Aperiodic lattices for tunable photonic bandgaps and localization

Photonic bandgap engineering using aperiodic lattices (ALs) is systematically studied. Up to now ALs have tended to be defined by specific formulae (e.g. Fibonacci, Cantor), and theories have neglected other useful ALs along with the vast majority of non-useful (random) ALs. Here we present a practical and efficient Fourier space-based general theory, to identify all those ALs having useful band properties, which are characterized by well-defined Fourier (i.e. lattice momentum) components. Direct real-space optimization of ALs tends to be computationally demanding, and is also difficult to generalise beyond 1D. However, via our Fourier space-based inverse optimization algorithm, we efficiently tailor the relative strength of the AL Fourier components for precise control of photonic band and localization properties.