McPhedran has made seminal contributions to the field of wave science, its techniques and applications. These have provided methods of unprecedented accuracy and insights which have enabled major developments in the performance of microstructured optical fibres, composite materials, diffraction gratings and photonic crystals. The multipole formulation has been developed as a major tool for solving scattering problems involving electromagnetic and elastic waves with both periodic and finite systems for applications like spectroscopy and photovoltaic and photothermal energy conversion. The associated tools of lattice sums, density of state functions, mode and defect analysis have advanced understanding and methodologies of wave science.