Classical and generalized geometric phase in electromagnetic metasurfaces

Yinghui Guo; Mingbo Pu; Fei Zhang; Mingfeng Xu; Xiong Li; Xiaoliang Ma; Xiangang Luo

doi:10.3788/PI.2022.R03

[1] P. K. Aravind. A simple proof of Pancharatnam’s theorem. Opt. Commun., 94, 191(1992).

[2] M. V. Berry. Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. Lond. A, 392, 45(1984).

[3] Y. Aharonov, D. Bohm. Significance of electromagnetic potentials in the quantum theory. Phys. Rev., 115, 485(1959).

[4] R. Y. Chiao, Y.-S. Wu. Manifestations of Berry’s topological phase for the photon. Phys. Rev. Lett., 57, 933(1986).

[5] Y. Aharonov, J. Anandan. Phase change during a cyclic quantum evolution. Phys. Rev. Lett., 58, 1593(1987).

[6] J. Zak. Berry’s phase for energy bands in solids. Phys. Rev. Lett., 62, 2747(1989).

[7] S. Pancharatnam. Generalized theory of interference and its applications. Proc. Indian Acad. Sci. A, 44, 398(1956).

[8] R. Simon, H. J. Kimble, E. C. G. Sudarshan. Evolving geometric phase and its dynamical manifestation as a frequency shift: an optical experiment. Phys. Rev. Lett., 61, 19(1988).

[9] R. Bhandari. SU (2) phase jumps and geometric phases. Phys. Lett. A, 157, 221(1991).

[10] M. V. Berry. The adiabatic phase and Pancharatnam’s phase for polarized light. J. Mod. Opt., 34, 1401(1987).

[11] N. Yu et al. Light propagation with phase discontinuities: generalized laws of reflection and refraction. Science, 334, 333(2011).

[12] C. P. Jisha, S. Nolte, A. Alberucci. Geometric phase in optics: from wavefront manipulation to waveguiding. Laser Photonics Rev., 15, 2100003(2021).

[13] J. Anandan. The geometric phase. Nature, 360, 307(1992).

[14] M. Berry. Geometric phase memories. Nat. Phys., 6, 148(2010).

[15] C. A. Mead. The geometric phase in molecular systems. Rev. Mod. Phys., 64, 51(1992).

[16] E. Cohen et al. Geometric phase from Aharonov–Bohm to Pancharatnam–Berry and beyond. Nat. Rev. Phys., 1, 437(2019).

[17] A. G. Fox. An adjustable wave-guide phase changer. Proc. IRE, 35, 1489(1947).

[18] S. Pancharatnam. Achromatic combinations of birefringent plates. Proc. Indian Acad. Sci. A, 41, 137(1955).

[19] Z. Bomzon, V. Kleiner, E. Hasman. Pancharatnam-Berry phase in space-variant polarization-state manipulations with subwavelength gratings. Opt. Lett., 26, 1424(2001).

[20] Z. Bomzon et al. Space-variant Pancharatnam-Berry phase optical elements with computer-generated subwavelength gratings. Opt. Lett., 27, 1141(2002).

[21] Y. Guo et al. Dispersion management of anisotropic metamirror for super-octave bandwidth polarization conversion. Sci. Rep., 5, 8434(2015).

[22] M. Pu et al. Spatially and spectrally engineered spin-orbit interaction for achromatic virtual shaping. Sci. Rep., 5, 9822(2015).

[23] D. Mawet et al. Annular groove phase mask coronagraph. Astrophys. J., 633, 1191(2005).

[24] G. Biener et al. Formation of helical beams by use of Pancharatnam-Berry phase optical elements. Opt. Lett., 27, 1875(2002).

[25] E. Hasman et al. Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics. Appl. Phys. Lett., 82, 328(2003).

[26] D. Tang et al. Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light focusing. Laser Photonics Rev., 9, 713(2015).

[27] E. Karimi et al. Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface. Light Sci. Appl., 3, e167(2014).

[28] G. Zheng et al. Metasurface holograms reaching 80% efficiency. Nat. Nanotechnol., 10, 308(2015).

[29] X. Ma et al. A planar chiral meta-surface for optical vortex generation and focusing. Sci. Rep., 5, 10365(2015).

[30] M. Pu et al. Catenary optics for achromatic generation of perfect optical angular momentum. Sci. Adv., 1, e1500396(2015).

[31] F. Zhang et al. Multistate switching of photonic angular momentum coupling in phase-change metadevices. Adv. Mater., 32, 1908194(2020).

[32] D. Lin et al. Dielectric gradient metasurface optical elements. Science, 345, 298(2014).

[33] F. Aieta et al. Multiwavelength achromatic metasurfaces by dispersive phase compensation. Science, 347, 1342(2015).

[34] A. Arbabi et al. Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission. Nat. Nanotechnol., 10, 937(2015).

[35] M. Khorasaninejad et al. Metalenses at visible wavelengths: diffraction-limited focusing and subwavelength resolution imaging. Science, 352, 1190(2016).

[36] F. Ding et al. Versatile polarization generation and manipulation using dielectric metasurfaces. Laser Photonics Rev., 14, 2000116(2020).

[37] M. Khorasaninejad et al. Multispectral chiral imaging with a metalens. Nano Lett., 16, 4595(2016).

[38] X. Luo. Principles of electromagnetic waves in metasurfaces. Sci. China Phys. Mech. Astron, 58, 594201(2015).

[39] Z. Li et al. Achromatic broadband super-resolution imaging by super-oscillatory metasurface. Laser Photonics Rev., 12, 1800064(2018).

[40] Z. Yue et al. Terahertz metasurface zone plates with arbitrary polarizations to a fixed polarization conversion. Opto-Electron. Sci., 1, 210014(2022).

[41] X. Zang et al. Metasurfaces for manipulating terahertz waves. Light Adv. Manuf., 2, 148(2021).

[42] K. Liu et al. Active tuning of electromagnetically induced transparency from chalcogenide-only metasurface. Light Adv. Manuf., 2, 251(2021).

[43] X. Luo et al. Broadband spin Hall effect of light in single nanoapertures. Light Sci. Appl., 6, e16276(2017).

[44] X. Ling et al. Giant photonic spin Hall effect in momentum space in a structured metamaterial with spatially varying birefringence. Light Sci. Appl., 4, e290(2015).

[45] Y. Meng et al. Optical meta-waveguides for integrated photonics and beyond. Light Sci. Appl., 10, 235(2021).

[46] L. Huang et al. Three-dimensional optical holography using a plasmonic metasurface. Nat. Commun., 4, 2808(2013).

[47] X. Li et al. Multicolor 3D meta-holography by broadband plasmonic modulation. Sci. Adv., 2, e1601102(2016).

[48] G. Qu et al. Reprogrammable meta-hologram for optical encryption. Nat. Commun., 11, 5484(2020).

[49] Y. Hu et al. Trichromatic and tripolarization-channel holography with noninterleaved dielectric metasurface. Nano Lett., 20, 994(2020).

[50] D. Wen et al. Helicity multiplexed broadband metasurface holograms. Nat. Commun., 6, 8241(2015).

[51] J.-H. Park, B. Lee. Holographic techniques for augmented reality and virtual reality near-eye displays. Light Adv. Manuf., 3, 1(2022).

[52] Z.-L. Deng et al. Multi-freedom metasurface empowered vectorial holography. Nanophotonics, 11, 0622(2022).

[53] H. Gao et al. Recent advances in optical dynamic meta-holography. Opto-Electronic Adv., 4, 210030(2021).

[54] Y. Ming et al. Creating composite vortex beams with a single geometric metasurface. Adv. Mater., 34, 2109714(2022).

[55] S. Zhang et al. Generation of achromatic auto-focusing Airy beam for visible light by an all-dielectric metasurface. J. Appl. Phys., 131, 043104(2022).

[56] Q. Zhou et al. Generation of perfect vortex beams by dielectric geometric metasurface for visible light. Laser Photon. Rev., 15, 2100390(2021).

[57] Y. Guo et al. High-efficiency and wide-angle beam steering based on catenary optical fields in ultrathin metalens. Adv. Opt. Mater., 6, 1800592(2018).

[58] S. Xiao et al. Flexible coherent control of plasmonic spin-Hall effect. Nat. Commun., 6, 8360(2015).

[59] T. Ma et al. Benchmarking deep learning-based models on nanophotonic inverse design problems. Opto-Electron. Sci., 1, 210012(2022).

[60] Y. Guo et al. Merging geometric phase and plasmon retardation phase in continuously shaped metasurfaces for arbitrary orbital angular momentum generation. ACS Photonics, 3, 2022(2016).

[61] Y. Guo et al. Scattering engineering in continuously shaped metasurface: an approach for electromagnetic illusion. Sci. Rep., 6, 30154(2016).

[62] X. Zhang et al. A quasi-continuous all-dielectric metasurface for broadband and high-efficiency holographic images. J. Phys. D, 53, 465105(2020).

[63] X. Zhang et al. Ultra-broadband metasurface holography via quasi-continuous nano-slits. J. Phys. D, 53, 104002(2019).

[64] D. Wang et al. Broadband high-efficiency chiral splitters and holograms from dielectric nanoarc metasurfaces. Small, 15, 1900483(2019).

[65] D. Hakobyan et al. Tailoring orbital angular momentum of light in the visible domain with metallic metasurfaces. Adv. Opt. Mater., 4, 306(2016).

[66] M. Xu et al. Topology-optimized catenary-like metasurface for wide-angle and high-efficiency deflection: from a discrete to continuous geometric phase. Opt. Express, 29, 10181(2021).

[67] Z. Gong et al. Broadband efficient vortex beam generation with metallic helix array. Appl. Phys. Lett., 113, 071104(2018).

[68] D. Hakobyan et al. Tailoring orbital angular momentum of light in the visible domain with metallic metasurfaces. Adv. Opt. Mater., 4, 306(2015).

[69] X. Luo et al. Catenary functions meet electromagnetic waves: opportunities and promises. Adv. Opt. Mater., 8, 2001194(2020).

[70] M. Pu et al. Nanoapertures with ordered rotations: symmetry transformation and wide-angle flat lensing. Opt. Express, 25, 31471(2017).

[71] F. Zhang et al. Extreme-angle silicon infrared optics enabled by streamlined surfaces. Adv. Mater., 33, 2008157(2021).

[72] Y. Guo et al. Polarization-controlled broadband accelerating beams generation by single catenary-shaped metasurface. Adv. Opt. Mater., 7, 1900503(2019).

[73] F. Zhang et al. Broadband and high-efficiency accelerating beam generation by dielectric catenary metasurfaces. Nanophotonics, 9, 20200057(2020).

[74] X. Chen et al. Dual-polarity plasmonic metalens for visible light. Nat. Commun., 3, 1198(2012).

[75] F. Zhang et al. Symmetry breaking of photonic spin-orbit interactions in metasurfaces. Opto-Electron. Eng., 44, 319(2017).

[76] F. Zhang et al. All-dielectric metasurfaces for simultaneous giant circular asymmetric transmission and wavefront shaping based on asymmetric photonic spin–orbit interactions. Adv. Fun. Mater., 27, 1704295(2017).

[77] J. P. B. Mueller et al. Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization. Phys. Rev. Lett., 118, 113901(2017).

[78] R. C. Devlin et al. Arbitrary spin-to-orbital angular momentum conversion of light. Science, 358, 896(2017).

[79] J. Cai et al. Simultaneous polarization filtering and wavefront shaping enabled by localized polarization-selective interference. Sci. Rep., 10, 14477(2020).

[80] Q. Fan et al. Independent amplitude control of arbitrary orthogonal states of polarization via dielectric metasurfaces. Phys. Rev. Lett., 125, 267402(2020).

[81] Y. Yuan et al. Independent phase modulation for quadruplex polarization channels enabled by chirality-assisted geometric-phase metasurfaces. Nat. Commun., 11, 4186(2020).

[82] Y. Bao et al. Toward the capacity limit of 2D planar Jones matrix with a single-layer metasurface. Sci. Adv., 7, eabh0365(2021).

[83] D. Wang et al. Efficient generation of complex vectorial optical fields with metasurfaces. Light Sci. Appl., 10, 67(2021).

[84] D. Wang et al. High-efficiency metadevices for bifunctional generations of vectorial optical fields. Nanophotonics, 10, 685(2021).

[85] I. Kim et al. Pixelated bifunctional metasurface-driven dynamic vectorial holographic color prints for photonic security platform. Nat. Commun., 12, 3614(2021).

[86] A. H. Dorrah et al. Metasurface optics for on-demand polarization transformations along the optical path. Nat. Photonics, 15, 287(2021).

[87] N. A. Rubin et al. Jones matrix holography with metasurfaces. Sci. Adv., 7, eabg7488(2021).

[88] M. Liu et al. Broadband generation of perfect Poincaré beams via dielectric spin-multiplexed metasurface. Nat. Commun., 12, 2230(2021).

[89] F. Zhang et al. Synthetic vector optical fields with spatial and temporal tenability. Sci. China Phys. Mech. Astron., 65, 254211(2022).

[90] J. Ni et al. Multidimensional phase singularities in nanophotonics. Science, 374, eabj0039(2021).

[91] S. Zhang et al. Broadband detection of multiple spin and orbital angular momenta via dielectric metasurface. Laser Photonics Rev., 14, 2000062(2020).

[92] Y. Guo et al. Spin-decoupled metasurface for simultaneous detection of spin and orbital angular momenta via momentum transformation. Light Sci. Appl., 10, 63(2021).

[93] X. Luo et al. Symmetric and asymmetric photonic spin-orbit interaction in metasurfaces. Prog. Quant. Electron., 79, 100344(2021).

[94] Z. Fei et al. Metasurfaces enabled by asymmetric photonic spin-orbit interactions. Opto-Electron Eng., 47, 200366(2020).

[95] M. Tymchenko et al. Gradient nonlinear Pancharatnam-Berry metasurfaces. Phys. Rev. Lett., 115, 207403(2015).

[96] G. Li et al. Continuous control of the nonlinearity phase for harmonic generations. Nat. Mater., 14, 607(2015).

[97] N. Segal et al. Controlling light with metamaterial-based nonlinear photonic crystals. Nat. Photonics, 9, 180(2015).

[98] S. Chen et al. Symmetry-selective third-harmonic generation from plasmonic metacrystals. Phys. Rev. Lett., 113, 033901(2014).

[99] K. Konishi et al. Polarization-controlled circular second-harmonic generation from metal hole arrays with threefold rotational symmetry. Phys. Rev. Lett., 112, 135502(2014).

[100] G. Li, S. Zhang, T. Zentgraf. Nonlinear photonic metasurfaces. Nat. Rev. Mater., 2, 17010(2017).

[101] G. Li et al. Spin and geometric phase control four-wave mixing from metasurfaces. Laser Photon. Rev., 12, 1800034(2018).

[102] M. Ma et al. Optical information multiplexing with nonlinear coding metasurfaces. Laser Photon. Rev., 13, 1900045(2019).

[103] Z. Li et al. Multiplexed nondiffracting nonlinear metasurfaces. Adv. Funct. Mater., 30, 1910744(2020).

[104] C. Schlickriede et al. Imaging through nonlinear metalens using second harmonic generation. Adv. Mater., 30, 1703843(2018).

[105] F. Walter et al. Ultrathin nonlinear metasurface for optical image encoding. Nano Lett., 17, 3171(2017).

[106] B. Reineke et al. Silicon metasurfaces for third harmonic geometric phase manipulation and multiplexed holography. Nano Lett., 19, 6585(2019).

[107] W. Zhao et al. Chirality-selected second-harmonic holography with phase and binary amplitude manipulation. Nanoscale, 12, 13330(2020).

[108] Z. Gao et al. Reconstruction of multidimensional nonlinear polarization response of Pancharatnam-Berry metasurfaces. Phys. Rev. B, 104, 054303(2021).

[109] C. McDonnell et al. Functional THz emitters based on Pancharatnam-Berry phase nonlinear metasurfaces. Nat. Commun., 12, 30(2021).

[110] W. Ye et al. Spin and wavelength multiplexed nonlinear metasurface holography. Nat. Commun., 7, 11930(2016).

[111] M. A. Kats et al. Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy. Proc. Nat. Acad. Sci., 109, 12364(2012).

[112] X. Xie et al. Generalizd Pancharatnam-Berry phase in rotationally symmetric meta-atoms. Phys. Rev. Lett., 126, 3902(2021).

[113] S. Yijia et al. Achromatic metalens based on coordinative modulation of propagation phase and geometric phase. Opto-Electron Eng., 47, 200237(2020).

[114] N. V. Tabiryan et al. Advances in transparent planar optics: enabling large aperture, ultrathin lenses. Adv. Opt. Mater., 9, 2001692(2021).

[115] Y. Tang et al. Nonlinear vectorial metasurface for optical encryption. Phys. Rev. Appl., 12, 024028(2019).

[116] Y. Zhang et al. Multidimensional manipulation of wave fields based on artificial microstructures. Opto-Electron. Adv., 3, 200002(2020).

[117] Y. Wang, Q. Fan, T. Xu. Design of high efficiency achromatic metalens with large operation bandwidth using bilayer architecture. Opto-Electron. Adv., 4, 200008(2021).

[118] R. Zhao et al. Multichannel vectorial holographic display and encryption. Light Sci. Appl., 7, 95(2018).

[119] E. Arbabi et al. Vectorial holograms with a dielectric metasurface: ultimate polarization pattern generation. ACS Photonics, 6, 2712(2019).

[120] L. Fang et al. Vectorial doppler metrology. Nat. Commun., 12, 4186(2021).

[121] E. Wang et al. Complete control of multichannel, angle-multiplexed, and arbitrary spatially varying polarization fields. Adv. Opt. Mater., 8, 1901674(2020).

[122] J. Wang et al. Shifting beams at normal incidence via controlling momentum-space geometric phases. Nat. Commun., 12, 6046(2021).

[123] Z. Zhang et al. Enhancing the efficiency of the topological phase transitions in spin–orbit photonics. Appl. Phys. Lett., 120, 181102(2022).

[124] W. Zhu et al. Wave-vector-varying Pancharatnam-Berry phase photonic spin hall effect. Phys. Rev. Lett., 126, 083901(2021).

[125] X. Ling et al. Topology-induced phase transitions in spin-orbit photonics. Laser Photon. Rev., 15, 2000492(2021).

[126] M. Pu et al. Revisitation of extraordinary Young’s interference: from catenary optical fields to spin-orbit interaction in metasurfaces. ACS Photonics, 5, 3198(2018).