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Abstract
Metasurfaces offer diverse wavefront control by manipulating amplitude, phase, and polarization of light which is beneficial to design subwavelength scaled integrated photonic devices. Metasurfaces based tunable circular polarization (CP) beam splitting is one functionality of interest in polarization control. Here, we propose and numerically realize metasurface based spin tunable beam splitter which splits the incoming CP beam into two different directions and tune the splitting angles by switching the handedness of incident light polarization. The proposed design approach has potential in applications such as optical communication, multiplexing, and imaging.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metasurfaces, subwavelength scaled engineered structures, have great potential to manipulate the light beams in transmission/reflection [1–5]. Metasurfaces can be classified according to material type into dielectric and plasmonic. Dielectric metasurfaces, high refractive index nanostructures which can engineer both the electric and magnetic components of incoming light, are preferable in the visible regime due to their low intrinsic material damping compared to plasmonic structures [6–8]. By redirecting the light in a desired direction, these miniaturized structures have been used for anomalous beam steering [1], vortex beam generation [2,9], computer-generated holograms [10–13], and ultra-thin lenses [14–16].
In the optical field, beam splitters are commonly used optical components which can split the incoming beam into multiple beams and play a vital role in optical communication, interferometers and display systems. There are several traditional ways to realize the different types of beam splitter such as cube beam splitter can be constructed by gluing the hypotenuse of a coated triangular prism to the low index thin transparent substrate with a partially transparent thin metal coating [17]. Waveguides [18], photonic crystals [19], and gratings [20,21] based structures have been reported for beam splitting. However, these designs are bulky which limits their functionality in integrated photonic systems. Fortunately, metasurfaces are providing an opportunity to perform beam splitting at ultrathin interface and considerable research effort has been made to design the metasurface based beam splitters for linearly and circular polarized light [22–34]. Current endeavors are benefiting either from propagation phase [22,23,28] or geometric phase [25,31] for metasurface based beam splitting and only few schemes have been proposed which simultaneously investigate propagation and geometric phases [35]. Moreover, tunable beam splitting especially for CP light remains challenging and only few methods have been studied to tune the CP beam splitting angle [36–38]. However, these proposed designs are either multi-layered or need physical alteration for tuning. Furthermore, they do not fully benefit from the modulation ability raised by hybrid propagation phase and geometric phase.
In this manuscript we proposed that by utilizing both propagation and geometric phases the desired phase for both transmitted cross left circular polarization (LCP) and right circular polarization (RCP) can be obtained by switching the handedness of input light. This scheme facilitates the design of CP light beam splitters which can tune the splitting angles by changing the spin of the incident light. We present two different single-layered metasurface designs which, while operating on similar principles have different functions. Both designs split incoming RCP light into two beams with equal and opposite angles from the normal. Changing the input polarization changes the splitting angle, in design 1, these angles are still equal and opposite but different from the case of the incident RCP light. In contrast, by switching the input polarization in design 2 the deflection angle of one beam is unchanged whereas the other is deflected onto the other side of the normal, in this case hence the design steers the incident beam into two different angles on the left side of the normal. It is expected that the proposed beam splitter designs can find applications in laser engraving [39], sensing [40], circular dichroism spectroscopy [41], information decoding [42], and imaging [43].
2. Working principle and numerical results
The underlying principle behind the designs presented here allows a range of new functions to be demonstrated. The basic concept is that the geometric phase reverses in sign when the input CP state is reversed, whereas the propagation phase remains unchanged. This provides opportunities to add and subtract phase shifts in ways that allow new functions to be implemented. The design principle is illustrated in Fig. 1(a), which presents the configuration of unit cell where silicon nanopillar is placed on a silicon dioxide substrate. The top view of the unit cell is presented in Fig. 1(a)(right-side); where $L_x\&L_y$ are the lengths of the nanopillars in “x”$\&$“y” directions. The “$u$”$\&$ “$v$” are the local coordinates of nanopillar, and “$u$” makes angle “$\theta (x,y)$” with x-axis. The period of the unit cell is $P_x=P_y=400nm$. The CP light ($\pm \sigma$) incident on the nanopillar will transmit a geometric phase $\mp 2\sigma \theta (x,y)$ on cross-polarized light. Here, $+\sigma$ is defined for RCP and $-\sigma$ is defined for LCP. The propagation phase of value $n\theta$ ($n$ is integer) can be merged with the geometric phase as an additional degree of freedom to manipulate the cross polarized CP light. By switching the spin direction of the incident light the sign of the geometric phase gets reversed, i.e., $\pm 2\sigma \theta (x,y)$, whereas the propagation phase, $n\theta$ remains unchanged. This scheme facilitates the manipulation of additional phase to the transmitted CP light and allows one to obtain several combinations of transmitted orthogonal CP light just by suitable selection of propagation phase value. The Jones matrix for CP light, both for geometric and propagation phases can be written as [44]:
Fig. 1. Schematic of the unit cell and metasurface based tunable beam splitter designs. (a) The propagation and geometric phases can be obtained through spatial structural parameters and rotation of nanopillar when CP light normally impinges on the unit cell(left side). By swapping the handedness of incident light, the sign of geometric phase is inverted (right side). (b) Two different designs are proposed which split the light for $+\sigma$ incident light. The splitting angles on either side of the normal can be tuned just by switching the handedness of incident light and through proper arrangement of nanopillars. (c,d) Working principle of design 1 $\&$ 2 where phase gradients are separated by distance $dx$ (Top view). The graphical presentation of spatial dimensions of nanopillars are for illustration purpose only and the actual parametric values are listed in Tab.1.
Table 1. Phase distribution, parametric values and CE of basic nanopillars for the proposed beam splitter designs.
Figure 1(b) illustrates the schematic of proposed designs for the normally incident CP light. For the $+\sigma$, the transmitted light splits into two specific angles, and the splitting angle of light can be tuned on either side from the normal just by switching the spin of the incident light, i.e., $-\sigma$. These designs are arranged with two sets of nanopillars, left (green) and right (blue) on substrate with equal number of phase gradients from the centre. The phase gradients on either side from the centre of the design determine the splitting direction and angle of transmitted light. The transmitted angle emerging from either set of phase gradients can be determined by the generalized Snell’s Law [1]:
In order to obtain the functionality proposed above, we need to find the unit cells which can give equally spaced phase differences. To this end, we arrange 24 unit cells in an array with two sets of phase gradients whose phase distribution is different from each other, as shown in Fig. 1(c,d). These nanopillars are separated from the centre “o”. Both green and blue sets of nanopillars are optimized and arranged such that for a specific input and output CP polarization particular number of nanopillars cover the complete phase shift. And, by switching the handedness of input light, the number of nanopillars covering the complete phase shift will be changed for the cross-polarized light. For instance, for the $+\sigma$ light, in the design 1, a supercell($\Lambda _g$) of four green nanopillar covers 0-2$\pi$ phase which results in beam deflection to the right side of the normal and on the other hand a supercell($\Lambda _b$) of four blue nanopillar covers 2$\pi$-0 phase which results in beam deflection to the left side of the normal. As a whole, the design works as a beam splitter that splits the CP light into different angles. The deflection angle from the each set of nanopillars can be obtained from the Eqs. (2)$\&$3 as: $\theta _{tg}=\sin ^{-1}\left (\frac {\lambda _{o}2\pi }{2\pi *1.45 *1600nm}\right )=19.64^\circ$ $\&$ $\theta _{tb}=\sin ^{-1}\left (\frac {-\lambda _{o}2\pi }{2\pi *1.45*1600nm}\right )=-19.64^\circ$. Here, $\Lambda _g=\Lambda _b=4*400nm=1600nm$, as the equal number of nanopillars, i.e., “4” covering complete phase shift thus the deflection value will be same. For the $\theta _{tb}$, in $\Lambda _b$ the reverse arrangement of phase gradients, i.e., “$2\pi -0$” introduces the “-” sign; therefore, the direction of deflection angle also gets reversed. Hence, design 1 splits the incoming $+\sigma$ light at $\pm 19.64^\circ$. By switching the spin direction of incident light to $-\sigma$, same nanopillars transforms into binary phase gradients with successively “$0/2\pi$” and “$\pi$” arranged nanopillars on the interface. Therefore, splitting angles tunes according to generalized Snell’s law as [22]: $\theta _{tb}=\theta _{tg}=\sin ^{-1}\left (\frac {\pm \pi \lambda _{o}}{2\pi *1.45 *400nm}\right )=\pm 42.25^\circ$.
On the same account, for design 2, when +$\sigma$ light impinges on nanopillars, then the sizes of supercells are $\Lambda _b=\Lambda _g=4*400nm=1600nm$. As discussed above, from each set of nanopillars, the angle of deflection will also be same. Collectively, both sets split the incoming beam at $\pm 19.64^\circ$ due to opposite phase distribution of green and blue sets. By switching the input light to $-\sigma$, the arrangement of phase distribution from the nanopillars transforms such that the number of green and blue nanopillars for the complete phase coverage will not be same; therefore, the size of green and blue supercells will also not be same, i.e., $\Lambda _b \ne \Lambda _g$. In this design three green nanopillars cover the complete phase shift therefore: $\Lambda _g=3*400nm=1200nm$, as illustrated in Fig. 1(d). When nanopillars in a supercell have phase coverage $0-2\pi$ then $\theta _{tg}=\sin ^{-1}\left (\frac {\lambda _{o}2\pi }{2\pi *1.45 *1200nm}\right )=26.63^\circ$ and nanopillars in a supercell have coverage $2\pi -0$ then $\theta _{tg}=\sin ^{-1}\left (\frac {-\lambda _{o}2\pi }{2\pi *1.45 *1200nm}\right )=-26.63^\circ$. However, four nanopillars in a blue supercell cover the complete phase shift; therefore beam can deflect either to $+19.64^\circ$ or $-19.64^\circ$ depending upon arrangement of nanopillars. Hence, as a whole, this design works as a beam splitter which can split incoming light into desired directions. Here, we only presented a beam splitter that splits the light into two different angles on the left side of normal for $-\sigma$ incidence. In this case, it keeps beam deflection angle same emerging from blue set of nanopillars, i.e., $-19.64^\circ$ and tunes the beam deflection angle emerging from green set of nanopillars to $-26.63^\circ$. Hence, both of splitting angles will be on the left side of the normal, i.e., $-19.64^\circ$ $\&$ $-26.63^\circ$. From the above discussion, it can be asserted that one can reconfigure these designs by the arrangement and number of the nanopillars covering complete phase shift. By switching the spin of the incident light, the approach of simultaneous manipulation of propagation and geometric phases provides the opportunity to switch the phase coverage arrangement coming from the nanopillars and change the count of phase gradient covering complete phase shift without altering the actual design.
The FDTD lumerical solutions tool was used to obtain the unit cell’s electromagnetic response and optimize the parametric values. Parametric sweep was carried out between the “$L_x$” and “$L_y$” for each rotation angle between “$\theta =0-180^\circ$ with step size of “$2.8125^\circ$”. The CE [46] of the basic unit cell under CP light is shown in Fig. 2(a), which guarantees the high efficiency. The Fig. 2(b) shows that equal phase shift can be obtained for the CP cross-polarization when nanopillar is rotated at “$\theta =0^\circ$”. Similarly, equal phase shift for the circularly orthogonal transmitted light can be obtained when the nanopillar is rotated at “$\theta =90^\circ$”. The required phase value on a particular rotation angle “$\theta$” for crossed CP light can be obtained in the similar fashion as the side dimensions of nanopillar rotated at “$\theta =67.5^\circ$” can be determined from the phase distribution shown Fig. 2(c$\&d$). To numerically realize proposed tunable beam splitters, multiple basic blue and green sets of phase gradient are periodically arranged on the substrate in five rows according to the phase distribution presented in Tab.1. For design 1, 12 green and blue nanopillars are distributed from the centre in x-direction whereas in design 2, the number of nanopillars on each side is 24. Figure 3 presents the nearfield electric field distribution in xz-plane and their corresponding farfield results for the designed beam splitters under $+\sigma$ and $-\sigma$ incident light. In each design, total blue and green sets of phase gradients deflect the light according to the phase distribution coming from the nanopillars. The nearfield distributions of these designs in xz-plane [Figs. 3(a$\&$b)] show that cross-polarized electric field for the $+\sigma$ incident light is splitting into two directions. Due to the two-way beam deflection at interface, these designs act as beam splitters which redirect the incoming light according to the analytically calculated angles and tune the splitting angles under $-\sigma$ incident light. Hence, the desired angle tuning from each beam splitter design is achieved just by switching the handedness of incident light. From the farfield analysis [Figs. 3(a$\&$b)], it can be observed that the beam splitting angles match the analytically calculated values under $+\sigma$ and $-\sigma$ incident light. And, the power of transmitted light mainly splits in beam splitting directions. It is worth noting here that strong outgoing can be observed in the direction for whom a large number of super cells are working even in case of beam misalignment [28]. Furthermore, under $+\sigma$ light, the calculated transmission power for the design 1 consisting of the 24-nanopillars in one row is $40\%$ to the left side and $41\%$ to the right side. By switching the spin of incident light to $-\sigma$, $41\%$ of the power transmits to the left side and $41\%$ to the right side. For the design 2 consisting of the 24-nanopillars in one row, the $38\%$ of the transmitted power shifts to the left side and $40\%$ of power transfers to right side for the $+\sigma$ incident light. By switching the spin of incident light to $-\sigma$, the power shift to the left is $41\%$ and to the right side is $48\%$. It is worth noting here that the change of spin does not significantly change the power transfer in each beam splitting channel.
Fig. 2. Electromagnetic response of unit cell under CP light. (a) Conversion efficiency (CE) and phase distribution of cross polarized CP light for 2D parametric optimization when nanopillar is rotated at (b) $\theta (x,y)=0^\circ$ $\&$ (c $\&$ d) $\theta (x,y)=67.5^\circ$. The structural parameters of basic nanopillars [Tab.1] are marked with red squares (design 1) and black dots (design 2).
Fig. 3. Numerical simulation results of proposed beam splitter designs. Nearfield (real part and phase) in xz-plane and their corresponding farfield results of (a) design 1 and (b) design 2 under $\pm \sigma$ light clearly indicate that beam is splitting under $+\sigma$ light and splitting angles are being tuned under $-\sigma$ incident light.
Under $\pm \sigma$ light, transmitted cross-polarization phase distribution of 24 basic nanopillars and their corresponding optimized side dimensions, rotation angles and CE for each beam splitter design are tabulated in Tab.1. These parameters are optimized through suitable selection of propagation phase $n\theta$ values and merging them with geometric phase for the particular input/output combination of CP light, as discussed earlier. It should be noted that the values $\phi _{RCP\rightarrow LCP}$, $\phi _{LCP\rightarrow RCP}$ $\&$ $\theta (x,y) (^\circ )$ obtained from modified expressions for manipulation of transmitted CP orthogonal polarizations are the global phase and the rotation angle values, respectively. Here, these phase values are wrapped into $0-2\pi$, and rotation angles are wrapped into $0^\circ -180^\circ$. And the transmission coefficient emerging from each nanopillar is more than $.90$ in glass substrate. These designs can be experimentally realized through standard electron beam lithography in a similar way as silicon nanopillars were fabricated on glass substrate in Refs. [35,47].
3. Summary
We proposed and numerically realized spin tunable beam splitter based on dielectric metasurface through simultaneous manipulation of propagation and geometric phases. We presented two different beam splitter designs that split the RCP light of wavelength $\lambda _{0}=780nm$ at $\pm 19.64^\circ$. By switching the handedness of input light to LCP the design1 tunes the splitting angles at $\pm 42.25^\circ$ and design 2 steers the light at $-19.64^\circ$ $\&$ $-26.63^\circ$. It is emphasized that, the transmission power mainly transfers into desired orders which does not significantly change by changing the spin of incident light. The parameters of unit cell including period of unit cell, side dimensions, height and rotation of nanopillar are carefully optimized. The suitable phase profiles for both spins are adjusted to validate both beam splitter designs. One may reconfigure these designs to tune either one or both splitting angles by suitable selection and placement of nanopillars within the limit of generalized Snell’s law. Moreover, additional tunability can be introduced in the proposed design approach through the incident angle and stretchable substrate via suitable selection of phase profiles. Furthermore, our spin switchable beam splitter design approach is expected to play an important role in optical systems, communication, circular dichroism spectroscopy, and imaging on an ultrathin platform.
Funding
National Natural Science Foundation of China (61905147, 61935013, 91750205, U1701661); Leading Talents Program of Guangdong Province (00201505); Natural Science Foundation of Guangdong Province (2016A030312010, 2019TQ05X750, 2020A1515010598); Science, Technology and Innovation Commission of Shenzhen Municipality (JCYJ20180507182035270, KQTD2017033011044403, KQTD20180412181324255).
Acknowledgments
Authors acknowledge the technical support from Nanophotonics Research Center of Shenzhen university.
Disclosures
The authors declare no competing financial 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. 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]
2. R. C. Devlin, A. Ambrosio, D. Wintz, S. L. Oscurato, A. Y. Zhu, M. Khorasaninejad, J. Oh, P. Maddalena, and F. Capasso, “Spin-to-orbital angular momentum conversion in dielectric metasurfaces,” Opt. Express 25(1), 377–393 (2017). [CrossRef]
3. 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]
4. Y. H. Ko, N. Razmjooei, H. Hemmati, and R. Magnusson, “Perfectly-reflecting guided-mode-resonant photonic lattices possessing mie modal memory,” Opt. Express 29(17), 26971–26982 (2021). [CrossRef]
5. N. Razmjooei, Y. H. Ko, F. A. Simlan, and R. Magnusson, “Resonant reflection by microsphere arrays with ar-quenched mie scattering,” Opt. Express 29(12), 19183–19192 (2021). [CrossRef]
6. B. Yang, H. Cheng, S. Chen, and J. Tian, “Structural colors in metasurfaces: principle, design and applications,” Mater. Chem. Front. 3(5), 750–761 (2019). [CrossRef]
7. J. Wang, J. Kühne, T. Karamanos, C. Rockstuhl, S. A. Maier, and A. Tittl, “All-dielectric crescent metasurface sensor driven by bound states in the continuum,” Adv. Funct. Mater. 31(46), 2104652 (2021). [CrossRef]
8. A. U. R. Khalid, J. Liu, N. Ullah, and S. Jia, “Tunable beam deflection based on plasmonic resonators mounted freestanding thermoresponsive hydrogel,” Chin. Opt. Lett. 18(6), 062402 (2020). [CrossRef]
9. R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. Balthasar Mueller, and F. Capasso, “Arbitrary spin-to–orbital angular momentum conversion of light,” Science 358(6365), 896–901 (2017). [CrossRef]
10. Y. Hu, L. Li, Y. Wang, M. Meng, L. Jin, X. Luo, Y. Chen, X. Li, S. Xiao, H. Wang, Y. Luo, C. W. Qiu, and H. Duan, “Trichromatic and Tripolarization-Channel Holography with Noninterleaved Dielectric Metasurface,” Nano Lett. 20(2), 994–1002 (2020). [CrossRef]
11. A. U. R. Khalid, J. Liu, Y. Han, N. Ullah, R. Zhao, and Y. Wang, “Multichannel polarization encoded reflective metahologram using vo2 spacer in visible regime,” Opt. Commun. 451, 211–215 (2019). [CrossRef]
12. A. U. R. Khalid, J. Liu, Y. Han, N. Ullah, S. Jia, and Y. Wang, “Multipurpose thermoresponsive hydrogel: a platform for dynamic holographic display,” Opt. Lett. 45(2), 479–482 (2020). [CrossRef]
13. X. Li, L. Chen, Y. Li, X. Zhang, M. Pu, Z. Zhao, X. Ma, Y. Wang, M. Hong, and X. Luo, “Multicolor 3d meta-holography by broadband plasmonic modulation,” Sci. Adv. 2(11), e1601102 (2016). [CrossRef]
14. W. T. Chen, A. Y. Zhu, J. Sisler, Z. Bharwani, and F. Capasso, “A broadband achromatic polarization-insensitive metalens consisting of anisotropic nanostructures,” Nat. Commun. 10(1), 355 (2019). [CrossRef]
15. M. Khorasaninejad and F. Capasso, “Metalenses: Versatile multifunctional photonic components,” Science 358(6367), 1 (2017). [CrossRef]
16. N. Ullah, W. Liu, G. Wang, Z. Wang, A. U. R. Khalid, B. Hu, J. Liu, and Y. Zhang, “Gate-controlled terahertz focusing based on graphene-loaded metasurface,” Opt. Express 28(3), 2789–2798 (2020). [CrossRef]
17. E. Hecht, Optics, 5e (Pearson Education India, 2002).
18. K. Wen, Y. Hu, L. Chen, J. Zhou, L. Lei, and Z. Guo, “Design of an optical power and wavelength splitter based on subwavelength waveguides,” J. Lightwave Technol. 32(17), 3020–3026 (2014). [CrossRef]
19. E. Ordouie, H. Alisafaee, and A. Siahmakoun, “Ultracompact polarizing beam splitter based on single-material birefringent photonic crystal,” Opt. Lett. 43(17), 4288–4291 (2018). [CrossRef]
20. J.-C. Song, W. K. Jung, N.-H. Kim, and K. M. Byun, “Plasmonic wavelength splitter based on a large-area dielectric grating and white light illumination,” Opt. Lett. 37(18), 3915–3917 (2012). [CrossRef]
21. J. Feng and Z. Zhou, “Polarization beam splitter using a binary blazed grating coupler,” Opt. Lett. 32(12), 1662–1664 (2007). [CrossRef]
22. A. Ozer, N. Yilmaz, H. Kocer, and H. Kurt, “Polarization-insensitive beam splitters using all-dielectric phase gradient metasurfaces at visible wavelengths,” Opt. Lett. 43(18), 4350–4353 (2018). [CrossRef]
23. D. Zhang, M. Ren, W. Wu, N. Gao, X. Yu, W. Cai, X. Zhang, and J. Xu, “Nanoscale beam splitters based on gradient metasurfaces,” Opt. Lett. 43(2), 267–270 (2018). [CrossRef]
24. J. Sung, G.-Y. Lee, C. Choi, J. Hong, and B. Lee, “Polarization-dependent asymmetric transmission using a bifacial metasurface,” Nanoscale Horiz. 5(11), 1487–1495 (2020). [CrossRef]
25. G. Yoon, D. Lee, K. T. Nam, and J. Rho, “Geometric metasurface enabling polarization independent beam splitting,” Sci. Rep. 8(1), 9468 (2018). [CrossRef]
26. M. Khorasaninejad, W. Zhu, and K. Crozier, “Efficient polarization beam splitter pixels based on a dielectric metasurface,” Optica 2(4), 376–382 (2015). [CrossRef]
27. A. Ozer, N. Yilmaz, H. Kocer, and H. Kurt, “Broadband asymmetric light transmission based on all-dielectric metasurfaces in the visible spectrum,” J. Opt. 21(5), 055104 (2019). [CrossRef]
28. M. Wei, Q. Xu, Q. Wang, X. Zhang, Y. Li, J. Gu, Z. Tian, X. Zhang, J. Han, and W. Zhang, “Broadband non-polarizing terahertz beam splitters with variable split ratio,” Appl. Phys. Lett. 111(7), 071101 (2017). [CrossRef]
29. J. Ding, L. Huang, W. Liu, Y. Ling, W. Wu, and H. Li, “Mechanism and performance analyses of optical beam splitters using all-dielectric oligomer-based metasurfaces,” Opt. Express 28(22), 32721–32737 (2020). [CrossRef]
30. J. Wang, Q. Jiang, and D. Han, “Multi-channel beam splitters based on gradient metasurfaces,” Results Phys. 24, 104084 (2021). [CrossRef]
31. M. Khorasaninejad and K. B. Crozier, “Silicon nanofin grating as a miniature chirality-distinguishing beam-splitter,” Nat. Commun. 5(1), 5386 (2014). [CrossRef]
32. S. Hu, S. Du, J. Li, and C. Gu, “Multidimensional image and beam splitter based on hyperbolic metamaterials,” Nano Lett. 21(4), 1792–1799 (2021). [CrossRef]
33. W. S. Lee, S. Nirantar, D. Headland, M. Bhaskaran, S. Sriram, C. Fumeaux, and W. Withayachumnankul, “Broadband terahertz circular-polarization beam splitter,” Adv. Opt. Mater. 6(3), 1700852 (2018). [CrossRef]
34. Z.-H. Wang, S.-C. Jiang, X. Xiong, R.-W. Peng, and M. Wang, “Generation of equal-intensity coherent optical beams by binary geometrical phase on metasurface,” Appl. Phys. Lett. 108(26), 261107 (2016). [CrossRef]
35. B. Wang, F. Dong, H. Feng, D. Yang, Z. Song, L. Xu, W. Chu, Q. Gong, and Y. Li, “Rochon-prism-like planar circularly polarized beam splitters based on dielectric metasurfaces,” ACS Photonics 5(5), 1660–1664 (2018). [CrossRef]
36. C. Wang, S. Liu, Y. Sun, X. Tao, P. Sun, J. Zhang, C. Tao, R. Wu, F. Wu, and Z. Zheng, “Tunable beam splitter using bilayer geometric metasurfaces in the visible spectrum,” Opt. Express 28(19), 28672–28685 (2020). [CrossRef]
37. X. Xie, M. Pu, K. Liu, X. Ma, X. Li, J. Yang, and X. Luo, “High-efficiency and tunable circular-polarization beam splitting with a liquid-filled all-metallic catenary meta-mirror,” Adv. Mater. Technol. 4(7), 1900334 (2019). [CrossRef]
38. H.-S. Ee and R. Agarwal, “Tunable metasurface and flat optical zoom lens on a stretchable substrate,” Nano Lett. 16(4), 2818–2823 (2016). [CrossRef]
39. O. J. Allegre, W. Perrie, K. Bauchert, D. Liu, S. P. Edwardson, G. Dearden, and K. G. Watkins, “Real-time control of polarisation in ultra-short-pulse laser micro-machining,” Appl. Phys. A 107(2), 445–454 (2012). [CrossRef]
40. E. Mohammadi, K. Tsakmakidis, A.-N. Askarpour, P. Dehkhoda, A. Tavakoli, and H. Altug, “Nanophotonic platforms for enhanced chiral sensing,” ACS Photonics 5(7), 2669–2675 (2018). [CrossRef]
41. P. Spaeth, S. Adhikari, L. Le, T. Jollans, S. Pud, W. Albrecht, T. Bauer, M. Caldarola, L. Kuipers, and M. Orrit, “Circular Dichroism Measurement of Single Metal Nanoparticles Using Photothermal Imaging,” Nano Lett. 19(12), 8934–8940 (2019). [CrossRef]
42. J. P. Balthasar Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface Polarization Optics: Independent Phase Control of Arbitrary Orthogonal States of Polarization,” Phys. Rev. Lett. 118(11), 113901 (2017). [CrossRef]
43. D.-C. Hu, J.-G. Lu, J.-L. Feng, S.-Y. Liu, and Y.-J. Wang, “Three-dimensional display with directional beam splitter array,” Opt. Express 25(2), 1564–1572 (2017). [CrossRef]
44. C. Chen, S. Gao, X. Xiao, X. Ye, S. Wu, W. Song, H. Li, S. Zhu, and T. Li, “Highly Efficient Metasurface Quarter-Wave Plate with Wave Front Engineering,” Adv. Photonics Res. 2(3), 2000154 (2021). [CrossRef]
45. A. U. R. Khalid, F. Feng, N. Ullah, M. Somekh, and X. Yuan, “Exploitation of geometric and propagation phases for spin-dependent rational rational multiple complete phase modulation using dielectric metasurfaces,” Photonics Res. 10(4), 877–885 (2022). [CrossRef]
46. J. Shi, H. Ma, C. Guan, Z. Wang, and T. Cui, “Broadband chirality and asymmetric transmission in ultrathin 90-twisted babinet-inverted metasurfaces,” Phys. Rev. B 89(16), 165128 (2014). [CrossRef]
47. Q.-T. Li, F. Dong, B. Wang, F. Gan, J. Chen, Z. Song, L. Xu, W. Chu, Y.-F. Xiao, Q. Gong, and L. Yan, “Polarization-independent and high-efficiency dielectric metasurfaces for visible light,” Opt. Express 24(15), 16309–16319 (2016). [CrossRef]
