We present designs of 2D, isotropic, disordered, photonic materials of arbitrary size with complete band gaps blocking all directions and polarizations. The designs with the largest band gaps are obtained by a constrained optimization method that starts from a hyperuniform disordered point pattern, an array of points whose number variance within a spherical sampling window grows more slowly than the volume. We argue that hyperuniformity, combined with uniform local topology and short-range geometric order, can explain how complete photonic band gaps are possible without long-range translational order. We note the ramifications for electronic and phononic band gaps in disordered materials.dielectric heterostructures ͉ electronic band gap ͉ disordered structures ͉ amorphous materials S ince their introduction in 1987, photonic band gap (PBG) materials (1, 2) have evolved dramatically, and their unusual properties have led to diverse applications, including efficient radiation sources (3), sensors (4), and optical computer chips (5). To date, although, the only known large-scale dielectric heterostructures with sizeable, complete band gaps (⌬ / C Ն 10%, say, where ⌬ is the width of the band gap and C is the midpoint frequency) have been periodic, which limits the rotational symmetry and defect properties critical for controlling the flow of light in applications.In this paper, we show that it is possible to design 2D, isotropic, translationally disordered photonic materials of arbitrary size with large, complete PBGs. The designs have been generated through a protocol that can be used to construct different types of disordered, hyperuniform structures in two or more dimensions, which are distinguished by their suppressed density fluctuations on long length scales (6) and may serve as templates for designer materials with various other novel physical properties, including electronic, phononic, elastic, and transport behavior.Here we focus on adapting the protocol for fabricating materials with optimal photonic properties because of their useful applications and because it is feasible to manufacture the dielectric heterostructure designs presented in this paper by using existing techniques. Although the goal here is to produce designs for isotropic, disordered heterostructures, we show elsewhere how the same procedure can be used to obtain photonic quasicrystals with complete PBGs (28).The design procedure includes a limited number of free parameters (two, in the cases considered here) that are varied to find the largest possible band gap in this constrained subspace of structures. The optimization requires modest computational cost as compared with full-blown optimizations that search over all possible dielectric designs. In practice, although, we find that the protocol produces band gap properties that are not measurably different from the optima obtained by the optimization methods in cases where those computations have been performed. To compute the PBGs for the various disordered structures, we employ a supercel...

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...

We describe the role of first non-Markovian corrections to resonance fluorescence in photonic crystals, using a perturbative expansion of the Heisenberg equations of motion in powers of the atom-field reservoir coupling strength. Non-Markovian effects arise from the rapid variation of the photonic density of states with frequency. Our method recaptures the physics of the photon-atom bound state in the presence of a full photonic band gap. For the anisotropic three-dimensional photonic band gap, it predicts remarkable features in the resonance fluorescence, such as atomic population inversion and switching behavior in a two-level atom for moderate values of the applied laser field. The magnitude of the switching effect depends sensitively on the external laser intensity and its detuning frequency from the atomic transition. The robustness of this effect against nonradiative decay and dephasing mechanisms is also investigated.

Abstract:We report the first experimental demonstration of a TEpolarization photonic band gap (PBG) in a 2D isotropic hyperuniform disordered solid (HUDS) made of dielectric media with a dielectric index contrast of 1.6:1, very low for PBG formation. The solid is composed of a connected network of dielectric walls enclosing air-filled cells. Direct comparison with photonic crystals and quasicrystals permitted us to investigate band-gap properties as a function of increasing rotational isotropy. We present results from numerical simulations proving that the PBG observed experimentally for HUDS at low index contrast has zero density of states. The PBG is associated with the energy difference between complementary resonant modes above and below the gap, with the field predominantly concentrated in the air or in the dielectric. The intrinsic isotropy of HUDS may offer unprecedented flexibilities and freedom in applications (i. e. defect architecture design) not limited by crystalline symmetries. 10970-10973 (1988). 27. M. Florescu, P. J. Steinhardt, and S. Torquato, "Optical cavities and waveguides in hyperuniform disordered photonic solids," Phys.

We introduce an optimization method to design examples of photonic quasicrystals with substantial, complete photonic band gaps; that is, a range of frequencies over which electromagnetic wave propagation is forbidden for all directions and polarizations. The method can be applied to photonic quasicrystals with arbitrary rotational symmetry; here, we illustrate the results for fivefold and eightfold symmetric quasicrystals. The optimized band gaps are highly isotropic, which may offer advantages over photonic crystals for certain applications.