1. Introduction

As techniques for nano-engineering complex optical media are developed and refined, there is a growing awareness of the synergy among artificial and natural systems [1,2]. There is a vast body of literature documenting functional colors in animals as a result of chemical pigmentation and bioluminescence. However, there is another category for this phenomenon, structural coloration. Structural colors result from the selectively enhanced reflection of incident light due to the physical nature of a structure. Between the systems for this structural phenomena are: (i) structures causing random scattering of light waves, (ii) single or multiple thin-layer reflectors and (iii) surface gratings [3,4].

We have focused our study on two optically different types of beetles which display this phenomenon of structural coloration, the Chrysina aurigans and the Chrysina limbata, Coleoptera: Scarabaeidae [5,6], the first one with a brilliant golden appearance and the second displaying a silver-like brilliant color. These beetles are two of the most spectacular tropical forest specimens because of their gold and silver metallic colors (see Fig. 1 ), and they constitute part of the rich biodiversity found in Costa Rica [7]. They measure between 25 and 35 mm of length and they are located in Central America and Southeast Mexico, especially in the mountain ranges 600 meters above sea level. The specimens used in our studies were captured in the University of Costa Rica’s Biological Reserve located in Alajuela, Costa Rica. This work will describe spectral photometric measurements of non polarized and circularly polarized light reflected by specimens of C. aurigans and C. limbata. Optical measurements using normal incidence of non polarized radiation are described in Section 2, and Section 3 is focused on modelling the reflection spectra characterizing broad band reflectors from application of a multilayer-transfer-matrix formalism. The measured reflection spectra show a low reflection band at low wavelengths followed by a structured high reflection band consisting of a sequence of maxima and minima reflectance values. Section 4 describes the experimental setup used to measured reflection of circularly polarized light from the beetles’ elytra. The measurements display the capacity of the beetle’s elytra for reflecting circularly polarized light in a differential way.

 

Fig. 1 Pictures of the Chrysina aurigans (left) and the Chrysina limbata (right) beetle specimens displaying their brilliant golden- and silver-like appearance, respectively.

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2. Reflection of non polarized radiation

Direct reflection spectra were taken from samples of the C. aurigans and C. limbata dorsal elytra. The reflection spectra were measured with an Avaspec 2048 fiber optic spectrometer in the range between 300 and 750 nm under non polarized light illumination with normal incidence. Spectra were taken from different points of the dorsal area and they show the same general features, the main difference being the intensity of the reflected light, which may be influenced by the difficulty on having the incident light falling perpendicularly on a curved elytra surface. To compensate for the curvature on the elytra, it was necessary to build an apparatus which allowed us to shine light normally on different points of the elytra keeping constant other variables. The device constructed to measure the direct reflection of the elytra is shown in Fig. 2 . It was designed to follow the contour of the beetle’s body having the probe perpendicular and with a constant distance from it at each position. The fiber optic probe is fixed on the centre of the plane and it can be adjusted up and down following the $z\text{'}-axis$. The black knob at the right allows displacement in the $x\text{'}-axis$, perpendicular to the $z\text{'}-axis$ _, and the knob in the left allows rotation about the y-axis. The video linked to Fig. 2 shows the available displacements and rotations when using the device to measure reflection spectra (see Media 1). Reflection from a calibrated mirror was used as reference.

 

Fig. 2 Device used to carry out the direct reflectance measurements under normal incidence of non-polarized light on the elytron of a beetle. The allowed displacements and rotations of the probe holder allow us to focus the beam on the beetle’s elytron perpendicularly, as shown in Media 1.

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The reflection spectra from the C. aurigans has a sharp drop for wavelengths shorter than 525 nm, a feature similar to the trend displayed in the reflectivity spectrum of gold, when it is evaluated from its optical constants: the refractive index and the extinction coefficient [8], as shown in Fig. 3 where we have also included the eye sensitivity curve and reflection spectra taken from the beetle’s head and from a hindmost section. The gold reflectivity $R(\lambda )=\left[{(n-1)}^2+k^2\right]/\left[{(n+1)}^2+k^2\right]$ with $n=n(\lambda )$ as the refractive index and $k=k(\lambda )$ as the extinction coefficient, with $\lambda$ as the wavelength of the incident radiation, has been included in Fig. 3 only for comparison purposes: it shows a wavelength range of low reflectivity values close to 40% followed by a range of increasing high reflectivity values, approaching the 95% in the red side of the visible spectrum.

 

Fig. 3 Reflection spectra of C. aurigans beetle when illuminating an area of its head or a rear section with non-polarized radiation under near normal illumination. The reflectivity spectrum of gold, evaluated from its optical constants taken from the literature [8], and the eye sensitivity curve are included in the figure.

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The reflection spectra of the C. aurigans also show two bands: one of low reflection on the blue side of the visible and other of high reflection on the red side. Of course different mechanisms are involved in each case to produce similar metallic appearance of C. aurigans beetles and gold samples. In this last case the reflectivity spectrum is characterized by low absorption of light due to surface screening of free electrons at low energies (large wavelengths), and by increased absorption owing to transitions of bound electrons at high energies (low wavelengths).

An interesting feature in this reflection spectrum from the elytra of the C. aurigans beetle is the oscillations in the high reflection range (λ >545 nm) with minima (or maxima) separated by 16 ± 1 nm, as seen in Fig. 4 . One could think initially that these well displayed oscillations are consistent with an interference pattern (Fabry-Perot interference fringes) by reflection from a multilayered structure located through the epicuticle, the exocuticle or the endocuticle [9]. But this explanation should be detailed because in the measured reflection spectra the wavelength distance between successive maxima or minima is basically constant, while interference fringes are characterized by an increasing separation with increasing wavelength. This is so even when the normal dispersion in the refractive index of the dielectric materials involved is neglected, and when constant values of the thicknesses of the layers through the cuticle are assumed. Normal dispersion means decreasing values of the refractive index with visible wavelengths. Reports on the chitin’s refractive index spectral dependence are very scarce. According to findings of Berthier et al., the chitin refractive index shows an anomalous dispersion in the range of visible wavelengths [10]. This could indicate the presence of an absorption band at lower wavelengths, with a tail approaching the visible, which would explain the low reflection bands observed in the spectra of C. aurigans and C. limbata beetles. The presence of melanin pigments at the bottom of the reflector multilayers would explain this absorption band. Melanin absorption increases with decreasing wavelength when approaching the ultraviolet wavelength range from the visible [11]. The Berthier et al. analysis was based on applying the Maxwell-Garnett model to evaluate the effective refractive index of cuticular structures in the scales of Morpho menelaus butterflies, for transverse electric and transverse magnetic incident light. They define transverse electric and transverse magnetic normal incident fields in terms of the orientation of the electric field with respect to the ridges along the lamellae in the scales of the butterfly’s wings. With these effective refractive indices they were able to fit very well, measured hemispherical reflection spectra taken from Morpho menelaus wings. In the case of non polarized incident light an average refractive index for chitin must be considered for each wavelength. Figure 5 depicts the spectral dependence of the average chitin refractive index, evaluated from the curves reported by Berthier et al. in their Fig. 9 .

 

Fig. 4 Reflection spectra from the C. aurigans and C. limbata beetle’s dorsal elytra. They are consistent with the color observed under white light illumination. Both show sequences of maxima and minima, as explained in the text.

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Fig. 5 Spectral dependence of the average refractive index of chitin, evaluated from the curves reported by Berthier et al. [10].

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Fig. 9 Smoothed reflection spectra of chirped multilayer structures with linearly decreasing values in the thickness of the sequence of layers, and low contrast between the refractive indices of successive layers. The number of layers is 68 for both cases: (a) C. aurigans, and (b) C. limbata. The larger and lower thicknesses values were set as indicated in the text. The blue thin solid lines correspond to reflection measurements.

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Within the context of a multilayer-transfer-matrix formalism [12], we have used these values of the chitin refractive index to evaluate reflection spectra of a stack of chitin-air layers of homogeneous thicknesses, with the aim of elucidating if the wavelength separation between interference fringes increases or decreases with wavelength. Our evaluations indicate an increment in the wavelength separation between successive maxima or minima. This effect is still more significant for dielectric materials with a normal dispersion of its refractive index [13]. As a consequence, the sequence of maxima and minima in the reflection spectra of the beetle’s elytra considered cannot be attributed to interference between successive cuticle layers of homogeneous thicknesses.

Going back to the reflection spectra displayed in Fig. 4, the sequence of maxima and minima is superimposed on a background oscillation or modulation curve showing two peaks and one valley, within the range of wavelengths considered. This background oscillation is similar to that characterizing the normalized scattering cross section of spherical dielectric particles [14]. Beetles with similar golden appearance, the C. gloriosa and the C. resplendens, do not show these well defined oscillations in their reflection spectra and the drop in the shorter wavelengths is less pronounced [15]. This probably involves mechanisms to create the golden metallic appearance related to different morphological structures through the elytra of the beetles, a topic which is being considered for further studies. Qualitatively, the reflection spectra of the C. aurigans resemble those reported in the literature for colloidal crystals. Rengarajan et al. have obtained samples of colloidal crystals by employing a convective self-assembly technique [16,17]. Their samples consist of layers of spherical particles distributed through a face-centered cubic lattice, with diameters between 250 and 350 nm, and with increasing dispersion in particle size.

The spectrum from the C. limbata beetle is fairly constant in the whole visible range, as expected from its visual appearance, and it is not reflective in the UV, i.e. for λ<390 nm, with a less pronounced reflection edge as compared with the edge displayed in the reflection spectrum of the C. aurigans. The reflectivity of silver, also evaluated from its optical constants [8], is over 97% for all visible wavelengths. Through the visible wavelength range, the C. limbata reflection spectrum also shows a background oscillation pattern with a superimposed ripple structure whose periodicity decreases toward longer wavelengths, from 30 to 18 nm. In this case the background oscillation shows three peaks and two valleys, within the spectral range considered. The ripple structure, as compared with the sequence of maxima and minima displayed in the reflection spectrum of the C. aurigans, is not as well defined and this could be related to the presence of structural defects. Spectra from other silver looking beetles such as the C. clypealis show similar oscillations but the broad peak is not displayed [15]. Despite the metallic appearance of both species, the surface elytra are not completely smooth and they show a rough surface perceptible without optical aid, which means that there is an important component of non-specular or diffuse reflection. The specular reflection spectra for the two beetles under study are shown in Fig. 4. From the measured reflection spectra ($R_b(\lambda )$), the solar spectral irradiance $I_S(\lambda )$ AM1.5 [18], and the tristimulus values specified by the International Commission on Illumination [19,20] (CIE: Commission Internationale de l’Eclairage), we evaluate the chromaticity coordinates (x,y) corresponding to both reflection spectra depicted in Fig. 4. They are x = 0.46 and y = 0.48 for the C. aurigans’ reflection spectrum, and x = 0.34 and y = 0.33 for the C. limbata’s spectrum. For the C. aurigans the coordinates locate a point close to the greenish-yellow and yellow regions, while for the C. limbata they correspond to a white region. The beetles look like gold and silver respectively owing to the constructive interference of specular reflection of light waves on successive interfaces. The luminous reflection values correspond to 17.4% and 23.4% respectively. Figure 6 displays these coordinates in the chromaticity diagram of the CIE. The coordinate values for silver and gold, evaluated from the reflectivity spectra, are (0.33, 0.33) and (0.40, 0.39) with luminous reflections of 97% and 69% respectively. Luminous reflections were evaluated from the discrete version of

 

Fig. 6 Chromaticity diagram of the International Commission on Illumination, showing the coordinates (x,y) obtained from the reflection spectra reported in Fig. 4, and by assuming the solar irradiance spectrum AM1.5.

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3. Modeling reflection spectra of multilayer reflectors

The descriptions given above for the measured reflection spectra of the C. aurigans and C. limbata beetles correspond to what characterize natural broad band or silver/gold reflectors [21,22]. By assuming successive layers of two different materials with corresponding refractive indices, three models have been proposed to explain the iridescence or metallic appearance of natural broad band mirrors. They are based on considering multilayer structures with varying thicknesses of the layers through the beetle’s cuticle: (i) composites of regular multilayer stacks each one tuned to give high reflection values for a specific wavelength, (ii) stacks with systematically changing optical thicknesses, and (iii) disordered arrangements of layer thicknesses about a mean value. Within the first kind of model one has that the larger the number of layers in the structure the higher the dominant peak of visible reflection and the lower its bandwidth. This is so when the difference between refractive indices of the high- and low-refractive index layers is low, while for a large difference a broad high reflection band is displayed, even if a low number of layers is considered [23].

3.1. Reflection from regular arrays of multilayers

When considering an ideal multilayer reflector characterized by several stacks of two-layers each one, under normal incidence (${\theta }_0=0$) the wavelength position of the dominant peak of visible reflection is given by the relation$2{\overline{n}}_{s}d={\lambda }_{peak}\text{ ,}$ where ${\overline{n}}_s=\left(n_1{d}_1+n_2{d}_2\right)/\left(d_1+d_2\right)$ is the average refractive index of each two-layers stacks, and $d=d_1+d_2$ is the spatial period of the structure. Each layer of a stack has a refractive index $n_i$ and a thickness $d_i$, with $i=1,2$, and the “ideal” nature of the multilayer is specified by the condition$n_1{d}_1=n_2{d}_2\text{.}$ Under oblique incidence (${\theta }_0\ne 0$), the wavelength position of the dominant visible reflection peak is given by${\lambda }_{peak}=2\left[n_1{d}_1\cos {\theta }_1+n_2{d}_2\cos {\theta }_2\right]\text{ ,}$ where ${\theta }_1$ and ${\theta }_2$ are the angles of refraction in the corresponding media of the two-layers stacks. From Snell’s law, they are evaluated by applying the relation ${\theta }_i={\sin }^{-1}\left(\sin {\theta }_0/n_i\right)$ with $i=1,2$. ${\lambda }_{peak}$ is the visible wavelength corresponding to the strongest constructive interference. Figure 7 displays two calculated reflection spectra of an ideal multilayer reflector showing the blue shift of the dominant peak of visible reflection when the angle of incidence is increased. The calculations were carried out from a multilayer-transfer-matrix formalism [12].

 

Fig. 7 Reflection spectra of a multilayer consisting of ten stacks of high (n₁ = 1.70) and low (n₂ = 1.40) refractive index materials, with corresponding thicknesses of 100 and 121 nm. Two different incidence angles (θ_o) have been considered, as indicated in the figure.

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A similar behavior is found for non-ideal multilayer reflectors. This effect explains the iridescence appearance of specific biological systems like some beetles. They display different colors depending on the view angle. The beetles we are considering do not show iridescence but they display a silver- or gold-like metallic appearance independently of the view angle. This fact indicates the presence of a broad reflection band over the entire visible wavelength range or over the red side of the visible spectrum, respectively.

3.2. Reflection from broad band multilayer reflectors

Parker et al. have been able to obtain, by applying a model structured from stacks with systematically changing optical thicknesses, a reflection spectrum for the gold beetle Aspidomorpha tecta displaying a sequence of maxima and minima of high reflection values, with a wavelength distance between successive minima around 75 nm [3]. Based on transmission electron micrographs of cuticle cross sections, they assumed a multilayer “chirped” structure with decreasing thicknesses for the high- and low- refractive index layers, protein-chitin rich and water rich layers respectively. From the published transmission electron microscope picture corresponding to the exocuticle cross section of the Aspidomorpha tecta we have estimated thicknesses of the successive layers [1]. They are around 200 nm at the top of the chirped multilayer which consists of a sequence of around 90 layers of high and low refractive indices. Both high and low refractive index layers decrease in thickness about 45% through the multilayer structure whose total thickness is around D = 10 μm. A multilayer chirped morphology has been proposed to explain the reflection spectra of the Charidotella egregia beetle in its “gold” state [24].

Chirped structures can have reflection bands broader than the bands obtained from structures with no dispersion in the thicknesses of the successive layers. Figure 8 displays a calculated reflection spectrum with a broad reflection band through visible wavelengths. It corresponds to a chirped structure with 82 layers, thickness and low refractive index of the top layer d_1max = 138 nm and n₁ = 1.40 respectively, thickness and high refractive index of the next layer d_2max = 113 nm and n₂ = 1.75 respectively, with two thick layers above the chirped structure: the first one 2.5 μm thick and refractive index of 1.40, and the second layer of 2.3 μm thick with refractive index of 1.75. These two thick layers on the top of the structure do not change significantly the reflection spectrum. Through the multilayer structure, the thickness of the low (high) refractive index layer decreases linearly down to p₁ = 50% (p₂ = 50%) from the corresponding thickness value at the top of the chirped structure, i. e. d_1min = 69 nm and d_2min = 56 nm with $p_i=\left(d_{i\max }-d_{i\min }\right)/d_{i\max }$ for i = 1,2. The total thickness of the chirped structure is D = 7.5 μm. At the bottom of the chirped multilayer structure we assume a light absorbing substrate of melanin whose extinction coefficient has been estimated from the absorption coefficient reported by Abbas et al. [11]. We do not consider light absorption through the sequence of chitin layers. Thickness values and decreasing rates are similar to estimations based on transmission electron microscopy pictures reported in the literature, as commented above. In Fig. 8 we define three values for visible wavelengths:

 

Fig. 8 Broad band reflection spectrum displayed for a chirped multilayer structure with a high contrast in the refractive index of successive layers ($n_2/n_1=1.25$). The total number of layers considered is 82, thickness and low refractive index of the top layer d_1max = 138 nm and n₁ = 1.40 respectively, thickness and high refractive index of the next layer d_2max = 113 nm and n₂ = 1.75 respectively, with a total thickness for the chirped structure of 7.5 μm.

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${\lambda }_{\min }$ is close to the wavelength corresponding to the half drop in the reflection edge. For wavelengths lower than ${\lambda }_{\min }$ a ripple structure is displayed. ${\lambda }_{\max }$ is a wavelength limiting the reflection band in the red side of the spectrum, and ${\lambda }_a$ is located close to the middle of the reflection band. For the spectrum of Fig. 8, ${\lambda }_{\min }=390nm$, ${\lambda }_a=585nm$, and ${\lambda }_{\max }=780nm$. Values of these three wavelengths are determined by the average refractive index and the corresponding minimum, maximum, and average value of the spatial period of the structure respectively: ${\lambda }_{\min }\simeq 2{\overline{n}}_N\left(d_{1\min }+d_{2\min }\right)\text{,}$ ${\lambda }_{\max }\simeq 2{\overline{n}}_N\left(d_{1\max }+d_{2\max }\right)\text{,}$ and ${\lambda }_a\simeq 2{\overline{n}}_N{d}_a$ where ${\overline{n}}_N$ is an average refractive index characterizing the whole multilayer structure, and the average spatial period is$d_a=\left(d_{1\min }+d_{1\max }\right)/2+\left(d_{2\min }+d_{2\max }\right)/2\text{.}$ In some way ${\overline{n}}_N$ depends on the number of layers in the structure incorporating the fact that the deeper the location of a layer through the structure, the lower the polarization it will experience due to the lower intensity of the radiation coming to this layer. Under normal incidence, the electric field is parallel to the successive interfaces of the multilayer structure. Within an electrostatic picture, i.e. neglecting retardation effects, the successive N layers are equivalent to N capacitors connected in parallel. The corresponding effective dielectric function of the system is [25]

We have applied a multilayer-transfer-matrix formalism to evaluate reflection spectra of chirped multilayer structures, similar to the one reported for the Aspidomorpha tecta, in order to display as much as possible the trends characterizing our measured reflection spectra. Low values of the luminous reflectance, as compared with other “metallic” beetles, indicate that the C. aurigans and C. limbata specimens are characterized by a low contrast between high and low refractive indices of the neighboring layers. From the measured reflection spectra we can estimate $d_{1\min }\sim d_{2\min }={\lambda }_{\min }/4{\overline{n}}_N$ with ${\overline{n}}_N\sim 1.5$, and ${\lambda }_{\min }\simeq 515nm$ according with the estimation from Fig. 4 for the C. aurigans. Figure 9a shows a reflection spectrum obtained from smoothing the corresponding reflection spectra calculated by means of a multilayer transfer matrix approach. In the non smoothed spectrum the variations between successive maximum and minimum values are larger than those displayed in the smoothed reflection spectrum. A smoothing in the measured reflection spectra could be related to a non linear variation of layer thickness with depth through the cuticle, and/or fluctuations in the layer thickness. We assume a sequence of 68 layers, with $d_{1\min }\sim d_{2\min }=85nm$, $d_{1\max }\sim d_{2\max }=170nm$, and $n_1=1.4$. The evaluation of the average refractive index from Eq. (2) gives ${\overline{n}}_N=1.44$, with a total thickness D = 8.1 μm. The contrast between the refractive indices was set to 1.08, in order to approach the average reflection band, R_top. As depicted in the figure, the trends displayed in the measured reflection spectrum can be approached from the assumed chirped multilayer structure. The drop in reflectance when going from red to blue wavelengths is less pronounced than the measured one. A sequence of maxima and minima in the calculated high reflection band is displayed, while the calculated reflectance values in the blue side of the spectrum are still higher than the measured ones. Figure 9b corresponds to the smoothed reflection spectrum for the C. limbata. In this case N = 68 layers, $d_{1\min }\simeq d_{2\min }=65nm$, $d_{1\max }\simeq d_{2\max }=190nm$, $n_1=1.4$, and $n_2/n_1=1.10$. The evaluation of the average refractive index from Eq. (2) gives ${\overline{n}}_N=1.45$, with a total thickness D = 7.6 μm. The general trends observed in the measured reflection spectrum are also displayed in the calculated spectra for the C. limbata beetle.

The estimation of minimum thickness values has also been carried out in this case from the experimental reflection spectra, by applying the relation ${\lambda }_{\min }\simeq 2{\overline{n}}_N\left(d_{1\min }+d_{2\min }\right)$ with $d_{1\min }\sim d_{2\min }$. Clearly, the assumption of a multilayer structure through the cuticle of the beetle specimens considered allows the evaluation of reflection spectra which display the general trends observed in the measured spectra. Reflection measurements through an extended wavelength range, approaching the near-infrared, will allow the estimation of $d_{1\max }+d_{2\max }$ decreasing the number of fitting parameters. Additionally, better fittings of the measured reflection spectra require knowing in detail the thickness distribution of the layers through the cuticle. For this reason, our efforts are now focused on characterizing for the C. aurigans and C. limbata beetles the kind of multilayer structure responsible for the observed reflection spectra, by using electron microscopy. In this way we will have a detailed description of the change of layer thickness with depth through the cuticle.

4. Reflection of circularly polarized radiation

The selective reflection of circularly polarized light (CPL) by beetles was first reported by Michelson in the beginning of the past century [26]. More recently, the effect has been attributed to the presence of optically anisotropic media similar to cholesteric liquid crystals [27,28]. Spatial distribution and wavelength dependency of linear and circularly polarized light reflected by metallic-shiny cuticles of different beetles have been reported a few years ago [29]. In order to check for the selective reflection of CPL reported in literature for other species of golden beetles [30], we measured the reflection of CPL from the elytra of C. aurigans and C. limbata beetles. An approach similar to the one used by Jewell et al. was followed [31]. The experimental set up used is shown in Fig. 10 . The source, indicated as A in this figure, is a tunable helium - neon laser. The beam from the laser passes first through a linear polarizer (B) with optical axis perpendicular to the direction of propagation, a 45° beam splitter (C) and a quarter wave crystal (D) set to produce CPL. The handedness of the CPL was defined in the standard way according to reference [32]. A lens (E) was used to focus the reflection from the sample (F). After the light is reflected by the sample, it passes again through the quarter wave crystal and is then transmitted or reflected by the 45° beam splitter. The transmitted beam passes through an analyzer (G), whose optical axis is rotated 0° (parallel) or 90° (crossed) with respect to the optical axis of the first linear polarizer (B) in order to determine the polarization of the resulting beam. Finally, the light is focused on a sensor (H) that measures the power of the incoming beam. In this way, if the handedness of the reflected light is different from the handedness of the incident light, the power measured by the sensor becomes a maximum when B and G are in crossed positions and minimum when they are set in parallel positions.

 

Fig. 10 Experimental set up used to measure the reflection of circularly polarized light: A- He-Ne tunable laser, B- linear polarizer, C- 45° beam splitter, D- λ/4 wave crystal, E- lens, F- sample, G- analyzer, and H- sensor.

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The experimental arrangement was tested first using a mirror in the place of the sample. When light was reflected by the mirror, it changed its handedness and therefore the power measured by the sensor was a maximum when the analyzer was in crossed position and minimum when it was in parallel position. In all cases (mirror and beetle’s elytra) a background was measured previously by blocking the reflection from the sample. The results for the reflection of CPL with different handedness and a wavelength of 543 nm for both beetles are summarized in Table 1 . In this table we present for each specimen, for each handedness of the CPL, and for each orientation of the analyzer, the weakest reflection measured by the sensor expressed as a percentage of the maximum power measured. When the C. aurigans beetle was illuminated with left-handed circularly polarized light (LHCPL), the handedness of the reflected light seemed to be conserved. This conclusion is supported by the fact that the signal in the sensor was stronger when the analyzer was set to parallel position. Nevertheless, the signal measured when the analyzer was set to crossed position represents 22% of the signal measured with the analyzer in parallel position. This non null result can be explained by the fact that the circular polarizer composed of the linear polarizer and the quarter wave plate is not ideal. For the reflection of right handed circularly polarized light (RHCPL), the power measured in the parallel position was only 0.1% of the power measured in the crossed position, meaning that the reflected beam did not conserve the handedness of the incident beam. Also, the power measured in the sensor was weaker compared to the maximum measured in the LHCPL. This could mean that the reflected RHCPL is being scattered over a large viewing angle with some fraction impinging on the detector. A similar fact has been reported for the C. boucardi specimens [31].

Table 1. Reflection of Light from the Beetle’s Elytra When Illuminating with Circularly Polarized Light of Wavelength 543 nm^a

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The reflection of LHCPL in the case of the C. limbata displays the same features commented above for the reflection of LHCPL for C. aurigans. In the case of reflection of RHCPL the signal measured when the analyzer was in parallel position was comparable to the reflection measured for LHCPL with the analyzer at crossed position. Also its magnitude was much higher than in the case of the C. aurigans, which indicates that the light is reflected in a more specular way. Our observations indicate that the phenomenon of selective reflection of CPL for the C. limbata might be weaker than for the C. aurigans. According to these findings, the beetles considered will reflect predominantly left-circularly polarized light when illuminated with circularly polarized radiation, which is in agreement with similar behaviors reported for other scarab beetles of the Chrysina’s genus [15].

As mentioned, the reflection of circularly polarized light selectively has been attributed to the presence of an anisotropic layer through the beetle’s outer exocuticle [27]. This layer consists of successive planes parallel to the surface of the cuticle. Each plane consists of chitin micro fibrils all oriented along a direction which differs from the orientation of the micro fibrils in the previous plane, until a complete rotation of 360° is reached through the sequence of planes, which constitute in this way a helicoidal structure similar to that observed in cholesteric liquid crystals [33–35]. In these beetles the property of differential reflection of circularly polarized light seems to be accompanied with the capacity of also detecting circular polarized light in a differential way [36]. These capabilities seem to be related to intricate aspects of communications, recognition, reproduction, and camouflage [37].

5. Summary and conclusions

The optical properties of two species of beetles have been initially considered through reflection spectra of non polarized visible light with normal incidence onto the elytra’s surface. The reflection spectra display low absorption bands at lower wavelengths, a significant rise followed by a high reflection band consisting of maxima and minima superimposed on a background oscillation. When approaching the low visible wavelength range, for the C. limbata beetle the half drop in reflection corresponds to 380 nm while it is located in the 515 nm for the C. aurigans specimens. The characteristic features of the reflection spectra of these natural broad band reflectors have been correlated previously by other authors with the presence of a multilayer structure through which the thicknesses of the layers change, decreasing smoothly with the depth through the cuticle. Following previous works, we assume that the reflection of circularly polarized light can be explained in terms of a more homogenous layer in the top of the exocuticle characterized by a helicoidal structure which behaves as an optical analogue of cholesteric liquid crystals.