The most common degrees of freedom used for the description of a photonic system are frequency, wave vector, polarization and phase of the propagating light wave. However, in the last few years a new degree of freedom entered photonics: Topology - a property of photonic materials that relates to the global structure of their frequency dispersions - has been emerging as another indispensable ingredient, opening a path forward to the discovery of fundamentally new states of light and possibly revolutionary applications, including photonic circuitry less dependent on isolators and slow light insensitive to disorder. Based on laser-written photonic waveguide lattices [J. Phys. B 43, 163001 (2010)], we investiage the impact of topological quantities on the evolution of light. Recent results include the first demonstration of topological insulation of light [Nature 496, 196 (2013)], supersymmetric mode conversion [Nature Commun. 5, 3698 (2014)], the demonstration of the topological creation and destruction of edge modes [Phys. Rev. Lett. 111, 103901 (2013)], in-band localized modes [Phys. Rev. Lett. 114, 245503 (2015)], and the first demonstration of novel edge states in the graphene geometry [Nature Mater. 13, 57 (2014)]. Importantly, we expand our work also to the non-hermitian regime [Phys. Rev. Lett. 113, 123903 (2014)], where we showed how to extract topological quantities from the evolution of a wave packet [Phys. Rev. Lett. (in press)] .

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Left: Waveguide structure for breaking time-reversal symmetry, which is required for the observation of topological protection of light [Nature 496, 196 (2013)]. Right: Artist´s impression of the light evolution in a non-hermitian waveguide lattice [Phys. Rev. Lett. 113, 123903 (2014)].

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