Symmetry-based topology optimization for skyrmion generation in symmetric infinitely long scatterers

Skyrmions, topologically stable vectorial configurations defined on a 2D or 3D domain, have attracted significant interests due to their potential in various applications including light - matter interaction, microscopy, high capacity communications. So far, studies have focused on the design of EM structures based on intuitive physical arguments. However, a systematic study on inverse design methodologies remains unexplored. In this work, we focus on a special class of EM structures, that is, infinitely long scatterers (which are good approximations for, e.g., waveguiding structures, wire-like scatterers) with cross-sectional symmetries, and establish a symmetry based topology optimization (TO) algorithm to realize efficient design of structures supporting different types of EM skyrmions. This is done by first categorizing skyrmions according to symmetry arguments, designing efficient computational algorithms to analyze symmetric structures and finally adapting the TO algorithm to incorporate the constraints imposed by symmetries. To validate, the developed symmetry based TO algorithm is applied to design scatterers that support the Néel-type skyrmion and the Bloch-type skyrmion at microwave frequencies. The output designs are tested in commercial solvers where good agreements are shown. This work lays down a solid foundation for exploring future symmetry-based inverse design tools for EM singularities (not limited to EM skyrmions, but also phase singularities, polarization vortices, to name a few) and thus can make a significant contribution to both the research domain of singular electromagnetics and computational electromagnetics/photonics.