(a) Optical properties
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 (a
). 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 [8
]. 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 (b
) and from orange to deep red/purple in the purple region (c
). This indicates that locally the multilayers below the surface, which cause the colour, can slightly vary in layer thickness and/or refractive index.
Figure 3. (a) Dorsal view of a female Japanese jewel beetle, Chrysochroa fulgidissima. The elytra and thorax are green with purple stripes (scale bar, 0.5 cm). (b,c) Details of the elytra. The surface of both the green (b) and purple (c) cuticle has a number of (more ...)
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 (b,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 (a) and atomic force microscopy (b,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 (b), 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.
(a) SEM and (b) AFM of the elytral surface (scale bar, 5 µm). (c) Height profile of the surface along the green line of (b) (note that the abscissa-ordinate aspect ratio is 10 : 1).
(b) Imaging scatterometry
That the elytra act as plane reflectors was confirmed with the ISM of a
. 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 a
). The illuminated area appeared as dotted (a
), 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
) are limited to 5° [11
], 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 b
. The resulting scattering patterns, documented by the far-field (ff) camera C2
) are shown superimposed in c
(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; a
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 c) by completely opening up (i.e. removing) diaphragm D4 (a). 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 (e). 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° (f). We emphasize here that e,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
]. We therefore inserted a (vertically) polarizing filter into the white illumination beam. This results in dark areas in the scatterograms (g
), apparently because the polarized light is poorly reflected in certain angular directions. Upon rotation of the polarization filter, the patterns of g
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 (a). 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 (). The TE- and TM-reflectance bands shifted hypsochromically for both the green and purple elytra (a,b). The TE reflectance increased in amplitude, but the TM reflectance decreased in amplitude (c,d).
Figure 6. Reflectance spectra of the (a,c) green and (b,d) purple elytral pieces for a few angular directions, measured with the spectrometer section of the imaging scatterometer (a). The angular directions (15°, 30°, 45° (more ...)
(c) Polarization- and angle-dependent spectrometry
For detailed spectrometry, especially concerning the angle dependence of the polarization, the set-up with two rotating fibres, diagrammatically shown in a, 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 , 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 (a–f). For TE-polarized light, the peak reflectance increased with an increasing angle of incidence, for both the green and purple areas (g,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 (c,d), but at the wavelengths where the TE-polarized light had a peak, the TM light then featured a trough (g,h).
Figure 7. Angle-dependent reflectance spectra for (a,b) TE- and (c,d) TM-polarized light measured with the fibre optic set-up of a for (a,c,e,g) green and (b,d,f,h) purple elytral pieces. With an increase in the angle of incidence, the peak wavelength (more ...)
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 (a) and purple (b) 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 (c).
Figure 8. Transmission electron micrograph of (a) green and (b) purple sections of the jewel beetle elytra (scale bar, 1 µm). The green and purple areas have about 16 and 12 layers, respectively, in the 1.3 µm thick epicuticle. The average optical (more ...)
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. 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.
A few normalized reflectance spectra measured microspectrophotometrically from single (a) green and (b) red/purple elytral tiles.
Usually, multilayers are treated as a stack of discrete layers that have an alternating low and high refractive index, nl
, with thicknesses dl
, 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
]. Interestingly, although the layers in a
are not discrete but graded, the density profiles have peaks that are sharper than the troughs (c
), so roughly similar to an ideal multilayer where dh
. For the green area of figures –, λmax
≈ 520 nm. Assuming heuristically that dl
= 82 nm and dh
= 78 nm (so that dl
= 160 nm), this would mean that nl
= 1.59 and nh
= 1.67. For the purple areas of figures –, λmax
≈ 670 nm. Assuming heuristically that dl
= 105 nm and dh
= 100 nm (so that dl
= 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 [10
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 (). 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
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 e
), as expected from the interference condition λmax
= 2 (nldl
), where the angles θl
at the interfaces are determined by Snell's Law: nl
) is given in e
by the green line). The peak wavelengths of the TM light were identical to those of the TE spectra for θ0
= 69.3°, where θB
is the generalized Brewster angle [17
], but for θ0
, 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 (e
). The amplitude of the TE spectra increased with θ0
), but the amplitude of the TM spectra decreased with θ0
, and for θ0
the amplitude increased again (c
Figure 10. Angle-dependent reflectance and absorptance spectra of an ideal multilayer with peak reflectance at 600 nm for normal incidence light. The (real parts of the) refractive indices of the 14 layers were nl = 1.60 and nh = 1.68. (a,c) Reflectance spectra (more ...)
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 (b
; see also [9
]). The peak wavelength as a function of angle of incidence was accordingly slightly bathochromic shifted (e
; 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
), is related to the imaginary component of the refractive index by α
) = 4πk
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 (a). 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 (c). 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. b,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 (a,b). From these spectra, the angle dependence of the peak wavelength (e) and amplitude (f) 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 . The absorptance spectra associated with the calculated reflectance spectra are presented in c,d.
Figure 12. (a,b) Reflectance spectra and (c,d) absorptance spectra calculated with the multilayer formalism of the appendix using the refractive index values for the green area of . (e) The peak wavelength of TE-polarized light as a function of (more ...)
presents the parallel results for the purple area, obtained with the refractive index values of c. 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 , but the peak wavelengths were bathochromic shifted. Given the local variability in spectral properties (), we conclude that the TEM section yielding the micrograph of b was from a more deep-red/purple area than that investigated in the reflectance spectra measurements of b,d.
Figure 13. (a,b) Reflectance spectra and (c,d) absorptance spectra calculated with the multilayer formalism of the appendix using the refractive index values for the red area of . (e) The peak wavelength of TE-polarized light as a function of angle (more ...)