The robustness of skyrmion numbers of structured optical fields in atmospheric turbulence

The development of vector optical fields has brought forth numerous applications. Among these optical fields, a particular class of vector vortex beams has emerged, leading to the emergence of intriguing optical skyrmion fields characterized by skyrmion numbers. The optical skyrmion fields are well-defined by their effective magnetization and possess topologically protected configurations. It is anticipated that this type of optical structure can be exploited for encoding information in optical communication, even under perturbations such as turbulent air, optical fibers, and even general random media. In this study, we numerically demonstrate that the skyrmion numbers of optical skyrmion fields exhibit a certain degree of robustness to atmospheric turbulence, even though their intensity, phase and polarization patterns are distorted. Intriguingly, it is also observed that a larger difference between the absolute values of two azimuthal indices of the vectorial structured light field can lead to a superior level of resilience. These properties not only enhance the versatility of skyrmion fields and their numbers, but also open up new possibilities for their use in various applications across noisy channels.