Exotic symmetry-induced effects in photonic and phononic systems

Predictive theory to geometrically engineer materials in continuum systems to have desired symmetry-induced effects is developed here by bridging the gap between quantum and continuum descriptions. We emphasise a predictive approach, the strength of which is demonstrated by the ability to design well-defined broadband edge states, valley-Hall networks and anisotropic quasicrystalline effects. We solely use semi-analytical models; this means we can concentrate cleanly upon issues such as group theory, and its influence upon the effects we see, without numerical distractions.