Against common intuition, light propagating in free space may exhibit various intriguing features that one would expect only from artificially structured media. The initial conditions, i.e., amplitude distribution and phase, of an optical beam can force him to evolve in a peculiar fashion. Recently, we were able to generate a quantum random walk in free space [Optica 1, 268 (2014)] by appropriately tailoring the initial wave field. Interestingly, the light evolves as if it follows a periodic potential, although free space is absolutely homogeneous. Moreover, the equations governing the light evolution allow even for spiraling trajectories in free space. We identified a new family of light beams that exhibit spatial rotations during propagation [Phys. Rev. Lett. 113, 183901 (2014)] and were able to develop a full theory and to show these new beams in a series of experiments.

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Left: Artist´s depiction of a free space quantum random walk [Optica 1, 268 (2014)].  Right: Spiraling trajectories of a new class of optical beams - radially self-accelerated beams [Phys. Rev. Lett. 113, 183901 (2014)].

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