The gyroid is a continuous and triply periodic cubic morphology which possesses a constant mean curvature surface across a range of volumetric fi ll fractions. Found in a variety of natural and synthetic systems which form through self-assembly, from butterfl y wing scales to block copolymers, the gyroid also exhibits an inherent chirality not observed in any other similar morphologies. These unique geometrical properties impart to gyroid structured materials a host of interesting optical properties. Depending on the length scale on which the constituent materials are organised, these properties arise from starkly different physical mechanisms (such as a complete photonic bandgap for photonic crystals and a greatly depressed plasma frequency for optical metamaterials). This article reviews the theoretical predictions and experimental observations of the optical properties of two fundamental classes of gyroid structured materials: photonic crystals (wavelength scale) and metamaterials (sub-wavelength scale).

By incorporating feedback around systems we wish to manipulate, it is possible to improve their performance and robustness properties to meet pre-specified design objectives. For decades control engineers have been successfully implementing feedback controllers for complex mechanical and electrical systems such as aircraft and sports cars. Natural biological systems use feedback extensively for regulation and adaptation but apart from the most basic designs, there is no systematic framework for designing feedback controllers in Synthetic Biology. In this paper we describe how classical approaches from linear control theory can be used to close the loop. This includes the design of genetic circuits using feedback control and the presentation of a biological phase lag controller.

Block copolymer (BCP) self-assembly is a promising route to manufacture functional nanomaterials for applications from nanolithography to optical metamaterials. Self-assembled cubic morphologies cannot, however, be conveniently optically characterized in the lab due to their structural isotropy. Here, the aligned crystallization behavior of a semicrystalline-amorphous polyisoprene-b-polystyrene-b-poly(ethylene oxide) (ISO) triblock terpolymer was utilized to visualize the grain structure of the cubic microphase-separated morphology. Upon quenching from a solvent swollen state, ISO first self-assembles into an alternating gyroid morphology, in the confinement of which the PEO crystallizes preferentially along the least tortuous pathways of the single gyroid morphology with grain sizes of hundreds of micrometers. Strikingly, the resulting anisotropic alignment of PEO crystallites gives rise to a unique optical birefringence of the alternating gyroid domains, which allows imaging of the self-assembled grain structure by optical microscopy alone. This study provides insight into polymer crystallization within a tortuous three-dimensional network and establishes a useful method for the optical visualization of cubic BCP morphologies that serve as functional nanomaterial templates.

Over the past two decades, metamaterials have led to an increasing number of biosensing and nanophotonic applications due to the possibility of a careful control of light propagating through subwavelength features. Chiral nanostructures (characterized by the absence of any mirror symmetry), in particular, give rise to unique chiro-optical properties such as circular dichroism and optical activity. Here, we present a gyroid optical metamaterial with a periodicity of 65 nm exhibiting a strong circular dichroism at visible wavelengths. Our bottom-up approach, based on metallic replication of the gyroid morphology in triblock terpolymer films, generates a large area of periodic optical metamaterials. We observe a strong circular dichroism in gold and silver gyroid metamaterials at visible wavelengths. We show that the circular dichroism is inherently linked to the handedness of the gyroid nanostructure, and demonstrate its tuneability. The optical effects are discussed and compared to other existing systems, showing the potential of bottom-up approaches for large-scale circular filters and chiral sensing.