Absence of Circular Polarisation in Reflections of Butterfly Wing Scales with Chiral Gyroid Structure

Thermotropic "Plumber's Nightmare"-A Tight Liquid Organic Double Framework

Gyroid, double diamond and the body-centred "Plumber's nightmare" are the three most common bicontinuous cubic phases in lyotropic liquid crystals and block copolymers. While the first two are also present in solvent-free thermotropics, the latter had never been found. Containing six-fold junctions, it was unlikely to form in the more common phases with rod-like cores normal to the network columns, where a maximum of four branches can join at a junction. The solution has therefore been sought in side-branched mesogens that lie in axial bundles joined at their ends by flexible "hinges". But for the tightly packed double framework, geometric models predicted that the side-chains should be very short. The true Plumber's nightmare reported here, using fluorescent dithienofluorenone rod-like mesogen, has been achieved with, indeed, no side chains at all, but with 6 flexible end-chains. Such molecules normally form columnar phases, but the key to converting a complex helical column-forming mesogen into a framework-forming one was the addition of just one methyl group to each pendant chain. A geometry-based explanation is given.

Supertwisted Chiral Gyroid Mesophase in Chiral Rod-Like Compounds

Among the intriguing bicontinuous self-assembled structures, the gyroid cubic is the most ubiquitous. It is found in block and star polymers, surfactants with or without solvent, in thermotropic liquid crystals with end- or side-chains, and in biosystems providing structural color and modelling cell mitosis. It contains two interpenetrating networks of opposite chirality and is thus achiral if, as usual, the content of the two nets is the same. However, we now find that this is not the case for strongly chiral compounds. While achiral molecules follow the opposite twists of nets 1 and 2, molecules with a chiral center in their rod-like core fail to follow the 70° twist between junctions in net 2 and instead wind against it by -110° to still match the junction orientation. The metastable chiral gyroid is a high-entropy high-heat-capacity mesophase. The homochirality of its nets makes the CD signal of the thienofluorenone compounds close to that in the stable I23 phase with 3 isochiral nets.

Using high-resolution microscopy data to generate realistic structures for electromagnetic FDTD simulations from complex biological models

Finite-difference time-domain (FDTD) electromagnetic simulations are a computational method that has seen much success in the study of biological optics; however, such simulations are often hindered by the difficulty of faithfully replicating complex biological microstructures in the simulation space. Recently, we designed simulations to calculate the trajectory of electromagnetic light waves through realistically reconstructed retinal photoreceptors and found that cone photoreceptor mitochondria play a substantial role in shaping incoming light. In addition to vision research and ophthalmology, such simulations are broadly applicable to studies of the interaction of electromagnetic radiation with biological tissue. Here, we present our method for discretizing complex 3D models of cellular structures for use in FDTD simulations using MEEP, the MIT Electromagnetic Equation Propagation software, including subpixel smoothing at mesh boundaries. Such models can originate from experimental imaging or be constructed by hand. We also include sample code for use in MEEP. Implementation of this algorithm in new code requires understanding of 3D mathematics and may require several weeks of effort, whereas use of our sample code requires knowledge of MEEP and C++ and may take up to a few hours to prepare a model of interest for 3D FDTD simulation. In all cases, access to a facility supercomputer with parallel processing capabilities is recommended. This protocol offers a practical solution to a significant challenge in the field of computational electrodynamics and paves the way for future advancements in the study of light interaction with biological structures.

A meta-analysis of butterfly structural colors: their color range, distribution and biological production

Butterfly scales are among the richest natural sources of optical nanostructures, which produce structural color and iridescence. Several recurring nanostructure types have been described, such as ridge multilayers, gyroids and lower lamina thin films. While the optical mechanisms of these nanostructure classes are known, their phylogenetic distributions and functional ranges have not been described in detail. In this Review, we examine a century of research on the biological production of structural colors, including their evolution, development and genetic regulation. We have also created a database of more than 300 optical nanostructures in butterflies and conducted a meta-analysis of the color range, abundance and phylogenetic distribution of each nanostructure class. Butterfly structural colors are ubiquitous in short wavelengths but extremely rare in long wavelengths, especially red. In particular, blue wavelengths (around 450 nm) occur in more clades and are produced by more kinds of nanostructures than other hues. Nanostructure categories differ in prevalence, phylogenetic distribution, color range and brightness. For example, lamina thin films are the least bright; perforated lumen multilayers occur most often but are almost entirely restricted to the family Lycaenidae; and 3D photonic crystals, including gyroids, have the narrowest wavelength range (from about 450 to 550 nm). We discuss the implications of these patterns in terms of nanostructure evolution, physical constraint and relationships to pigmentary color. Finally, we highlight opportunities for future research, such as analyses of subadult and Hesperid structural colors and the identification of genes that directly build the nanostructures, with relevance for biomimetic engineering.

Modelling structural colour from helicoidal multi-layer thin films with natural disorder

A coupled mode theory based on Takagi-Taupin equations describing electromagnetic scattering from distorted periodic arrays is applied to the problem of light scattering from beetles. We extend the method to include perturbations in the permittivity tensor to helicoidal arrays seen in many species of scarab beetle and optically anisotropic layered materials more generally. This extension permits analysis of typical dislocations arising from the biological assembly process and the presence of other structures in the elytra. We show that by extracting structural information from transmission electron microscopy data, including characteristic disorder parameters, good agreement with spectral specular and non-specular reflectance measurements is obtained.

High-resolution three-dimensional structural determination of unstained double-gyroid block copolymers through scanning transmission electron microscopy

Block copolymer-based multicomponent materials have garnered considerable attention because of tunable properties due to their various constituents. The use of electron tomography through transmission electron microscopy (TEM) for the three-dimensional (3D) imaging of stained block copolymers is an established approach for investigating structure-property relationships. Recently, scanning transmission electron microscopy (STEM) with an annular dark-field (ADF) detector has emerged as a method for the 3D structural analysis of unstained block copolymers. However, because of a lack of electron contrast, only a few low-resolution 3D reconstructions were reported for light elements. Herein, we report the first 3D structural analysis of a 200-nm-thick film composed of unstained double-gyroid block copolymers-polystyrene-b-poly(2-vinylpyridine) (PS-P2VP)-at a resolution of 8.6 nm through spherical aberration Cs-corrected STEM. At this resolution, P2VP molecules can be distinguished from PS molecules in z-contrast 3D reconstructions obtained both experimentally and theoretically. The 3D reconstructions revealed structural differences between stained and unstained specimens.

Broadband circular dichroism in chiral plasmonic woodpiles

The circular dichroism (CD) of a material is the difference in optical absorption under left- and right-circularly polarized illumination. It is crucial for a number of applications, from molecular sensing to the design of circularly polarized thermal light sources. The CD in natural materials is typically weak, leading to the exploitation of artificial chiral materials. Layered chiral woodpile structures are well known to boost chiro-optical effects when realized as a photonic crystal or an optical metamaterial. We here demonstrate that light scattering at a chiral plasmonic woodpile, which is structured on the order of the wavelength of the light, can be well understood by considering the fundamental evanescent Floquet states within the structure. In particular, we report a broadband circular polarization bandgap in the complex band structure of various plasmonic woodpiles that spans the optical transparency window of the atmosphere between 3 and 4 μ m and leads to an average CD of up to 90% within this spectral range. Our findings could pave the way for an ultra-broadband circularly polarized thermal source.

Curvature in Biological Systems: Its Quantification, Emergence, and Implications across the Scales

Surface curvature both emerges from, and influences the behavior of, living objects at length scales ranging from cell membranes to single cells to tissues and organs. The relevance of surface curvature in biology is supported by numerous experimental and theoretical investigations in recent years. In this review, first, a brief introduction to the key ideas of surface curvature in the context of biological systems is given and the challenges that arise when measuring surface curvature are discussed. Giving an overview of the emergence of curvature in biological systems, its significance at different length scales becomes apparent. On the other hand, summarizing current findings also shows that both single cells and entire cell sheets, tissues or organisms respond to curvature by modulating their shape and their migration behavior. Finally, the interplay between the distribution of morphogens or micro-organisms and the emergence of curvature across length scales is addressed with examples demonstrating these key mechanistic principles of morphogenesis. Overall, this review highlights that curved interfaces are not merely a passive by-product of the chemical, biological, and mechanical processes but that curvature acts also as a signal that co-determines these processes.

Pachyrhynchus Weevils Use 3D Photonic Crystals with Varying Degrees of Order to Create Diverse and Brilliant Displays

The brilliant appearance of Easter Egg weevils, genus Pachyrhynchus (Coleoptera, Curculionidae), originates from complex dielectric nanostructures within their elytral scales and elytra. Previous work, investigating singular members of the Pachyrhynchus showed the presence of either quasi-ordered or ordered 3D photonic crystals based on the single diamond ( Fd3¯m ) symmetry in their scales. However, little is known about the diversity of the structural coloration mechanisms within the family. Here, the optical properties within Pachyrhynchus are investigated by systematically identifying their spectral and structural characteristics. Four principal traits that vary their appearance are identified and the evolutionary history of these traits to identify ecological trends are reconstructed. The results indicate that the coloration mechanisms across the Easter Egg weevils are diverse and highly plastic across closely related species with features appearing at multiple independent times across their phylogeny. This work lays a foundation for a better understanding of the various forms of quasi-ordered and ordered diamond photonic crystal within arthropods.

Butterfly wing architectures inspire sensor and energy applications

Natural biological systems are constantly developing efficient mechanisms to counter adverse effects of increasing human population and depleting energy resources. Their intelligent mechanisms are characterized by the ability to detect changes in the environment, store and evaluate information, and respond to external stimuli. Bio-inspired replication into man-made functional materials guarantees enhancement of characteristics and performance. Specifically, butterfly architectures have inspired the fabrication of sensor and energy materials by replicating their unique micro/nanostructures, light-trapping mechanisms and selective responses to external stimuli. These bio-inspired sensor and energy materials have shown improved performance in harnessing renewable energy, environmental remediation and health monitoring. Therefore, this review highlights recent progress reported on the classification of butterfly wing scale architectures and explores several bio-inspired sensor and energy applications.

Formation of Double-Helical Structures by Silica Nanotubes Templated by Mixtures of Common Nonionic Surfactants in Aqueous Solutions

Micelles of Pluronic F108 (EO₁₃₂PO₅₀EO₁₃₂)/P104 (EO₂₇PO₆₁EO₂₇) surfactant mixtures swollen with toluene were found to template silica nanotubes that formed double-helical structures under appropriately selected aqueous acidic solution conditions. In particular, the double-helical nanotube structure (DHNTS) formed as a main product at 15 °C for 30-37.5 wt % of Pluronic P104 in a surfactant mixture, with 35 wt % being particularly suitable. The formation of DHNTSs appears to involve a spontaneous wrapping of micelle-templated nanotubes around one another, while a similar structure was known to form only under confinement of anodic alumina pores of appropriate diameter. In addition to DHNTSs, other helical or circular structures, such as a helical nanotube tightly wrapped around a straight nanotube, or nanotube(s) wrapped around a sphere, were observed in many cases as minor components. DHNTSs formed as a major component at a well-defined proportion of silica precursor to surfactant at 15 °C, while the relative amount of the swelling agent and the hydrochloric acid concentration could be varied considerably. The hydrothermal treatment temperature was used to adjust the pore diameter of the DHNTS. However, structures formed without the hydrothermal treatment or with the treatment at a moderate temperature appeared very soft, while the treatment at excessively high temperature resulted in a development of significant gaps in the nanotube walls. Our results establish DHNTS as a well-defined ordered mesoporous silica with ultralarge (∼35 nm) helical mesopores of some degree of diameter adjustability, accessible under aqueous conditions using common nonionic surfactants as templating agents.

Discovery of single gyroid structure in self-assembly of block copolymer with inorganic precursors

Triply periodic hyperbolic surfaces have attracted great attention due to their unique geometries and physical properties. Among them, the single gyroid (SG) is of significant interest due to its inherent chirality as well as the potential applications in energy and environmental science. However, the formation of the thermodynamically unstable structure is still unclear. In this work, we show the formation of SG structure in the structural transformation from the cylindrical to shifted double diamond (SDD) scaffold in a self-assembly system of diblock copolymer and silica precursors in solution. It has been found that the cylindrical tubes with zero Gaussian curvature were split and curved into hyperbolic surfaces and extruded to form SG structures and further evolved into the SDD networks. This growth or extrusion process suggests the SG structure is an intermediate phase of the cylindrical and SDD, and this transformation is found similar to the formation of butterfly wing scales (Thecla opisena), which has not been observed in neither the theoretical calculation nor the experimental self-assembly of amphiphilic molecules. We hope the structural relationship may bring new insights in understanding the formation of single networks in the biological system and the creation of new functional materials.

Chirality Induction through Nano-Phase Separation: Alternating Network Gyroid Phase by Thermotropic Self-Assembly of X-Shaped Bolapolyphiles

The single gyroid phase as well as the alternating double network gyroid, composed of two alternating single gyroid networks, hold a significant place in ordered nanoscale morphologies for their potential applications as photonic crystals, metamaterials and templates for porous ceramics and metals. Here, we report the first alternating network cubic liquid crystals. They form through self-assembly of X-shaped polyphiles, where glycerol-capped terphenyl rods lie on the gyroid surface while semiperfluorinated and aliphatic side-chains fill their respective separate channel networks. This new self-assembly mode can be considered as a two-color symmetry-broken double gyroid morphology, providing a tailored way to fabricate novel chiral structures with sub-10 nm periodicities using achiral compounds.

Metasurfaces Atop Metamaterials: Surface Morphology Induces Linear Dichroism in Gyroid Optical Metamaterials

Optical metamaterials offer the tantalizing possibility of creating extraordinary optical properties through the careful design and arrangement of subwavelength structural units. Gyroid-structured optical metamaterials possess a chiral, cubic, and triply periodic bulk morphology that exhibits a redshifted effective plasma frequency. They also exhibit a strong linear dichroism, the origin of which is not yet understood. Here, the interaction of light with gold gyroid optical metamaterials is studied and a strong correlation between the surface morphology and its linear dichroism is found. The termination of the gyroid surface breaks the cubic symmetry of the bulk lattice and gives rise to the observed wavelength- and polarization-dependent reflection. The results show that light couples into both localized and propagating plasmon modes associated with anisotropic surface protrusions and the gaps between such protrusions. The localized surface modes give rise to the anisotropic optical response, creating the linear dichroism. Simulated reflection spectra are highly sensitive to minute details of these surface terminations, down to the nanometer level, and can be understood with analogy to the optical properties of a 2D anisotropic metasurface atop a 3D isotropic metamaterial. This pronounced sensitivity to the subwavelength surface morphology has significant consequences for both the design and application of optical metamaterials.

Multiscale Mechanics of Triply Periodic Minimal Surfaces of Three-Dimensional Graphene Foams

The mechanics of triply periodic minimal surfaces (TPMSs) with three-dimensional (3D) graphene foams are systematically studied to understand the effects of structure and size on the mechanical properties, for example, elasticity, strength, and fracture. The design of lightweight open-shell porous solid materials with TPMSs has shown excellent and tunable load-bearing properties. However, fracture properties and their relations with surface topologies are largely unknown. Utilizing reactive molecular dynamics simulations, here we investigate the elastic and fracture properties of three different surface topologies with 3D graphene foams: P (primitive), D (diamond), and G (gyroid), called Schwarzites. Models with different lattice sizes are utilized to derive power laws, which can connect the properties along different sizes to shed light on the multiscale mechanics of TPMSs. Our study provides a systematic understanding of the relation between TPMS topologies and their mechanical properties, including failure mechanisms of graphene foams, opening opportunities to explore designable structures with tailored properties.

Anatomy of triply-periodic network assemblies: characterizing skeletal and inter-domain surface geometry of block copolymer gyroids

Triply-periodic networks (TPNs), like the well-known gyroid and diamond network phases, abound in soft matter assemblies, from block copolymers (BCPs), lyotropic liquid crystals and surfactants to functional architectures in biology. While TPNs are, in reality, volume-filling patterns of spatially-varying molecular composition, physical and structural models most often reduce their structure to lower-dimensional geometric objects: the 2D interfaces between chemical domains; and the 1D skeletons that thread through inter-connected, tubular domains. These lower-dimensional structures provide a useful basis of comparison to idealized geometries based on triply-periodic minimal, or constant-mean curvature surfaces, and shed important light on the spatially heterogeneous packing of molecular constituents that form the networks. Here, we propose a simple, efficient and flexible method to extract a 1D skeleton from 3D volume composition data of self-assembled networks. We apply this method to both self-consistent field theory predictions as well as experimental electron microtomography reconstructions of the double-gyroid phase of an ABA triblock copolymer. We further demonstrate how the analysis of 1D skeleton, 2D inter-domain surfaces, and combinations therefore, provide physical and structural insight into TPNs, across multiple length scales. Specifically, we propose and compare simple measures of network chirality as well as domain thickness, and analyze their spatial and statistical distributions in both ideal (theoretical) and non-ideal (experimental) double gyroid assemblies.

It's Not a Bug, It's a Feature: Functional Materials in Insects

Over the course of their wildly successful proliferation across the earth, the insects as a taxon have evolved enviable adaptations to their diverse habitats, which include adhesives, locomotor systems, hydrophobic surfaces, and sensors and actuators that transduce mechanical, acoustic, optical, thermal, and chemical signals. Insect-inspired designs currently appear in a range of contexts, including antireflective coatings, optical displays, and computing algorithms. However, as over one million distinct and highly specialized species of insects have colonized nearly all habitable regions on the planet, they still provide a largely untapped pool of unique problem-solving strategies. With the intent of providing materials scientists and engineers with a muse for the next generation of bioinspired materials, here, a selection of some of the most spectacular adaptations that insects have evolved is assembled and organized by function. The insects presented display dazzling optical properties as a result of natural photonic crystals, precise hierarchical patterns that span length scales from nanometers to millimeters, and formidable defense mechanisms that deploy an arsenal of chemical weaponry. Successful mimicry of these adaptations may facilitate technological solutions to as wide a range of problems as they solve in the insects that originated them.

Selection of the intrinsic polarization properties of animal optical materials creates enhanced structural reflectivity and camouflage

Many animals use structural coloration to create bright and conspicuous visual signals. Selection of the size and shape of the optical structures animals use defines both the colour and intensity of the light reflected. The material used to create these reflectors is also important; however, animals are restricted to a limited number of materials: commonly chitin, guanine and the protein, reflectin. In this work we highlight that a particular set of material properties can also be under selection in order to increase the optical functionality of structural reflectors. Specifically, polarization properties, such as birefringence (the difference between the refractive indices of a material) and chirality (which relates to molecular asymmetry) are both under selection to create enhanced structural reflectivity. We demonstrate that the structural coloration of the gold beetle Chrysina resplendens and silvery reflective sides of the Atlantic herring, Clupea harengus are two examples of this phenomenon. Importantly, these polarization properties are not selected to control the polarization of the reflected light as a source of visual information per se. Instead, by creating higher levels of reflectivity than are otherwise possible, such internal polarization properties improve intensity-matching camouflage.

This article is part of the themed issue ‘Animal coloration: production, perception, function and application’.

Metallic gyroids with broadband circular dichroism

Circular dichroism is a useful property for filtering or separating beams containing opposite spin angular momentum. Of the many geometries exhibiting circular dichroism, the gyroid has proven to be an excellent template for exploring circular dichroism in three dimensions. However, the bandwidth of the circular dichroism from dielectric gyroids is limited by its narrow circularly polarized stop band. Here we investigate conductive silver gyroid micro-structures using direct laser writing of polymeric templates followed by the electroless deposition of a uniform silver coating. We show that the transformation from dielectric to silver gyroid micro-structure can increase the circular dichroism bandwidth by close to a factor of 3.

Trapping Structural Coloration by a Bioinspired Gyroid Microstructure in Solid State

In theory, gyroid photonic crystals in butterfly wings exhibit advanced optical properties as a result of their highly interconnected microstructures. Because of the difficulties in synthesizing artificial gyroid materials having periodicity corresponding to visible wavelengths, human-made visible gyroid photonic crystals are still unachievable by self-assembly. In this study, we develop a physical approach-trapping of structural coloration (TOSC)-through which the visible structural coloration of an expanded gyroid lattice in a solvated state can be preserved in the solid state, thereby allowing the fabrication of visible-wavelength gyroid photonic crystals. Through control over the diffusivity and diffusive distance for solvent evaporation, the single-molecular-weight gyroid block copolymer photonic crystal can exhibit desired structural coloration in the solid state without the need to introduce any additives, namely, evapochromism. Also, greatly enhanced reflectivity is observed arising from the formation of porous gyroid nanochannels, similar to those in butterfly wings. As a result, TOSC facilitates the fabrication of the human-made solid gyroid photonic crystal featuring tunable and switchable structural coloration without the synthesis to alter the molecular weight. It appears to be applicable in the fields of optical communication, energy, light-emission, sensors, and displays.

Purely entropic self-assembly of the bicontinuous Ia3d gyroid phase in equilibrium hard-pear systems

We investigate a model of hard pear-shaped particles which forms the bicontinuous Ia[Formula: see text]d structure by entropic self-assembly, extending the previous observations of Barmes et al. (2003 Phys. Rev. E68, 021708. (doi:10.1103/PhysRevE.68.021708)) and Ellison et al. (2006 Phys. Rev. Lett.97, 237801. (doi:10.1103/PhysRevLett.97.237801)). We specifically provide the complete phase diagram of this system, with global density and particle shape as the two variable parameters, incorporating the gyroid phase as well as disordered isotropic, smectic and nematic phases. The phase diagram is obtained by two methods, one being a compression-decompression study and the other being a continuous change of the particle shape parameter at constant density. Additionally, we probe the mechanism by which interdigitating sheets of pears in these systems create surfaces with negative Gauss curvature, which is needed to form the gyroid minimal surface. This is achieved by the use of Voronoi tessellation, whereby both the shape and volume of Voronoi cells can be assessed in regard to the local Gauss curvature of the gyroid minimal surface. Through this, we show that the mechanisms prevalent in this entropy-driven system differ from those found in systems which form gyroid structures in nature (lipid bilayers) and from synthesized materials (di-block copolymers) and where the formation of the gyroid is enthalpically driven. We further argue that the gyroid phase formed in these systems is a realization of a modulated splay-bend phase in which the conventional nematic has been predicted to be destabilized at the mesoscale due to molecular-scale coupling of polar and orientational degrees of freedom.

On the colour of wing scales in butterflies: iridescence and preferred orientation of single gyroid photonic crystals

Lycaenid butterflies from the genera Callophrys, Cyanophrys and Thecla have evolved remarkable biophotonic gyroid nanostructures within their wing scales that have only recently been replicated by nanoscale additive manufacturing. These nanostructures selectively reflect parts of the visible spectrum to give their characteristic non-iridescent, matte-green appearance, despite a distinct blue–green–yellow iridescence predicted for individual crystals from theory. It has been hypothesized that the organism must achieve its uniform appearance by growing crystals with some restrictions on the possible distribution of orientations, yet preferential orientation observed in Callophrys rubi confirms that this distribution need not be uniform. By analysing scanning electron microscope and optical images of 912 crystals in three wing scales, we find no preference for their rotational alignment in the plane of the scales. However, crystal orientation normal to the scale was highly correlated to their colour at low (conical) angles of view and illumination. This correlation enabled the use of optical images, each containing up to 10⁴–10⁵ crystals, for concluding the preferential alignment seen along the at the level of single scales, appears ubiquitous. By contrast, orientations were found to occur at no greater rate than that expected by chance. Above a critical cone angle, all crystals reflected bright green light indicating the dominant light scattering is due to the predicted band gap along the direction, independent of the domain orientation. Together with the natural variation in scale and wing shapes, we can readily understand the detailed mechanism of uniform colour production and iridescence suppression in these butterflies. It appears that the combination of preferential alignment normal to the wing scale, and uniform distribution within the plane is a near optimal solution for homogenizing the angular distribution of the band gap relative to the wings. Finally, the distributions of orientations, shapes, sizes and degree of order of crystals within single scales provide useful insights for understanding the mechanisms at play in the formation of these biophotonic nanostructures.

Butterfly gyroid nanostructures as a time-frozen glimpse of intracellular membrane development

The formation of the biophotonic gyroid material in butterfly wing scales is an exceptional feat of evolutionary engineering of functional nanostructures. It is hypothesized that this nanostructure forms by chitin polymerization inside a convoluted membrane of corresponding shape in the endoplasmic reticulum. However, this dynamic formation process, including whether membrane folding and chitin expression are simultaneous or sequential processes, cannot yet be elucidated by in vivo imaging. We report an unusual hierarchical ultrastructure in the butterfly Thecla opisena that, as a solid material, allows high-resolution three-dimensional microscopy. Rather than the conventional polycrystalline space-filling arrangement, a gyroid occurs in isolated facetted crystallites with a pronounced size gradient. When interpreted as a sequence of time-frozen snapshots of the morphogenesis, this arrangement provides insight into the formation mechanisms of the nanoporous gyroid material as well as of the intracellular organelle membrane that acts as the template.

Harmonic distortions enhance circular dichroism of dielectric single gyroids

The departure from strict periodic order in two-phase dielectric materials can offer properties that are otherwise inaccessible to perfectly ordered photonic crystals. Herewith, we investigate the circular dichroism of the single gyroid photonic crystal in the presence of spatial distortions. FDTD simulations and microwave transmission measurements on 3D-printed replicas show that certain harmonic long-wavelength spatial distortions ("sinusoidal chirp") nearly doubles the imbalance of the circular polarisation reflectances, as well as significantly strengthens polarisation-incoherent reflectance. The observed changes are partially rationalised by comparison with simpler distortion models (linear chirp and tetragonal deformation) of the Gyroid.

Gyroid Optical Metamaterials: Calculating the Effective Permittivity of Multidomain Samples

Gold gyroid optical metamaterials are known to possess a reduced plasma frequency and linear dichroism imparted by their intricate subwavelength single gyroid morphology. The anisotropic optical properties are, however, only evident when a large individual gyroid domain is investigated. Multidomain gyroid metamaterials, fabricated using a polyisoprene-b-polystyrene-b-poly(ethylene oxide) triblock terpolymer and consisting of multiple small gyroid domains with random orientation and handedness, instead exhibit isotropic optical properties. Comparing three effective medium models, we here show that the specular reflectance spectra of such multidomain gyroid optical metamaterials can be accurately modeled over a broad range of incident angles by a Bruggeman effective medium consisting of a random wire array. This model accurately reproduces previously published results tracking the variation in normal incidence reflectance spectra of gold gyroid optical metamaterials as a function of host refractive index and volume fill fraction of gold. The effective permittivity derived from this theory confirms the change in sign of the real part of the permittivity in the visible spectral region (so, that gold gyroid metamaterials exhibit both dielectric and metallic behavior at optical wavelengths). That a Bruggeman effective medium can accurately model the experimental reflectance spectra implies that small multidomain gold gyroid optical metamaterials behave both qualitatively and quantitatively as an amorphous composite of gold and air (i.e., nanoporous gold) and that coherent electromagnetic contributions arising from the subwavelength gyroid symmetry are not dominant.

Simulation of light scattering from exoskeletons of scarab beetles

An approach for simulation of light scattering from beetles exhibiting structural colors originating from periodic helicoidal structures is presented. Slight irregularities of the periodic structure in the exoskeleton of the beetles are considered as a major cause of light scattering. Two sources of scattering are taken into account: surface roughness and volume non-uniformity. The Kirchhoff approximation is applied to simulate the effect of surface roughness. To describe volume non-uniformity, the whole structure is modeled as a set of domains distributed in space in different orientations. Each domain is modeled as an ideal uniformly twisted uniaxial medium and differs from each other by the pitch. Distributions of the domain parameters are assumed to be Gaussian. The analysis is performed using the Mueller matrix formalism which, in addition to spectral and spatial characteristics, also provides polarization properties of the scattered light.

Coexistence of both gyroid chiralities in individual butterfly wing scales of Callophrys rubi

The wing scales of the Green Hairstreak butterfly Callophrys rubi consist of crystalline domains with sizes of a few micrometers, which exhibit a congenitally handed porous chitin microstructure identified as the chiral triply periodic single-gyroid structure. Here, the chirality and crystallographic texture of these domains are investigated by means of electron tomography. The tomograms unambiguously reveal the coexistence of the two enantiomeric forms of opposite handedness: the left- and right-handed gyroids. These two enantiomers appear with nonequal probabilities, implying that molecularly chiral constituents of the biological formation process presumably invoke a chiral symmetry break, resulting in a preferred enantiomeric form of the gyroid structure. Assuming validity of the formation model proposed by Ghiradella H (1989) J Morphol 202(1):69-88 and Saranathan V, et al. (2010) Proc Natl Acad Sci USA 107(26):11676-11681, where the two enantiomeric labyrinthine domains of the gyroid are connected to the extracellular and intra-SER spaces, our findings imply that the structural chirality of the single gyroid is, however, not caused by the molecular chirality of chitin. Furthermore, the wing scales are found to be highly textured, with a substantial fraction of domains exhibiting the <001> directions of the gyroid crystal aligned parallel to the scale surface normal. Both findings are needed to completely understand the photonic purpose of the single gyroid in gyroid-forming butterflies. More importantly, they show the level of control that morphogenesis exerts over secondary features of biological nanostructures, such as chirality or crystallographic texture, providing inspiration for biomimetic replication strategies for synthetic self-assembly mechanisms.

Dual circular polarization gaps in helix photonic metamaterials

Chiral structures exhibit strong interactions with circularly polarized light, and have been demonstrated to show many polarization-dependent properties. Various chiral structures exhibit some level of circular dichroism, where right-handed and left-handed circularly polarized waves experience different transmission. In this study, we use a dielectric helix array as a model system to examine the interactions of circularly polarized light with helical structures. Our results show that circular polarization band gaps can be formed in a dielectric helix array not only by light having the same handedness with the structure but also by light with the opposite handedness, resulting from additional chiral motifs induced by the arrangement of helices. Dual polarization band gaps can thus be tailored by varying the geometrical parameters, and circular-polarization dependent properties can be manipulated for optoelectronic devices and applications.