Polarization Engineering via Metamaterials and Metasurfaces

Polarization, an intrinsic property of transverse waves, encapsulates a wealth of information and serves as a crucial degree of freedom. In recent decades, thanks to the rapid advancement of metamaterials and metasurfaces, unprecedented control over various physical systems has been achieved. Through meticulous engineering subwavelength structures, known as meta-atoms, of varying sizes, shapes, and materials, a multitude of polarization-related studies have emerged in the domains of electromagnetic waves, acoustic waves, and elastic waves. In contrast to conventional polarization elements, novel devices based on metamaterials achieve unique polarization-dependent phenomena by manipulating fundamental physical parameters through resonance tuning. Moreover, metasurfaces, the two-dimensional counterpart of metamaterials, demonstrate exceptional control capabilities over waves and possess unparalleled integration, providing a broad platform for polarization manipulation. In this thesis, our research efforts are directed towards the generation and application of polarization. We have successfully produced a series of polarizers in the optical and acoustic domains using 2D metasurfaces and 3D metamaterials, respectively. Furthermore, leveraging their polarization conversion capabilities, we explore novel physical phenomena and present a variety of polarization-related applications.

       In Chapter 1, this thesis commences by outlining and reviewing the fundamental principles of polarization, metamaterials and metasurfaces, along with summarizing representative works related to polarization engineering.

       The thesis proceeds with a logical progression from theory to experiment, and from generation to utilization, presenting three researches conducted during the doctoral period in the following three chapters.

       In Chapter 2, a series of dielectric metasurface polarizers are introduced. To ensure the polarization conversion performance in the design wavelength, we have established a method for characterizing the real Jones matrix of metasurface polarizers. This method offers a novel solution to the problems of dispersion and high demands on nano-fabrication that are commonly encountered in polarization meta-devices. Furthermore, by decomposing the Jones matrix, encryption and extraction of polarization information have been achieved.

       In Chapter 3, we conducted further research based on two unique types of metasurface polarizers, left and right circular polarizers. By applying rotation operations to the circular polarizer unit, we achieved simultaneous control of phase and polarization. Furthermore, by designing different phase distributions for different kinds of circular polarizer units, we achieved a leap from scalar holography to vectorial holography. Vectorial holography possessing arbitrary polarization distributions are generated based on circular polarizers, with the twin image problem which often plagues geometric phase holography solved.

       In Chapter 4, we continue to study circular polarization, a particular state with spin angular momentum, but in the context of sound waves. By designing an acoustic metamaterial composed by helical structures, we obtained a circular polarizer for sound waves that can generate circularly polarized states. Through simulations and experiments conducted in both momentum space, the spin-orbit interaction of sound has been observed, providing further evidence for generation circular polarization state of sound. This research fills the missing degree of freedom in traditional acoustics and provides a new perspective for manipulating sound.

       Our research makes full use of the capabilities of metasurfaces and metamaterials to manipulate classical waves, resulting in the successful generation and utilization of polarization states in both light and sound. We believe that the various polarizer-type devices introduced in this thesis may be applied to a wide range of fields, including polarization detection, complex field generation, and high-capacity communication, among others.

[1] J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1999).
[2] M. Born, E. Wolf, and A. B. Bhatia, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light, Seventh (expanded) anniversary edition, 60th anniversary edition (Cambridge University Press, Cambridge, 2019).
[3] D. H. Goldstein, Polarized Light, 3rd ed. (CRC Press, Boca Raton, 2017).
[4] W. F. Magie, A Source Book in Physics (Harvard U. P., Cambridge, 1965).
[5] A. Rodger and B. Nordén, Circular Dichroism and Linear Dichroism (Oxford University Press, Oxford, 1997).
[6] E. Hecht, Optics, 5 ed (Pearson Education, Inc, Boston, 2017).
[7] D. Brewster, IX. On the Laws Which Regulate the Polarisation of Light by Reflexion from Transparent Bodies. By David Brewster, LL. D. F. R. S. Edin. and F. S. A. Edin. In a Letter Addressed to Right Hon. Sir Joseph Banks, Bart. K. B. P. R. S, Philos. Trans. R. Soc. Lond. 105, 125 (1997).
[8] L. Kristjánsson, Iceland Spar and Its Influence on the Development of Science and Technology in the Period 1780–1930, 3rd ed. (University of Iceland, Reykjavík, 2010).
[9] R. A. Chipman, G. Young, and W. S. T. Lam, Polarized Light and Optical Systems (Taylor & Francis, CRC Press, Boca Raton, 2018).
[10] G. Ma and P. Sheng, Acoustic Metamaterials: From Local Resonances to Broad Horizons, Sci. Adv. 2, e1501595 (2016).
[11] C. Shi, R. Zhao, Y. Long, S. Yang, Y. Wang, H. Chen, J. Ren, and X. Zhang, Observation of Acoustic Spin, Natl. Sci. Rev. 6, 707 (2019).
[12] M. R. Scheinfein, J. Unguris, M. H. Kelley, D. T. Pierce, and R. J. Celotta, Scanning Electron Microscopy with Polarization Analysis (SEMPA), Rev. Sci. Instrum. 61, 2501 (1990).
[13] S. Hénon and J. Meunier, Microscope at the Brewster Angle: Direct Observation of First‐order Phase Transitions in Monolayers, Rev. Sci. Instrum. 62, 936 (1991).
[14] S. G. Demos and R. R. Alfano, Optical Polarization Imaging, Appl. Opt. 36, 150 (1997).
[15] P. J. Winzer, D. T. Neilson, and A. R. Chraplyvy, Fiber-Optic Transmission and Networking: The Previous 20 and the next 20 Years [Invited], Opt. Express 26, 24190 (2018).
[16] D. J. Richardson, J. M. Fini, and L. E. Nelson, Space-Division Multiplexing in Optical Fibres, Nat. Photonics 7, 354 (2013).
[17] E. Komatsu, New Physics from the Polarized Light of the Cosmic Microwave Background, Nat. Rev. Phys. 4, 452 (2022).
[18] T. R. Seshadri and K. Subramanian, Cosmic Microwave Background Polarization Signals from Tangled Magnetic Fields, Phys. Rev. Lett. 87, 101301 (2001).
[19] M. J. Stephen and J. P. Straley, Physics of Liquid Crystals, Rev. Mod. Phys. 46, 617 (1974).
[20] T. K. Das and S. Prusty, Review on Conducting Polymers and Their Applications, Polym.-Plast. Technol. Eng. 51, 1487 (2012).
[21] L. A. Nguyen, H. He, and C. Pham-Huy, Chiral Drugs: An Overview, Int. J. Biomed. Sci. IJBS 2, 85 (2006).
[22] R. Naaman, Y. Paltiel, and D. H. Waldeck, Chiral Molecules and the Electron Spin, Nat. Rev. Chem. 3, 250 (2019).
[23] S. Crampin, Seismic-Wave Propagation through a Cracked Solid: Polarization as a Possible Dilatancy Diagnostic, Geophys. J. Int. 53, 467 (1978).
[24] T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, Quantum Computers, Nature 464, 7285 (2010).
[25] J. L. O’Brien, Optical Quantum Computing, Science 318, 1567 (2007).
[26] N. Gisin and R. Thew, Quantum Communication, Nat. Photonics 1, 165 (2007).
[27] P. W. Shor and J. Preskill, Simple Proof of Security of the BB84 Quantum Key Distribution Protocol, Phys. Rev. Lett. 85, 441 (2000).
[28] Y.-A. Chen et al., An Integrated Space-to-Ground Quantum Communication Network over 4,600 Kilometres, Nature 589, 7841 (2021).
[29] C. Couteau, S. Barz, T. Durt, T. Gerrits, J. Huwer, R. Prevedel, J. Rarity, A. Shields, and G. Weihs, Applications of Single Photons to Quantum Communication and Computing, Nat. Rev. Phys. 5, 326 (2023).
[30] V. G. Veselago, Electrodynamics of Substances with Simultaneously Negative Values of ε and μ, Sov. Phys. Uspekhi 10, 509 (1968).
[31] J. B. Pendry, Negative Refraction Makes a Perfect Lens, Phys. Rev. Lett. 85, 3966 (2000).
[32] C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, All-Angle Negative Refraction without Negative Effective Index, Phys. Rev. B 65, 201104 (2002).
[33] D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Metamaterials and Negative Refractive Index, Science 305, 788 (2004).
[34] D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Composite Medium with Simultaneously Negative Permeability and Permittivity, Phys. Rev. Lett. 84, 4184 (2000).
[35] R. A. Shelby, D. R. Smith, and S. Schultz, Experimental Verification of a Negative Index of Refraction, Science 292, 77 (2001).
[36] J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Photonic Crystals: Putting a New Twist on Light, Nature 386, 6621 (1997).
[37] M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, Acoustic Band Structure of Periodic Elastic Composites, Phys. Rev. Lett. 71, 2022 (1993).
[38] S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, Experimental Demonstration of Near-Infrared Negative-Index Metamaterials, Phys. Rev. Lett. 95, 137404 (2005).
[39] C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, Experimental Verification and Simulation of Negative Index of Refraction Using Snell’s Law, Phys. Rev. Lett. 90, 107401 (2003).
[40] A. A. Houck, J. B. Brock, and I. L. Chuang, Experimental Observations of a Left-Handed Material That Obeys Snell’s Law, Phys. Rev. Lett. 90, 137401 (2003).
[41] C. M. Soukoulis, S. Linden, and M. Wegener, Negative Refractive Index at Optical Wavelengths, Science 315, 47 (2007).
[42] V. M. Shalaev, Optical Negative-Index Metamaterials, Nat. Photonics 1, 41 (2007).
[43] C. García-Meca, J. Hurtado, J. Martí, A. Martínez, W. Dickson, and A. V. Zayats, Low-Loss Multilayered Metamaterial Exhibiting a Negative Index of Refraction at Visible Wavelengths, Phys. Rev. Lett. 106, 067402 (2011).
[44] Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, Locally Resonant Sonic Materials, Science 289, 1734 (2000).
[45] Y. Ding, Z. Liu, C. Qiu, and J. Shi, Metamaterial with Simultaneously Negative Bulk Modulus and Mass Density, Phys. Rev. Lett. 99, 093904 (2007).
[46] S. H. Lee, C. M. Park, Y. M. Seo, Z. G. Wang, and C. K. Kim, Composite Acoustic Medium with Simultaneously Negative Density and Modulus, Phys. Rev. Lett. 104, 054301 (2010).
[47] T. Brunet, A. Merlin, B. Mascaro, K. Zimny, J. Leng, O. Poncelet, C. Aristégui, and O. Mondain-Monval, Soft 3D Acoustic Metamaterial with Negative Index, Nat. Mater. 14, 384 (2015).
[48] M. Yang, G. Ma, Z. Yang, and P. Sheng, Coupled Membranes with Doubly Negative Mass Density and Bulk Modulus, Phys. Rev. Lett. 110, 134301 (2013).
[49] Y. Wu, Y. Lai, and Z.-Q. Zhang, Elastic Metamaterials with Simultaneously Negative Effective Shear Modulus and Mass Density, Phys. Rev. Lett. 107, 105506 (2011).
[50] Y. Lai, Y. Wu, P. Sheng, and Z.-Q. Zhang, Hybrid Elastic Solids, Nat. Mater. 10, 620 (2011).

[51] X. N. Liu, G. K. Hu, G. L. Huang, and C. T. Sun, An Elastic Metamaterial with Simultaneously Negative Mass Density and Bulk Modulus, Appl. Phys. Lett. 98, 251907 (2011).

[52] M. Kadic, G. W. Milton, M. van Hecke, and M. Wegener, 3D Metamaterials, Nat. Rev. Phys. 1, 198 (2019).

[53] P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, Realization of an All-Dielectric Zero-Index Optical Metamaterial, Nat. Photonics 7, 791 (2013).

[54] W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, Optical Cloaking with Metamaterials, Nat. Photonics 1, 224 (2007).

[55] N. Fang, H. Lee, C. Sun, and X. Zhang, Sub-Diffraction-Limited Optical Imaging with a Silver Superlens, Science 308, 534 (2005).

[56] N. Kaina, F. Lemoult, M. Fink, and G. Lerosey, Negative Refractive Index and Acoustic Superlens from Multiple Scattering in Single Negative Metamaterials, Nature 525, 7567 (2015).

[57] J. Christensen and F. J. G. de Abajo, Anisotropic Metamaterials for Full Control of Acoustic Waves, Phys. Rev. Lett. 108, 124301 (2012).

[58] J. Zhu, J. Christensen, J. Jung, L. Martin-Moreno, X. Yin, L. Fok, X. Zhang, and F. J. Garcia-Vidal, A Holey-Structured Metamaterial for Acoustic Deep-Subwavelength Imaging, Nat. Phys. 7, 52 (2011).

[59] S. Zhang, C. Xia, and N. Fang, Broadband Acoustic Cloak for Ultrasound Waves, Phys. Rev. Lett. 106, 024301 (2011).

[60] G. W. Milton, M. Briane, and J. R. Willis, On Cloaking for Elasticity and Physical Equations with a Transformation Invariant Form, New J. Phys. 8, 248 (2006).

[61] J. Mei, G. Ma, M. Yang, Z. Yang, W. Wen, and P. Sheng, Dark Acoustic Metamaterials as Super Absorbers for Low-Frequency Sound, Nat. Commun. 3, 756 (2012).

[62] J. Hao, Q. Ren, Z. An, X. Huang, Z. Chen, M. Qiu, and L. Zhou, Optical Metamaterial for Polarization Control, Phys. Rev. A 80, 023807 (2009).

[63] C. Menzel, C. Helgert, C. Rockstuhl, E.-B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, Asymmetric Transmission of Linearly Polarized Light at Optical Metamaterials, Phys. Rev. Lett. 104, 253902 (2010).

[64] C. Pfeiffer, C. Zhang, V. Ray, L. J. Guo, and A. Grbic, High Performance Bianisotropic Metasurfaces: Asymmetric Transmission of Light, Phys. Rev. Lett. 113, 023902 (2014).

[65] J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, Manipulating Electromagnetic Wave Polarizations by Anisotropic Metamaterials, Phys. Rev. Lett. 99, 063908 (2007).

[66] E. Plum, X.-X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, and N. I. Zheludev, Metamaterials: Optical Activity without Chirality, Phys. Rev. Lett. 102, 113902 (2009).

[67] A. C. Strikwerda, K. Fan, H. Tao, D. V. Pilon, X. Zhang, and R. D. Averitt, Comparison of Birefringent Electric Split-Ring Resonator and Meanderline Structures as Quarter-Wave Plates at Terahertz Frequencies, Opt. Express 17, 136 (2009).

[68] N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H.-T. Chen, Terahertz Metamaterials for Linear Polarization Conversion and Anomalous Refraction, Science 340, 1304 (2013).

[69] L. Cong, W. Cao, Z. Tian, J. Gu, J. Han, and W. Zhang, Manipulating Polarization States of Terahertz Radiation Using Metamaterials, New J. Phys. 14, 115013 (2012).

[70] J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, Gold Helix Photonic Metamaterial as Broadband Circular Polarizer, Science 325, 1513 (2009).

[71] J. Kaschke and M. Wegener, Gold Triple-Helix Mid-Infrared Metamaterial by STED-Inspired Laser Lithography, Opt. Lett. 40, 3986 (2015).

[72] C. Wu, H. Li, X. Yu, F. Li, H. Chen, and C. T. Chan, Metallic Helix Array as a Broadband Wave Plate, Phys. Rev. Lett. 107, 177401 (2011).

[73] C. Rockstuhl, C. Menzel, T. Paul, and F. Lederer, Optical Activity in Chiral Media Composed of Three-Dimensional Metallic Meta-Atoms, Phys. Rev. B 79, 035321 (2009).

[74] Y. Zhao, M. A. Belkin, and A. Alù, Twisted Optical Metamaterials for Planarized Ultrathin Broadband Circular Polarizers, Nat. Commun. 3, 870 (2012).

[75] Y. Zhao, A. N. Askarpour, L. Sun, J. Shi, X. Li, and A. Alù, Chirality Detection of Enantiomers Using Twisted Optical Metamaterials, Nat. Commun. 8, 14180 (2017).

[76] V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, Asymmetric Propagation of Electromagnetic Waves through a Planar Chiral Structure, Phys. Rev. Lett. 97, 167401 (2006).

[77] I. D. Toftul, K. Y. Bliokh, M. I. Petrov, and F. Nori, Acoustic Radiation Force and Torque on Small Particles as Measures of the Canonical Momentum and Spin Densities, Phys. Rev. Lett. 123, 183901 (2019).

[78] Y. Long, H. Ge, D. Zhang, X. Xu, J. Ren, M.-H. Lu, M. Bao, H. Chen, and Y.-F. Chen, Symmetry Selective Directionality in Near-Field Acoustics, Natl. Sci. Rev. 7, 1024 (2020).

[79] Y. Long, D. Zhang, C. Yang, J. Ge, H. Chen, and J. Ren, Realization of Acoustic Spin Transport in Metasurface Waveguides, Nat. Commun. 11, 4716 (2020).

[80] K. Y. Bliokh, H. Punzmann, H. Xia, F. Nori, and M. Shats, Field Theory Spin and Momentum in Water Waves, Sci. Adv. 8, eabm1295 (2022).

[81] L. D. Landau, E. M. Lifshitz, A. M. Kosevich, and L. P. Pitaevskii, Theory of Elasticity: Volume 7 (Elsevier, 1986).

[82] S. Brûlé, E. H. Javelaud, S. Enoch, and S. Guenneau, Experiments on Seismic Metamaterials: Molding Surface Waves, Phys. Rev. Lett. 112, 133901 (2014).

[83] G. Ma, C. Fu, G. Wang, P. Del Hougne, J. Christensen, Y. Lai, and P. Sheng, Polarization Bandgaps and Fluid-like Elasticity in Fully Solid Elastic Metamaterials, Nat. Commun. 7, 13536 (2016).

[84] G. J. Chaplain, J. M. De Ponti, and R. V. Craster, Elastic Orbital Angular Momentum, Phys. Rev. Lett. 128, 064301 (2022).

[85] K. Y. Bliokh, Elastic Spin and Orbital Angular Momenta, Phys. Rev. Lett. 129, 204303 (2022).

[86] M. F. Groß, J. L. G. Schneider, Y. Wei, Y. Chen, S. Kalt, M. Kadic, X. Liu, G. Hu, and M. Wegener, Tetramode Metamaterials as Phonon Polarizers, Adv. Mater. 35, 2211801 (2023).

[87] T. Frenzel, M. Kadic, and M. Wegener, Three-Dimensional Mechanical Metamaterials with a Twist, Science 358, 1072 (2017).

[88] Y. Long, J. Ren, and H. Chen, Intrinsic Spin of Elastic Waves, Proc. Natl. Acad. Sci. 115, 9951 (2018).

[89] W. Yuan, C. Yang, D. Zhang, Y. Long, Y. Pan, Z. Zhong, H. Chen, J. Zhao, and J. Ren, Observation of Elastic Spin with Chiral Meta-Sources, Nat. Commun. 12, 6954 (2021).

[90] H.-T. Chen, A. J. Taylor, and N. Yu, A Review of Metasurfaces: Physics and Applications, Rep. Prog. Phys. 79, 076401 (2016).

[91] B. Assouar, B. Liang, Y. Wu, Y. Li, J.-C. Cheng, and Y. Jing, Acoustic Metasurfaces, Nat. Rev. Mater. 3, 12 (2018).

[92] J. Park, D. Lee, and J. Rho, Recent Advances in Non-Traditional Elastic Wave Manipulation by Macroscopic Artificial Structures, Appl. Sci. 10, 2 (2020).

[93] 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, 1190 (2016).

[94] G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, Metasurface Holograms Reaching 80% Efficiency, Nat. Nanotechnol. 10, 308 (2015).

[95] S. Linden, F. B. P. Niesler, J. Förstner, Y. Grynko, T. Meier, and M. Wegener, Collective Effects in Second-Harmonic Generation from Split-Ring-Resonator Arrays, Phys. Rev. Lett. 109, 015502 (2012).

[96] Y. Tang, K. Li, X. Zhang, J. Deng, G. Li, and E. Brasselet, Harmonic Spin–Orbit Angular Momentum Cascade in Nonlinear Optical Crystals, Nat. Photonics 14, 658 (2020).

[97] T. Santiago-Cruz, S. D. Gennaro, O. Mitrofanov, S. Addamane, J. Reno, I. Brener, and M. V. Chekhova, Resonant Metasurfaces for Generating Complex Quantum States, Science 377, 991 (2022).

[98] J. Karst, M. Floess, M. Ubl, C. Dingler, C. Malacrida, T. Steinle, S. Ludwigs, M. Hentschel, and H. Giessen, Electrically Switchable Metallic Polymer Nanoantennas, Science 374, 612 (2021).

[99] A. Komar, Z. Fang, J. Bohn, J. Sautter, M. Decker, A. Miroshnichenko, T. Pertsch, I. Brener, Y. S. Kivshar, I. Staude, and D. N. Neshev, Electrically Tunable All-Dielectric Optical Metasurfaces Based on Liquid Crystals, Appl. Phys. Lett. 110, 071109 (2017).

[100] L. Li, T. Jun Cui, W. Ji, S. Liu, J. Ding, X. Wan, Y. Bo Li, M. Jiang, C.-W. Qiu, and S. Zhang, Electromagnetic Reprogrammable Coding-Metasurface Holograms, Nat. Commun. 8, 197 (2017).

[101] K. Wang, K. De Greve, L. A. Jauregui, A. Sushko, A. High, Y. Zhou, G. Scuri, T. Taniguchi, K. Watanabe, M. D. Lukin, H. Park, and P. Kim, Electrical Control of Charged Carriers and Excitons in Atomically Thin Materials, Nat. Nanotechnol. 13, 128 (2018).

[102] 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, 333 (2011).

[103] X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, Ultra-Thin, Planar, Babinet-Inverted Plasmonic Metalenses, Light Sci. Appl. 2, e72 (2013).

[104] X. Ni, A. V. Kildishev, and V. M. Shalaev, Metasurface Holograms for Visible Light, Nat. Commun. 4, 2807 (2013).

[105] S. Sun, K.-Y. Yang, C.-M. Wang, T.-K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W.-T. Kung, G.-Y. Guo, L. Zhou, and D. P. Tsai, High-Efficiency Broadband Anomalous Reflection by Gradient Meta-Surfaces, Nano Lett. 12, 6223 (2012).

[106] S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, Gradient-Index Meta-Surfaces as a Bridge Linking Propagating Waves and Surface Waves, Nat. Mater. 11, 426 (2012).

[107] K. Koshelev and Y. Kivshar, Dielectric Resonant Metaphotonics, ACS Photonics 8, 102 (2021).

[108] M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. M. Litchinitser, High-Efficiency All-Dielectric Metasurfaces for Ultracompact Beam Manipulation in Transmission Mode, Nano Lett. 15, 6261 (2015).

[109] 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: High-Transmission Dielectric Metasurface with 2π Phase Control at Visible Wavelengths, Laser Photonics Rev. 9, 412 (2015).

[110] A. Zhan, S. Colburn, R. Trivedi, T. K. Fryett, C. M. Dodson, and A. Majumdar, Low-Contrast Dielectric Metasurface Optics, ACS Photonics 3, 209 (2016).

[111] 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, 937 (2015).

[112] M. V. Berry, Quantal Phase Factors Accompanying Adiabatic Changes, Proc. R. Soc. Lond. Math. Phys. Sci. 392, 45 (1997).

[113] S. Pancharatnam, Generalized Theory of Interference, and Its Applications, Proc Indian Acad Sci Sect A 44, 247 (1956).

[114] Z. Bomzon, V. Kleiner, and E. Hasman, Pancharatnam–Berry Phase in Space-Variant Polarization-State Manipulations with Subwavelength Gratings, Opt. Lett. 26, 1424 (2001).

[115] F. Gori, Measuring Stokes Parameters by Means of a Polarization Grating, Opt. Lett. 24, 584 (1999).

[116] N. M. Litchinitser, Photonic Multitasking Enabled with Geometric Phase, Science 352, 1177 (2016).

[117] R. C. Jones, A New Calculus for the Treatment of Optical SystemsI Description and Discussion of the Calculus, J. Opt. Soc. Am. 31, 488 (1941).

[118] G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, Continuous Control of the Nonlinearity Phase for Harmonic Generations, Nat. Mater. 14, 607 (2015).

[119] 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, 1558 (2016).

[120] 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, 1198 (2012).

[121] L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, Dispersionless Phase Discontinuities for Controlling Light Propagation, Nano Lett. 12, 5750 (2012).

[122] B. R. Brown and A. W. Lohmann, Complex Spatial Filtering with Binary Masks, Appl. Opt. 5, 967 (1966).

[123] C. Min, J. Liu, T. Lei, G. Si, Z. Xie, J. Lin, L. Du, and X. Yuan, Plasmonic Nano-Slits Assisted Polarization Selective Detour Phase Meta-Hologram: Plasmonic Nano-Slits Assisted Polarization Selective Detour Phase Meta-Hologram, Laser Photonics Rev. 10, 978 (2016).

[124] K. Zhang, Y. Wang, S. N. Burokur, and Q. Wu, Generating Dual-Polarized Vortex Beam by Detour Phase: From Phase Gradient Metasurfaces to Metagratings, IEEE Trans. Microw. Theory Tech. 70, 200 (2022).

[125] J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, Nanostructured Holograms for Broadband Manipulation of Vector Beams, Nano Lett. 13, 4269 (2013).

[126] B. Auguié and W. L. Barnes, Collective Resonances in Gold Nanoparticle Arrays, Phys. Rev. Lett. 101, 143902 (2008).

[127] Y. Zhao and A. Alù, Tailoring the Dispersion of Plasmonic Nanorods To Realize Broadband Optical Meta-Waveplates, Nano Lett. 13, 1086 (2013).

[128] Y. Zhao and A. Alù, Manipulating Light Polarization with Ultrathin Plasmonic Metasurfaces, Phys. Rev. B 84, 205428 (2011).

[129] S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, Invited Article: Broadband Highly Efficient Dielectric Metadevices for Polarization Control, APL Photonics 1, 030801 (2016).

[130] 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, 1394 (2014).

[131] 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, 2000154 (2021).

[132] N. A. Rubin, A. Zaidi, M. Juhl, R. P. Li, J. P. B. Mueller, R. C. Devlin, K. Leósson, and F. Capasso, Polarization State Generation and Measurement with a Single Metasurface, Opt. Express 26, 21455 (2018).

[133] D. Wen, F. Yue, S. Kumar, Y. Ma, M. Chen, X. Ren, P. E. Kremer, B. D. Gerardot, M. R. Taghizadeh, G. S. Buller, and X. Chen, Metasurface for Characterization of the Polarization State of Light, Opt. Express 23, 10272 (2015).

[134] M. Khorasaninejad and K. B. Crozier, Silicon Nanofin Grating as a Miniature Chirality-Distinguishing Beam-Splitter, Nat. Commun. 5, 5386 (2014).

[135] J. Bar-David and U. Levy, Nonlinear Diffraction in Asymmetric Dielectric Metasurfaces, Nano Lett. 19, 1044 (2019).

[136] B. Reineke, B. Sain, R. Zhao, L. Carletti, B. Liu, L. Huang, C. De Angelis, and T. Zentgraf, Silicon Metasurfaces for Third Harmonic Geometric Phase Manipulation and Multiplexed Holography, Nano Lett. 19, 6585 (2019).

[137] B. Liu, B. Sain, B. Reineke, R. Zhao, C. Meier, L. Huang, Y. Jiang, and T. Zentgraf, Nonlinear Wavefront Control by Geometric-Phase Dielectric Metasurfaces: Influence of Mode Field and Rotational Symmetry, Adv. Opt. Mater. 8, 1902050 (2020).

[138] M. Khorasaninejad, A. Ambrosio, P. Kanhaiya, and F. Capasso, Broadband and Chiral Binary Dielectric Meta-Holograms, Sci. Adv. 2, e1501258 (2016).

[139] Z.-L. Deng, J. Deng, X. Zhuang, S. Wang, T. Shi, G. P. Wang, Y. Wang, J. Xu, Y. Cao, X. Wang, X. Cheng, G. Li, and X. Li, Facile Metagrating Holograms with Broadband and Extreme Angle Tolerance, Light Sci. Appl. 7, 78 (2018).

[140] J. Li, S. Chen, H. Yang, J. Li, P. Yu, H. Cheng, C. Gu, H.-T. Chen, and J. Tian, Simultaneous Control of Light Polarization and Phase Distributions Using Plasmonic Metasurfaces, Adv. Funct. Mater. 25, 704 (2015).

[141] D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, Dielectric Gradient Metasurface Optical Elements, Science 345, 298 (2014).

[142] 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, 6328 (2012).

[143] P. C. Wu, W.-Y. Tsai, W. T. Chen, Y.-W. Huang, T.-Y. Chen, J.-W. Chen, C. Y. Liao, C. H. Chu, G. Sun, and D. P. Tsai, Versatile Polarization Generation with an Aluminum Plasmonic Metasurface, Nano Lett. 17, 445 (2017).

[144] Z. Deng, M. Jin, X. Ye, S. Wang, T. Shi, J. Deng, N. Mao, Y. Cao, B. Guan, A. Alù, G. Li, and X. Li, Full‐Color Complex‐Amplitude Vectorial Holograms Based on Multi‐Freedom Metasurfaces, Adv. Funct. Mater. 30, 1910610 (2020).

[145] 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, 113901 (2017).

[146] Y. Bao, L. Wen, Q. Chen, C.-W. Qiu, and B. Li, Toward the Capacity Limit of 2D Planar Jones Matrix with a Single-Layer Metasurface, Sci. Adv. 7, eabh0365 (2021).

[147] Q. Song, M. Odeh, J. Zúñiga-Pérez, B. Kanté, and P. Genevet, Plasmonic Topological Metasurface by Encircling an Exceptional Point, Science 373, 1133 (2021).

[148] B. Xiong, Y. Liu, Y. Xu, L. Deng, C.-W. Chen, J.-N. Wang, R. Peng, Y. Lai, Y. Liu, and M. Wang, Breaking the Limitation of Polarization Multiplexing in Optical Metasurfaces with Engineered Noise, Science 379, 294 (2023).

[149] D. Wang, F. Liu, T. Liu, S. Sun, Q. He, and L. Zhou, Efficient Generation of Complex Vectorial Optical Fields with Metasurfaces, Light Sci. Appl. 10, 67 (2021).

[150] M. Khorasaninejad, W. Zhu, and K. B. Crozier, Efficient Polarization Beam Splitter Pixels Based on a Dielectric Metasurface, Optica 2, 376 (2015).

[151] Z. Shi, A. Y. Zhu, Z. Li, Y.-W. Huang, W. T. Chen, C.-W. Qiu, and F. Capasso, Continuous Angle-Tunable Birefringence with Freeform Metasurfaces for Arbitrary Polarization Conversion, Sci. Adv. 6, eaba3367 (2020).

[152] N. Mao, G. Zhang, Y. Tang, Y. Li, Z. Hu, X. Zhang, K. Li, K. Cheah, and G. Li, Nonlinear Vectorial Holography with Quad-Atom Metasurfaces, Proc. Natl. Acad. Sci. 119, e2204418119 (2022).

[153] P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, New High-Intensity Source of Polarization-Entangled Photon Pairs, Phys. Rev. Lett. 75, 4337 (1995).

[154] Y. Kozawa and S. Sato, Generation of a Radially Polarized Laser Beam by Use of a Conical Brewster Prism, Opt. Lett. 30, 3063 (2005).

[155] K. V. Chellappan, E. Erden, and H. Urey, Laser-Based Displays: A Review, Appl. Opt. 49, F79 (2010).

[156] M. De and L. Sévigny, Polarization Holography, J. Opt. Soc. Am. 57, 110_1 (1967).

[157] C. He, H. He, J. Chang, B. Chen, H. Ma, and M. J. Booth, Polarisation Optics for Biomedical and Clinical Applications: A Review, Light Sci. Appl. 10, 194 (2021).

[158] K. Sassen, The Polarization Lidar Technique for Cloud Research: A Review and Current Assessment, Bull. Am. Meteorol. Soc. 72, 1848 (1991).

[159] A. C. S. Readhead et al., Polarization Observations with the Cosmic Background Imager, Science 306, 836 (2004).

[160] R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso, Arbitrary Spin-to–Orbital Angular Momentum Conversion of Light, Science 358, 896 (2017).

[161] Z. Shi, N. A. Rubin, J.-S. Park, and F. Capasso, Nonseparable Polarization Wavefront Transformation, Phys. Rev. Lett. 129, 167403 (2022).

[162] Y. Bao, F. Nan, J. Yan, X. Yang, C.-W. Qiu, and B. Li, Observation of Full-Parameter Jones Matrix in Bilayer Metasurface, Nat. Commun. 13, 7550 (2022).

[163] N. A. Rubin, A. Zaidi, A. H. Dorrah, Z. Shi, and F. Capasso, Jones Matrix Holography with Metasurfaces, Sci. Adv. 7, eabg7488 (2021).

[164] P.-N. Ni, P. Fu, P.-P. Chen, C. Xu, Y.-Y. Xie, and P. Genevet, Spin-Decoupling of Vertical Cavity Surface-Emitting Lasers with Complete Phase Modulation Using on-Chip Integrated Jones Matrix Metasurfaces, Nat. Commun. 13, 7795 (2022).

[165] S. Wang, Z.-L. Deng, Y. Wang, Q. Zhou, X. Wang, Y. Cao, B.-O. Guan, S. Xiao, and X. Li, Arbitrary Polarization Conversion Dichroism Metasurfaces for All-in-One Full Poincaré Sphere Polarizers, Light Sci. Appl. 10, 24 (2021).

[166] A. H. Dorrah, N. A. Rubin, A. Zaidi, M. Tamagnone, and F. Capasso, Metasurface Optics for On-Demand Polarization Transformations along the Optical Path, Nat. Photonics 15, 287 (2021).

[167] N. A. Rubin, G. D’Aversa, P. Chevalier, Z. Shi, W. T. Chen, and F. Capasso, Matrix Fourier Optics Enables a Compact Full-Stokes Polarization Camera, Science 365, eaax1839 (2019).

[168] S. Wang, S. Wen, Z.-L. Deng, X. Li, and Y. Yang, Metasurface-Based Solid Poincaré Sphere Polarizer, Phys. Rev. Lett. 130, 123801 (2023).

[169] A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, Intrinsic and Extrinsic Nature of the Orbital Angular Momentum of a Light Beam, Phys. Rev. Lett. 88, 053601 (2002).

[170] S. M. Kelly, T. J. Jess, and N. C. Price, How to Study Proteins by Circular Dichroism, Biochim. Biophys. Acta BBA - Proteins Proteomics 1751, 119 (2005).

[171] N. Berova, K. Nakanishi, and R. W. Woody, Circular Dichroism: Principles and Applications, 2nd ed. (John Wiley & Sons, 2000).

[172] H. L. Zhu, S. W. Cheung, K. L. Chung, and T. I. Yuk, Linear-to-Circular Polarization Conversion Using Metasurface, IEEE Trans. Antennas Propag. 61, 4615 (2013).

[173] X. Zhang, Y. Liu, J. Han, Y. Kivshar, and Q. Song, Chiral Emission from Resonant Metasurfaces, Science 377, 1215 (2022).

[174] D. Gabor, A New Microscopic Principle, Nature 161, 4098 (1948).

[175] R. Collier, Optical Holography (Elsevier, 2013).

[176] Z.-L. Deng and G. Li, Metasurface Optical Holography, Mater. Today Phys. 3, 16 (2017).

[177] F. Zhang, M. Pu, X. Li, P. Gao, X. Ma, J. Luo, H. Yu, and X. Luo, All-Dielectric Metasurfaces for Simultaneous Giant Circular Asymmetric Transmission and Wavefront Shaping Based on Asymmetric Photonic Spin-Orbit Interactions, Adv. Funct. Mater. 27, 1704295 (2017).

[178] Q. Wang, E. Plum, Q. Yang, X. Zhang, Q. Xu, Y. Xu, J. Han, and W. Zhang, Reflective Chiral Meta-Holography: Multiplexing Holograms for Circularly Polarized Waves, Light Sci. Appl. 7, 25 (2018).

[179] M. Wang, Y. Li, Y. Tang, J. Chen, R. Rong, G. Li, T. Cao, and S. Chen, Nonlinear Chiroptical Holography with Pancharatnam–Berry Phase Controlled Plasmonic Metasurface, Laser Photonics Rev. 16, 2200350 (2022).

[180] L. Nikolova and P. S. Ramanujam, Polarization Holography (Cambridge University Press, 2009).

[181] Y. Tang, Y. Intaravanne, J. Deng, K. F. Li, X. Chen, and G. Li, Nonlinear Vectorial Metasurface for Optical Encryption, Phys. Rev. Appl. 12, 024028 (2019).

[182] L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Orbital Angular Momentum of Light and the Transformation of Laguerre-Gaussian Laser Modes, Phys. Rev. A 45, 8185 (1992).

[183] J. Petersen, J. Volz, and A. Rauschenbeutel, Chiral Nanophotonic Waveguide Interface Based on Spin-Orbit Interaction of Light, Science 346, 67 (2014).

[184] S. B. Wang and C. T. Chan, Lateral Optical Force on Chiral Particles near a Surface, Nat. Commun. 5, 3307 (2014).

[185] K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, Spin-Orbit Interactions of Light, Nat. Photonics 9, 796 (2015).

[186] M. Onoda, S. Murakami, and N. Nagaosa, Hall Effect of Light, Phys. Rev. Lett. 93, 083901 (2004).

[187] O. Hosten and P. Kwiat, Observation of the Spin Hall Effect of Light via Weak Measurements, Science 319, 787 (2008).

[188] L. Marrucci, C. Manzo, and D. Paparo, Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media, Phys. Rev. Lett. 96, 163905 (2006).

[189] G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, Free-Space Information Transfer Using Light Beams Carrying Orbital Angular Momentum, Opt. Express 12, 5448 (2004).

[190] A. Anhäuser, R. Wunenburger, and E. Brasselet, Acoustic Rotational Manipulation Using Orbital Angular Momentum Transfer, Phys. Rev. Lett. 109, 034301 (2012).

[191] K. Y. Bliokh and F. Nori, Spin and Orbital Angular Momenta of Acoustic Beams, Phys. Rev. B 99, 174310 (2019).

[192] T. Frenzel, J. Köpfler, E. Jung, M. Kadic, and M. Wegener, Ultrasound Experiments on Acoustical Activity in Chiral Mechanical Metamaterials, Nat. Commun. 10, 3384 (2019).

[193] Y. Chen, M. Kadic, S. Guenneau, and M. Wegener, Isotropic Chiral Acoustic Phonons in 3D Quasicrystalline Metamaterials, Phys. Rev. Lett. 124, 235502 (2020).

[194] S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, Waves and Energy in Chiral Nihility, J. Electromagn. Waves Appl. 17, 695 (2003).

[195] J. B. Pendry, A Chiral Route to Negative Refraction, Science 306, 1353 (2004).

[196] S. Zhang, Y.-S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, Negative Refractive Index in Chiral Metamaterials, Phys. Rev. Lett. 102, 023901 (2009).

[197] B. A. Auld, Acoustic Fields and Waves in Solids (Wiley, 1973).

[198] A. C. Eringen, Microcontinuum Field Theories (Springer, New York, 1999).

[199] R. S. Lakes and R. L. Benedict, Noncentrosymmetry in Micropolar Elasticity, Int. J. Eng. Sci. 20, 1161 (1982).

[200] S. Duan, W. Wen, and D. Fang, A Predictive Micropolar Continuum Model for a Novel Three-Dimensional Chiral Lattice with Size Effect and Tension-Twist Coupling Behavior, J. Mech. Phys. Solids 121, 23 (2018).

[201] Y. Chen, T. Frenzel, S. Guenneau, M. Kadic, and M. Wegener, Mapping Acoustical Activity in 3D Chiral Mechanical Metamaterials onto Micropolar Continuum Elasticity, J. Mech. Phys. Solids 137, 103877 (2020).

[202] S. A. Cummer, J. Christensen, and A. Alù, Controlling Sound with Acoustic Metamaterials, Nat. Rev. Mater. 1, 16001 (2016).

[203] Q. Tong, J. Li, and S. Wang, Acoustic Circular Dichroism in a Three-Dimensional Chiral Metamaterial, Phys. Rev. B 107, 134103 (2023).