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The elytra of the Japanese jewel beetle Chrysochroa fulgidissima are metallic green with purple stripes. Scanning electron microscopy and atomic force microscopy demonstrated that the elytral surface is approximately flat. The accordingly specular green and purple areas have, with normal illumination, 100–150 nm broad reflectance bands, peaking at about 530 and 700 nm. The bands shift progressively towards shorter wavelengths with increasing oblique illumination, and the reflection then becomes highly polarized. Transmission electron microscopy revealed that the epicuticle of the green and purple areas consists of stacks of 16 and 12 layers, respectively. Assuming gradient refractive index values of the layers between 1.6 and 1.7 and applying the classical multilayer theory allowed modelling of the measured polarization- and angle-dependent reflectance spectra. The extreme polarized iridescence exhibited by the elytra of the jewel beetle may have a function in intraspecific recognition.
Structural colours created by multilayers are widely used in the animal kingdom for display and/or camouflage [1–3]. Striking examples are the jewel beetles, woodboring beetles of the Buprestidae family, which display resplendent metallic colours owing to multilayers in the cuticle . For Euchroma gigantea, the ceiba borer beetle, Durrer & Villiger  concluded that the epicuticle consists of a stack of five melanin-containing layers, 60–80 nm thick and embedded at a regular distance of 60 nm in chitin. Similar layered structures have been demonstrated to exist in other Buprestidae, e.g. the jewel beetles Chrysochroa vittata [6,7], Chrysochroa fulgidissima [8,9] and Chrysochroa raja .
The Japanese jewel beetle, C. fulgidissima, has beautiful, brilliant green elytra with longitudinal purplish stripes. Because of their striking iridescence, this jewel beetle was used as ornament in ancient Japanese times. Indeed, its Japanese name, Tamamushi-no-zushi, derives from archaic Japanese ‘Tama’, meaning jewels or beautiful things and ‘Mushi’, meaning small animals. The famous seventh century Japanese national treasure Tamamushi-no-zushi, the beetle wing shrine, was decorated with innumerous iridescent elytra of C. fulgidissima.
Previous optical studies of the iridescence of jewel beetles have attempted to establish a quantitative description of measured reflectance spectra using multilayer modelling [8,10] and furthermore have shown that the beetles' photonic structures can inspire biomimetic applications . Here, we extend the previous work by presenting a comprehensive set of reflectance spectra, measured as a function of angle and polarization. By using various optical approaches, among others a novel imaging scatterometer (ISM) , we establish that the epicuticle of the beetle's elytra can be well treated as an ideal multilayer interference reflector that creates a strong polarized iridescence. We show that a classical multilayer with a gradient refractive index is an appropriate model for the jewel beetle elytra, providing an in-depth understanding of the Chrysochroa beetle's coloration. The range of the refractive index gradient realized in the jewel beetle cuticle appears to be surprisingly narrow.
Chrysochroa fulgidissima specimens were collected at the campus of the Hamamatsu University School of Medicine, in Shizuoka Prefecture, Japan, from June to August 2004.
The elytra were removed from the body, using a razor blade and fine scissors, for studying their anatomy. Details of the elytral surface were photographed with an Olympus SZX16 stereomicroscope equipped with an Olympus DP70 digital camera, and with a Philips XL-30 ESEM scanning electron microscope (SEM).
The elytral surface was scanned with a Veeco Dimension 3100 atomic force microscope (AFM), used in dynamic mode with Olympus AC240TS tips with tip radius less than 7 nm.
For transmission electron microscopy (TEM), the elytra were immersed in primary fixative solution (2.5% glutaraldehyde, 2.5% paraformaldehyde in 0.1 M phosphate buffer, pH = 7.4) and placed for 12 h in a refrigerator at 4°C. Tissues were rinsed several times in phosphate buffer solution, post-fixed for 2 h with 1 per cent OsO4 in the same buffer at room temperature, dehydrated through a graded series of ethanol solutions and after transfer to propylene oxide embedded in a mixed solution of Epon 812 (TAAB) and Araldite (TAAB). Dehydration effects of the dry cuticle were assumed to be of minor size. Sections were cut with an ultramicrotome and picked up with 100-mesh copper grids. The sections were double-stained with 2 per cent uranyl acetate and 0.4 per cent lead citrate solution for 5 and 3 min, respectively, and observed with a JEM-1220 (JEOL) transmission electron microscope at 80 kV emission voltage.
Using Matlab, the TEM micrographs revealing the multilayer in the epicuticle were evaluated by determining the average value of the image pixels in 10 nm thick layers, I(z), where z is the coordinate perpendicular to the cuticle surface. Subsequently, the optical density, D(z) = −log10[I(z)], was calculated, assuming that the density is proportional to the concentration of electron-dense material.
The spatial distribution of the light scattered by the elytra was visualized with an ISM, a diagram of which is shown in figure 1a. A small piece of an elytron was therefore glued to a tip of a glass micropipette. The wing piece, the object, was positioned in the first focal plane (F1) of an elliptical mirror (E), where it was viewed and photographed via a small, about 5°, axial hole in the mirror with camera C1 (Jenoptik ProgRes C10). The object was illuminated with the primary beam, delivered by light source S1 via diaphragms D1,2 and lenses L1,2, and/or by the secondary beam, from light source S2 via diaphragms D3–5, lenses L4,5 and half-mirror H1. The light scattered by the object into the frontal hemisphere was focused by the elliptical mirror in its second focal plane, F2, and imaged by lens L6 in its back focal plane, I, which thus received the object's spatial distribution of scattered light. An opaque object positioned axially in plane I served as a spatial filter, blocking the transmitted light from the primary beam. The scattered light pattern of plane I was imaged by lens L7 onto camera C2 (Olympus DP70). The images, corrected for the optical distortions of the set-up, were converted into polar plots (figure 5). Figure 1b diagrammatically shows how light from the axial primary beam is reflected by a specular object rotated in steps of 15°, from 0° to 45°, and figure 1c diagrammatically shows how light from the secondary beam with angles of incidence 30° and 60° is reflected by a specular object, normal to the axis of the scatterometer. The red circles in the hemispheres of figure 1b,c indicate angular directions of 5°, 30°, 60° and 90°, which are also drawn in the polar plots.
The set-up shown in figure 1a is a slight modification of that described by Stavenga et al. (; see also [12,13]). The added facility, a CCD detector array spectrometer (SP; AvaSpec-2048-2, Avantes, Eerbeek, The Netherlands), samples a small area of the scattered light pattern via half-mirror H2, lens L8 and one channel of a bifurcated light guide (effective aperture approx. 4°). The other channel of the bifurcated light guide was connected to a source S3, the light of which was focused by L8 onto mirror M, which is conjugated to plane I by half-mirror H2. The light beam reflected by mirror M and subsequently reflected by H2 towards lens L7 reached camera C2, and thus allowed identification of the area sampled by spectrometer. Laterally displacing the fibre tip together with lens L8 allowed sampling of any area of choice of the scattering pattern in plane I, and hence of any chosen spatial direction of the light scattered by the object. A small piece of MgO served as a white diffusing reference object. The differences in spatial scattering profiles of the object and reference were accounted for in the calculations of the reflectance spectra.
The reflectance spectra of small elytral areas were measured with a microspectrophotometer (MSP), consisting of a xenon light source, a Leitz Ortholux microscope and an S2000 fibre optic spectrometer (Ocean Optics). The microscope objective was an Olympus 20×, NA 0.46.
The polarization and angle dependence of the reflectance spectra of the elytra were measured by using two optical fibres (figure 2a). One end of the first optical fibre was connected to a deuterium/halogen light source (AvaLight-D(H)-S) or a xenon lamp, and its other end was mounted on a goniometer together with a small lens, which focused the fibre tip at the goniometer's rotation axis. The second fibre was mounted with one end at a second goniometer, together with a similarly focusing lens and a polarization filter that could be rotated around the optical axis of lens and fibre entrance; the other end was connected to a CCD detector array spectrometer (AvaSpec-2048-2). The rotation axes of the two goniometers coincided and the two fibres rotated in the same plane. The patch to be measured was positioned in that plane, at the axis of rotation of the goniometers. The aperture of the fibres was 5° (full width at half maximum, FWHM) and the distance of the tips to the centre of the illuminated spot was 4 and 12 cm, respectively. The receiving fibre thus sampled a larger area than the illuminated spot, but it did not fully capture all the reflected light. The spatial reflectance profile of a mirror illuminated with a static illumination fibre and measured with a rotating receiving fibre was approximately Gaussian, with aperture 5° (FWHM; figure 2b). The beetle cuticle approximated an ideal reflector; the aperture of the reflected light was 12° (FWHM), independent of the angle of light incidence (figure 2b). Therefore, at all illumination angles, the same fraction of the reflected light was captured. In the reflectance measurements, a white diffusing reference tile (Avantes WS-2) served as reference. The reflectance spectra were corrected for the difference in spatial scattering properties of the object and reference.
The reflectance of the multilayer in the epicuticle of the jewel beetles' elytra was calculated by applying the classical multilayer theory for dielectric media (see the appendix). Both the real (n) and imaginary (k) part of the refractive index of the cuticle were assumed to be proportional to the optical density derived from the TEM micrographs: n(z) = 1.58 + aD(z) and k(z, λ) = b κ(λ)D(z), with a = 0.15 and b = 1 for the green area, and a = 0.1 and b = 2 for the purple area, with κ(λ) = (λ/4π)*α(λ) and α(λ) the absorption spectrum for melanin, determined from transmission measurements, normalized at 500 nm (the dimension of α is µm−1 when taking λ in µm; see figure 11a). The parameters a and b were determined heuristically to optimize agreement between the model and the experiment.
The Japanese jewel beetle, C. fulgidissima, has a brightly reflecting cuticle in virtually all body parts. The elytra, which mainly determine the beetles' appearance when at rest, reflect maximally in the green region, with longitudinal, dark-purple stripes interrupting the pattern; at the borders in between the green and purple areas, the cuticle is red/orange (figure 3a). The female and male are coloured almost identically, and the only apparent difference between the two sexes is that the males have more prominent eyes . Observing the elytra at higher magnification reveals that the colour of the elytral surface is not unique and can vary between yellow and violet in the green region (figure 3b) and from orange to deep red/purple in the purple region (figure 3c). This indicates that locally the multilayers below the surface, which cause the colour, can slightly vary in layer thickness and/or refractive index.
The elytral surface is dotted with distinct pits having distances about 100 µm together with numerous minor indentations, with distances of the order of 10 µm (figure 3b,c), which form a tessellated pattern of more or less hexagonal tiles. The irregular surface will affect the reflection properties, and therefore we investigated the elytral surface with scanning electron microscopy (figure 4a) and atomic force microscopy (figure 4b,c). The surface in between the minor indentations appeared to be indeed not flat, but the radius of curvature of the tiles is rather large, about 100 µm (figure 4b), so that the normal to the surface changes over no more than approximately 6–7°. Over a large area, the direction of the normal to the surface will vary more, of course, especially near the pits and indentations, but the latter structures make up only a minor part of the surface, and therefore we conclude that in fair approximation the elytra will locally act as approximately plane reflectors.
That the elytra act as plane reflectors was confirmed with the ISM of figure 1a. Small pieces of the green as well as purple elytral areas were mounted in the scatterometer and, using the white light primary beam (S1) with a small diaphragm (D1), an area with diameter 40 µm was illuminated (indicated by the circle in figure 5a,b). The illuminated area appeared as dotted (figure 5a,b), with each dot representing a tile of the tessellated cuticle, because the aperture of the primary beam as well as that of the near-field (nf) camera C1 (figure 1a) are limited to 5° , and thus the scattered light from the rims of the tiles could not be captured by the camera. The scattering of the illuminated elytral piece was investigated in four cases where the angle of incidence was 0°, 15°, 30° and 45°, respectively. This was realized by rotating the elytral pieces around an axis perpendicular to the direction of illumination in steps of 15° as indicated in figure 1b. The resulting scattering patterns, documented by the far-field (ff) camera C2 (figure 1a) are shown superimposed in figure 5c (green) and d (purple). For both the green and the purple elytra, the scattering patterns were directionally very restricted spots, with half-width of the spatial profile about 10°, centred around the directional angles 0°, 30°, 60° and 90° (as expected for an ideal mirror; the central reflection spot, representing reflection on the surface oriented perpendicularly to the illuminating beam, is incomplete, because of the 10° central black hole in the elliptical mirror and the blocking spatial filter in plane I; figure 1a).
The beetle's cuticle is of course not an ideal mirror, but a multilayer reflector, as witnessed by the dependence of the colour of the reflected spots on the angle of illumination. Illumination of the cuticle with a white, wide-aperture beam should therefore result in a variety of colours. A wide-aperture illumination was realized with the secondary beam (see the diagram in figure 1c) by completely opening up (i.e. removing) diaphragm D4 (figure 1a). With unpolarized light, a green elytron reflects green into angles up to about 45°, which changes at larger angles into blue and violet, and at angles above 70°, a broad-band white reflection results (figure 5e). The angular scattering pattern is virtually circular and symmetrical, except for the black bar at 180° of the polar diagram, which is due to the pipette holding the elytral piece obstructing the light reflected by the elliptical mirror. The purple elytral piece reflects dark-red/brown into angles up to about 30°, changing into red/orange at angles around 60°, and into yellow and broad-band white above an angle of incidence and reflection of 60° (figure 5f). We emphasize here that figure 5e,f demonstrates that the ISM in a single picture captures the angle dependence of the colour of the reflected light.
It is well known that multilayer reflectance not only depends on the angle of illumination, but also on the degree of polarization [14–16]. We therefore inserted a (vertically) polarizing filter into the white illumination beam. This results in dark areas in the scatterograms (figure 5g,h), apparently because the polarized light is poorly reflected in certain angular directions. Upon rotation of the polarization filter, the patterns of figure 5g,h rotated simultaneously, demonstrating the rotational symmetry of the elytral scattering.
The angle-dependent reflection of the polarized light was studied in more detail with the spectrometer attachment of our scatterometer (figure 1a). The spectra for both TE- (transverse electric or s-) and TM- (transverse magnetic or p-) polarized light were obtained for a few different angular directions (15°, 30°, 45° and 60°) in the vertical plane of the scattering pattern (figure 6). The TE- and TM-reflectance bands shifted hypsochromically for both the green and purple elytra (figure 6a,b). The TE reflectance increased in amplitude, but the TM reflectance decreased in amplitude (figure 6c,d).
For detailed spectrometry, especially concerning the angle dependence of the polarization, the set-up with two rotating fibres, diagrammatically shown in figure 2a, appeared to be more flexible than the scatterometer. Small spots of the green and purple areas of the elytra were illuminated with focused white light from one fibre and the reflected light was collected by the second fibre, which was equipped with a polarizing filter. With about normal illumination, the reflectance spectra obtained from various areas showed a distinct band, peaking at 500–550 nm (green) or 650–720 nm (purple), with half-width approximately 100 (green) and approximately 150 nm (purple). As to be expected from the scattering patterns of figure 5, the reflectance spectra strongly depended on the angle of light incidence. We changed the angle of light incidence, θ0, in steps of 10° when θ0 < 50° and in steps of 5° when θ0 > 50°, and simultaneously changed the angle of the measurement fibre, symmetrical with respect to the normal to the elytral surface. It thus appeared again that for both TE- and TM-polarized light, the peak wavelength shifted to shorter wavelengths (figure 7a–f). For TE-polarized light, the peak reflectance increased with an increasing angle of incidence, for both the green and purple areas (figure 7g,h), but for TM-polarized light, the peak reflectance decreased, becoming minimal at an angle of incidence of approximately 65–70°; at larger angles, the overall spectral reflectance increased again (figure 7c,d), but at the wavelengths where the TE-polarized light had a peak, the TM light then featured a trough (figure 7g,h).
The observed polarization-dependent phenomena are quite characteristic for a multilayer. To interpret the angle-dependent reflectance spectra quantitatively, the thicknesses of the layers and the values of the refractive indices have to be known. The multilayer thicknesses were obtained by TEM of pieces of cuticle from the green (figure 8a) and purple (figure 8b) areas. In both cases, an about 1.3 µm thick distal sheet, forming the epicuticle, features several layers with alternating high and low electron density, about 16 in the green area and about 12 in the purple area. The more proximal exocuticle is approximately uniformly stained. The electron density is presumably related to the refractive index of the material that creates the light-reflecting multilayer. The average density of the images calculated in 10 nm thick slabs parallel to the surface appeared to oscillate more or less sinusoidally as a function of depth, with oscillation periods about 160 and 205 nm for the green and purple areas, respectively (figure 8c).
The transmission electron micrographs are of course from a very local area and not necessarily representative for all areas of the elytra cuticle. To assess the variability of the cuticular properties, we did not perform extensive anatomy, but instead measured reflectance spectra of several single tiles of the green and purple areas wtih a microspectrometer. We thus found that the reflectance spectra are somewhat variable in both peak wavelength and amplitude. Figure 9 gives a few spectra, normalized for clarity's sake. The reflectance amplitudes of the green and purple areas were rather similar, but varied within a range of a factor 1.5. Presumably, therefore, the layering of the elytra will vary accordingly.
Usually, multilayers are treated as a stack of discrete layers that have an alternating low and high refractive index, nl and nh, with thicknesses dl and dh, respectively. In the case of a so-called ideal multilayer, the optical path length of the layers is constant, nl dl = nh dh, and for normal incident light, the peak reflectance then is at wavelength λmax = 4nl dl = 4nh dh [3,16]. Interestingly, although the layers in figure 8a,b are not discrete but graded, the density profiles have peaks that are sharper than the troughs (figure 8c), so roughly similar to an ideal multilayer where dh < dl. For the green area of figures 5–7, λmax ≈ 520 nm. Assuming heuristically that dl = 82 nm and dh = 78 nm (so that dl + dh = 160 nm), this would mean that nl = 1.59 and nh = 1.67. For the purple areas of figures 5–7, λmax ≈ 670 nm. Assuming heuristically that dl = 105 nm and dh = 100 nm (so that dl + dh = 205 nm), this would mean that nl = 1.60 and nh = 1.68. These refractive index values are similar to those estimated for the green and red areas of the elytra of C. raja where for normal light incidence the reflectance peak wavelengths are about 550 and 610 nm. The values nl = 1.55 and nh = 1.68 were obtained by modelling the multilayers as a stack of 16 discrete layers with varying thicknesses .
To improve our insight into the polarization- and angle-dependent reflectance spectra of a multilayer, we have calculated the spectra for an ideal multilayer consisting of 14 layers that maximally reflects normal incident light with wavelength 600 nm (figure 10). We first considered the case that the layers were non-absorbing and had alternating refractive indices nl = 1.60 and nh = 1.68. At the front side, the stack faced the air, with refractive index n0 = 1, and at the end, the refractive index was taken to be (nl + nh)/2. Figure 10a,c presents the reflectance spectra for TE- and TM-polarized light for angles of incidence, θ0, increasing in steps of 10°. The peak wavelength, λmax, of the TE spectra decreased with an increasing angle of incidence (blue symbols in figure 10e), as expected from the interference condition λmax = 2 (nldl cos θl + nhdh cos θh), where the angles θl and θh at the interfaces are determined by Snell's Law: nl sin θl = nh sin θh = n0 sin θ0 (λmax(θ0) is given in figure 10e by the green line). The peak wavelengths of the TM light were identical to those of the TE spectra for θ0 < θB = 69.3°, where θB is the generalized Brewster angle , but for θ0 > θB, the spectral shape of the TM spectra was inversed so that then the trough wavelength of TM spectra equalled the peak wavelength of the TE spectra (figure 10e). The amplitude of the TE spectra increased with θ0 (figure 10a,g), but the amplitude of the TM spectra decreased with θ0 for θ0 < θB, and for θ0 > θB the amplitude increased again (figure 10c,g).
In the second case considered, the high refractive index layers were absorbing, with imaginary component k = 0.1. For both TE- and TM-polarized light, the resulting reflectance spectra showed an enhanced reflectance at the long-wavelength side of the peak (figure 10b,d; see also [9,13]). The peak wavelength as a function of angle of incidence was accordingly slightly bathochromic shifted (figure 10e; red line symbols and line). The absorptance spectra associated with the constant k showed a trough where the reflectance spectra had a peak, and outside that wavelength range, the absorptance gradually decreased with increasing wavelength. This was to be expected, because the absorption coefficient, α(λ), is related to the imaginary component of the refractive index by α(λ) = 4πk/λ.
Transmission measurements of the elytra demonstrated that the absorption decreases much more strongly with wavelength than follows from a constant k. In our further calculations, we therefore have used a wavelength-dependent imaginary component of the refractive index derived from the transmission measurements (figure 11a). Furthermore, the graded density of the transmission electron micrographs strongly suggests that treating the beetle epicuticle as a stack of discrete layers with constant refractive indices is a very crude approximation (figure 8c). A better approximation presumably is that the refractive index is a function of the derived optical density. This was implemented in a model treating the multilayer as a large stack of thin (10 nm thick) layers with a refractive index, the real and imaginary components of which are linearly proportional to the determined average density. Figure 11b,c presents the depth profiles of the real and imaginary parts of the refractive index for the green and purple areas that were used in the calculations of the polarization- and angle-dependent reflectance spectra (figure 12a,b). From these spectra, the angle dependence of the peak wavelength (figure 12e) and amplitude (figure 12f) were derived. The range of real and imaginary parts of the refractive index was chosen so that the calculated reflectance spectra resembled those for the green area of the experiment of figure 7. The absorptance spectra associated with the calculated reflectance spectra are presented in figure 12c,d.
Figure 13 presents the parallel results for the purple area, obtained with the refractive index values of figure 11c. Using similar refractive index values as those chosen for the green area produced reflectance spectra with a similar shape as those for the purple area of figure 7, but the peak wavelengths were bathochromic shifted. Given the local variability in spectral properties (figure 9), we conclude that the TEM section yielding the micrograph of figure 8b was from a more deep-red/purple area than that investigated in the reflectance spectra measurements of figure 7b,d.
Reflecting multilayers in insect cuticle have been extensively studied in various beetle species [18–22]. In transmission electron micrographs, the multilayers are recognized as a stack of layers with alternating high and low electron density. The multilayers in the epicuticle of jewel beetles exhibit a strong polarized iridescence, a well-known property of optical multilayers, which has been amply applied in reflecting polarizers (e.g. ). The jewel beetle's multilayers are presumably homogeneous, causing only linear polarization, whereas circular polarization is a dominant feature in scarab beetles [18,20,23,24]. For scarab beetles, Caveney  concluded that the reflective layers had a high concentration of uric acid, causing a high refractive index value of about 1.70. Durrer & Villiger  noticed for the elytra of the buprestid E. gigantea that the distribution of the high refractive material was patchy, but without further evidence they stated that the material would be melanin, with a refractive index of 2.0. In their wake, Schultz & Rankin  concluded that Cicindela tiger beetle cuticle contains melanoprotein producing a refractive index near 2.0. A refractive index value of 2.0 for beetle cuticle is most probably much too high [8,10,19], but we agree with Durrer & Villiger  that the material of the cuticular multilayers, probably melanin, is not deposited in discrete layers, as is commonly assumed (e.g. [10,21,25]).
Taking into account that for multilayers the wave nature of light is of predominant importance, we concluded that the refractive index profile of a multilayer changes gradually instead of stepwise. The measured reflectance spectra were modelled with refractive index values that varied between 1.60 and 1.70 (figures 12 and and13),13), where the latter value is similar to the maximal refractive index values derived for scarab beetle cuticle by Caveney  and for C. raja by Noyes et al. . The modelling showed that the peak wavelength and amplitude of the reflectance spectra are quite sensitive for the range of the refractive index. In the presence of absorption, the side bands start to vanish (figure 10a,b). Side bands were indeed not prominent in the reflectance spectra measured with the scatterometer and the two-fibre set-up (figures 6 and and7),7), but distinct side bands were found in the reflectance spectra measured microspectrophotometrically from individual elytral tiles (figure 9a). The spectra measured from neighbouring tiles appeared to vary in amplitude and peak position, and therefore the spectra from areas comprising several tiles would have lost fine structure. We therefore tentatively conclude that modelling of the spectra from the larger areas overestimates the imaginary component of the refractive index. In other words, the absorptance spectra calculated for the epicuticle (figures 12c,d and and1313c,d) may be somewhat too large. Given the variability in the experimental spectra and the difficulty of connecting the local anatomy with the spectral properties of the elytra, a fully quantitative treatment is presently impossible. Nevertheless, we expect that the actual profiles of both the real and imaginary parts of the refractive index will not strongly deviate from the present estimates.
The range of the refractive index appears to be quite narrow, but with a large stack of 16 (green) or 12 (purple) layers, a bright reflection nevertheless results. In fact, the spectral reflectance values of the jewel beetles are not very different from those of green leaves, which however usually scatter rather diffusely. Female jewel beetles remain stationary, with closed elytra, on leaves or twigs of a host tree when searched by male jewel beetles . Males can detect a potential female mate from a distance of several metres, but the applied detection criteria have not yet been satisfactorily established. Studies with models constructed from male and female elytra showed that they were equally attractive, but models made from light-emitting diodes with emission spectra similar to those of the elytral reflection spectra were fully unattractive . Imaging scatterometry of the jewel beetle's elytra demonstrated that the light reflected at angles around 60° is highly (linearly) polarized. This will determine the appearance and thus the visibility of the beetles in nature. Polarized reflection patterns appear to be widespread among insects [26,27] and can serve for intraspecific signalling . Our present hypothesis, that the polarized iridescence exhibited by the reflecting elytra provides valuable clues for the presence of a sitting female, will be tested in the near future.
We thank S. Mouchet and M. F. Wehling for reading the manuscript. SEM and AFM were performed within the University of Groningen Materials Science department (Prof. J. Th. de Hosson, Dr G. Palasantzas, G. H. ten Brink). Financial support was given by AFOSR/EOARD grant no. FA8655-08-1-3012.
The reflectance and transmittance of a multilayer can be effectively calculated with a matrix formalism describing the propagation of light from layer to layer. Yeh  provides a most accessible treatise, which is summarized here and slightly expanded.
We consider a general multilayer consisting of N infinite wide layers of homogeneous dielectric media, separated by parallel surfaces, faced by media with real refractive indices n0 and nN+1 (figure 14). The layer thickness is dj and the (in general complex) refractive index is ñj = nj − ikj (j = 1, 2, … , N); the imaginary part of the refractive index, kj, is related to the absorption coefficient of the medium, αj, by kj = αjλ/4π, where λ is the light wavelength. The propagation of light through this multilayer is governed by Snell's Law:
where the angle of incidence θj of the light ray at the interface of media j and j + 1 can be complex. The light propagation through the multilayer is described by the transfer matrix
with pj = 1 and qj = ñj cos θj for TE waves, pj = cos θj and qj = ñj for TM waves and sj = exp (ij), with j = 2/λ ñj dj cos θj. The reflectance of the multilayer then is
and the transmittance is
Diagram of light propagation through a multilayer existing of N layers with refractive indices nj, j = 1, 2, … , N, bordered by media with refractive index n0 and nN+1. The angles of light incidence and refraction at the interface of media j and ...
One contribution of 20 to a Theme Issue ‘New directions in biological research on polarized light’.