Complex edge states in tailored photonic graphene

In condensed matter physics, the peculiar Dirac dynamics of electrons in graphene enables a plethora of novel applications, ranging from composite materials to photovoltaics and energy storage. This thesis demonstrates that also in integrated photonics the unique structural properties of graphene open up new possibilities. This is realized by the transfer of the honeycomb lattice structure to an array of evanescently coupled waveguides called photonic graphene - exhibiting the same extraordinary tight-binding band structure as atomic graphene. Within this work, femtosecond laser written photonic graphene allows the exploration of various novel phenomena. Especially, the relatively easy experimental access to the characteristic edge states of the honeycomb lattice is advantageous in the photonic system. Edge states of the system are shown to undergo a transition under linear deformation of the lattice. In a further experiment, measurement of light confinement at the edge is used to demonstrate the formation of Landau levels. This special band structure usually occurs under application of a magnetic field to an atomic lattice. Here, it arises from a pseudomagnetic field caused by a certain non-uniform strain implemented in photonic graphene. However, to derive breaking of the time-reversal symmetry as found under a real magnetic field, here another method is applied. By periodical modulation of the lattice along the propagation direction, the principle of Floquet topological insulators is implemented. The first realization of a photonic topological insulator demonstrates the unique robust one-way light transport along the edges of the system. Such extraordinary topological transport properties hold immense potential for the improvement of various photonic functionalities. Hence, the work transfers ideas originally based on solid state systems to optics allowing to evolve above and beyond these fundamental notions opening up new avenues in the field of photonics.