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...

Photonic crystals are metamaterials designed to display a periodic modulation of the refractive index. [ 1,2 ] For light wavelengths that match the Bragg condition, such materials display a photonic gap. For suffi cient refractive index contrast, a complete band gap emerges, the density of states in the gap is zero, transmission vanishes and incident light is specularly refl ected. The concept was initially proposed by Yablonovitch and John 25 years ago. Research in the fi eld initially developed rapidly but has matured over the last decade. Although materials with complete band gaps have been reported from the infrared to the visible, there still exist many challenges in fabrication and for possible applications. [ 3,4 ] For example only recently threedimensional guiding of photons in photonic crystals has been demonstrated. [ 5,6 ] Interestingly disordered photonic structures are also candidates for complete band gap materials. Numerical data show that peculiar hyperuniform disordered materials can display complete bandgaps in two dimensions [ 7 ] that allows the design of cavities and optical waveguides. [ 8 ] Recent experimental data for two-dimensional hyperuniform structures in the microwave regime provide support for these claims. [ 9,10 ] Independent numerical calculations suggest that these concepts can also be applied to three-dimensional hyperuniform structures where a band gap is predicted to open for refractive indices n ≥ 3 in air. [ 11 ] Here we present such hyperuniform structures made from silicon with a broad and pronounced gap in the shortwave infrared for the fi rst time.One of the intrinsic shortcomings of photonic crystals is the highly selective refl ection from Bragg planes due to crystalline symmetries. For many practical applications this feature is detrimental. For example dye-free refl ective color displays, colored packing materials or cosmetics are preferentially noniridescent and thus non-crystalline. Moreover the design of optical integrated devices is based on the realization of waveguides, switches and optical cavities that suffer from the anisotropic optical response of crystalline solids. [ 8 ] While initially largely ignored, the design of amorphous photonic materials has gained increasing attention over the last decade. [12][13][14][15][16] Disordered dielectric structures with short-range order display wideangle refl ection and broad spectral features. Early experiments demonstrated that the transmission and refl ection properties are governed by an interplay between Mie scattering and local order via the modulation of the single scattering cross section. [ 13,14 ] To some extent both properties can be tuned independently which in turn allows to tailor solid and liquid materials with a specifi c optical response, fi nding use in random lasers [ 15 ] or for materials where angle-independent structural colors are desired. [ 16 ] While engineering disordered photonic materials is just at its beginning, many examples can already be found in nature such as in non-iridescent colo...

We report on the mesoscale fabrication and characterization of polymeric templates for isotropic photonic materials derived from hyper-uniform point patterns using direct laser writing in a polymer photoresist. We study experimentally the microscopic structure by electron microscopy and small angle light scattering. Reducing the refractive index mismatch by liquid infiltration we find good agreement between the scattering data and numerical calculations in the single scattering limit. Our work thus demonstrates the feasibility of fabricating such random designer materials on technologically relevant length scales.

No abstract