Role of Short-Range Order and Hyperuniformity in the Formation of Band Gaps in Disordered Photonic Materials

Abstract

We study photonic band gap formation in two-dimensional high-refractive-index disordered materials where the dielectric structure is derived from packing disks in real and reciprocal space. Numerical calculations of the photonic density of states demonstrate the presence of a band gap for all polarizations in both cases. We find that the band gap width is controlled by the increase in positional correlation inducing short-range order and hyperuniformity concurrently. Our findings suggest that the optimization of shortrange order, in particular the tailoring of Bragg scattering at the isotropic Brillouin zone, are of key importance for designing disordered PBG materials. DOI: 10.1103/PhysRevLett.117.053902 Photonic band gap (PBG) materials exhibit frequency bands where the propagation of light is strictly prohibited. Such materials are usually designed by arranging highrefractive-index dielectric material on a crystal lattice [1,2]. The description of wave transport in a periodically repeating environment provides a clear physical mechanism for the emergence of PBGs, in analogy to common electronic semiconductors. It is also known that certain aperiodic dielectric structures, such as quasicrystals [3][4][5], can display a full PBG. Over the last decade disordered or amorphous photonic materials have gained growing attention [6][7][8][9][10][11][12][13][14][15][16][17][18]. This trend is motivated by the many disordered photonic materials found in nature that reveal fascinating structural color effects in plants, insects, and mammals [19]. At the same time, fabricating perfect crystalline structures with photonic properties at optical wavelengths has proven to be more difficult than initially anticipated [20]. It has been argued that disordered PBG materials should be less sensitive to fabrication errors or defects and thus promise a more robust design platform [15]. Moreover PBGs in disordered dielectrics are isotropic, which could make it easier to achieve a full PBG while at the same time offering better performance in wave guiding, design of noniridescent stable pigments, and display applications [21][22][23][24].Yet, until recently, direct evidence for the existence of full PBGs in disordered photonic materials had been scarce and the fabrication principles and physical-optical mechanism leading to PBG formation remained obscure. Although the importance of appropriate short-range order for the development of PBGs in disordered photonic materials was discovered early on [6-9], a strategy to maximize the PBG width was lacking.In 2009 Florescu and co-workers [25] proposed a new approach for the design of disordered PBG materials that has attracted widespread attention. They introduced the concept of hyperuniformity for photonic structures, which enforces a certain type of short-range order. In particular, so-called stealthy hyperuniform (SHU) disordered patterns were reported to be fully transparent to incident long-wavelength radiation [26,27] and lead to strong isotropic PBGs at shorter wavelengths [25]. Ot...

High-density hyperuniform materials can be transparent

“…Regarding wave propagation, it has been shown that bandgaps could be observed for electromagnetic waves in two-dimensional (2D) disordered hyperuniform materials [26][27][28][29][30]. Although understanding the origin of the bandgaps is still a matter of study [31,32], these results have stimulated the design and fabrication of threedimensional (3D) hyperuniform structures for wave control at optical frequencies [33,34].In this Letter, we demonstrate that stealth hyperuniform point patterns, a special class of hyperuniform structures for which S(q) = 0 in a finite domain around |q| = 0, offer the possibility to design disordered materials that can be both dense and transparent, in a specific and broad range of frequencies and directions of incidence. The analysis is based on full numerical simulations and theoretical modelling.…”

On‐Chip Hyperuniform Lasers for Controllable Transitions in Disordered Systems

“…Hyperuniform patterns are generated with the approach explained in refs. [], which makes use of molecular dynamics simulations with particles subjected to the potential energy Φ. where N is the total number of the particles, their position, a discrete wavenumber in the reciprocal space, and the corresponding structure factor.…”

Hyperuniformity disorder length spectroscopy for extended particles

“…The second is by direct integration using Eqs. (12)(13)(14)(15). Note that the effect of pixelated space (i.e.…”

“…Examples include jamming in amorphous materials [4,5,[7][8][9][10], complete optical band gaps in disordered photonics materials [11][12][13][14][15], and reversibility/irreversibility in periodically driven systems [16][17][18]. Hyperunformity is also important in the arrangement of photoreceptors in the retina [19], and in the large-scale structure of the universe [2].…”