Bachelor/Master Thesis "Light propagation on two-dimensional gratings"

By coupling two optical fiber rings, light propagation on a 1+1D grating can be investigated. The low losses in optical fibers are exploited to realize even propagation lengths of more than 1000 km. In addition, the use of standardized telecommunication equipment makes it possible to modulate the amplitude and phase of light pulses virtually at will. Furthermore, high peak power allows the investigation of nonlinear effects such as solitons. Because of this versatility, circulating light pulses in optical fibers are excellent for studying light propagation in discrete spaces under the influence of arbitrary potentials. Despite the numerous possibilities, however, the system can always be reduced to simple model systems. Thus, numerous analogies can be made to different physical fields such as: Particle physics, physics of ultracold gases, geometric phases and topological phenomena, parity-time symmetry and discrete systems leading to fractal patterns. By using additional fiber optic rings, the number of dimensions can be further increased, allowing the study of additional phenomena.

The thesis will involve simulations and calculations of linear and nonlinear light propagation on two-dimensional gratings. The work is intended to serve as a theoretical foundation for an experimental implementation in the form of an optical fiber setup. Accordingly, experimental investigation of the predicted phenomena would also be possible at a later stage.

Possible topics would be:

• Interaction between chaotic potentials and nonlinearities.
• Superfluidity and vortex evolution in two-dimensional systems
• Influence of gain and loss on two-dimensional systems (antidiffusion, fractal evolution and formation of the Hofstadter Butterfly)

Further reading

• Wimmer, M. et al. Optical diametric drive acceleration through action-reaction symmetry breaking. Nat. Phys. 9, 780-784 (2013).
• Regensburger, A. et al. Parity-time synthetic photonic lattices. Nature 488, 167-71 (2012).
• Regensburger, A. et al. Photon Propagation in a Discrete Fiber Network: An Interplay of Coherence and Losses. Phys. Rev. Lett. 107, 233902 (2011).