Reflectivity of the gyroid biophotonic crystals in the ventral wing scales of the Green Hairstreak butterfly,Callophrys rubi

We present a comparison of the computer simulation data of gyroid nanostructures with optical measurements (reflectivity spectra and scattering diagrams) of ventral wing scales of the Green Hairstreak butterfly, Callophrys rubi. We demonstrate that the omnidirectional green colour arises from the gyroid cuticular structure grown in the domains of different orientation. We also show that this three-dimensional structure, operating as a biophotonic crystal, gives rise to various polarization effects. We briefly discuss the possible biological utility of the green coloration and polarization effects.     

Triply periodic bicontinuous structures through interference lithography: a level-set approach

Interference lithography holds the promise of fabricating large-area, defect-free photonic structures on the sub-micrometer scale both rapidly and cheaply. There is a need for a procedure to establish a connection between the structures that are formed and the parameters of the interfering beams. There is also a need to produce self-supporting three-dimensional bicontinuous structures. A generic technique correlating parameters of the interfering beams with the symmetry elements present in the resultant structures by a level-set approach is developed. A particular space group is ensured by equating terms of the intensity equation to a representative level surface of the desired space group. Single- and multiple-exposure techniques are discussed. The beam parameters for certain cubic bicontinuous structures relevant to photonic crystals, viz.,the diamond(D), the simple cubic (P), and the chiral gyroid (G) are derived by utilizing either linear or elliptically polarized light.     

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.     

Epitaxial growth of three-dimensionally architectured optoelectronic devices

Optoelectronic devices have long benefited from structuring in multiple dimensions on microscopic length scales. However, preserving crystal epitaxy, a general necessity for good optoelectronic properties, while imparting a complex three-dimensional structure remains a significant challenge. Three-dimensional (3D) photonic crystals are one class of materials where epitaxy of 3D structures would enable new functionalities. Many 3D photonic crystal devices have been proposed, including zero-threshold lasers, low-loss waveguides, high-efficiency light-emitting diodes (LEDs) and solar cells, but have generally not been realized because of material limitations. Exciting concepts in metamaterials, including negative refraction and cloaking, could be made practical using 3D structures that incorporate electrically pumped gain elements to balance the inherent optical loss of such devices. Here we demonstrate the 3D-template-directed epitaxy of group III-V materials, which enables formation of 3D structured optoelectronic devices. We illustrate the power of this technique by fabricating an electrically driven 3D photonic crystal LED.     

Block copolymer morphologies in dye-sensitized solar cells: probing the photovoltaic structure-function relation

We integrate mesostructured titania arrays into dye-sensitized solar cells by replicating ordered, oriented one-dimensional (1D) columnar and three-dimensional (3D) bicontinuous gyroid block copolymer phases. The solar cell performance, charge transport, and recombination are investigated. We observe faster charge transport in 1D "wires" than through 3D gyroid arrays. However, owing to their structural instability, the surface area of the wire arrays is low, inhibiting the solar cell performance. The gyroid morphology, on the other hand, outperforms the current state-of-the-art mesoporous nanoparticle films.     

Hemispherical Brillouin zone imaging of a diamond-type biological photonic crystal

The brilliant structural body colours of many animals are created by three-dimensional biological photonic crystals that act as wavelength-specific reflectors. Here, we report a study on the vividly coloured scales of the diamond weevil, Entimus imperialis. Electron microscopy identified the chitin and air assemblies inside the scales as domains of a single-network diamond (Fd3m) photonic crystal. We visualized the topology of the first Brillouin zone (FBZ) by imaging scatterometry, and we reconstructed the complete photonic band structure diagram (PBSD) of the chitinous photonic crystal from reflectance spectra. Comparison with calculated PBSDs indeed showed a perfect overlap. The unique method of non-invasive hemispherical imaging of the FBZ provides key insights for the investigation of photonic crystals in the visible wavelength range. The characterized extremely large biophotonic nanostructures of E. imperialis are structurally optimized for high reflectance and may thus be well suited for use as a template for producing novel photonic devices, e.g. through biomimicry or direct infiltration from dielectric material.     

Photonic bandgaps of different unit cells in the basic structural unit of germanium-based two-dimensional decagonal photonic quasi-crystals

Based on the infrared optical material germanium, in the basic structural unit of a two-dimensional decagonal photonic quasi-crystal, photonic bandgaps of four square unit cells with a scattering radius in the range of [0,0.3a] have been calculated within two cases of construction (i.e., air cylinders arranged in germanium and germanium cylinders arranged in air) by using the plane wave expansion method. In considering the Bragg-like scattering effect in two-dimensional photonic quasi-crystals as the elastic collision in physics, we put forward the photonic bandgap impact function F=q(1)q(2)q(3)επr(2) for the first time, to the best of our knowledge. A certain unit cell structure shares some similar photonic bandgap properties with a periodic structure. For a certain structure of the unit cell, the center frequency change trends of the photonic bandgap and the type of photonic bandgap generated are not related with the period of the photonic crystal, but with the relative dielectric constant and the construction, respectively. Different unit cell structures own different photonic bandgap structures. This occurs because the high degree of rotational symmetry of the quasi-periodic structure and weak long-range order of the basic structural unit lead to different Bragg-like scattering effects within the unit cell structures.     

Enlarged Photonic Band Gap in Heterostructure of Metallic Photonic and Superconducting Photonic Crystals

We show theoretically that the frequency range of photonic band gap of a hetero-structure which is made of a metallic photonic and superconducting photonic crystal can be enlarged due to the combination of the reflection band properties of the superconductor–dielectric (PC1) and metallic–dielectric (PC2) periodic structures. The transmittance and band structure of the considered structures are calculated using simple transfer matrix method and the Bloch theorem. Beside this, we have also calculated the transmittance of the superconducting photonic structure (PC1), metallic photonic structure (PC2) and heterostructure of metallic photonic and superconductor photonic crystals (PC1/PC2) for TE and TM-mode at the different angles of incidence.     

Advanced lightweight 316L stainless steel cellular lattice structures fabricated via selective laser melting

This paper investigates the manufacturability and performance of advanced and lightweight stainless steel cellular lattice structures fabricated via selective laser melting (SLM). A unique cell type called gyroid is designed to construct periodic lattice structures and utilise its curved cell surface as a self-supported feature which avoids the building of support structures and reduces material waste and production time. The gyroid cellular lattice structures with a wide range of volume fraction were made at different orientations, showing it can reduce the constraints in design for the SLM and provide flexibility in selecting optimal manufacturing parameters. The lattice structures with different volume fraction were well manufactured by the SLM process to exhibit a good geometric agreement with the original CAD models. The strut of the SLM-manufactured lattice structures represents a rough surface and its size is slightly higher than the designed value. When the lattice structure was positioned with half of its struts at an angle of 0° with respect to the building plane, which is considered as the worst building orientation for SLM, it was manufactured with well-defined struts and no defects or broken cells. The compression strength and modulus of the lattice structures increase with the increase in the volume fraction, and two equations based on Gibson–Ashby model have been established to predict their compression properties.     

Three-dimensional titania pore structures produced by using a femtosecond laser pulse technique and a dip coating procedure

In this work, the preparation of three-dimensional hierarchical pore structures by a combination of laser-based templates and the self-organization process of mesostructured titania is presented. For this purpose macrostructured polymers produced by two-photon polymerization act as a template for the deposition of a mesostructured titania film from a solution containing an amphiphilic block copolymer by dip coating. A carefully applied calcination procedure removes both the macrotemplating polymer and the mesotemplating surfactant molecules so that a replica of the initial polymer structure with a hierarchical (macro- and meso-) pore system is obtained. In addition, the titania, which is amorphous after deposition, is transferred into crystalline anatase during calcination. Materials with dual pore systems are interesting for possible applications in catalysis and sorption, and three-dimensional crystalline structures from materials with high refraction index are attractive for photonic applications, for example as photonic crystals.     

Inverse Mopho butterfly: a new approach to photonic crystal

In this paper we showed a new approach for the fabrication of a photonic crystal with a three-dimensional structure. By replicating biomaterials such as the wing of Mopho butterfly with TiO2 nanoparticles using the nanoparticles infiltration method, we can derive photonic crystals with unique structures, which is difficult to fabricate by other approaches. New optical properties are anticipated.     

Preconditioned superprism-based photonic crystal demultiplexers: analysis and design

We present the analysis and design of a new type of photonic crystal (PC) demultiplexers (i.e., preconditioned demultiplexer), in which the simultaneous existence of the superprism effect and the negative effective index for diffraction results in a compact structure by canceling the second-order spectral phase to avoid beam broadening inside the PC. This approach considerably relaxes the requirements for the large area of the structure and the small divergence of the input beam. As a result, the size of the preconditioned demultiplexers varies as N(2.5) (N being the number of wavelength channels) compared to the N(4) variation in the conventional superprism-based PC demultiplexers. We use a generalized effective index model to analyze, design, and optimize these demultiplexing structures. This approximate model can be used to extract all the basic properties of the PC device simply from the band structure and eliminates the need to go through tedious simulations especially for three-dimensional structures. Our results show that the preconditioned superprism-based PC demultiplexers have 2 orders of magnitude smaller size compared to the conventional ones.     

Analysis of surface modes in photonic crystals by a plane-wave transfer-matrix method

We have developed a plane-wave transfer-matrix method (PWTMM) with the aid of the interpolation technique to analyze the dispersion relation of surface modes in photonic crystal or photonic crystal surface waveguide. The proposed approach has been applied to several surface structures in two-dimensional photonic crystals. The calculated dispersion relation of the surface modes is in good agreement with the result obtained by the conventional plane-wave expansion method in combination with the supercell technique. The developed PWTMM needs to handle only a single unit-cell layer domain and is therefore numerically friendly. The proposed approach can become an efficient and accurate numerical tool to understand and design surface modes in different two-dimensional and three-dimensional photonic crystals with complex geometries.     

Nonlinear optical responses in two-dimensional photonic crystals

A two-dimensional (2D) highly nonlinear lithium niobate (LN) photonic crystal (PhC) waveguide is fabricated with the aim of studying its nonlinear optical properties. We show a large enhancement of the second-harmonic generation (SHG) in the 2D LN PhCs, originating from resonance between the external pump laser field and a photonic band mode. The SHG enhancement results agree well with the experimental photonic band structure obtained by an angle-dependent optical reflectivity and the theoretical band structure generated by three-dimensional finite-difference time-domain calculations. These results open new possibilities for the use of 2D LN PhC waveguide in integrated nonlinear optical applications.     

Dual gratings interspersed on a single butterfly scale

Iridescent butterfly wing colours result from the interaction of light with sub-micrometre structures in the scales. Typically, one scale contains one such photonic structure that produces a single iridescent signal. Here, however, we show how the dorsal wings of male Lamprolenis nitida emit two independent signals from two separate photonic structures in the same scale. Multiple independent signals from separate photonic structures within the same sub-micrometre device are currently unknown in animals. However, they would serve to increase the complexity and specificity of the optical signature, enhancing the information conveyed. This could be important during intrasexual encounters, in which iridescent male wing colours are employed as threat displays. Blazed diffraction gratings, like those found in L. nitida, are asymmetric photonic structures and drive most of the incident light into one diffraction order. Similar gratings are used in spectrometers, limiting the spectral range over which the spectrometer functions. By incorporating two interchangeable gratings onto a single structure, as they are in L. nitida, the functional range of spectrometers could be extended.     

Symmetry reduction for maximization of higher-order stop-bands in two-dimensional photonic crystals

A large absolute higher-order stop-band is achieved in two-dimensional (2D) photonic crystals of square lattice. A genetic algorithm is used to search through a large number of possible structures. In this algorithm, the unit cell is divided into a grid of square pixels and a 2D binary chromosome is assigned to each filling pattern of the pixels. An initial structure with a small higher-order stop-band is included in the initial population to accelerate the search procedure. This initial structure is formed by breaking the symmetry of the supercell of a photonic crystal having a square lattice of square dielectric rods in air. In the optimization process, the effect of reducing the symmetry of the unit cell on the photonic band-gap is investigated. A structure showing an absolute higher-order band-gap as large as 0.1522(2πc/a) is obtained, which is larger than the values reported so far for photonic stop-bands.     

Anomalous behaviour of light reflection in crystals with different homogeneity

The light reflection as a function of the sample length has been studied for an ideal two-dimensional photonic crystal and for a two-dimensional photonic structure with smaller homogeneity with respect to the photonic crystal. We have found that, although the number of the scattering elements is constant for the two structures, the behaviour of the light reflection increases linearly with the sample length in the less homogeneous photonic structure, while it is strongly sub-linear in the photonic crystals.     

Investigation of TE-polarized photonic band gap properties in matallodielectric photonic crystals composed of metal coated dielectric cylinders

Using the Dirichlet-to-Neumann map method and generalization of this method, we have been able to calculate the photonic band structure of two-dimensional (2D) metallodielectric photonic crystals composed of metal-coated circular dielectric rods. The rods are embedded in an air background with a square array. We are interested in considering transverse electric (TE) mode of electromagnetic waves. The resulting band structures show the existence of photonic band gaps as well as some flat band regions. We theoretically study the effect of the dielectric constant and radius of the dielectric core on the photonic band structures. There are some interesting results compared to the case of solid metallic rods (without dielectric core) such as appearing the new photonic band gaps and a flat band region with the characteristic of cavity modes.     

Rapid fabrication of 2D and 3D photonic crystals and their inversed structures

In this paper a new technique is proposed for the fabrication of two-dimensional (2D) and three-dimensional (3D) photonic crystals using monodisperse polystyrene microspheres as the templates. In addition, the approaches toward the creation of their corresponding inversed structures are described. The inversed structures were prepared by subjecting an introduced silica source to a sol-gel process; programmed heating was then performed to remove the template without spoiling the inversed structures. Utilizing these approaches, 2D and 3D photonic crystals and their highly ordered inversed hexagonal multilayer or monolayer structures were obtained on the substrate.     

A triple-network tricontinuous cubic liquid crystal

Soft matter such as surfactant-water systems, block copolymers or liquid crystals can form periodic structures on nanometre to micrometre scales. This property can be used for templating nanoporous ceramics, surface patterning for electronic devices, or generation of photonic materials. Much attention has been paid to structures appearing between the layer and cylinder phases, the three so-called bicontinuous cubic phases. These are formed by two continuous interpenetrating networks of channels. In this article we describe a related phase, which has the first reported structure consisting of three interpenetrating infinite networks. It is a thermotropic (solvent-free) liquid crystal of cubic symmetry Im3m. The structure is one of the most complex in liquid crystals, and is determined by direct Fourier reconstruction of electron density. We discuss the possible rationale for the existence of such a phase, its structural relationship with the bicontinuous phases, and its position in the phase diagram.