Skyrmions are quasi-particles with a topologically stable structure

having widespread relevance in fields like condensed matter physics

plasmonics

and photonics. Initially proposed to describe baryons and atomic nuclei

they have since been extensively studied in spintronic devices for their unique magnetic properties. Recently

the exploration of optical skyrmions generation and their interaction of matters has attracted wide interest in optics and photonics. Previous studies have been mostly limited in the linear optical regime. The nonlinear interaction and topological transformation of optical skyrmions with matters has not been well explored. In this work

we report the second and third nonlinear harmonic generation driven by optical skyrmions by interacting with crystals possessing different rotational symmetries. We demonstrate the nonlinear transformation of optical skyrmions with different topological charges in solids. The nonlinear optical harmonic skyrmions are formed with coherent superpositions of higher-order skyrmions

allowing conversions between skyrmions and anti-skyrmions. A quantum urn model is introduced to explain the generation of low-order and high-order harmonic skyrmions. This work presents the nonlinear interaction of the topological light fields with crystalline symmetry and provides novel insights into the efficient generation and robust control of the harmonics of skyrmions. It has implications on the application of secure communication

precise metrology

and quantum information.