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Knots play a fundamental role in the dynamics of biological and physical systems, from DNA to turbulent plasmas, as well as in climbing, weaving, sailing, and surgery. Despite having been studied for centuries, the subtle interplay between topology and mechanics in elastic knots remains poorly understood. Here, we combined optomechanical experiments with theory and simulations to analyze knotted fibers that change their color under mechanical deformations. Exploiting an analogy with long-range ferromagnetic spin systems, we identified simple topological counting rules to predict the relative mechanical stability of knots and tangles, in agreement with simulations and experiments for commonly used climbing and sailing bends. Our results highlight the importance of twist and writhe in unknotting processes, providing guidance for the control of systems with complex entanglements.

Materials in nature are characterized by structural order over multiple length scales have evolved for maximum performance and multifunctionality, and are often produced by self-assembly processes. A striking example of this design principle is structural coloration, where interference, diffraction, and absorption effects result in vivid colors. Mimicking this emergence of complex effects from simple building blocks is a key challenge for manmade materials. Here, we show that a simple confined selfassembly process leads to a complex hierarchical geometry that displays a variety of optical effects. Colloidal crystallization in an emulsion droplet creates micron-sized superstructures, termed photonic balls. The curvature imposed by the emulsion droplet leads to frustrated crystallization. We observe spherical colloidal crystals with ordered, crystalline layers and a disordered core. This geometry produces multiple optical effects. The ordered layers give rise to structural color from Bragg diffraction with limited angular dependence and unusual transmission due to the curved nature of the individual crystals. The disordered core contributes nonresonant scattering that induces a macroscopically whitish appearance, which we mitigate by incorporating absorbing gold nanoparticles that suppress scattering and macroscopically purify the color. With increasing size of the constituent colloidal particles, grating diffraction effects dominate, which result from order along the crystal’s curved surface and induce a vivid polychromatic appearance. The control of multiple optical effects induced by the hierarchical morphology in photonic balls paves the way to use them as building blocks for complex optical assemblies—potentially as more efficient mimics of structural color as it occurs in nature.

Micro-scale optical components play a crucial role in imaging and display technology, biosensing, beam shaping, optical switching, wavefront-analysis, and device miniaturization. Herein, we demonstrate liquid compound micro-lenses with dynamically tunable focal lengths. We employ bi-phase emulsion droplets fabricated from immiscible hydrocarbon and fluorocarbon liquids to form responsive micro-lenses that can be reconfigured to focus or scatter light, form real or virtual images, and display variable focal lengths. Experimental demonstrations of dynamic refractive control are complemented by theoretical analysis and wave-optical modelling. Additionally, we provide evidence of the micro-lenses’ functionality for two potential applications—integral micro-scale imaging devices and light field display technology—thereby demonstrating both the fundamental characteristics and the promising opportunities for fluid-based dynamic refractive micro-scale compound lenses. Micro-lenses are critical components in miniaturized optical devices for imaging and sensing, yet it is challenging to design them with on-demand variable optical properties. Here, Nagelberg et al . use bi-phase emulsion droplets to design reconfigurable micro-lenses with variable focal length.

Many species rely on diverse selections of entirely organic photonic structures for the manipulation of light and the display of striking colours. Here we report the discovery of a mineralized hierarchical photonic architecture embedded within the translucent shell of the blue-rayed limpet Patella pellucida . The bright colour of the limpet’s stripes originates from light interference in a periodically layered zig-zag architecture of crystallographically co-oriented calcite lamellae. Beneath the photonic multilayer, a disordered array of light-absorbing particles provides contrast for the blue colour. This unique mineralized manifestation of a synergy of two distinct optical elements at specific locations within the continuum of the limpet’s translucent protective shell ensures the vivid shine of the blue stripes, which can be perceived under water from a wide range of viewing angles. The stripes’ reflection band coincides with the spectral range of minimal light absorption in sea water, raising intriguing questions regarding their functional significance. Mollusks have evolved an exquisite diversity of complex mineralized shells for protection. One such example, the blue-rayed limpet, incorporates a vivid display of blue lines, which originate from the interference of light in a nano-periodic photonic architecture buried within the animal's translucent shell.

Mechanical forces in the cell’s natural environment have a crucial impact on growth, differentiation and behaviour. Few areas of biology can be understood without taking into account how both individual cells and cell networks sense and transduce physical stresses. However, the field is currently held back by the limitations of the available methods to apply physiologically relevant stress profiles on cells, particularly with sub-cellular resolution, in controlled in vitro experiments. Here we report a new type of active cell culture material that allows highly localized, directional and reversible deformation of the cell growth substrate, with control at scales ranging from the entire surface to the subcellular, and response times on the order of seconds. These capabilities are not matched by any other method, and this versatile material has the potential to bridge the performance gap between the existing single cell micro-manipulation and 2D cell sheet mechanical stimulation techniques. Mechanical forces within the cell’s environment play a crucial role in their growth, differentiation and behaviour. Here, the authors develop a photothermal responsive cell culture substrate for the assessment of how cell growth can be affected by manipulating the strain profile of the substrate.

Recently, diffraction elements that reverse the color sequence normally observed in planar diffraction gratings have been found in the wing scales of the butterfly Pierella luna . Here, we describe the creation of an artificial photonic material mimicking this reverse color-order diffraction effect. The bioinspired system consists of ordered arrays of vertically oriented microdiffraction gratings. We present a detailed analysis and modeling of the coupling of diffraction resulting from individual structural components and demonstrate its strong dependence on the orientation of the individual miniature gratings. This photonic material could provide a basis for novel developments in biosensing, anticounterfeiting, and efficient light management in photovoltaic systems and light-emitting diodes. Significance In the course of evolution, many organisms have developed unique light manipulation strategies that rely on intriguing combinations of a broad range of optical effects generated by materials with sophisticated multiscale hierarchical structural arrangements. By exploiting the optical principles underlying natural structural color, we can generate new photonic materials. Researchers have only just begun to match nature’s morphological and compositional complexity in man-made materials using nanofabrication. We present a bioinspired photonic material that mimics the reverse color-order diffraction found in the butterfly Pierella luna . Exploiting and improving the butterfly’s strategy, we create photonic materials that increase our basic understanding of the optical interplay of hierarchical structures and provide a platform for the development of novel photonic devices.

Iridescence, the change in hue of a surface with varying observation angles, is used by insects, birds, fish, and reptiles for species recognition and mate selection. We identified iridescence in flowers of Hibiscus trionum and Tulipa species and demonstrated that iridescence is generated through diffraction gratings that might be widespread among flowering plants. Although iridescence might be expected to increase attractiveness, it might also compromise target identification because the object's appearance will vary depending on the viewer's perspective. We found that bumblebees (Bombus terrestris) learn to disentangle flower iridescence from color and correctly identify iridescent flowers despite their continuously changing appearance. This ability is retained in the absence of cues from polarized light or ultraviolet reflectance associated with diffraction gratings.

Dark-field microscopy is a standard imaging technique widely employed in biology that provides high image contrast for a broad range of unstained specimens1. Unlike bright-field microscopy, it accentuates high spatial frequencies and can therefore be used to emphasize and resolve small features. However, the use of dark-field microscopy for reliable analysis of blood cells, bacteria, algae and other marine organisms often requires specialized, bulky microscope systems, as well as expensive additional components, such as dark-field-compatible objectives or condensers2,3. Here, we propose to simplify and downsize dark-field microscopy equipment by generating the high-angle illumination cone required for dark-field microscopy directly within the sample substrate. We introduce a luminescent photonic substrate with a controlled angular emission profile and demonstrate its ability to generate high-contrast dark-field images of micrometre-sized living organisms using standard optical microscopy equipment. This new type of substrate forms the basis for miniaturized lab-on-chip dark-field imaging devices that are compatible with simple and compact light microscopes.A luminescent photonic substrate with a controlled angular emission profile is introduced and its ability to generate high-contrast dark-field images of micrometre-sized living organisms is demonstrated using standard optical microscopy equipment.

Mechanoresponsive, soft, photonic materials with tunable structural coloration represent a class of materials that have potential benefits for a wide range of applications. While many lab‐scale fabrication approaches afford control over the nano‐ and microscale morphology of these materials, upscaling their manufacture remains a challenge. Herein, a scalable fabrication concept is proposed that centers on the modular assembly of color‐changing materials from microscale building blocks. The building blocks consist of hydrogel‐based spherical photonic crystals. They are formed through a water‐in‐oil emulsification of nanoscale colloidal particles suspended in the aqueous phase. Once formed, the photonic crystal microspheres are then assembled into macroscale photonic materials, such as stretchable fibers or sheets. The resulting materials respond to a mechanical deformation with a reversible, dynamic change in color. Fabricated via a scalable, modular‐assembly approach, these mechanoresponsive photonic fibers and sheets, in turn, form a valuable building block for sensing systems or visual communication in healthcare, architecture, and consumer product design. Macroscale production of mechanoresponsive color‐changing materials is achieved by utilizing hydrogel‐based photonic microspheres as building blocks for the modular design of stretchable photonic fibers and sheets. The resulting soft photonic materials exhibit a dynamic change in color when subjected to mechanical deformation.

Structurally coloured materials that change their colour in response to mechanical stimuli are uniquely suited for optical sensing and visual communication 1 – 4 . The main barrier to their widespread adoption is a lack of manufacturing techniques that offer spatial control of the materials’ nanoscale structures across macroscale areas. Here, by adapting Lippmann photography 5 , we report an approach for producing large-area, structurally coloured sheets with a rich and easily controlled design space of colour patterns, spectral properties, angular scattering characteristics and responses to mechanical stimuli. Relying on just a digital projector and commercially available photosensitive elastomers, our approach is fast, scalable, affordable and relevant for a wide range of manufacturing settings. We also demonstrate prototypes for mechanosensitive healthcare materials and colorimetric strain and stress sensing for human–computer interaction and robotics. Desired for optical sensing or visual communications, structural colour-changing materials are hindered by the lack of scalable manufacturing. Here, by adapting Lippmann photography, large-area manufacturing of colour patterns in photosensitive elastomers is realized.