The fundamental connection between geometrical and topological characteristics of structured photonic materials and advanced photonic functionalities is central to the design of novel photonic materials. Here, we explore new metrics, hyperuniformity and local self-uniformity, as measures of the structural order of photonic network structures. The hyperuniformity concept is built upon the properties of the structure in the reciprocal space and is associated with a constrained randomness such that density fluctuations on large scales behave more like those of ordered solids, crystals or quasicrystals, rather than those of conventional amorphous materials. Local self-uniformity on the other hand characterises the intimate connection between uniformity on local and global length scales and provides a measure of a random network’s internal structural similarity that can be used to rank networks on a continuous scale from crystalline, through glassy intermediate states, to chaotic configurations. Despite their very distinct characteristics, both metrics provide novel design strategies for achieving advanced photonic functionalities in non-periodic materials.

In this talk, I will explore the connection between the hyperuniformity and local self-uniformity and the photonic band gap formation and introduce novel photonic-network architectures, the local self-uniform amorphous diamond network and the amorphous gyroid network or triamond. I will demonstrate that all architectures displaying large photonic band gaps, be they periodic or disordered, are characterized by large values of the newly introduced disordered metrics. And will discuss the implications for advanced optical phenomena including photonic band gaps, localisation and waveguiding. A comparison between their predicted properties and recent experimental results will also be provided.
In the end, a series of applications of the new disordered photonic networks will be discussed including novel structuring for solar cell absorbers, the connection to the wing-scale structuring in the Pseudolycaena marsyas butterfly and new designs for photonic integrated circuits and micro-opto-mechanical filters and modulators.