Isotropic band gaps and freeform waveguides observed in hyperuniform disordered photonic solids

Abstract

Recently, disordered photonic media and random textured surfaces have attracted increasing attention as strong light diffusers with broadband and wide-angle properties. We report the experimental realization of an isotropic complete photonic band gap (PBG) in a 2D disordered dielectric structure. This structure is designed by a constrained optimization method, which combines advantages of both isotropy due to disorder and controlled scattering properties due to low-density fluctuations (hyperuniformity) and uniform local topology. Our experiments use a modular design composed of Al 2 O 3 walls and cylinders arranged in a hyperuniform disordered network. We observe a complete PBG in the microwave region, in good agreement with theoretical simulations, and show that the intrinsic isotropy of this unique class of PBG materials enables remarkable design freedom, including the realization of waveguides with arbitrary bending angles impossible in photonic crystals. This experimental verification of a complete PBG and realization of functional defects in this unique class of materials demonstrate their potential as building blocks for precise manipulation of photons in planar optical microcircuits and has implications for disordered acoustic and electronic band gap materials. The first examples of synthetic materials with complete photonic band gaps (PBGs) (1, 2) were photonic crystals using Bragg interference to block light over a finite range of frequencies. Because of their crystallinity, the PBGs are highly anisotropic, a potential drawback for many applications. The idea that a complete PBG (blocking all directions and all polarizations) can exist in isotropic disordered systems is striking, because it contradicts the longstanding intuition that periodic translational order is necessary to form PBGs. The paradigm for PBG formation is Bloch's theorem (3): a periodic modulation of the dielectric constant mixes degenerate waves propagating in opposite directions and leads to standing waves with high electric field intensity in the low dielectric region for states just above the gap and in the high dielectric region for states just below the gap. Long-range periodic order, as evidenced by Bragg peaks, is necessary for this picture to hold. The intrinsic anisotropy associated with periodicity may limit the scope of PBG applications greatly and places a major constraint on device design. For example, although 3D photonic crystals with complete PBGs have been fabricated for two decades (4), 3D waveguiding continues to be a challenge. Very recently, Noda and coworkers reported the first successful demonstration of 3D waveguiding (5). However, they found that because of the mismatch of the propagation modes in line defects along various symmetry orientations, vertical-trending waveguides must follow one particular major symmetry direction to effectively guide waves out of the horizontal symmetry plane in a 3D woodpile photonic crystal (5).Recently, disordered photonic media and random textured surfaces have attracted incr...

High-density hyperuniform materials can be transparent

“…The geometrical properties of hyperuniform point patterns have been extensively studied, in particular in terms of packing properties [21][22][23][24][25]. 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].…”

High-Qoptical cavities in hyperuniform disordered materials

“…We demonstrate that quality factors Q > 10 9 can be achieved for purely two-dimensional structures, and that for three-dimensional finite-height photonic slabs, quality factors Q > 20 000 can be maintained. A special class of disordered photonic heterostructures has recently been shown to display large isotropic band gaps comparable in width to band gaps found in photonic crystals [1][2][3]. The large band gaps found in these structures are facilitated by the hyperuniform geometrical properties of the underlying point-pattern template upon which the structures are built.…”

“…A point pattern in real space is hyperuniform if for large R the number variance σ (R) 2 within a spherical sampling window of radius R (in d dimensions) grows more slowly than the window volume, i.e., more slowly than R d . In Fourier space, hyperuniformity means that the structure factor S(k) approaches zero as |k| → 0 [5,6].…”

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].…”