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

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.