Segmented waveguide arrays: deriving discrete diffraction relations in a square lattice photonic crystal

Segmented strip-loaded waveguide arrays are investigated within a rigorous square lattice photonic crystal model. We derive a full multiband discrete diffraction approach for near-axial injection in the direction of a lattice vector. We obtain an effective waveguide array picture, with quasi-linear dependence on the segmentation ratio in a simplified single-band scheme. Our results are validated by beam deviation experiments. Such a diffraction framework allows for efficient shaping of the phase map in waveguide arrays and enriches the engineering toolkit of photonic crystals with the in-plane free propagation structures of discrete photonics.