Determining intrinsic potentials and validating optical binding forces between colloidal particles using optical tweezers.

Understanding the interactions between small, submicrometer-sized colloidal particles is crucial for numerous scientific disciplines and technological applications. In this study, we employ optical tweezers as a powerful tool to investigate these interactions. We utilize a full image reconstruction technique to achieve high precision in characterizing particle pairs that enable nanometer-scale measurement of their positions. This approach captures intricate details and provides a comprehensive understanding of the spatial arrangement between particles, overcoming previous limitations in resolution. Moreover, our research demonstrates that properly accounting for optical binding forces to determine the intrinsic interaction potential is vital. We employ a discrete dipole approximation approach to calculate optical binding potentials and achieve a good agreement between the calculated and observed binding forces. We incorporate the findings from these simulations into the assessment of the intrinsic interaction potentials and validate our methodology by using short-range depletion attraction induced by micelles as an example.

Structural color from pigment-loaded nanostructures.

Color can originate from wavelength-dependence in the absorption of pigments or the scattering of nanostructures. While synthetic colors are dominated by the former, vivid structural colors found in nature have inspired much research on the latter. However, many of the most vibrant colors in nature involve the interactions of structure and pigment. Here, we demonstrate that pigment can be exploited to efficiently create bright structural color at wavelengths outside its absorption band. We created pigment-enhanced Bragg reflectors by sequentially spin-coating layers of poly-vinyl alcohol (PVA) and polystyrene (PS) loaded with ß-carotene (BC). With only 10 double layers, we achieved a peak reflectance over 0.8 at 550 nm and normal incidence. A pigment-free multilayer made of the same materials would require 25 double layers to achieve the same reflectance. Further, pigment loading suppressed the Bragg reflector's characteristic iridescence. Using numerical simulations, we further show that similar pigment loadings could significantly expand the gamut of non-iridescent colors addressable by photonic glasses.

Bandgap fluctuations and robustness in two-dimensional hyperuniform dielectric materials.

We numerically study the statistical fluctuations of photonic band gaps in ensembles of stealthy hyperuniform disordered patterns. We find that at low stealthiness, where correlations are weak, band gaps of different system realizations appear over a wide frequency range, are narrow, and generally do not overlap. Interestingly, above a critical value of stealthiness χ≳0.35, the bandgaps become large and overlap significantly from realization to realization, while a second gap appears. These observations extend our understanding of photonic bandgaps in disordered systems and provide information on the robustness of gaps in practical applications.

Transport through Amorphous Photonic Materials with Localization and Bandgap Regimes.

We propose a framework that unifies the description of light transmission through three-dimensional amorphous dielectric materials that exhibit both localization and a photonic bandgap. We argue that direct, coherent reflection near and in the bandgap attenuates the generation of diffuse or localized photons. Using the self-consistent theory of localization and considering the density of states of photons, we can quantitatively describe the total transmission of light for all transport regimes: transparency, light diffusion, localization, and bandgap. Comparison with numerical simulations of light transport through hyperuniform networks supports our theoretical approach.

Macroporous Silica Foams Fabricated via Soft Colloid Templating.

Macroporous materials with controlled pore sizes are of high scientific and technological interest, due to their low specific weight, as well as unique acoustic, thermal, or optical properties. Solid foams made of titania, silica, or silicon, as representative materials, have been previously obtained with several hundred nanometer pore sizes, by using sacrificial templates such as spherical emulsion droplets or colloidal particles. Macroporous structures in particular are excellent candidates as photonic materials with applications in structural coloration and photonic bandgap devices. However, whereas using spherical building blocks as templates may provide tight control over pore shape and size, it results in materials with an often unfavorable local topology. Templating dry-foam or compressed-emulsion structures appear as attractive alternatives, but have not been demonstrated so far for submicron pore sizes. Herein, the use of soft, flexible microgel colloids decorated with silica nanoparticles as templates of macroporous foams is reported. These purposely synthesized core-shell colloids are assembled at ultra-high effective volume fractions by centrifuging and thermal swelling, thereby resulting in uniform disordered materials with facetted pores, mimicking dry foams. After removal of the polymer component via calcination, lightweight pure silica structures are obtained with a well-defined cellular or network topology.

Light scattering from colloidal aggregates on a hierarchy of length scales.

Disordered dielectrics with structural correlations on length scales comparable to visible light wavelengths exhibit interesting optical properties. Such materials exist in nature, leading to beautiful structural non-iridescent color, and they are also increasingly used as building blocks for optical materials and coatings. In this article, we explore the angular resolved single-scattering properties of micron-sized, disordered colloidal assemblies. The aggregates act as structurally colored supraparticles or as building blocks for macroscopic photonic glasses. We obtain first experimental data for the differential scattering and transport cross-section. Based on existing macroscopic models, we develop a theoretical framework to describe the scattering from densely packed colloidal assemblies on a hierarchy of length scales.

Experimental Tuning of Transport Regimes in Hyperuniform Disordered Photonic Materials.

We present wave transport experiments in hyperuniform disordered arrays of cylinders with high dielectric permittivity. Using microwaves, we show that the same material can display transparency, photon diffusion, Anderson localization, or a full band gap, depending on the frequency ν of the electromagnetic wave. Interestingly, we find a second weaker band gap, which appears to be related to the second peak of the structure factor. Our results emphasize the importance of spatial correlations on different length scales for the formation of photonic band gaps.

Transition from light diffusion to localization in three-dimensional amorphous dielectric networks near the band edge.

Localization of light is the photon analog of electron localization in disordered lattices, for whose discovery Anderson received the Nobel prize in 1977. The question about its existence in open three-dimensional materials has eluded an experimental and full theoretical verification for decades. Here we study numerically electromagnetic vector wave transmittance through realistic digital representations of hyperuniform dielectric networks, a new class of highly correlated but disordered photonic band gap materials. We identify the evanescent decay of the transmitted power in the gap and diffusive transport far from the gap. Near the gap, we find that transport sets off diffusive but, with increasing slab thickness, crosses over gradually to a faster decay, signaling localization. We show that we can describe the transition to localization at the mobility edge using the self-consistent theory of localization based on the concept of a position-dependent diffusion coefficient.

Band gap formation and Anderson localization in disordered photonic materials with structural correlations.

Disordered dielectric materials with structural correlations show unconventional optical behavior: They can be transparent to long-wavelength radiation, while at the same time have isotropic band gaps in another frequency range. This phenomenon raises fundamental questions concerning photon transport through disordered media. While optical transparency in these materials is robust against recurrent multiple scattering, little is known about other transport regimes like diffusive multiple scattering or Anderson localization. Here, we investigate band gaps, and we report Anderson localization in 2D disordered dielectric structures using numerical simulations of the density of states and optical transport statistics. The disordered structures are designed with different levels of positional correlation encoded by the degree of stealthiness [Formula: see text] To establish a unified view, we propose a correlation-frequency ([Formula: see text]-[Formula: see text]) transport phase diagram. Our results show that, depending only on [Formula: see text], a dielectric material can transition from localization behavior to a band gap crossing an intermediate regime dominated by tunneling between weakly coupled states.

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

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 short-range order, in particular the tailoring of Bragg scattering at the isotropic Brillouin zone, are of key importance for designing disordered PBG materials.

High-quality photonic crystals with a nearly complete band gap obtained by direct inversion of woodpile templates with titanium dioxide.

Photonic crystal materials are based on a periodic modulation of the dielectric constant on length scales comparable to the wavelength of light. These materials can exhibit photonic band gaps; frequency regions for which the propagation of electromagnetic radiation is forbidden due to the depletion of the density of states. In order to exhibit a full band gap, 3D PCs must present a threshold refractive index contrast that depends on the crystal structure. In the case of the so-called woodpile photonic crystals this threshold is comparably low, approximately 1.9 for the direct structure. Therefore direct or inverted woodpiles made of high refractive index materials like silicon, germanium or titanium dioxide are sought after. Here we show that, by combining multiphoton lithography and atomic layer deposition, we can achieve a direct inversion of polymer templates into TiO2 based photonic crystals. The obtained structures show remarkable optical properties in the near-infrared region with almost perfect specular reflectance, a transmission dip close to the detection limit and a Bragg length comparable to the lattice constant.

Controlling dispersion forces between small particles with artificially created random light fields.

Appropriate combinations of laser beams can be used to trap and manipulate small particles with optical tweezers as well as to induce significant optical binding forces between particles. These interaction forces are usually strongly anisotropic depending on the interference landscape of the external fields. This is in contrast with the familiar isotropic, translationally invariant, van der Waals and, in general, Casimir-Lifshitz interactions between neutral bodies arising from random electromagnetic waves generated by equilibrium quantum and thermal fluctuations. Here we show, both theoretically and experimentally, that dispersion forces between small colloidal particles can also be induced and controlled using artificially created fluctuating light fields. Using optical tweezers as a gauge, we present experimental evidence for the predicted isotropic attractive interactions between dielectric microspheres induced by laser-generated, random light fields. These light-induced interactions open a path towards the control of translationally invariant interactions with tuneable strength and range in colloidal systems.

Self-assembled photonic structures.

Photonic crystals have proven their potential and are nowadays a familiar concept. They have been approached from many scientific and technological flanks. Among the many techniques devised to implement this technology self-assembly has always been one of great popularity surely due to its ease of access and the richness of results offered. Self-assembly is also probably the approach entailing more materials aspects owing to the fact that they lend themselves to be fabricated by a great many, very different methods on a vast variety of materials and to multiple purposes. To these well-known material systems a new sibling has been born (photonic glass) expanding the paradigm of optical materials inspired by solid state physics crystal concept. It is expected that they may become an important player in the near future not only because they complement the properties of photonic crystals but because they entice the researchers' curiosity. In this review a panorama is presented of the state of the art in this field with the view to serve a broad community concerned with materials aspects of photonic structures and more so those interested in self-assembly.

Threshold of a random laser with cold atoms.

We address the problem of achieving an optical random laser with a cloud of cold atoms, in which gain and scattering are provided by the same atoms. The lasing threshold can be defined using the on-resonance optical thickness b0 as a single critical parameter. We predict the threshold quantitatively, as well as power and frequency of the emitted light, using two different light transport models and the atomic polarizability of a strongly pumped two-level atom. We find a critical b0 on the order of 300, which is within reach of state-of-the-art cold-atom experiments. Interestingly, we find that random lasing can already occur in a regime of relatively low scattering.

Spatial wave intensity correlations in quasi-one-dimensional wires.

Spatial intensity correlations between waves transmitted through random media are analyzed within the framework of the random matrix theory of transport. Assuming that the statistical distribution of transfer matrices is isotropic, we found that the spatial correlation function can be expressed as the sum of three terms, with distinctive spatial dependences. This result coincides with the one obtained in the diffusive regime from perturbative calculations, but holds all the way from quasiballistic transport to localization. While correlations are positive in the diffusive regime, we predict a transition to negative correlations as the length of the system decreases.