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Summary form only given. Using the transfer matrix method the transmission co-efficient was determined for periodic defect states in a hexagonal lattice. The hexagonal lattice is created by removing cylindrical air holes from a background dielectric media with a dielectric constant of 7.9. This value was chosen to represent a half-wavelength thick GaAs waveguide from which the cylindrical holes were removed. The holes were chosen to have a radius to lattice spacing ratio of 0.35. Defects were created within the lattice by completely in-filling a superlattice of air cylinder sites with the same constituent waveguide material.