My research has been primarily in theoretical optics and photonics—hence the acronym (TOP) for my research team. Structured light has emerged as a recurring research theme of the team. Coherent light fields with controllable amplitude, phase and polarization distributions in space and/or time fall into the realm of structured light; in the case of partially coherent (speckled) light fields, space-time (space-frequency) field correlations can be structured. Exploring structured space-time light packets and topologically nontrivial states of light, such as optical vortices, hopfions, skyrmions, knots and links, establishes a gateway into the fundamental behavior of analogous fields in more complex and less experimentally accessible settings in condensed matter physics and quantum field theory. At the same time, structured light has found applications to free-space and multi-mode fiber optical communications and imaging. With this in mind, we have been exploring topological states of light as well as optical wave packets with classically non-separable (entangled) degrees of freedom which mimic local quantum entanglement and can therefore be employed in quantum-like communication protocols with classical light for which no quantum non-locality is required.

We have also studied novel manifestations of periodic revivals of wave packets of light, such as the celebrated Talbot effect, arising from such classical non-separability of their various degrees of freedom. These studies uncovered intriguing links between the physics of structured light and number theory that can be employed to efficiently factorize large numbers into primes on an analogue optical computer.

Further, we have been concerned with structured light-matter interactions at spatial and temporal interfaces in optical media. Such temporal boundaries can model event horizons of general relativity; thus, structured light optics has emerged as a promising laboratory to explore otherwise inaccessible cosmological phenomena, often unfolding over astronomically large scales in space and time.

Sometimes light structuring occurs naturally in nonlinear wave systems via a subtle interplay between the medium nonlinearity and linear diffraction and/or dispersion, as well as gain/loss and medium inhomogeneity. We have been studying such nonlinear light structures or patterns, including optical solitons, similaritons and rogue waves. Similaritons are waves that maintain their shape and identity but scale on propagation in the medium, while rogue waves are random bursts of extreme amplitudes emerging faster than is anticipated by conventional Gaussian statistics.