The physics and applications of topologically complex light*

This talk will describe the propagation, control and manipulation of light that manifests spatial complexity. In free space and bulk media, such higher order eigenstates of light possess intriguing characteristics such as the ability to carry spin and orbital angular momentum and the ability to self-heal. Upon confinement, either by focusing them, or by guiding them in fibers, even more exotic behaviour, akin to spin-orbit interactions of confined electrons in atomic and molecular systems, is observed – light's polarisation as well as phase and group velocities become dependent on the intrinsic as well as extrinsic geometric path that the light beam takes. Such attributes have spawned applications as diverse as super-resolution microscopy, deep-tissue imaging, DNA sorting, classical and quantum communications, remote sensing and directed-energy defence strategies. This talk will describe recent applications, after elucidating the fundamental phenomena that make singular light beams behave dramatically differently from commonly encountered, conventional, Gaussian-shaped beams of light.