7. (a) The longitudinal magnetization component (Mz) at the focal plane upon LCP (top) and RCP (bottom) illumination respectively. (b) The simulated (left) and measured (right) intensity distribution at the xz-plane.
4. Conclusion
In conclusion, we demonstrated a bifunctional triplex metalens to integrate the functionalities of three bulky optical devices on a planar metalens for all-optical magnetic storage. The direction of the longitudinal magnetization at the focal spot can be conveniently switched by reversing the handedness of the incident light. The elementary tetratomic macropixel of the bifunctional triplex metalens is composed of two pairs of twin elliptical nanoposts to inhibit the contribution of light in l-polarization owing to the destructive interference between them. FAPV beam was generated and focused into almost perfect circular polarization spot with neglectable longitudinal component of electric field. The focal spot and its polarization distribution are experimentally characterized, which are in well consistence with the FDTD simulations. The measured conversion efficiency of the bifunctional triplex metalens under the incident LCP and RCP light is 13.7% and 13% respectively. The bifunctional triplex metalens demonstrated in this work paves the way for the application of metalens in all-optical magnetic storage.
Funding
National Key Research and Development Program of China (2020YFB2007501); National Natural Science Foundation of China (U20A20216).
Acknowledgments
This work was partially carried out at the USTC Center for Micro and Nanoscale Research and Fabrication.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and T. Rasing, “Ultrafast non-thermal control of magnetization by instantaneous photomagnetic pulses,” Nature 435(7042), 655–657 (2005). [CrossRef]
2. C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99(4), 047601 (2007). [CrossRef]
3. K. Vahaplar, A. M. Kalashnikova, A. V. Kimel, D. Hinzke, U. Nowak, R. Chantrell, A. Tsukamoto, A. Itoh, A. Kirilyuk, and T. Rasing, “Ultrafast path for optical magnetization reversal via a strongly nonequilibrium state,” Phys. Rev. Lett. 103(11), 117201 (2009). [CrossRef]
4. C. H. Lambert, S. Mangin, B. S. D. Ch, S. Varaprasad, Y. K. Takahashi, M. Hehn, M. Cinchetti, G. Malinowski, K. Hono, Y. Fainman, M. Aeschlimann, and E. E. Fullerton, “All-optical control of ferromagnetic thin films and nanostructures,” Science 345(6202), 1337–1340 (2014). [CrossRef]
5. Y. S. Jiang, X. P. Li, and M. Gu, “Generation of sub-diffraction-limited pure longitudinal magnetization by the inverse Faraday effect by tightly focusing an azimuthally polarized vortex beam,” Opt. Lett. 38(16), 2957–2960 (2013). [CrossRef]
6. L. P. Pitaevskii, “Electric forces in a transparent dispersive medium,” Phys. Rev. E 58(5), 6685–6694 (1998). [CrossRef]
7. J. P. van der Ziel, P. S. Pershan, and L. D. Malmstrom, “Optically-induced magnetization resulting from the inverse Faraday effect,” Phys. Rev. Lett. 15(5), 190–193 (1965). [CrossRef]
8. S. Mangin, M. Gottwald, C.-H. Lambert, D. Steil, V. Uhlíř, L. Pang, M. Hehn, S. Alebrand, M. Cinchetti, G. Malinowski, Y. Fainman, M. Aeschlimann, and E. E. Fullerton, “Engineered materials for all-optical helicity-dependent magnetic switching,” Nat. Mater. 13(3), 286–292 (2014). [CrossRef]
9. S. Wang, X. Li, J. Zhou, and M. Gu, “Ultralong pure longitudinal magnetization needle induced by annular vortex binary optics,” Opt. Lett. 39(17), 5022–5025 (2014). [CrossRef]
10. W. Yan, Z. Nie, X. Zhang, Y. Wang, and Y. Song, “Generation of an ultralong pure longitudinal magnetization needle with high axial homogeneity using an azimuthally polarized beam modulated by pure multi-zone plate phase filter,” J. Opt. 19(8), 085401 (2017). [CrossRef]
11. S. Wang, C. Wei, Y. Feng, Y. Cao, H. Wang, W. Cheng, C. Xie, A. Tsukamoto, A. Kirilyuk, T. Rasing, A. V. Kimel, and X. Li, “All-optical helicity-dependent magnetic switching by first-order azimuthally polarized vortex beams,” Appl. Phys. Lett. 113(17), 171108 (2018). [CrossRef]
12. 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]
13. A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013). [CrossRef]
14. A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015). [CrossRef]
15. A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6(1), 7069 (2015). [CrossRef]
16. M. Khorasaninejad, W. 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]
17. G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015). [CrossRef]
18. X. Ni, A. V. Kildishev, and V. M. Shalaev, “Metasurface holograms for visible light,” Nat. Commun. 4(1), 2807 (2013). [CrossRef]
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]
20. 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]
21. E. Karimi, S. A. Schulz, I. D. Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light: Sci. Appl. 3(5), e167 (2014). [CrossRef]
22. B. Wang, F. Dong, Q. T. Li, D. Yang, C. Sun, J. Chen, Z. Song, L. Xu, W. Chu, Y. F. Xiao, Q. Gong, and Y. Li, “Visible-frequency dielectric metasurfaces for multiwavelength achromatic and highly dispersive holograms,” Nano Lett. 16(8), 5235–5240 (2016). [CrossRef]
23. E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “Multiwavelength polarization-insensitive lenses based on dielectric metasurfaces with meta-molecules,” Optica 3(6), 628 (2016). [CrossRef]
24. B. H. Chen, P. C. Wu, V. C. Su, Y. C. Lai, C. H. Chu, I. C. Lee, J. W. Chen, Y. H. Chen, Y. C. Lan, C. H. Kuan, and D. P. Tsai, “GaN metalens for pixel-level full-color routing at visible light,” Nano Lett. 17(10), 6345–6352 (2017). [CrossRef]
25. S. M. Kamali, E. Arbabi, A. Arbabi, Y. Horie, M. Faraji-Dana, and A. Faraon, “Angle-multiplexed metasurfaces: encoding independent wavefronts in a single metasurface under different illumination angles,” Phys. Rev. X 7(4), 041056 (2017). [CrossRef]
26. S. Wan, C. W. Wan, C. J. Dai, Z. Li, J. Tang, G. X. Zheng, and Z. Y. Li, “Angular-multiplexing metasurface: building up independent-encoded amplitude/phase dictionary for angular illumination,” Adv. Opt. Mater. 9(22), 2101547 (2021). [CrossRef]
27. D. Wen, F. Yue, G. Li, G. Zheng, K. Chan, S. Chen, M. Chen, K. F. Li, P. W. H. Wong, K. W. Cheah, E. Y. B. Pun, S. Zhang, and X. Chen, “Helicity multiplexed broadband metasurface holograms,” Nat. Commun. 6(1), 8241 (2015). [CrossRef]
28. M. Khorasaninejad, W. T. Chen, A. Y. Zhu, J. Oh, R. C. Devlin, D. Rousso, and F. Capasso, “Multispectral chiral imaging with a metalens,” Nano Lett. 16(7), 4595–4600 (2016). [CrossRef]
29. S. Gao, C. S. Park, S. S. Lee, and D. Y. Choi, “A highly effcient bifunctional dielectric metasurface enabling polarization-tuned focusing and deflection for visible light,” Adv. Opt. Mater. 7(9), 1801337 (2019). [CrossRef]
30. K. Zhao, Z. Y. Zhang, H. F. Zang, J. Du, Y. H. Lu, and P. Wang, “Generation of pure longitudinal magnetization focal spot with a triplex metalens,” Opt. Lett. 46(8), 1896–1899 (2021). [CrossRef]
31. Q. B. Fan, M. Z. Liu, C. Zhang, W. Q. Zhu, Y. L. Wang, P. C. Lin, F. Yan, L. Chen, H. J. Lezec, Y. Q. Lu, A. Agrawal, and T. Xu, “Independent amplitude control of arbitrary orthogonal states of polarization via dielectric metasurfaces,” Phys. Rev. Lett. 125(26), 267402 (2020). [CrossRef]
32. M. Z. Liu, W. Q. Zhu, P. C. Huo, L. Feng, M. W. Song, C. Zhang, L. Chen, H. J. Lezec, Y. Q. Lu, A. Agrawal, and T. Xu, “Multifunctional metasurfaces enabled by simultaneous and independent control of phase and amplitude for orthogonal polarization states,” Light: Sci. Appl. 10(1), 107 (2021). [CrossRef]
33. T. Wu, X. Q. Zhang, Q. Xu, E. Plum, K. J. Chen, Y. H. Xu, Y. C. Lu, H. F. Zhang, Z. Y. Zhang, X. Y. Chen, G. H. Ren, L. Niu, Z. Tian, J. G. Han, and W. L. Zhang, “Dielectric metasurfaces for complete control of phase, amplitude, and polarization,” Adv. Opt. Mater. 10(1), 2101223 (2022). [CrossRef]
34. R. Hertel, “Theory of the inverse Faraday effect in metals,” J. Magn. Magn. Mater. 303(1), L1–L4 (2006). [CrossRef]
