This thesis deals with the theoretical description of photonic waveguides for the simulation of non-Abelian gauge fields as well as the study of non-Hermitian systems. The artifical gauge fields emerge from a closed, adiabatic curve in the parameter manifold of a waveguide system with degeneracies. An optimisation process allows to find ideal parameters of an experimental implementation. Additionally, two Lie-algebraic methods that solve the quantum master equation of an arbitrary, lossy waveguide system are developed, which allow to study non-Hermitian systems, e.g. parity-time-symmetry.<eng>
