Optical vortices are beams of light that carry orbital angular momentum¹, which represents an extra degree of freedom that can be generated and manipulated for photonic applications^{2,3,4,5,6,7,8}. Unlike vortices in other physical entities, the generation of optical vortices requires structural singularities^9,10,11,12, but this affects their quasiparticle nature and hampers the possibility of altering their dynamics or making them interacting^{13,14,15,16,17}. Here we report a platform that allows the spontaneous generation and active manipulation of an optical vortex–antivortex pair using an external field. An aluminium/silicon dioxide/nickel/silicon dioxide multilayer structure realizes a gradient-thickness optical cavity, where the magneto-optic effects of the nickel layer affect the transition between a trivial and a non-trivial topological phase. Rather than a structural singularity, the vortex–antivortex pairs present in the light reflected by our device are generated through mathematical singularities in the generalized parameter space of the top and bottom silicon dioxide layers, which can be mapped onto real space and exhibit polarization-dependent and topology-dependent dynamics driven by external magnetic fields. We expect that the field-induced engineering of optical vortices that we report will facilitate the study of topological photonic interactions and inspire further efforts to bestow quasiparticle-like properties to various topological photonic textures such as toroidal vortices, polarization and vortex knots, and optical skyrmions.