Abstract
In this thesis we investigate designer disordered complex media for photonics and phononics applications. Initially we focus on the photonic properties and we analyse hyperuniform disordered structures (HUDS) using numerical simulations. Photonic HUDS are a new class of photonic solids, which display large, isotropic photonic band gaps (PBG) comparable in size to the ones found in photonic crystals (PC). We review their complex interference properties, including the origin of PBGs and potential applications. HUDS combine advantages of both isotropy due to disorder (absence of long-range order) and controlled scattering properties from uniform local topology due to hyperuniformity (constrained disorder). The existence of large band gaps in HUDS contradicts the long-standing intuition that Bragg scattering and long-range translational order is required in PBG formation, and demonstrates that interactions between Mie-like local resonances and multiple scattering can induce on their own PBGs. The discussion is extended to finite height effects of planar architectures such as pseudo-band-gaps in photonic slabs as well as the vertical confinement in the presence of disorder. The particular case of a silicon-on-insulator compatible hyperuniform disordered network structure is considered for TE polarised light. We address technologically realisable designs of HUDS including localisation of light in point-defect-like optical cavities and the guiding of light in free-form PC waveguide analogues. Using finite-difference time domain and band structure computer simulations, we show that it is possible to construct optical cavities in planar hyperuniform disordered solids with isotropic band gaps that efficiently confine TE polarised radiation. We thus demonstrate that HUDS are a promising general-purpose design platform for integrated optical micro-circuitry. After analysing HUDS for photonic applications we investigate them in the context of elastic waves towards phononics applications. We demonstrate the first phononic band gaps (PnBG) for HUDS. We find that PnBGs in phononic HUDS can confine and guide elastic waves similar to photonic HUDS for EM radiation.