This thesis investigates the intricate relationship between structural complexity and electromagnetic wave behaviour in photonic media, with a focus on quasiperiodic, disordered,

and absorptive systems. The work aims to understand how deterministic aperiodicity, statistical disorder, and material absorption influence the formation of photonic band gaps, the localization of modes, and the transport of optical energy.

Quasiperiodic photonic structures, particularly Penrose networks, are shown to support both fundamental and sub-fundamental photonic band gaps. These gaps arise from distinct physical mechanisms: the fundamental gap is driven by local scattering and Bragg-like resonances, while the sub-fundamental gap emerges from long-range geometric correlations and the infinite repetition of local motifs. A key result is the identification of spatial resonances that dominate the modal landscape near these gaps. By varying the local isomorphism class of the quasiperiodic pattern, the study demonstrates how geometric deformation suppresses localization near the sub-fundamental gap and enhances defect-like modes in the fundamental gap. Scaling analysis reveals that most modes in these structures are critical, exhibiting multifractal behaviour, with only a few truly localised or extended states.

Hyperuniform disordered networks provide a statistically isotropic platform for studying light localization in non-periodic media. By tuning the hyperuniformity parameter χ, the research identifies clear transitions between Anderson and defect-type localization regimes. Localization length spectra and level-spacing statistics show that near the band edges, modes become strongly confined. In highly ordered configurations, defect-type localization dominates, while in more disordered patterns, Anderson localization prevails. A particularly novel result is the emergence of photonic molecules—bondingand anti-bonding states formed by coupling between defect modes centered on four-sided air-hole cavities. These molecules are observed both in simulations and experimentally, with photoluminescence spectra confirming their presence and spatial distribution. The study also identifies a frequency inversion point in the lower band, marking the transition between Anderson and defect-type localization, a feature not previously reported in the literature.

To incorporate material absorption and dispersion, the thesis develops a quantum electro-dynamical framework based on polaritonic mode decomposition. This formalism enables the computation of absorptive band structures for materials such as Gallium Arsenide. The results reveal novel features including dispersionless flat bands and sub-band resonances, which arise from the interplay between the material’s frequency-dependent dielectric response and the structural geometry. The breakdown of conventional scaling laws is demonstrated, showing that absorptive effects introduce a length scale that alters the band structure in ways not captured by traditional models. The photonic energy ratio is introduced as a metric for quantifying the electromagnetic character of modes, and its variation across frequency and wavevector space provides insight into the degree

of absorption and confinement.

Together, these investigations advance the theoretical and experimental understanding of light localization, band gap formation, and absorption in complex photonic systems. The results have direct implications for the design of next-generation optical materials and devices, including waveguides, filters, and sensors, that exploit structural disorder and material response for enhanced functionality. By bridging deterministic and statistical

design paradigms with quantum optical modelling, the thesis lays the groundwork for a unified approach to engineering photonic media with tailored spectral and spatial properties.