Research

Topological photonics

According to Bloch's theorem, propagating waves in periodic media form energy bands separated by band gaps. Within the band gaps the waves are evanescent and spatially localized. Band structures describe a variety of phenomena in condensed matter physics, such as the electrical properties of metals, semiconductors, and insulators. In analogy to the crystalline structure of these materials, in 1987 Yablonovich and John introduced the concept of photonic crystals to trap and guide light using band gaps for light waves.

Relatively recently, condensed matter physicists have discovered that the energy band structure alone is insufficient to classify all phases of periodic crystalline materials; one also needs to use certain topological invariants to distinguish between otherwise identical energy bands. Topological invariants are quantized numbers that do not change under smooth deformations of a system, analogous to distinguishing a sphere from a coffee mug by counting the number of holes each has. Importantly, these topological invariants are not just a mathematical curiosity, but they can also predict and explain the robust "topologically protected" surface conductivity of surface materials.

Following a seminal 2005 paper by Haldane and Raghu showing that photonic band structures may also be described by topological invariants, researchers in photonics started to apply these ideas to the design of novel photonic devices. For example, topologically protected surface states may be used to create one-way optical waveguides that do not suffer from backscattering. The first proof of concept experiments (at microwave frequencies) were performed in 2009, and since then there has been tremendous interest in realizing different families of topological phases and refining designs towards eventual device applications. One direction we are currently pursuing is how to combine these topologically protected surface waves with nonlinear functionalities such as optical switching and self-focusing. Recently we have shown that the Kerr effect may be used for power-controlled switching and focusing of topological surface states [Phys. Rev. Lett. 117, 143901 (2016)], or to achieve nonlinear optical isolation [New J. Phys. 19, 095002 (2017)]. Another area of interest is how to generalise the topological invariants originally derived for Hermitian (energy-conserving) quantum mechanical systems to photonic systems with gain or loss that do not conserve the energy of the optical field [Phys. Rev. Lett. 118, 040401 (2017)]. This is an important consideration for harnessing topological invariants in devices such as lasers.

Conical intersections

Conical intersections are peculiar points in a wave's dispersion relation at which two or more bands intersect and become degenerate, resulting in a singularity of the wave group velocity. This singularity imparts interesting signatures on wave propagation, such as conical diffraction and vortex generation. The most famous example of a conical intersection is the Dirac cone occurring in honeycomb lattice systems such as graphene, but they have a much longer history dating back to the study of conical refraction in biaxial crystals in 1832. In two-dimensional systems the degeneracies are fragile and require either fine-tuning of the system parameters or protection by some symmetry. In three dimensional systems, however, conical intersections are generic (i.e. they occur without any special fine-tuning) and are known as "Weyl points". Less familiar, but just as interesting are "higher order" conical intersections involving three or more intersecting bands, which have recently been observed using Lieb photonic lattices. Our work on this topic includes theoretical predictions [Phys. Rev. A 86, 031805 (2012)], experimental collaborations (Phys. Rev. Lett. 116, 183902 (2016), Nature Phys. 13, 611 (2017)], and a review article [Adv. in Phys.: X 1, 101 (2016)].

Flat bands

Lattices with perfectly flat spectral bands have many interesting properties, such as a macroscopic degeneracy and diverging density of states which make them very sensitive to external perturbations. They are also closely connected connections to other branches of physics such as highly frustrated magnetism. Flat bands often host "compact localized modes" which have nonzero amplitude on only a finite number of lattice sites, with diffraction to other sites prevented by destructive interference.

We have been studying how to characterise the properties of flat bands using the structure of their compact localised modes. In many cases, these compact states provide an intuitive way to understand the behaviour of flat bands. For example, in systems where flat and dispersive bands coexist, disorder will couple the localised flat band states into a continuum of states belonging to the dispersive bands, leading to Fano resonances and a host of interesting effects including wave transport governed by heavy-tailed statistics reminiscent of large fluctuations occurring at phase transitions [Phys. Rev. B 88, 224203 (2013)], the emergence of anomalous disorder scaling laws originally predicted in an exactly solvable model introduced by Lloyd in 1969[EPL 105, 30001 (2014)], and the generation of different types of singularities in the density of states under correlated disorder [Phys. Rev. Lett. 113, 236403 (2014)]. More recently, we have investigated the peculiar impact of non-Hermitian wave dynamics on flat band phenomena [Phys. Rev. B 96, 064305 (2017)].

Discrete vortex solitons

An optical vortex is a phase singularity in a scalar field, with a quantized topological charge which takes integer values. Arrays of coupled waveguides can host discrete analogues of optical vortices, called discrete vortices, which have a nontrivial phase winding around a contour of discrete sites. We have studied the properties of discrete vortices in nonlinear waveguide arrays, in particular the existence and stability of nonlinear modes (stationary states) in ring-like structures. The existence of a degenerate family of nonlinear modes leads to peculiar "vortex spiralling" dynamics. Additionally, strong perturbations of stable modes can lead a periodic reversal (flipping) of the vortex handedness [Opt. Lett. 36, 4806 (2011)]. These different types of nonlinear dynamics could form the basis for all-optical (intensity-controlled) switches of the vortex topological charge [Phys. Rev. A 86, 043812 (2012)]. For example, we demonstrated in a proof-of- concept experiment the power-controlled switching of the vortex handedness in a coupler formed by four nonlinear waveguides [App. Phys. Lett. 104, 261111 (2014)]. We have also considered generalizations of this idea. In PT (parity-time) symmetric waveguide arrays with balanced gain and loss, the sign of the vortex charge becomes important [Opt. Lett. 38, 371 (2013)]. Multi-component fields (eg. two orthogonal polarizations) coupled via cross-phase modulation can host composite nonlinear modes, with different topological charges in the two components. Stability of nonlinear modes becomes sensitive to the total charge, with higher charges being stable over a larger range of parameters [J. Opt. 15, 044016 (2013)].