3D airfoil-shaped grating

M. robinsoni and M. chrysomelas have two types of visually distinct abdominal scales: rainbow-iridescent scales and velvet black scales (Fig. 2a, b and Supplementary Fig. 1). These scales show strikingly different morphologies: the black scales are brush-like and randomly oriented (Fig. 2c, d black arrowhead, Supplementary Fig. 2), while the rainbow-iridescent scales are more orderly aligned, cling to the cuticle surface and have bulky 3D shapes (Fig. 2c, d white arrowhead). Closer observation of the iridescent scales shows parallel grating structures on each individual scale for both spider species (Fig. 2e, f). The gratings are more regularly spaced on the scales of M. robinsoni (Fig. 2g) than those of M. chrysomelas (Fig. 2h). TEM on the transverse section of the iridescent scales reveals airfoil-shaped profiles (i.e. the curvatures are not concentric arcs; Fig. 2i, j). The surfaces of these airfoil-shaped scales are covered by prominent binary-phase grating structures with depths ~ 500 nm or more, and periods between 500 and 800 nm. Images of TEM sections (Fig. 2i, j) agree well with SEM images (Fig. 2e–h) and show the spacing of the gratings is more regular on the scales of M. robinsoni than that on the scales of M. chrysomelas (Table 1 and Supplementary Fig. 3). In addition, the gratings are asymmetrical between the two sides of the airfoil-shaped scales of M. robinsoni, with one side thinner and more densely distributed than the other, while the gratings are evenly, and more randomly, distributed on both sides of M. chrysomelas scales (Table 1).

Fig. 2 Optical and electron micrographs for the abdominal scales of M. robinsoni and M. chrysomelas. a, b Optical micrographs of the abdominal scales of M. robinsoni (a) and M. chrysomelas (b), showing two types of scales, iridescent and black. c, d SEM micrographs for the abdominal scales of M. robinsoni (c) and M. chrysomelas (d). At the centre of the image are the iridescent scales (white arrowhead). Black scales can be seen on both sides of the image (black arrowhead). The stems (white arrows) and the sockets (white circles) of detached scales can be observed. e–h Zoom-in views of SEM micrographs of the iridescent scales of M. robinsoni (e, g) and M. chrysomelas (f, h) showing grating structures. The grating period for the iridescent scales of M. robinsoni is more regular than that of M. chrysomelas. i, j TEM micrographs revealing the airfoil-shaped profiles and the surface nanogratings in the iridescent scales of M. robinsoni (i) and M. chrysomelas (j). Scale bar: a, b 200 μm; c, d 20 μm; e–j 5 μm Full size image

Table 1 The thickness and spacing measured from TEM micrographs (Fig. 2i, j) Full size table

Separating the full visible spectrum over small angles

The unique grating configuration of each M. robinsoni scale disperses the visible spectrum over a small angle, such that at short distances, the entire visible spectrum is resolved, and that a static microscopic rainbow pattern distinctly emerges (Fig. 3a). Hyperspectral analyses also demonstrate an array of full-spectrum reflectance spectra from the iridescent scales of both M. robinsoni (Fig. 3b) and M. chrysomelas (Supplementary Fig. 4a). On the basis of the SEM/TEM images, we hypothesize that the acute angle-sensitive rainbow-iridescence of M. robinsoni and M. chrysomelas result from the interaction of the surface nanograting and the microscopic airfoil-shape of the scales.

Fig. 3 Observed microscopic colour patterns. a Light micrograph of rainbow patterned M. robinsoni scales. Black centre square: 4 × 4 μm2. b Reflectance spectra collected by hyperspectral imaging of the iridescent scales. c SEM micrograph of the 3D printed foil grating (left, scale bar: 10 μm), and a hyperspectral image of the 3D printed foil grating (right) showing arbitrarily assigned, false-colour rainbow patterns emerging from the tip of the foil grating. Pixels show the same false-colour have the same reflectance spectrum and vice versa. d Reflectance spectra collected by hyperspectral imaging from the entire 3D printed foil grating image. For b, d the colours of the curves are estimated based on the “spec2rgb” function in R script “pavo”49 Full size image

To evaluate our hypothesis, we design three different grating configurations, all using the same surface nanograting with a period of 670 nm (thickness: 170 nm, spacing: 500 nm), and a depth of 300 nm, but with different shapes/geometries: the first configuration is a conventional 2D grating (flat, Fig. 4a); the second configuration is a pentagonal prism that roughly resembles the shape of the scales with flat surfaces and abrupt joints (prism, Fig. 4b); lastly the third configuration is a spider scale-mimic structure, with nanogratings on the two lenticular curved (i.e., with concentric convex curvature) sides (foil, Fig. 4c). For the pentagonal prism configuration, the nanogratings are on the four upward-facing surfaces except for the base and the sides (Fig. 4b). This design is partly inspired by the iridescence-enhancing boomerang-shaped feather barbules of the bird-of-paradise Parotia lawesii 17,18.

Fig. 4 Different grating configuration designs and their SEM micrographs. a The flat grating. b The prism grating. c The foil grating. d The lenticular prism (foil-shaped structure without the surface nanograting). e–g The SEM micrographs for the flat (e), prism (f) and foil (g) gratings. Scale bar: a–d 5 μm; insets, 2 μm. e–g 2 μm Full size image

We fabricate our designs using two-photon nanolithography, and verify the structure of the final products using SEM (Fig. 4e–g) and their optical output using hyperspectral imaging and scatterometry. These analyses demonstrate that only the foil grating (Fig. 3c, d) successfully reproduced the colour pattern from the spider scales (Fig. 3a, b), whereas the flat (Supplementary Fig. 4b) and prism gratings (Supplementary Fig. 4c) did not.

We further simulate the angle-dependent scattering spectra of the designed structures using finite-element modelling (FEM) and plot the simulated reflectance spectra of the three designed structures against their scattering/viewing angles (Fig. 5). The foil grating appears to show all the colours in a rainbow simultaneously in many simulated angles, but the rainbow pattern shows up especially well at three particular angles (Fig. 5a). This agrees well with the properties of the iridescent spider scales (Fig. 3a, b, Supplementary Fig. 4a) and the 3D printed foil grating (Fig. 3c, d). Nevertheless, the flat grating shows a pure colour at each individual viewing angle, and can display most colours sequentially from 40° to 60° (Figs. 5b and 6c, g). By contrast, the prism grating cannot show either the rainbow pattern or the high purity colours (except for exactly 0°) (Fig. 5c). Again, these results matche well with the results of hyperspectral analyses with the 3D printed flat (Supplementary Fig. 4b) and the prism (Supplementary Fig. 4c) gratings.

Fig. 5 Simulated reflectance spectra. The simulated reflectance spectra plotted against different viewing angles based on results from Fig. 6g–i. Each spectrum is smoothed, normalized to the highest value of spectra plotted within the panel and assigned to an arbitrary colour. a The foil grating is capable of showing all the colours in a rainbow simultaneously in many different angles, and the rainbow pattern shows up particularly well at angles 12°, 16°, and 33°. b The flat grating can only show a single high purity colour at each viewing angle, and it takes > 20° rotation to shift the colour from one end of the spectrum to the other end (40°, peak wavelength ~ 400 nm → 60°, peak wavelength just below 600 nm). c The prism grating can only show the rainbow pattern at exactly 0°. In all other angles simulated, it cannot show the rainbow pattern like the foil grating (a), nor high purity colours as the flat grating (b) does Full size image

Fig. 6 Imaging scatterograms and finite element optical simulation. a–e Scatterograms from iridescent scales of M. robinsoni (a), M. chrysomelas (b), from 3D printed flat grating (c), prism grating (d), and foil grating (e). The red circles from the centre out indicate 5°, 30°, 60°, 90° accordingly. The black centre of c–e is due to the 3D printed samples blocking the near-axis reflection in the scatterometer. Reverse-ordered diffraction patterns are observed in a, b, d, and e (see also insets). Fine banded patterns are observed in d and e only. f, Diagram of finite element optical simulations. g–i Results of finite element optical simulations for the 3D printed flat (g), prism (h) and foil (i) gratings. h, i Reverse-ordered diffraction patterns corresponding with d and e. Only i shows increased resolving power (i.e., finer diffraction features) Full size image

Reversed diffraction order

Imaging scatterometry further supports the detailed mechanism of the M. robinsoni and M. chrysomelas diffraction gratings (Fig. 6a, b). The order of the diffraction pattern of the spider scales is reversed relative to a conventional 2D (flat) grating (i.e., red⟶blue rather than blue⟶red, Fig. 6a, b vs. c). The scatterograms of the prism (Fig. 6d) and foil (Fig. 6e) gratings also show reverse-ordered diffraction patterns. This is because the surface gratings are oriented vertically on the airfoil-shaped scales, as previously reported in Pierella butterflies28,29.

The FEM simulated angle-dependent scattering spectra of the designed structures are shown in Fig. 6f–i. To keep the simulated results in accordance with experimental results, we consider a plane-wave Gaussian pulse entering at the normal incident angle, and calculate the angle-dependent light scattering. The results of FEM optical simulation closely agree with the scatterograms showing reverse-ordered diffraction pattern for the prism (Fig. 6h), and foil (Fig. 6i) gratings.

The flat grating produces a discrete diffraction profile (Fig. 6g) allowing only three diffraction orders (−1, 0, 1) in the visible spectrum (400 ~ 700 nm). This is well predicted by the grating equation (Supplementary Note 1)30:

$$m_{\mathrm{h}}\lambda _{\mathrm{h}} = d_{\mathrm{h}}({\mathrm{sin}}\theta _{\mathrm{i}} + {\mathrm{sin}}\theta _{\mathrm{s}})$$ (1)

Here, m h is the diffraction order (or spectral order), which is an integer for a horizontal period of d h , and θ i , θ s are the incident and scattering (diffraction) angles, respectively. The reverse diffraction order can be explained by implementing the vertical grating equation and considering an exact vertical orientation of the surface grating to the surface normal28,29:

$$m_{\mathrm{v}}\lambda _{\mathrm{v}} = d_{\mathrm{v}}({\mathrm{cos}}\theta _{\mathrm{i}} + {\mathrm{cos}}\theta _{\mathrm{s}})$$ (2)

At normal incidence of light (θ i =0), the diffraction wavelength peak for a specific order varies proportionally to the cosine of the diffraction angle, which explains the curve-shaped reverse order diffraction profiles in Fig. 6h, i. To understand the microscopic shape effect, we further modified the vertical grating equation for a triangular horizontal grating. Considering the top angle of the triangular grating α, the vertical grating equation is modified into:

$$m_{\mathrm{v}}\lambda _{\mathrm{v}} = 2d_{\mathrm{v}}{\mathrm{cos}}\left( {\alpha {\mathrm{/}}2} \right)({\mathrm{cos}}\theta _{\mathrm{i}} + {\mathrm{cos}}\theta _{\mathrm{s}})$$ (3)

The superposition of Eq. 1 with Eq. 2 and Eq. 3 is plotted in Supplementary Fig. 5a and b, respectively. The higher order diffraction wavelength peak appears for a scattering angle θ s = 0 at normal incidence of light in the red spectral region due to the vertical surface grating period d v (Supplementary Fig. 5b). This explained the red colour of the reflection at the crest of the spider scales as well as the biomimetic (foil) prototype. Along the gradient of the scales, with increasing scattering angle, the colour changes from red to blue in an acute manner as seen in Fig. 3a. The abrupt microscopic shape of the prism grating might be the cause of the anomalous weak distribution of the diffraction pattern. However, the microscopic shape effect allows a large number of horizontal and vertical mode superposition in foil and prism gratings, thereby improving the diffraction efficiency (i.e., total diffracted power (P) over total incident power (P 0 )).

High resolving power

The detailed fine features in both the experimental and simulated scattering profiles of the foil grating are clearly evident in Fig. 6e, i, respectively. Both prism and flat gratings show a coarser pattern in the scattering profiles than the foil grating (Fig. 6c, d, g, h), despite the fact that only the shape differs between the three types of gratings. These fine scattering features of the foil grating can be explained by its high resolving power (the ability to separate adjacent spectral lines of average wavelength λ) and low angular dispersion properties. The curved surfaces of the foil grating accumulate higher numbers of grooves under specific illumination conditions, in contrast to the flat grating. As the resolving power of a diffraction grating is proportional to the illuminated number of grooves and the periodicity30, the microscopic shape provides an advantage for achieving high resolving power. To be precise, the microscopic triangular shape increases the number of grooves by a factor of cosec(α/2). That results in two times the number of effective grooves when α = 60° for a fixed illumination spot compared to a flat grating with the same period. Moreover, according to Eq. 3, the microscopic triangular shape reduces the angular dispersion (Note: not to be confused with chromatic dispersion, see Supplementary Note 2) for any order m and period d v by a factor of 2cos(α/2). This reduces the angular spread of a spectrum of any order m. Therefore, the smaller angular spread of the foil grating enhances its “degree of iridescence” (here, we define the “degree of iridescence” as the change in reflectance peak wavelength with the same amount of scattering angle variation) compared to regular binary phase gratings.

We further derived the vertical grating equation for the biomimetic foil grating from Eq. (3) by approximating the ellipsoidal curvature of the foil shape:

$$m_{\mathrm{v}}\lambda _{\mathrm{v}} = ({\mathrm{\pi /}}\surd 2)d_{\mathrm{v}}{\mathrm{cos}}\left( {{\it{\alpha }}{\mathrm{/}}2} \right)({\mathrm{cos}}\theta _{\mathrm{i}} + {\mathrm{cos}}\theta _{\mathrm{s}})$$ (4)

According to Eq. 4, the curvature of the foil grating further increases the resolving power and decreases the angular spread by another ~ 10% (π/√8) when comparing the triangular grating with the same top angle (Eq. 3). Overall, the foil grating prototype is about twice as iridescent [(π/√2)cos(α/2), α = 56°, the top angle of the foil prototype] as a conventional 2D grating of the same period (flat). Hyperspectral analyses show that natural spider scales (Fig. 3b and Supplementary Fig. 4a) have an even higher resolving power than the foil prototype (Fig. 3d), suggesting that some aspect of the nanostructure (e.g. airfoil curvature) remains to be replicated and integrated into the next generation of prototypes to provide optimal resolving power closer to the natural system.

Due to the large period (~ 10 μm) of the microscopic grating, the angular separation between adjacent diffraction orders and the free spectral range of each individual order is small (Supplementary Fig. 6). However, introduction of the small-period (670 nm), surface vertical nanogratings modulates the horizontal diffraction orders and increases the diffraction efficiency and resolving power (Fig. 6i). This further demonstrates that resolving power increases due to the nanogratings on the microscopic curved surfaces, rather than simply angle and/or orientation17,18 like that in the prism grating (Fig. 6h). The combination of vertical and horizontal grating effects in iridescent scales of M. robinsoni and M. chrysomelas provides saturated and intense diffraction outputs relative to the previously described natural example of a vertical grating in Pierella butterflies28 (Supplementary Note 3). Due to the large horizontal period of Pierella butterfly scales ( > 50 μm), the diffraction pattern is dominated by the vertical nanograting. We note that the banded pattern shown in the scatterograms of the prism (Fig. 6d) and foil (Fig. 6e) gratings is an artifact of the nanolithography production that results in the superposition of wavelengths (Supplementary Note 4). Since natural spider iridescent scales are partially disordered and not aligned in parallel (i.e., reduction in micrograting effect) (Fig. 2c, d) in the same manner as the synthetic ones (Fig. 4f, g), the banded pattern is not observed in the scatterograms of iridescent spider scales and the scattering pattern is mostly dominated by the vertical grating effect from the airfoil-shaped spider scales (Fig. 6a, b).

Dark melanosome background

We previously detected eumelanin in the black scales of M. robinsoni and M. chrysomelas using Raman spectroscopy31. TEM images of the M. robinsoni black scale sections show that eumelanin is diffusely and heterogeneously deposited in the black scales, because areas of different electron densities (shown in different levels of greyscale) and granular depositions were observed in the TEM micrographs of the scales (Supplementary Fig. 2b&c). Melanosomes are also observed in the hypodermis under the abdominal cuticle for both M. robinsoni (Fig. 7a) and M. chrysomelas (Fig. 7b), as previously reported in M. splendens and M. anomalus 32. The dense layer of melanosomes likely functions to enhance the colour contrast.