Exploring topological physics with photonics

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Condensed matter physics and optics have long been fields that feed each other with new ideas and techniques. A recent example of this synergy comes from topological physics. Under the right conditions, periodic systems can be characterized by a non-trivial topological invariant in reciprocal space (a quantity that does not change if the band structure of the system is smoothly deformed). This leads to the appearance of states with very interesting properties, such as those existing at the boundaries of bulk crystals. These states are protected against disorder. Important recent advances in discovering materials that display topological behaviour provide exciting opportunities to elucidate their properties and exploit their applications. Topological materials are restricted to naturally occurring crystal lattices, which cannot be easily modified. In addition, most materials are three-dimensional, so the experimental study of topological physics in 1D and 2D is challenging. Fortunately, it is possible to construct optical systems that show topological behaviour. Optical systems offer the freedom to design arbitrary periodic lattices, as well as very accessible experiments, which can be used to examine issues in topological physics. Studying topological physics with photons will provide novel insights, some that will be directly applicable to electronic systems, continuing the cross-pollination of new ideas between optics and condensed matter physics. From the applications point of view, increased understanding of topological photonics will inform the design of photonic devices that are immune to fabrication imperfections.******The long-term aim of my research program is to exploit optical techniques to develop versatile experimental platforms to study 1D and 2D systems that possess topological features. Using these platforms, we will experimentally explore problems in topological physics that are hard to study in materials. Key short-term projects under this umbrella are: (i) The design, fabrication, and characterization of 1D topological structures with edge states, (ii) the study of light transport in edge states in 2D topological photonic insulators, and (iii) the exploitation of the topological properties to develop ways to manipulate light in structures that are imperfect.******The anticipated advances in topological photonics from the research proposed here will be of a two-fold benefit: (i) An improved understanding of the physics of lattice systems (essentially systems relevant to condensed matter physics), and (ii) new photonic devices will be designed that will be robust against fabrication imperfections. Notably, (i) can also be investigated in the microwave regime, but (ii) requires working with near infrared or visible light. Our proposed platforms will allow straightforward exploration, using standard telecommunication or visible lasers, of topological phenomena in 1D and 2D.