Investigation of a negative next-nearest-neighbor-coupling in evanescently coupled dielectric waveguides

The tight-binding model is an approximation that is able to reduce the complexity of a system to the point where the dynamics can be described by discrete coupled mode equations. This allows to experiment with interesting theoretical models at different physical platforms. Often in these systems, only the couplings to the nearest neighbor sites are considered and those further away are neglected. However, in some cases the next nearest neighbour (NNN) coupling is necessary for the creation of topological non-trivial phases [1]. Since under the tight-binding approximation the coupling coefficient between waveguides is defined by the overlap integral of their evanescent electric fields [2], this does not correctly give the coupling coefficient for higher order coupling.