Coupled-mode calculation with the R-matrix propagator for the dispersion of surface waves on a truncated photonic crystal

We describe a modal expansion method with an R-matrix propagation algorithm that can be applied to calculate the dispersion of surface and guided waves supported by a finite thickness photonic crystal. Easy to implement, the R matrix has the advantage of inherent numerical stability and allows photonic crystals of complex structure, which are many waves in thickness to be analyzed. This method is also computationally simpler that the supercell method when looking for surface modes. It can also be applied to many other dispersion problems including multilayer gratings and waveguides with internal structure. We apply this method to calculate dispersion of surface waves supported by a slablike photonic crystal structure, which consists of several rows of an infinitely periodic array of square dielectric cylinders. In the bulk, the periodic array has a photonic band gap and for the finite thickness structure, we calculate dispersion of surface waves that propagate along the boundaries at frequencies within the band gap. We vary the thickness of the cylinders in the outer layer and calculate the change in dispersion. When the overall thickness of the photonic slab is decreased, coupling and splitting between surface modes at each interface is observed.