Circular dichroism in biological photonic crystals and cubic chiral nets

Polarization resolved hyperspectral imaging of the beetle Protaetia speciosa jousselini

Understanding and classifying chiral structural color of scarab beetles across the phylogenetic tree is an important scientific tool to explore the origins of the homochiral optical response in biological structures with a potential relation to the homochirality of (chitin) molecules. We report hyperspectral polarization resolved images of the scarab beetle Protaetia speciosa jousselini (Gory & Percheron, 1833) and resolve the state of polarization as a function of both position (spatial resolution of ~20 μm × 10 μm) and wavelength (spectral resolution of 5.5 nm). We observe a strong left-handed chiral Bragg reflectance and analyze the center wavelength and width of the spectrum. The reflectance and state of polarization match scale with the center wavelength of the Bragg reflection, while the relative width of reflectance spectrum is characterized by a chiral photonic strength parameter ψC ≈ 0.14 that is independent of the reflected color and position. Based on the self-similarity of the reflectance spectra we interpret variation in reflectance as variations in the thickness of the chiral Bragg reflector across the beetle.

Elucidating nanostructural organization and photonic properties of butterfly wing scales using hyperspectral microscopy

Biophotonic nanostructures in butterfly wing scales remain fascinating examples of biological functional materials, with intriguing open questions with regard to formation and evolutionary function. One particularly interesting butterfly species, Erora opisena (Lycaenidae: Theclinae), develops wing scales that contain three-dimensional photonic crystals that closely resemble a single gyroid geometry. Unlike most other gyroid-forming butterflies, E. opisena develops discrete gyroid crystallites with a pronounced size gradient hinting at a developmental sequence frozen in time. Here, we present a novel application of a hyperspectral (wavelength-resolved) microscopy technique to investigate the ultrastructural organization of these gyroid crystallites in dry, adult wing scales. We show that reflectance corresponds to crystallite size, where larger crystallites reflect green wavelengths more intensely; this relationship could be used to infer size from the optical signal. We further successfully resolve the red-shifted reflectance signal from wing scales immersed in refractive index liquids with varying refractive index, including values similar to water or cytosol. Such photonic crystals with lower refractive index contrast may be similar to the hypothesized nanostructural forms in the developing butterfly scales. The ability to resolve these fainter signals hints at the potential of this facile light microscopy method for in vivo analysis of nanostructure formation in developing butterflies.

Programmed Self-Assembly of Single Colloidal Gyroids for Chiral Photonic Crystals

Gyroid structures are of extensive interest because they provide a rich platform for chiroptics as well as topological photonics. While the double-gyroid morphology as a bicontinuous structure is not uncommon in self-assembled soft materials, direct self-assembly of single-network gyroids has proven elusive. Here, an enantiomorphic pair of single-gyroid crystals comprising colloidal spheres is presented, and two distinct routes are demonstrated for programmed self-assembly of each single colloidal gyroid enantiomorph from rationally designed patchy spheres. The designer colloidal patchy spheres, which closely hew to their synthetic feasibility, are chiral, having either two staggered rectangular patches at opposite poles or four circular patches arranged in a well-defined geometry. The single colloidal gyroid, as well as its inverse structure, is shown to support a wide complete photonic bandgap in addition to exhibiting rich chiroptical properties, making them attractive chiral photonic crystals. The versatility of this single colloidal gyroid, the bottom-up routes devised here in silico, and the robustness of the design space for the chiral colloidal patchy spheres together make a strong case for single colloidal gyroids to supersede colloidal diamond, as a target for programmed self-assembly, in the quest for photonic crystals operating at optical frequencies.

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.

Topological Surface States in a Gyroid Acoustic Crystal

The acoustic properties of an acoustic crystal consisting of acoustic channels designed according to the gyroid minimal surface embedded in a 3D rigid material are investigated. The resulting gyroid acoustic crystal is characterized by a spin-1 Weyl and a charge-2 Dirac degenerate points that are enforced by its nonsymmorphic symmetry. The gyroid geometry and its symmetries produce multi-fold topological degeneracies that occur naturally without the need for ad hoc geometry designs. The non-trivial topology of the acoustic dispersion produces chiral surface states with open arcs, which manifest themselves as waves whose propagation is highly directional and remains confined to the surfaces of a 3D material. Experiments on an additively manufactured sample validate the predictions of surface arc states and produce negative refraction of waves at the interface between adjoining surfaces. The topological surface states in a gyroid acoustic crystal shed light on nontrivial bulk and edge physics in symmetry-based compact continuum materials, whose capabilities augment those observed in ad hoc designs. The continuous shape design of the considered acoustic channels and the ensuing anomalous acoustic performance suggest this class of phononic materials with semimetal-like topology as effective building blocks for acoustic liners and load-carrying structural components with sound proofing functionality.

Angle-selective chiral absorption induced by diffractive coupling in metasurfaces

Here we report that a simple chiral metasurface with twisted metallic cut-wire arrays enables highly efficient and continuously tunable chiral absorption over a broad spectral range by scanning the incidence angle over a few degrees. The angle-selective chiral absorption results from the surface plasmon resonance (SPR) excited by diffractive effects of the metasurface. The diffraction-assisted chiral metasurface provides a straightforward strategy for achieving dynamically tunable chiral devices and offers intriguing possibilities for various applications in on-chip chiral detectors/emitters, chiral spectrometers, chiral lasers, and so on.

Polarization-dependent reflection of I-WP minimal-surface-based photonic crystal

Brilliantly colored butterflies and weevils are known to utilize photonic crystals for their coloration. Interestingly, the morphology of such crystals made of cuticle is based on triply periodic minimal surfaces such as gyroid and diamond surfaces. Recently, a different minimal-surface-based photonic crystal, the I-WP surface, was discovered inside the scale of a longhorn beetle. The letter I is derived from expressing the body center symmetry and WP is derived from a wrapped package. It was reported that the brilliant green color is produced by the photonic band gap existing along the [110] direction of this crystal. In this study, the polarization dependence of the reflection from this photonic crystal was investigated. A peculiar reflectance spectrum with two peaks was observed under the crossed polarizers. This characteristic is theoretically reproduced by calculating the reflectance from a finite-sized photonic crystal, and the spectral shape is explained based on the symmetry of the electromagnetic modes. In addition, inspired by this longhorn beetle, a photonic crystal structure consisting of colloidal particles is proposed, which has a similar polarization effect.

Block copolymer gyroids for nanophotonics: significance of lattice transformations

A gyroid crystal possesses a peculiar structural feature that can be conceptualized as a triply periodic surface with a constant mean curvature of zero. The exotic optical properties such as the photonic bandgap and optical chirality can emerge from this three-dimensional (3D) morphological feature. As such, gyroid crystals have been considered as the promising structures for photonic crystals and optical metamaterials. To date, several methods have been proposed to materialize gyroid crystals, including 3D printing, layer-by-layer stacking, two-photon lithography, interference lithography, and self-assembly. Furthermore, the discovery of Weyl points in gyroid crystals has further stimulated these advancements. Among such methods, the self-assembly of block copolymers (BCPs) is unique, because this soft approach can provide an easy-to-craft gyroid, especially at the nanoscale. The unit-cell scale of a gyroid ranging within 30-300 nm can be effectively addressed by BCP self-assembly, whereas other methods would be challenging to achieve this size range. Therefore, a BCP gyroid has provided a material platform for metamaterials and photonic crystals functioning at optical frequencies. Currently, BCP gyroid nanophotonics is ready to take the next step toward topological photonics beyond the conventional photonic crystals and metamaterials. In particular, the intrinsic lattice transformations occurring during the self-assembly of BCP into a gyroid crystal could promise a compelling advantage for advancing Weyl photonics in the optical regime. Lattice transformations are routinely considered as limitations, but in this review, we argue that it is time to widen the scope of the lattice transformations for the future generation of nanophotonics. Thus, our review provides a comprehensive understanding of the gyroid crystal and its lattice transformations, the relevant optical properties, and the recent progress in BCP gyroid self-assembly.

The emergence of valency in colloidal crystals through electron equivalents

Colloidal crystal engineering of complex, low-symmetry architectures is challenging when isotropic building blocks are assembled. Here we describe an approach to generating such structures based upon programmable atom equivalents (nanoparticles functionalized with many DNA strands) and mobile electron equivalents (small particles functionalized with a low number of DNA strands complementary to the programmable atom equivalents). Under appropriate conditions, the spatial distribution of the electron equivalents breaks the symmetry of isotropic programmable atom equivalents, akin to the anisotropic distribution of valence electrons or coordination sites around a metal atom, leading to a set of well-defined coordination geometries and access to three new low-symmetry crystalline phases. All three phases represent the first examples of colloidal crystals, with two of them having elemental analogues (body-centred tetragonal and high-pressure gallium), while the third (triple double-gyroid structure) has no known natural equivalent. This approach enables the creation of complex, low-symmetry colloidal crystals that might find use in various technologies.

Observation of a Charge-2 Photonic Weyl Point in the Infrared

Weyl points are robust point degeneracies in the band structure of a periodic material, which act as monopoles of Berry curvature. They have been at the forefront of research in three-dimensional topological materials as they are associated with novel behavior both in the bulk and on the surface. Here, we present the experimental observation of a charge-2 photonic Weyl point in a low-index-contrast photonic crystal fabricated by two-photon polymerization. The reflection spectrum obtained via Fourier-transform infrared spectroscopy closely matches simulations and shows two bands with quadratic dispersion around a point degeneracy.

Quo vadis biophotonics? Wearing serendipity and slow science as a badge of pride, and embracing biology

This article is a reflection on the themes of the Faraday Discussion meeting on 'Biological and bio-inspired optics' held from 20 to 22 July 2020. It is a personal perspective on the nature of this field as a broad and interdisciplinary field that has led to a sound understanding of the material properties of biological nanostructured and optical materials. The article describes how the nature of the field and the themes of the conference are reflected in particular in work on the 3D bicontinuous biophotonic nanostructures known as single gyroids and in bicontinuous structures more broadly. Such single gyroid materials are found for example in the butterfly Thecla opisena, where the questions of biophotonic response, of bio-inspired optics, of the relationship between structure and function, and of the relationship between natural and synthetic realisations are closely interlinked. This multitude of facets of research on single gyroid structures reflects the beauty of the broader field of biophotonics, namely as a field that lives through embracing the serendipitous discovery of the biophotonic marvels that nature offers to us as seeds for in-depth analysis and understanding. The meandering nature of its discoveries, and the need to accept the slowness that comes from exploration of intellectually new or foreign territory, mean that the field shares some traits with biological evolution itself. Looking into the future, I consider that a closer engagement with living tissue and with the biological questions of function and formation, rather than with the materials science of biological materials, will help ensure the continuing great success of this field.

3D Helix Engineering in Chiral Photonic Materials

Engineering the helical structure of chiral photonic materials in three dimensions remains a challenge. 3D helix engineered photonic materials are fabricated by local stratification in a photopolymerizable chiral nematic liquid crystal. The obtained chiral photonic materials reflect both handedness of circular polarized light and show super-reflectivity. Simulations match the experimentally observed photonic properties and reveal a distorted helical structure. 3D engineered polymer films can be made that reflect both left- and right handed circular and linear polarized light dependent and exhibit a changing color contrast upon altering the polarization of incident light. Hence, these 3D engineered photonic materials are of interest for new and emerging applications ranging from anti-counterfeit labels and data encryption to aesthetics and super-reflective films.

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.

A Literal Elytral Rainbow: Tunable Structural Colors Using Single Diamond Biophotonic Crystals in Pachyrrhynchus congestus Weevils

The brilliant colors of many insects arise from the interference of incident light with complex nanostructured biomaterials that are present in their cuticle. Here, the rainbow-colored spots on the elytra of a snout weevil, Pachyrrhynchus congestus pavonius (Coleoptera: Curculionidae), are investigated using synchrotron small-angle X-ray scattering, scanning electron microscopy, microspectrophotometry, and photonic bandgap modeling. It is shown that the iridescent scales present in the rainbow-hued spots are due to a 3D photonic crystal network of chitin in air with a single diamond (Fd-3m) symmetry. In many insects, different orientations of photonic crystal domains are used to create various hues. In this weevil, however, both the chitin volume fractions as well as the lattice parameters of the biologically self-assembled single diamond nanostructure are varied to achieve the remarkable tuning of the structural colors across the visible light spectrum on a scale-by-scale basis. Uncovering the precise mechanism of color tuning employed by this weevil has important implications for further structural and developmental research on biophotonic nanostructures and may provide fresh impetus for bioinspired and biomimetic multifunctional applications, as synthesis of photonic crystals at visible length scales is currently challenging.

Impact of Cubic Symmetry on Optical Activity of Dielectric 8-srs Networks

Photonic crystals are engineered structures able to control the propagation and properties of light. Due to this ability, they can be fashioned into optical components for advanced light manipulation and sensing. For these applications, a particularly interesting case study is the gyroid srs-network, a three-dimensional periodic network with both cubic symmetry and chirality. In this work we present the fabrication and characterization of three-dimensional cubically symmetric 8-srs photonic crystals derived from combination of eight individual gyroid srs-networks. We numerically and experimentally investigate optical properties of these photonic crystals and study in particular, the impact of cubic symmetry on transmission and optical activity (OA). Gyroid photonic crystals fabricated in this work can lead to the development of smaller, cheaper, and more efficient optical components with functionalities that go beyond the concept of lenses.

Liquid-crystal-loaded chiral metasurfaces for reconfigurable multiband spin-selective light absorption

Light absorption plays a key role in numerous photonic devices. In this work, we theoretically demonstrate that multiband circularly polarized light can be spin-selectively absorbed with a single-layered metasurface. The difference of absorption efficiency between left- and right-handed circularly polarized light can reach 40%. This giant chiroptical effect originates from different plasmonic resonances induced by the incident circularly polarized light with opposite spin states. Furthermore, by integrating the metasurface with nematic liquid crystals, the spin-selective absorption and the chirality can be dynamically reconfigured via applying a bias voltage. The advantageous features of being multiband-absorptive, backplane-free and reconfigurable make our proposed liquid-crystal-loaded chiral metasurfaces potentially useful for various photonic applications.

Self-Assembled Chiral Photonic Crystals from a Colloidal Helix Racemate

Chiral crystals consisting of microhelices have many optical properties, while presently available fabrication processes limit their large-scale applications in photonic devices. Here, by using a simplified simulation method, we investigate a bottom-up self-assembly route to build up helical crystals from the smectic monolayer of a colloidal helix racemate. With increasing the density, the system undergoes an entropy-driven cocrystallization by forming crystals of various symmetries with different helical shapes. In particular, we identify two crystals of helices arranged in binary honeycomb and square lattices, which are essentially composed of two sets of opposite-handed chiral crystals. Photonic calculations show that these chiral structures can have large complete photonic band gaps. In addition, in the self-assembled chiral square crystal, we also find dual polarization band gaps that selectively forbid the propagation of circularly polarized light of a specific handedness along the helical axis direction. The self-assembly process in our proposed system is robust, suggesting possibilities of using chiral colloids to assemble photonic metamaterials.

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.

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.

Broadband angle- and permittivity-insensitive nondispersive optical activity based on planar chiral metamaterials

Because of the strong inherent resonances, the giant optical activity obtained via chiral metamaterials generally suffers from high dispersion, which has been a big stumbling block to broadband applications. In this paper, we propose a type of planar chiral metamaterial consisting of interconnected metal helix slat structures with four-fold symmetry, which exhibits nonresonant Drude-like response and can therefore avoid the highly dispersive optical activity resulting from resonances. It shows that the well-designed chiral metamaterial can achieve nondispersive and pure optical activity with high transmittance in a broadband frequency range. And the optical activity of multi-layer chiral metamaterials is proportional to the layer numbers of single-layer chiral metamaterial. Most remarkably, the broadband behaviors of nondispersive optical activity and high transmission are insensitive to the incident angles of electromagnetic waves and permittivity of dielectric substrate, thereby enabling more flexibility in polarization manipulation.

Origin and manipulation of band gaps in three-dimensional dielectric helix structures

In this study, we present a comprehensive analysis to examine the origin of circular polarization stop bands in a dielectric helix structure. We show that band gaps in a helix structure may result from Bragg resonance or non-Bragg mechanism. The two types of gaps exhibit distinct optical properties and display an opposite dependence with respect to structural periodicity. The interplay of gaps not only gives rise to various operation scenarios, but results in pronounced modifications to dispersion characteristics that lead to abnormal propagation properties of circularly polarized waves. Our findings reveal versatile behaviors of circularly polarized light interacted with a three-dimensional helix medium, which can be of great importance for the design and implementation of circular polarization-dependent devices and applications.

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.

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.

Bragg-mirror-like circular dichroism in bio-inspired quadruple-gyroid 4srs nanostructures

The smooth and tailorable spectral response of Bragg mirrors has driven their pervasive use in optical systems requiring customizable spectral control of beam propagation. However, the simple nature of Bragg mirror reflection prevents their application to the control of important polarization states such as circular polarization. While helical and gyroid-based nanostructures exhibiting circular dichroism have been developed extensively to address this limitation, they are often restricted by the spectral inconsistency of their optical response. Here we present the fabrication and characterization of quadruple-gyroid 4srs nanostructures exhibiting bio-inspired Bragg-mirror-like circular dichroism: a smooth and uniform band of circular dichroism reminiscent of the spectrum of a simple multilayer Bragg-mirror. Furthermore, we demonstrate that the circular dichroism produced by 4srs nanostructures are robust to changes in incident angle and beam collimation, providing a new platform to create and engineer circular dichroism for functional circular polarization manipulation.

From insect scales to sensor design: modelling the mechanochromic properties of bicontinuous cubic structures

Many of the three-dimensional photonic crystals occurring in the scales of insects have bicontinuous cubic structures. Their optical properties have been studied extensively, however little is known about their mechanical properties and their optical response under deformation. We demonstrated a mechanochromic effect by deforming the scales of a weevil and calculated the elastic, optical and mechanochromic (assuming homogeneous deformation) properties of the three types of bicontinuous cubic structures occurring in nature: P-structure (primitive), G-structure (gyroid) and D-structure (diamond). The results show that all investigated properties of these three structure types strongly depend on their geometry, structural parameters such as volume fractions of the two constituting phases and the directions of the incident light or applied stress, respectively. Interestingly, the mechanochromic simulation results predict that these structures may show blue-shift or even red-shift under compression along certain directions. Our results provide design guidelines for mechanochromic sensing materials operating in the elastic regime, including parameters such as sensitivity and direction of spectral shift.

Domain morphology, boundaries, and topological defects in biophotonic gyroid nanostructures of butterfly wing scales

Many organisms in nature have evolved sophisticated cellular mechanisms to produce photonic nanostructures and, in recent years, diverse crystalline symmetries have been identified and related to macroscopic optical properties. However, because we know little about the distributions of domain sizes, the orientations of photonic crystals, and the nature of defects in these structures, we are unable to make the connection between the nanostructure and its development and functionality. We report on nondestructive studies of the morphology of chitinous photonic crystals in butterfly wing scales. Using spatially and angularly resolved x-ray diffraction, we find that the domains are highly oriented with respect to the whole scale, indicating growth from scale boundaries. X-ray coherent diffractive imaging reveals two types of crystalline domain interfaces: abrupt changes between domains emerging from distinct nucleation sites and smooth transitions with edge dislocations presumably resulting from internal stresses during nanostructure development. Our study of the scale structure reveals new aspects of photonic crystal growth in butterfly wings and shows their similarity to block copolymer materials. It opens new avenues to exploration of fundamental processes underlying the growth of biological photonic nanostructures in a variety of species.

Biomimetic gyroid nanostructures exceeding their natural origins

Using optical two-beam lithography with improved resolution and enhanced mechanical strength, we demonstrate the replication of gyroid photonic nanostructures found in the butterfly Callophrys rubi. These artificial structures are shown to have size, controllability, and uniformity that are superior to those of their biological counterparts. In particular, the elastic Young's modulus of fabricated nanowires is enhanced by up to 20%. As such, the circular dichroism enabled by the gyroid nanostructures can operate in the near-ultraviolet wavelength region, shorter than that supported by the natural butterfly wings of C. rubi. This fabrication technique provides a unique tool for extracting three-dimensional photonic designs from nature and will aid the investigation of biomimetic nanostructures.

Chiral metamaterials: enhancement and control of optical activity and circular dichroism

The control of the optical activity and ellipticity of a medium has drawn considerable attention due to the recent developments in metamaterial design techniques and a deeper understanding of the light matter interaction in composite metallic structures. Indeed, recently proposed designs of metaatoms have enabled the realisation of materials with unprecedented chiral optical properties e.g. strong optical activity, broadband optical activity, and nondispersive zero ellipticity. Combining chiral metamaterials with nonlinear materials has opened up new possibilities in the field of nonlinear chirality as well as provided the foundation for switchable chiral devices. Furthermore, chirality together with hyperbolicity can be used to realise new exciting materials such as photonic topological insulators. In this review, we will outline the fundamental principles of chiral metamaterials and report on recent progress in providing the foundations for promising applications of switchable chiral metamaterials.

Observation of optical activity in dielectric biomimetic 8-srs networks

We demonstrate the first experimental realization of the 8-srs network by direct laser writing in a dielectric medium. The optical properties of this photonic crystal are both numerically simulated and experimentally measured. The numerical simulations indicate a strong optical activity (OA) for regions of the spectrum close to the unit cell size (3 μm) and a high sensitivity to angular resolution. Experimentally, we observe 40° of OA for a region of the spectrum between 3 and 3.5 μm, confirming both simulation predictions.

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.

Engineering Gyroid-Structured Functional Materials via Templates Discovered in Nature and in the Lab

In search of optimal structures for functional materials fabrication, the gyroid (G) structure has emerged as a promising subject of widespread research due to its distinct symmetry, 3D interconnected networks, and inherent chiral helices. In the past two decades, researchers have made great progress fabricating G-structured functional materials (GSFMs) based on G templates discovered both in nature and in the lab. The GSFMs demonstrate extraordinary resonance when interacting with light and matter. The superior properties of GSFMs can be divided into two categories based on the dominant structural properties, namely, dramatic optical performances dominated by short-range symmetry and well-defined texture, and effective matter transport due to long-range 3D interconnections and high integrity. In this review, G templates suitable for fabrication of GSFMs are summarized and classified. State-of-the-art optical applications of GSFMs, including photonic bandgap materials, chiral devices, plasmonic materials, and matamaterials, are systematically discussed. Applications of GSFMs involved in effective electron transport and mass transport, including electronic devices, ultrafiltration, and catalysis, are highlighted. Existing challenges that may hinder the final application of GSFMS together with possible solutions are also presented.

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.

Ideal geometry of periodic entanglements

Three-dimensional entanglements, including knots, knotted graphs, periodic arrays of woven filaments and interpenetrating nets, form an integral part of structure analysis because they influence various physical properties. Ideal embeddings of these entanglements give insight into identification and classification of the geometry and physically relevant configurations in vivo . This paper introduces an algorithm for the tightening of finite, periodic and branched entanglements to a least energy form. Our algorithm draws inspiration from the Shrink-On-No-Overlaps (SONO) (Pieranski 1998 In Ideal knots (eds A Stasiak, V Katritch, LH Kauffman), vol. 19, pp. 20–41.) algorithm for the tightening of knots and links: we call it Periodic-Branched Shrink-On-No-Overlaps (PB-SONO). We reproduce published results for ideal configurations of knots using PB-SONO. We then examine ideal geometry for finite entangled graphs, including θ -graphs and entangled tetrahedron- and cube-graphs. Finally, we compute ideal conformations of periodic weavings and entangled nets. The resulting ideal geometry is intriguing: we see spontaneous symmetrisation in some cases, breaking of symmetry in others, as well as configurations reminiscent of biological and chemical structures in nature.

Cryptic iridescence in a fossil weevil generated by single diamond photonic crystals

Nature's most spectacular colours originate in integumentary tissue architectures that scatter light via nanoscale modulations of the refractive index. The most intricate biophotonic nanostructures are three-dimensional crystals with opal, single diamond or single gyroid lattices. Despite intense interest in their optical and structural properties, the evolution of such nanostructures is poorly understood, due in part to a lack of data from the fossil record. Here, we report preservation of single diamond (Fd-3m) three-dimensional photonic crystals in scales of a 735,000 year old specimen of the brown Nearctic weevil Hypera diversipunctata from Gold Run, Canada, and in extant conspecifics. The preserved red to green structural colours exhibit near-field brilliancy yet are inconspicuous from afar; they most likely had cryptic functions in substrate matching. The discovery of pristine fossil examples indicates that the fossil record is likely to yield further data on the evolution of three-dimensional photonic nanostructures and their biological functions.

Well-ordered nanohybrids and nanoporous materials from gyroid block copolymer templates

The design of nanostructured materials and their corresponding morphologies has attracted intense attention because of their effectiveness in tuning electronic, optical, magnetic, and catalytic properties, as well as mechanical properties. Although many technologies have been explored to fabricate nanostructured materials, templated synthesis is one of the most important approaches to fabricate nanostructured materials with precisely controlled structures and morphologies from their constituent components. In this review article, we aim to highlight the use of the self-assembly of block copolymers as an emerging and powerful tool to fabricate well-defined nanomaterials with precise control over the structural dimensions and shape, as well as over the composition and corresponding spatial arrangement. After providing a brief introduction to the synthesis of regular porous materials, including silica- and carbon-based mesoporous materials, the review focuses on the fabrication of well-ordered nanoporous polymers from the selfassembly of degradable block copolymers, in particular with gyroid-forming network morphologies, as templates for the syntheses of various materials with different entities. We highlight the principles of different templated syntheses, from the fundamentals to their practical uses in the fabrication of nanohybrids and nanoporous materials; moreover, we provide an introduction to templates, precursors, solvents, and processing. Finally, some recent examples using block copolymer structure-directed nanomaterials for applications, such as solar cells, catalysis, and drug delivery, are presented. In particular, by taking advantage of the "well-ordered" structural characteristics of the gyroid texture, the properties and applications of 3D regular nanostructures, such as the photonic behavior and optical properties of gyroid-forming nanostructures, as well as of gyroid-forming metamaterials, will be emphasized. Special attention is also given to present new developments and future perspectives in this field.

Polarization-sensitive color in butterfly scales: polarization conversion from ridges with reflecting elements

Polarization-sensitive color originates from polarization-dependent reflection or transmission, exhibiting abundant light information, including intensity, spectral distribution, and polarization. A wide range of butterflies are physiologically sensitive to polarized light, but the origins of polarized signal have not been fully understood. Here we systematically investigate the colorful scales of six species of butterfly to reveal the physical origins of polarization-sensitive color. Microscopic optical images under crossed polarizers exhibit their polarization-sensitive characteristic, and micro-structural characterizations clarify their structural commonality. In the case of the structural scales that have deep ridges, the polarization-sensitive color related with scale azimuth is remarkable. Periodic ridges lead to the anisotropic effective refractive indices in the parallel and perpendicular grating orientations, which achieves form-birefringence, resulting in the phase difference of two different component polarized lights. Simulated results show that ridge structures with reflecting elements reflect and rotate the incident p-polarized light into s-polarized light. The dimensional parameters and shapes of grating greatly affect the polarization conversion process, and the triangular deep grating extends the outstanding polarization conversion effect from the sub-wavelength period to the period comparable to visible light wavelength. The parameters of ridge structures in butterfly scales have been optimized to fulfill the polarization-dependent reflection for secret communication. The structural and physical origin of polarization conversion provides a more comprehensive perspective on the creation of polarization-sensitive color in butterfly wing scales. These findings show great potential in anti-counterfeiting technology and advanced optical material design.

Phase behavior and complex crystal structures of self-assembled tethered nanoparticle telechelics

Motivated by growing interest in the self-assembly of nanoparticles for applications such as photonics, organic photovoltaics, and DNA-assisted designer crystals, we explore the phase behavior of tethered spherical nanoparticles. Here, a polymer tether is used to geometrically constrain a pair of nanoparticles creating a tethered nanoparticle "telechelic". Using simulation, we examine how varying architectural features, such as the size ratio of the two end-group nanospheres and the length of the flexible tether, affects the self-assembled morphologies. We demonstrate not only that this hybrid building block maintains the same phase diversity as linear triblock copolymers, allowing for a variety of nanoparticle materials to replace polymer blocks, but also that new structures not previously reported are accessible. Our findings imply a robust underlying ordering mechanism is common among these systems, thus allowing flexibility in synthesis approaches to achieve a target morphology.

Adaptive optics enhanced direct laser writing of high refractive index gyroid photonic crystals in chalcogenide glass

Chiral gyroid photonic crystals are fabricated in the high refractive index chalcogenide glass arsenic trisulfide with an adaptive optics enhanced direct laser writing system. The severe spherical aberration imparted when focusing into the arsenic trisulfide is mitigated with a defocus decoupled aberration compensation technique that reduces the level of aberration that must be compensated by over an order of magnitude. The fabricated gyroids are shown to have excellent uniformity after our adaptive optics method is employed, and the transmission spectra of the gyroids are shown to have good agreement with numerical simulations that are based on a uniform and diffraction limited fabrication resolution.