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 ...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.展开更多
In this work,we apply the group representation theory to systematically study polarization singularities in the inplane components of the electric fields supported by a planar electromagnetic(EM)resonator with generic...In this work,we apply the group representation theory to systematically study polarization singularities in the inplane components of the electric fields supported by a planar electromagnetic(EM)resonator with generic rotation and reflection symmetries.We reveal the intrinsic connections between the symmetries and the topological features,i.e.,the spatial configuration of the in-plane fields and the associated polarization singularities.The connections are substantiated by a simple relation that links the topological charges of the singularities and the symmetries of the resonator.To verify,a microwave planar resonator with the D8group symmetries is designed and numerically simulated,which demonstrates the theoretical findings well.Our discussions can be applied to generic EM resonators working in a wide EM spectrum,such as circular antenna arrays,microring resonators,and photonic quasi-crystals,and provide a unique symmetry perspective on many effects in singular optics and topological photonics.展开更多
基金supported by the National Natural Science Foun-dation of China(62301596 and 62288101)Shaanxi Provincial Science and Technology Innovation Team(23-CX-TD-48)+4 种基金the KU Leuven internal funds:the C1 Project(C14/19/083)the Interdisciplinary Network Project(IDN/20/014)the Small Infrastructure Grant(KA/20/019)the Research Foundation of Flanders(FWO)Project(G090017N,G088822N,and V408823N)the Danish National Research Foundation(DNRF165).
文摘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.
基金Fonds Wetenschappelijk Onderzoek(G090017N)KU Leuven(C14/19/083,IDN/20/014,KA/20/019)+1 种基金National Natural Science Foundation of China(61771485,62288101)National Key Research and Development Program of China(SQ2017YFA0700201,SQ2017YFA0700202,SQ2017YFA0700203)。
文摘In this work,we apply the group representation theory to systematically study polarization singularities in the inplane components of the electric fields supported by a planar electromagnetic(EM)resonator with generic rotation and reflection symmetries.We reveal the intrinsic connections between the symmetries and the topological features,i.e.,the spatial configuration of the in-plane fields and the associated polarization singularities.The connections are substantiated by a simple relation that links the topological charges of the singularities and the symmetries of the resonator.To verify,a microwave planar resonator with the D8group symmetries is designed and numerically simulated,which demonstrates the theoretical findings well.Our discussions can be applied to generic EM resonators working in a wide EM spectrum,such as circular antenna arrays,microring resonators,and photonic quasi-crystals,and provide a unique symmetry perspective on many effects in singular optics and topological photonics.
