Shaping and controlling electromagnetic waves have wide-ranging scientific and practical implications. In this talk, I will present a few theoretical proposals to generate novel topological structures in light. In particular, I show that the transmission nodal lines are general topological responses from non-local metasurfaces and can be used to generate spatiotemporal optical vortices. Additionally, I discuss the possible topological structures that can occur in electromagnetic waves. I show that three-dimensional topological structures, known as hopfions and Shankar skyrmions can be created in free-space electromagnetic waves. Such complex shaping of light may be used for optical emulation of new topological physics, or be used in optical trapping and manipulation applications.
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