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Evolutionary-Optimized Photonic Network Structure in White Beetle Wing Scales

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Evolutionary-Optimized Photonic Network Structure in White Beetle Wing Scales Evolutionary-Optimized Photonic Network Structure in White Beetle Wing Scales Bodo D. Wilts#,∗, Xiaoyuan Sheng∗, Mirko Holler, Ana Diaz, Manuel Guizar-Sicairos, J¨orgRaabe, Robert Hoppe, Shu-Hao Liu, Richard Langford, Olimpia D. Onelli, Duyu Chen, Salvatore Torquato, Ullrich Steiner, Christian G. Schroer, Silvia Vignolini, and Alessandro Sepe# Whiteness arises from the random scattering of inci- of the diffusion approximation is limited, since sin- dent light from disordered structures.[1] Opaque white gle scattering elements are difficult to be identified.[7] materials have to contain a sufficiently large num- To fully understand the correlation between the struc- ber of scatterers and therefore usually require thicker, ture and (optical) properties of complex materials, the material-rich nanostructures than structural color aris- detailed real-space structure in combination with a ing from the coherent interference of light.[2,3] In na- suitable model unravels this relationship. In optics, ture, bright white appearance arises from the dense these include finite-element modeling (FEM) or finite- arrays of pterin pigments in pierid butterflies,[4] gua- difference time-domain (FDTD) techniques, which can nine crystals in spiders,[5] or leucophore cells in the be employed for materials with arbitrary structures.[11] [6] flexible skin of cuttlefish. A striking example of such Distortion-free three-dimensional imaging of biolog- whiteness is found in the chitinous networks of white ical tissue with sub-micrometer resolution in a large [7{9] beetles, e.g. Lepidiota stigma and Cyphochilus sp. volume is cumbersome and often relies on destructive Previous research investigating these beetle structures techniques, i.e. FIB-SEM serial tomography or elec- has shown that the chitinous network is one of the most tron tomography.[7,12] Multi-keV ptychographic X-ray strongly scattering materials in nature and therefore computed tomography (PXCT)[13] overcomes this lim- the question arises whether this structure is evolution- itation, achieving below 15 nm resolution in radiation- ary optimized for strong scattering whilst minimizing hard materials at room temperature.[14] In radiation- the amount of employed material, thus reducing the sensitive materials, however, the PXCT resolution used weight of the organism. The brilliant white reflection to be much worse (> 100 nm), limited by either ra- from Cyphochilus beetles is assumed to be important diation damage at room temperature or by drifts of for camouflage among white fungi and in a shady en- the setup at cryogenic temperatures.[15,16] Here, we vironment. use \OMNY" (\tOMography Nano crYo", see SI), an In contrast to periodic photonic materials, for which instrument that allows cryo-PXCT of biological mate- the optical response is straightforward to calculate, the rials, overcoming these imaging limitation. Cryogenic reflection of light from such disordered network mor- conditions preserve the structure of the sample during phologies requires a detailed knowledge of local ge- the measurement time, and interferometric positioning ometry.[2,3,9,10] For these complex cases, the validity control eliminates thermal drifts.[17] We use OMNY to image single wing scales of the brilliant white bee- Dr. B. D. Wilts, X. Sheng, Prof. U. Steiner, Dr. A. Sepe tle Cyphochilus sp. These measurements provide a full Adolphe Merkle Institute, Chemin des Verdiers, 1700 Fribourg, CH structural characterization of the network morphology #e-mail: [email protected], [email protected] ∗ Contributed equally. within the scales, clearly demonstrating the power of cryo-PXCT to extract quantitative structural informa- Dr. M. Holler, Dr. A. Diaz, Dr. M. Guizar-Sicairos, Dr. J¨orgRaabe Swiss Light Source, Paul Scherrer Institute, 5232 Villigen, CH tion from biological tissues in a non-invasive, damage- resistant fashion. R. Hoppe Institute of Structural Physics, Technische Universit¨at Dresden, Cyphochilus beetles (Coleoptera: Scarabaeidae: 01062 Dresden, Germany Melolonthinae) occur widely across Southeast Asia. X. Sheng, S.-H. Liu, Dr. R. Langford The entire exoskeleton of the beetle (Figure 1a) is Department of Physics, University of Cambridge, JJ Thompson Av- patterned with single wing scales covering the else vel- enue, CB3 0HE Cambridge, UK vet black exocuticle, which can be clearly seen by opti- O. D. Onelli, Dr. S. Vignolini cal microscopy (Figure 1b). Each scale spans approx- Department of Chemistry, University of Cambridge, Lensfield Road, imately 200 µm in length and 60 µm in width. These CB2 1EW Cambridge, UK scales strongly scatter incident light and the reflectance D. Chen, Prof. S. Torquato is more or less constant across the visible wavelength Department of Chemistry, Princeton University, Princeton, NJ range (Figure S3 and[7]). 08544, USA Closer inspection of the white scales using scanning Prof. C. G. Schroer electron microscopy (SEM) reveals that the scale inte- Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany and Department of Physics, Universit¨atHam- rior comprises a network of interconnected, chitinous burg, Luruper Chaussee 149, 22761 Hamburg, Germany fibres surrounded by air.[7{9,18,19] Earlier interpreta- 1 a b c 1 cm d e f X-rays z y x Figure 1: The brilliant white beetle Cyphochilus sp. (a) Macrophotograph. (b) Light micrograph of the scale arrangement on the beetle's elytra. (c) Scanning electron micrograph of the sample pillar on a nanotomography pin-holder obtained from a beetle scale by focused ion-beam milling. (d) Sketch of the X-ray nanotomography setup. The sample is scanned and rotated through the beam (indicated by arrows) while recording the diffraction pattern (see SI for more details). (e) High-resolution tomographic slice (see movies S2, S3) and (f) 3D reconstruction of a 7 × 7 × 7 µm3 inset of the volume obtained by cryo-PXCT of the inner structure of a beetle wing scale. tions of the optical response of the scales[7,9] was ham- reflectivity. pered by the lack of artifact-free, three-dimensional The FDTD modeling results, Figure 2a, show that visualisation of the complex chitinous cuticle struc- the reflectance strongly depends on the orientation of ture, and claims concerning the evolutionary optimized the network volume. The reflectance is significantly white color of the beetle were therefore anecdotal. higher for the typical orientation of the scale (in-plane) To gain insight into the optical function of the and reaches a peak reflectance of ≈ 0.65, while orienta- scales, we investigated the wing scales using PXCT. A tions perpendicular (out-of-plane) to the scale normal first attempt was aimed at reconstructing the network are significantly less reflective, with reflectances of ≈ morphology inside the beetle scale using conventional 0.5. This confirms previous results by Cortese et al.,[8] room-temperature PXCT,[20] achieving a 3D resolution which showed that the time-of-flight of a laser pulse of 70 nm. Significant sample deformation was observed through the structure is strongly anisotropic. by visually comparing projections recorded at the be- To further elucidate the nature of the optical ginning and end of the PXCT measurement at the same anisotropy and its possible function, the network struc- projection angle. ture was digitally stretched and compressed. Figure To overcome this critical issue, the nanotomogra- 2b shows that compression along the z-axis lowers the phy measurements were repeated, using another beetle in-plane reflectance. Stretching of the structure, i.e. scale, at 92 K. Cryogenic conditions dramatically re- making it more isotropic, results only in a slightly duced structural deformation caused by the measure- increased reflectance (0.69 vs. 0.65). This indicates ment (see SI), enabling an isotropic 3D resolution of that the scales' structural anisotropy reduces the thick- 28 nm over a sample volume of ≈ 350 µm3, which ness needed to produce strong scattering resulting in hinges on the minimization of in-situ sample deforma- the observed brilliant whiteness. The scale thickness tion, a typical problem for organic materials. While is functionally important for flying insects, as larger still somewhat worse than that of other techniques, e.g. structures embedded on the wing require more mate- serial transverse sectioning and imaging using trans- rial along the elytra. mission electron microscopy or X-ray crystallography, By affinely expanding or contracting the network cryo-PXCT is non-invasive and does not rely on com- morphology, it is possible to test whether the scale plicated embedding and/or staining protocols. structure has an optimized volume distribution of scat- The spectral properties of the beetles are particu- terers that maximize broadband reflectivity (Figure larly interesting as they provide a very efficient inco- 2c). Uniform compression along all spatial directions herent broad-band reflector with a comparable white- results in a severe reduction of the reflectivity, which ness of common white paper but with a thickness of eventually (below 20% of the original size) disappears only about 1/10 of a typical paper sheet.[7{9,19] To un- all together, i.e. the material becomes transparent. derstand the key parameters governing this unusually This result is unsurprising since for a distribution of strong scattering strength, the rendered 3D network of scattering centers that is comparable to the incident Figure 1f can be directly used to perform FDTD sim- wavelength, propagating light \averages" over its dis- ulations of the structure's optical response to incident crete structure, entering the \optical crowding" or white light. The strength of this approach lies i.e. in “effective medium" regime.[21] Uniform expansion of the ability to digitally modify the network morphology the network morphology changes the broad-band re- displayed in Figure 1f to test the changes in optical flectance very little. This result again indicates that 2 1.0 a data use. in-plane e 00.8.8 out-of-plane c Fundamentally, the scattering power in single and n a 0.6 t multiple scattering systems depends strongly on the re- c e l f 0.4 fractive index.
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