Topological robustness and phase transitions of optical skyrmions determined by singularities

Skyrmions are topologically stable quasiparticles that have been predicted and demonstrated in various fields and came into optics in recent years. For the diverse controllable degrees-of-freedom of light, it provides the capability to form the higher-order topologies flexibly. Previously, most research has been focused on the generation of novel topologies in optical systems, whereas the underlying mechanisms of topological robustness and phase transitions of optical quasiparticles have been rarely studied till now. Here, we demonstrate an interesting mechanism related to the topological charges of optical singularities underlying topological robustness and phase transitions in optical skyrmions under a focusing configuration. Using Poynting vector skyrmions as an example, when the sum of topological charges of incident singularities is 2, optical skyrmions emerge with topological robustness against random disturbances, whereas when sum of topological charges of incident singularities is larger than 2, topological phase transitions occur and the maximal modulated skyrmion number depends solely on the topological charge of incident polarization singularity. We construct a comprehensive theoretical model to uncover the underlying mechanisms behind the performance of robustness and the capacity of topological phase transitions under three types of random disturbances, including amplitude, phase, and simultaneous amplitude and phase disturbances. Finally, we present a scheme to solve the lack of robustness for optical skyrmions when the sum of topological charges of incident singularities is not 2 by tailoring the zone of a skyrmion texture to form a meron topology. The findings can give a guidance for switching topological robustness and phase transitions of optical skyrmions in one system and offer applications in topologically robust optical manipulations, communications, and quantum communications.