His research is primarily in the physics of waves (optical, electromagnetic, quantum, …), and how geometry and topology may be used to understand and control their propagation and scattering.
Particular interests include singular optics and structured light (optical vortices, optical angular momentum, polarization singularities), and applied topology in physics (especially applications of knot theory in optics, quantum mechanics and molecular biology).
He has published over 100 research papers, proceedings, reviews, and book chapters, working with various other theorists and experimentalists around the world.