Optical Singularities in Photonic Microstructures with Rosette Symmetries: A Unified Theoretical Scheme

Jie Yang; Jiafu Wang; Xinmin Fu; Yueting Pan; Tie Jun Cui; Xuezhi Zheng

doi:10.1016/j.eng.2024.10.011

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Engineering ›› 2025, Vol. 45 ›› Issue (2) : 59-69. DOI: 10.1016/j.eng.2024.10.011

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Optical Singularities in Photonic Microstructures with Rosette Symmetries: A Unified Theoretical Scheme

Jie Yang^a^,^b^,^c ,
Jiafu Wang^a^,^b^,^d^,^* ,
Xinmin Fu^a^,^b ,
Yueting Pan^e ,
Tie Jun Cui^f^,^* ,
Xuezhi Zheng^c^,^g^,^*

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Abstract

Optical singularities are topological defects of electromagnetic fields; they include phase singularity in scalar fields, polarization singularity in vector fields, and three-dimensional (3D) singularities such as optical skyrmions. The exploitation of photonic microstructures to generate and manipulate optical singularities has attracted wide research interest in recent years, with many photonic microstructures having been devised to this end. Accompanying these designs, scattered phenomenological theories have been proposed to expound the working mechanisms behind individual designs. In this work, instead of focusing on a specific type of microstructure, we concentrate on the most common geometric features of these microstructures—namely, symmetries—and revisit the process of generating optical singularities in microstructures from a symmetry viewpoint. By systematically employing the projection operator technique in group theory, we develop a widely applicable theoretical scheme to explore optical singularities in microstructures with rosette (i.e., rotational and reflection) symmetries. Our scheme agrees well with previously reported works and further reveals that the eigenmodes of a symmetric microstructure can support multiplexed phase singularities in different components, such as out-of-plane, radial, azimuthal, and left- and right-handed circular components. Based on these phase singularities, more complicated optical singularities may be synthesized, including C points, V points, L lines, Néel- and bubble-type optical skyrmions, and optical lattices, to name a few. We demonstrate that the topological invariants associated with optical singularities are protected by the symmetries of the microstructure. Lastly, based on symmetry arguments, we formulate a so-called symmetry matching condition to clarify the excitation of a specific type of optical singularity. Our work establishes a unified theoretical framework to explore optical singularities in photonic microstructures with symmetries, shedding light on the symmetry origin of multidimensional and multiplexed optical singularities and providing a symmetry perspective for exploring many singularity-related effects in optics and photonics.

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Optical singularity / Optical vortex / Photonic microstructures / Symmetries / Group representation theory

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Jie Yang, Jiafu Wang, Xinmin Fu, Yueting Pan, Tie Jun Cui, Xuezhi Zheng. Optical Singularities in Photonic Microstructures with Rosette Symmetries: A Unified Theoretical Scheme. Engineering, 2025, 45(2): 59‒69 https://doi.org/10.1016/j.eng.2024.10.011

References

Publishing order | Descend order by publishing year | Descend order by cited within

[1]	Liu W, Liu W, Shi L, Kivshar Y.Topological polarization singularities in metaphotonics.Nanophotonics 2021; 10(5):1469-1486.

[2]	Mond D, Montaldi J.Singularity theory and its applications. Springer, Berlin (1991)

[3]	Ori A.Structure of the singularity inside a realistic rotating black hole.Phys Rev Lett 1992; 68(14):2117-2120.

[4]	Kosterlitz JM, Thouless DJ.Ordering, metastability and phase transitions in two-dimensional systems.J Phys C Solid State Phys 1973; 6(7):1181-1203.

[5]	Dirac PAM.Quantised singularities in the electromagnetic field.Proc R Soc Lond A Contain Pap Math Phys Character 1931; 133(821):60-72.

[6]	Bliokh KY, Alonso MA, Dennis MR.Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects.Rep Prog Phys 2019; 82(12):122401.

[7]	Tsesses S, Ostrovsky E, Cohen K, Gjonaj B, Lindner NH, Bartal G.Optical skyrmion lattice in evanescent electromagnetic fields.Science 2018; 361(6406):993-996.

[8]	Du L, Yang A, Zayats AV, Yuan X.Deep-subwavelength features of photonic skyrmions in a confined electromagnetic field with orbital angular momentum.Nat Phys 2019; 15(7):650-654.

[9]	Dai Y, Zhou Z, Ghosh A, Mong RS, Kubo A, Huang CB, et al.Plasmonic topological quasiparticle on the nanometre and femtosecond scales.Nature 2020; 588(7839):616-619.

[10]	Shen Y.Topological bimeronic beams.Opt Lett 2021; 46(15):3737-3740.

[11]	Sugic D, Droop R, Otte E, Ehrmanntraut D, Nori F, Ruostekoski J, et al.Particle-like topologies in light.Nat Commun 2021; 12:6785.

[12]	Shen Y, Yu B, Wu H, Li C, Zhu Z, Zayats AV.Topological transformation and free-space transport of photonic hopfions.Adv Photonics 2023; 5(1):015001.

[13]	Freund I.Optical Möbius strips in three-dimensional ellipse fields: I. lines of circular polarization.Opt Commun 2010; 283(1):1-15.

[14]	Bauer T, Banzer P, Karimi E, Orlov S, Rubano A, Marrucci L, et al.Observation of optical polarization Möbius strips.Science 2015; 347(6225):964-966.

[15]	Dennis MR, King RP, Jack B, O K’holleran, Padgett MJ.Isolated optical vortex knots.Nat Phys 2010; 6(2):118-121.

[16]	Zhong J, Liu S, Guo X, Li P, Wei B, Han L, et al.Observation of optical vortex knots and links associated with topological charge.Opt Express 2021; 29(23):38849-38857.

[17]	Davis TJ, Janoschka D, Dreher P, Frank B, Meyer zu Heringdorf FJ, Giessen H.Ultrafast vector imaging of plasmonic skyrmion dynamics with deep subwavelength resolution.Science 2020; 368(6489):eaba6415.

[18]	Yuan GH, Zheludev NI.Detecting nanometric displacements with optical ruler metrology.Science 2019; 364(6442):771-775.

[19]	Heeres RW, Zwiller V.Subwavelength focusing of light with orbital angular momentum.Nano Lett 2014; 14(8):4598-4601.

[20]	Kim H, Park J, Cho SW, Lee SY, Kang M, Lee B.Synthesis and dynamic switching of surface plasmon vortices with plasmonic vortex lens.Nano Lett 2010; 10(2):529-536.

[21]	Spektor G, Kilbane D, Mahro AK, Frank B, Ristok S, Gal L, et al.Revealing the subfemtosecond dynamics of orbital angular momentum in nanoplasmonic vortices.Science 2017; 355(6330):1187-1191.

[22]	Yang Y, Wu L, Liu Y, Xie D, Jin Z, Li J, et al.Deuterogenic plasmonic vortices.Nano Lett 2020; 20(9):6774-6779.

[23]	Ni J, Huang C, Zhou LM, Gu M, Song Q, Kivshar Y, et al.Multidimensional phase singularities in nanophotonics.Science 2021; 374(6566):eabj0039.

[24]	Tsai WY, Huang JS, Huang CB.Selective trapping or rotation of isotropic dielectric microparticles by optical near field in a plasmonic archimedes spiral.Nano Lett 2014; 14(2):547-552.

[25]	Jin Z, Janoschka D, Deng J, Ge L, Dreher P, Frank B, et al.Phyllotaxis-inspired nanosieves with multiplexed orbital angular momentum.eLight 2021; 1:5.

[26]	Krenn M, Handsteiner J, Fink M, Fickler R, Ursin R, Malik M, et al.Twisted light transmission over 143 km.Proc Natl Acad Sci USA 2016; 113(48):13648-13653.

[27]	Cheng W, Zhang W, Jing H, Gao S, Zhang H.Orbital angular momentum for wireless communications.IEEE Wirel Commun 2019; 26(1):100-107.

[28]	Ren Y, Li L, Xie G, Yan Y, Cao Y, Huang H, et al.Line-of-sight millimeter-wave communications using orbital angular momentum multiplexing combined with conventional spatial multiplexing.IEEE Trans Wirel Commun 2017; 16(5):3151-3161.

[29]	Carlon Zambon N, St-Jean P, Mili Mćević, Lema Aître, Harouri A, Le Gratiet L, et al.Optically controlling the emission chirality of microlasers.Nat Photonics 2019; 13(4):283-288.

[30]	Sala VG, Solnyshkov DD, Carusotto I, Jacqmin T, Lema Aître, Ter Hças, et al.Spin–orbit coupling for photons and polaritons in microstructures.Phys Rev X 2015; 5(1):011034.

[31]	Williams MD, Coles MM, Bradshaw DS, Andrews DL.Direct generation of optical vortices.Phys Rev A 2014; 89(3):033837.

[32]	Williams MD, Coles MM, Saadi K, Bradshaw DS, Andrews DL.Optical vortex generation from molecular chromophore arrays.Phys Rev Lett 2013; 111(15):153603.

[33]	Coles MM, Williams MD, Saadi K, Bradshaw DS, Andrews DL.Chiral nanoemitter array: a launchpad for optical vortices.Laser Photonics Rev 2013; 7(6):1088-1092.

[34]	Mohammadi SM, Daldorff LK, Bergman JE, Karlsson RL, Thid Bé, Forozesh K, et al.Orbital angular momentum in radio–a system study.IEEE Trans Antenn Propag 2010; 58(2):565-572.

[35]	Cai X, Wang J, Strain MJ, Johnson-Morris B, Zhu J, Sorel M, et al.Integrated compact optical vortex beam emitters.Science 2012; 338(6105):363-366.

[36]	Miao P, Zhang Z, Sun J, Walasik W, Longhi S, Litchinitser NM, et al.Orbital angular momentum microlaser.Science 2016; 353(6298):464-467.

[37]	Zhang Z, Qiao X, Midya B, Liu K, Sun J, Wu T, et al.Tunable topological charge vortex microlaser.Science 2020; 368(6492):760-763.

[38]	Zhang Z, Zhao H, Pires DG, Qiao X, Gao Z, Jornet JM, et al.Ultrafast control of fractional orbital angular momentum of microlaser emissions.Light Sci Appl 2020; 9:179.

[39]	Spektor G, Kilbane D, Mahro AK, Hartelt M, Prinz E, Aeschlimann M, et al.Mixing the light spin with plasmon orbit by nonlinear light–matter interaction in gold.Phys Rev X 2019; 9(2):021031.

[40]	Dai Y, Ghosh A, Yang S, Zhou Z, Huang C, Petek H.Poincaré engineering of surface plasmon polaritons.Nat Rev Phys 2022; 4(9):562-564.

[41]	Dai Y, Zhou Z, Ghosh A, Kapoor K, D Mąbrowski, Kubo A, et al.Ultrafast microscopy of a twisted plasmonic spin skyrmion.Appl Phys Rev 2022; 9(1):011420.

[42]	Tsesses S, Cohen K, Ostrovsky E, Gjonaj B, Bartal G.Spin–orbit interaction of light in plasmonic lattices.Nano Lett 2019; 19(6):4010-4016.

[43]	Yang Y, Thirunavukkarasu G, Babiker M, Yuan J.Orbital–angular–momentum mode selection by rotationally symmetric superposition of chiral states with application to electron vortex beams.Phys Rev Lett 2017; 119(9):094802.

[44]	Chen MLN, Jiang LJ, Wei EI.Generation of orbital angular momentum by a point defect in photonic crystals.Phys Rev Appl 2018; 10(1):014034.

[45]	Zhao C, Gan X, Liu S, Pang Y, Zhao J.Generation of vector beams in planar photonic crystal cavities with multiple missing-hole defects.Opt Express 2014; 22(8):9360-9367.

[46]	Su H, Shen X, Su G, Li L, Ding J, Liu F, et al.Efficient generation of microwave plasmonic vortices via a single deep-subwavelength meta-particle.Laser Photonics Rev 2018; 12(9):1800010.

[47]	Yang J, Zheng X, Wang J, Zhang A, Cui TJ, Vandenbosch GAE.Customizing the topological charges of vortex modes by exploiting symmetry principles.Laser Photonics Rev 2022; 16(4):2100373.

[48]	Zhang Y, Zhang Q, Chan CH, Li E, Jin J, Wang H.Emission of orbital angular momentum based on spoof localized surface plasmons.Opt Lett 2019; 44(23):5735-5738.

[49]	Yang J, Zheng X, Wang J, Zhang A, Cui TJ, Vandenbosch G.Polarization singularities in planar electromagnetic resonators with rotation and mirror symmetries.Photon Res 2023; 11(6):936.

[50]	Yang J, Zheng X, Wang J, Pan Y, Zhang A, Cui TJ, et al.Symmetry-protected spoof localized surface plasmonic skyrmion.Laser Photonics Rev 2022; 16(6):2200007.

[51]	Shi P, Du L, Li M, Yuan X.Symmetry-protected photonic chiral spin textures by spin–orbit coupling.Laser Photonics Rev 2021; 15(9):2000554.

[52]	Arikawa T, Hiraoka T, Morimoto S, Blanchard F, Tani S, Tanaka T, et al.Transfer of orbital angular momentum of light to plasmonic excitations in metamaterials.Sci Adv 2020; 6:eaay1977.

[53]	Yang J, Feng P, Han F, Zheng X, Wang J, Jin Z, et al.Symmetry-compatible angular momentum conservation relation in plasmonic vortex lenses with rotational symmetries 2022.arXiv:2209.14735.

[54]	Chen W, Yang Q, Chen Y, Liu W.Extremize optical chiralities through polarization singularities.Phys Rev Lett 2021; 126(25):253901.

[55]	Che Z, Zhang Y, Liu W, Zhao M, Wang J, Zhang W, et al.Polarization singularities of photonic quasicrystals in momentum space.Phys Rev Lett 2021; 127(4):043901.

[56]	Peng B, ŞÖzdemir K, Liertzer M, Chen W, Kramer J, Y Hılmaz, et al.Chiral modes and directional lasing at exceptional points.Proc Natl Acad Sci USA 2016; 113(25):6845-6850.

[57]	Sebbag Y, Levy U.Arbitrarily directed emission of integrated cylindrical vector vortex beams by geometric phase engineering.Opt Lett 2020; 45(24):6779-6782.

[58]	Shao Z, Zhu J, Zhang Y, Chen Y, Yu S.On-chip switchable radially and azimuthally polarized vortex beam generation.Opt Lett 2018; 43(6):1263-1266.

[59]	Arikawa T, Morimoto S, Tanaka K.Focusing light with orbital angular momentum by circular array antenna.Opt Express 2017; 25(12):13728-13735.

[60]	Cogn KGée, Doeleman HM, Lalanne P, Koenderink AF.Generation of pure OAM beams with a single state of polarization by antenna-decorated microdisk resonators.ACS Photonics 2020; 7(11):3049-3060.

[61]	Yue F, Wen D, Xin J, Gerardot BD, Li J, Chen X.Vector vortex beam generation with a single plasmonic metasurface.ACS Photonics 2016; 3(9):1558-1563.

[62]	Chew WC, Tong MS, Hu B.Integral equation methods for electromagnetic and elastic waves. Springer International Publishing, Cham (2009)

[63]	Zheng X, Kupresak M, Verellen N, Moshchalkov VV, Vandenbosch GAE.A review on the application of integral equation-based computational methods to scattering problems in plasmonics.Adv Theory Simul 2019; 2(9):1900087.

[64]	Chew WC.Waves and fields in inhomogenous media. John Wiley & Sons, Hoboken (1999)

[65]	Tung WK.Group theory in physics. World Scientific, Singapore (1985)

[66]	Dresselhaus MS, Dresselhaus G, Jorio A.Group theory: application to the physics of condensed matter. Springer Science & Business Media, Berlin (2007)

[67]	Serre JP.Linear representations of finite groups. Springer, Berlin (1977)

[68]	Collins JT, Zheng X, Braz NV, Slenders E, Zu S, Vandenbosch GA, et al.Enantiomorphing chiral plasmonic nanostructures: a counterintuitive sign reversal of the nonlinear circular dichroism.Adv Opt Mater 2018; 6(14):1800153.

[69]	Kuppe C, Zheng X, Williams C, Murphy AW, Collins JT, Gordeev SN, et al.Measuring optical activity in the far-field from a racemic nanomaterial: diffraction spectroscopy from plasmonic nanogratings.Nanoscale Horiz 2019; 4(5):1056-1062.

[70]	Zheng X, Verellen N, Vercruysse D, Volskiy V, Van Dorpe P, Vandenbosch GA, et al.On the use of group theory in understanding the optical response of a nanoantenna.IEEE Trans Antennas Propag 2015; 63(4):1589-1602.

[71]	Senthilkumaran P, Pal SK.Phase singularities to polarization singularities. Int J Opt (2020), Article 2812803

[72]	Wang Q, Tu CH, Li YN, Wang HT.Polarization singularities: progress, fundamental physics, and prospects.APL Photonics 2021; 6(4):040901.

[73]	Schulz SA, Machula T, Karimi E, Boyd RW.Integrated multi vector vortex beam generator.Opt Express 2013; 21(13):16130-16141.

[74]	Zhang X, Cui TJ.Single-particle dichroism using orbital angular momentum in a microwave plasmonic resonator.ACS Photonics 2020; 7(12):3291-3297.

[75]	Garcia-Etxarri A.Optical polarization mobius strips on all-dielectric optical scatterers.ACS Photonics 2017; 4(5):1159-1164.

[76]	Shen Y, Zhang Q, Shi P, Du L, Yuan X, Zayats AV.Optical skyrmions and other topological quasiparticles of light.Nat Photonics 2024; 18(1):15-25.

[77]	Kouznetsov D, Deng Q, Van Dorpe P, Verellen N.Revival and expansion of the theory of coherent lattices.Phys Rev Lett 2020; 125(18):184101.

[78]	Zhang R, Zhang Y, Ma L, Zeng X, Li X, Zhan Z, et al.Nanoscale optical lattices of arbitrary orders manipulated by plasmonic metasurfaces combining geometrical and dynamic phases.Nanoscale 2019; 11(29):14024-14031.

[79]	Wang Y, Xu Y, Feng X, Zhao P, Liu F, Cui K, et al.Optical lattice induced by angular momentum and polygonal plasmonic mode.Opt Lett 2016; 41(7):1478-1481.