Anisotropic Optical Shock Waves in Isotropic Media with Giant Nonlocal Nonlinearity.

Dispersive shock waves in thermal optical media are nonlinear phenomena whose intrinsic irreversibility is described by time asymmetric quantum mechanics. Recent studies demonstrated that the nonlocal wave breaking evolves in an exponentially decaying dynamics ruled by the reversed harmonic oscillator, namely, the simplest irreversible quantum system in the rigged Hilbert spaces. The generalization of this theory to more complex scenarios is still an open question. In this work, we use a thermal third-order medium with an unprecedented giant Kerr coefficient, the m-cresol/nylon mixed solution, to access an extremely nonlinear, highly nonlocal regime and realize anisotropic shock waves with internal gaps. We compare our experimental observations to results obtained under similar conditions but in hemoglobin solutions from human red blood cells, and found that the gap formation strongly depends on the nonlinearity strength. We prove that a superposition of Gamow vectors in an ad hoc rigged Hilbert space, that is, a tensorial product between the reversed and the standard harmonic oscillators spaces, describes the beam propagation beyond the shock point. The anisotropy turns out from the interaction of trapping and antitrapping potentials. Our work furnishes the description of novel intriguing shock phenomena mediated by extreme nonlinearities.

Hyperuniform disordered waveguides and devices for near infrared silicon photonics.

We introduce a hyperuniform-disordered platform for the realization of near-infrared photonic devices on a silicon-on-insulator platform, demonstrating the functionality of these structures in a flexible silicon photonics integrated circuit platform unconstrained by crystalline symmetries. The designs proposed advantageously leverage the large, complete, and isotropic photonic band gaps provided by hyperuniform disordered structures. An integrated design for a compact, sub-volt, sub-fJ/bit, hyperuniform-clad, electrically controlled resonant optical modulator suitable for fabrication in the silicon photonics ecosystem is presented along with simulation results. We also report results for passive device elements, including waveguides and resonators, which are seamlessly integrated with conventional silicon-on-insulator strip waveguides and vertical couplers. We show that the hyperuniform-disordered platform enables improved compactness, enhanced energy efficiency, and better temperature stability compared to the silicon photonics devices based on rib and strip waveguides.

Local self-uniformity in photonic networks.

The interaction of a material with light is intimately related to its wavelength-scale structure. Simple connections between structure and optical response empower us with essential intuition to engineer complex optical functionalities. Here we develop local self-uniformity (LSU) as a measure of a random network's internal structural similarity, ranking networks on a continuous scale from crystalline, through glassy intermediate states, to chaotic configurations. We demonstrate that complete photonic bandgap structures possess substantial LSU and validate LSU's importance in gap formation through design of amorphous gyroid structures. Amorphous gyroid samples are fabricated via three-dimensional ceramic printing and the bandgaps experimentally verified. We explore also the wing-scale structuring in the butterfly Pseudolycaena marsyas and show that it possesses substantial amorphous gyroid character, demonstrating the subtle order achieved by evolutionary optimization and the possibility of an amorphous gyroid's self-assembly.

Light localization and nonlinear beam transmission in specular amorphous photonic lattices.

We demonstrate specular photonic "lattices" with random index variations at disordered positions of lattice sites. These amorphous lattice structures, optically induced in a bulk nonlinear crystal, remain invariant during propagation since they are constructed from random components residing on a fixed ring in momentum space. We observe linear spatial localization of a light beam when probing through different "defect" points in such specular lattices, as well as the nonlinear destruction of localized modes. In addition, we illustrate the possibility of image transmission through the disordered lattices, when a self-defocusing nonlinearity is employed.

Unfolding the band structure of non-crystalline photonic band gap materials.

Non-crystalline photonic band gap (PBG) materials have received increasing attention, and sizeable PBGs have been reported in quasi-crystalline structures and, more recently, in disordered structures. Band structure calculations for periodic structures produce accurate dispersion relations, which determine group velocities, dispersion, density of states and iso-frequency surfaces, and are used to predict a wide-range of optical phenomena including light propagation, excited-state decay rates, temporal broadening or compression of ultrashort pulses and complex refraction phenomena. However, band calculations for non-periodic structures employ large super-cells of hundreds to thousands building blocks, and provide little useful information other than the PBG central frequency and width. Using stereolithography, we construct cm-scale disordered PBG materials and perform microwave transmission measurements, as well as finite-difference time-domain (FDTD) simulations. The photonic dispersion relations are reconstructed from the measured and simulated phase data. Our results demonstrate the existence of sizeable PBGs in these disordered structures and provide detailed information of the effective band diagrams, dispersion relation, iso-frequency contours, and their angular dependence. Slow light phenomena are also observed in these structures near gap frequencies. This study introduces a powerful tool to investigate photonic properties of non-crystalline structures and provides important effective dispersion information, otherwise difficult to obtain.

Using microwave and macroscopic samples of dielectric solids to study the photonic properties of disordered photonic bandgap materials.

Recently, disordered photonic materials have been suggested as an alternative to periodic crystals for the formation of a complete photonic bandgap (PBG). In this article we will describe the methods for constructing and characterizing macroscopic disordered photonic structures using microwaves. The microwave regime offers the most convenient experimental sample size to build and test PBG media. Easily manipulated dielectric lattice components extend flexibility in building various 2D structures on top of pre-printed plastic templates. Once built, the structures could be quickly modified with point and line defects to make freeform waveguides and filters. Testing is done using a widely available Vector Network Analyzer and pairs of microwave horn antennas. Due to the scale invariance property of electromagnetic fields, the results we obtained in the microwave region can be directly applied to infrared and optical regions. Our approach is simple but delivers exciting new insight into the nature of light and disordered matter interaction. Our representative results include the first experimental demonstration of the existence of a complete and isotropic PBG in a two-dimensional (2D) hyperuniform disordered dielectric structure. Additionally we demonstrate experimentally the ability of this novel photonic structure to guide electromagnetic waves (EM) through freeform waveguides of arbitrary shape.

Optical nonlinearities and enhanced light transmission in soft-matter systems with tunable polarizabilities.

We demonstrate a new class of synthetic colloidal suspensions capable of exhibiting negative polarizabilities, and observe for the first time robust propagation and enhanced transmission of self-trapped light over long distances that would have been otherwise impossible in conventional suspensions with positive polarizabilities. Such light penetration through the strong scattering environment is attributed to the interplay between optical forces and self-activated transparency effects while no thermal effect is involved. By judiciously mixing colloidal particles of both negative and positive polarizabilities, we show that the resulting nonlinear response of these systems can be fine-tuned. Our experimental observations are in agreement with theoretical analysis based on a thermodynamic model that takes into account particle-particle interactions. These results may open up new opportunities in developing soft-matter systems with engineered optical nonlinearities.

Interactions between self-channeled optical beams in soft-matter systems with artificial nonlinearities.

We demonstrate optical interactions between stable self-trapped optical beams in soft-matter systems with pre-engineered saturable self-focusing optical nonlinearities. Our experiments, carried out in dilute suspensions of particles with negative polarizabilities, show that optical beam interactions can vary from attractive to repulsive, or can display an energy exchange depending on the initial relative phases. The corresponding observations are in good agreement with theoretical predictions.

Photonic band gap in isotropic hyperuniform disordered solids with low dielectric contrast.

We report the first experimental demonstration of a TE-polarization 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.

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

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 Al2O3 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.

Direct measurements of critical stresses and cracking in thin films of colloid dispersions.

Useful films can be formed by drying colloidal dispersions, but the negative capillary pressure generated often promotes cracks. Complex lateral flows during drying compromised previous measurements of the pressure required for cracking. Here we report data for the onset of cracking, and the additional cracks that appear at higher pressures, from high-pressure ultrafiltration experiments on homogeneously compressed films. A comparison of the data with expectations from theory confirms that cracking is controlled by elastic recovery, though an energy criterion only provides a lower bound. Our experiments also identify the role of flaws as nucleation sites that initiate cracks.

Generalized Hertzian model for the deformation and cracking of colloidal packings saturated with liquid.

The process of drying colloidal dispersions generally produces particulate solids under stress as a result of capillary or interparticle forces. The derivation of a constitutive relation on the basis of Hertzian contact mechanics between spheres provides a model for quantitatively predicting the conditions under which close-packed colloidal layers form continuous void-free films or homogeneous porous films or crack under tensile stresses.

Experiments on random packings of ellipsoids.

Recent simulations indicate that ellipsoids can pack randomly more densely than spheres and, remarkably, for axes ratios near 1.25:1:0.8 can approach the densest crystal packing (fcc) of spheres, with a packing fraction of 74%. We demonstrate that such dense packings are realizable. We introduce a novel way of determining packing density for a finite sample that minimizes surface effects. We have fabricated ellipsoids and show that, in a sphere, the radial packing fraction phi(r) can be obtained from V(h), the volume of added fluid to fill the sphere to height h. We also obtain phi(r) from a magnetic resonance imaging scan. The measurements of the overall density phi(avr), phi(r) and the core density phi(0) = 0.74 +/- 0.005 agree with simulations.

Experimental measurement of the photonic properties of icosahedral quasicrystals.

Quasicrystalline structures may have optical bandgap properties-frequency ranges in which the propagation of light is forbidden-that make them well-suited to the scientific and technological applications for which photonic crystals are normally considered. Such quasicrystals can be constructed from two or more types of dielectric material arranged in a quasiperiodic pattern whose rotational symmetry is forbidden for periodic crystals (such as five-fold symmetry in the plane and icosahedral symmetry in three dimensions). Because quasicrystals have higher point group symmetry than ordinary crystals, their gap centre frequencies are closer and the gaps widths are more uniform-optimal conditions for forming a complete bandgap that is more closely spherically symmetric. Although previous studies have focused on one-dimensional and two-dimensional quasicrystals, where exact (one-dimensional) or approximate (two-dimensional) band structures can be calculated numerically, analogous calculations for the three-dimensional case are computationally challenging and have not yet been performed. Here we circumvent the computational problem by doing an experiment. Using stereolithography, we construct a photonic quasicrystal with centimetre-scale cells and perform microwave transmission measurements. We show that three-dimensional icosahedral quasicrystals exhibit sizeable stop gaps and, despite their quasiperiodicity, yield uncomplicated spectra that allow us to experimentally determine the faces of their effective Brillouin zones. Our studies confirm that they are excellent candidates for photonic bandgap materials.