Polarization-sensitive color in butterfly scales: polarization conversion from ridges with reflecting elements

Ke Zhang; Yiwen Tang; Jinsong Meng; Ge Wang; Han Zhou; Tongxiang Fan; Di Zhang

doi:10.1364/OE.22.027437

Introduction

Polarization-sensitive color originates from polarization-dependent reflection or transmission, exhibiting abundant optical information, including intensity, spectral distribution, and polarization [1, 2]. Polarized light can be caused by differential reflection or differential scattering, double reflection, differential absorption (dichroism and trichroism), and form-birefringence [1, 3–5]. In nature, many organisms having polarization-sensitive photoreceptors utilize the polarized light for biological communication [6–11]. Especially, some insects utilize their polarization signals as a secret signaling channel, minimizing detection by predators while maximizing recognition among intra-specific species, because their main predators probably cannot use polarization vision for object recognition [8, 9, 12]. Compared with nature, a multitude of optical measurement and imaging techniques, such as medical diagnostics, sensing, liquid-crystal display, and anti-counterfeiting, are based on polarized light [13–16].

The polarized light signal is widely utilized by butterflies, for example Monarch, Heliconius, and Papilio aegeus, in navigation, mate recognition, and finding oviposition sites, etc [9–11]. The utilization of polarized light greatly increases the adaptive capacity of butterflies inhabiting complex light environments, and is highly propitious to biological signaling functions [8]. Due to a variety of butterfly wings exhibiting polarization reflectance patterns, the origins and mechanisms of polarization in butterfly scales have been of great scientific interest. Previous studies showed that the polarization-sensitive color of wing scales in some species of butterfly originated from their elaborated scale microstructures [17–19]. For instance, the retro-reflection structure in the wing scales of butterfly Papilio palinurus causes a polarization effect [17], and the gyroid-structure in the wing scales of butterflies Callophrys rubi and Parides sesostris results in a strong circularly-polarized light [18,19]. Aside from a few butterflies with specific micro-structures, more general polarization mechanisms for diverse forms of known butterfly microstructures have not been investigated.

Gaining an overall perspective and precise characterizations of the microstructures of butterfly wing scales is critical for revealing the polarization mechanisms. Various scale microstructures were categorized into three typical types: ridge-lamellae (Type I scales), body-lamellae (Type II scales), and photonic crystal (Type III scales) [20]. Furthermore, almost all kinds of the three typical scales have diverse ridges forms. Previous studies showed that ridges in butterfly wing scales contributed to diverse optical effects, such as metallic white, light trapping, and broad angular Morpho blue [21–26]. However, the relationship between polarization-sensitive color and the ridge structures in butterfly wing scales is still not well understood.

In this paper, we investigated the polarization conversion originating from ridges with diverse reflecting elements in six species of butterfly. The morphology characterizations and optical spectra of the iridescent scales were investigated with optical microscope, emission scanning electron microscopy (FESEM), transmission electron microscope (TEM), and spectrometer. The polarization-sensitive characteristic related with scale azimuth was revealed through the images under crossed polarized microscope and Finite Differential Time Domain (FDTD) simulation. The polarization conversion originating from the ridges with reflecting elements was well explained by form-birefringence theory and the corresponding parameter factors of ridges were discussed.

Material and method

Butterflies

The dried samples of investigated butterflies were provided by the Shanghai Entomological museum, China. We investigated the colorful wing scales of six species of butterfly, includingCymothoe excels (C.excels), Troides aeacus kaguya (T.a.kaguya), Ornithoptera priamus poseidon (O.p.poseidon), Morpho sulkowskyi (M.sulkowskyi), Ancyluris meliboeus eudaemon (A.m.eudaemon), and Parides sesostris (P.sesostris).

Morphology characterization

The digital photographs of butterflies were taken with a Canon EOS 60D digital camera. In order to characterize the microstructures of the butterfly scales, the butterfly scales were investigated through field emission scanning electron microscope (FESEM; FEI NOVA NanoSEM 230) and transmission electron microscopy (TEM; FEI Tecnai G2 spirit Biotwin). For obtaining TEM images, the samples were embedded in epoxy resin at 60 °C for 48 hours, and ultrathin sections (70 nm) were cut with low temperature sectioning system (Leica ULTRACUT UC6) and post-stained in lead citrate for 6 minutes.

Spectra

We investigated the reflectance spectra and absorption spectra of butterfly scales. The reflectance spectra of intact wings were measured with a normal UV-Vis-NIR spectrometer (Varian Cary 500 infrared-visible-ultraviolet spectrometer) with an integrating sphere, and 1cm² area of color wing patch was subjected to the incident light. To obtain the absorption spectrum of the color scale pigments with micro-spectrophotometer (CraicQDI2010), color scales were removed with adhesive tape, then a single scale was immersed in bromoform, whose refractive index (RI) is 1.6, and 10μm² area of a single scale was illuminated by the incident light.

Polarization-sensitive characteristics

To investigate the polarization-sensitive characteristics of butterfly scales, microscopic images were obtained by an optical microscope with crossed polarizers (Zeiss Axio Scope A1 Microscope) observing the single butterfly wing scale at 90°azimuth, 45°azimuth, and 0°azimuth under the same incident light intensity. To reveal the polarization-dependent reflection, simulated calculation was carried out with the commercial OptiFDTD software from Optiwave Systems Inc. For Finite Differential Time Domain (FDTD) simulation, a Gaussian modulated light source was adopted. The parameters of scales were statistically obtained from the SEM and TEM images. Anisotropic perfect matching layer (APML) boundary condition was employed, and the resulted calculation data was transferred from time domain to frequency domain by discrete Fourier transform generating the simulated spectra.

Results

Figure 1 presents the digital photographs of the wings of the six species of butterfly. Butterfly C.excels exhibits a distinct red color, and the under-wings of Butterfly T.a.kaguya exhibit yellow patterns (Fig. 1(A) and 1(B)). Butterfly O.p.poseidon and butterfly P.sesostris feature with green patterns (Fig. 1(C) and 1(D)). Butterfly M.sulkowsky and butterfly A.m.eudaemon exhibit striking blue hues (Fig. 1(E) and 1(F)).

Fig. 1 Morphology and polarized microscope images of the investigated butterflies. (A) Photograph of C.excels dorsal surface. (A’) Polarized microscope image of C.excels scales at 90° azimuth. (A”) Polarized microscope image of C.excels scales at 45° azimuth. (A”’) Polarized microscope image of C.excels scales at 0° azimuth. (B) Photograph of T.a.kaguya dorsal surface. (B’) Polarized microscope image of T.a.kaguya scales at 90° azimuth. (B”) Polarized microscope image of T.a.kaguya scales at 45° azimuth. (B”’) Polarized microscope image of T.a.kaguya scales at 0° azimuth. (C) Photograph of O.p.poseidon dorsal surface. (C’) Polarized microscope image of O.p.poseidon scales at 90° azimuth. (C”) Polarized microscope image of O.p.poseidon scales at 45° azimuth. (C”’) Polarized microscope image of O.p.poseidon scales at 0° azimuth. (D) Photograph of M.sulkowskyi dorsal surface. (D’) Polarized microscope image of M.sulkowskyi scales at 90°azimuth. (D”) Polarized microscope image of M.sulkowskyi scales at 45° azimuth. (D”’) Polarized microscope image of M.sulkowskyi scales at 0° azimuth. (E) Photograph of A.m.eudaemon ventral surface. (E’) Polarized microscope image of A.m.eudaemon scales at 90° azimuth. (E”) Polarized microscope image of A.m.eudaemon scales at 45° azimuth. (E”’) Polarized microscope image of A.m.eudaemon scales at 0° azimuth. (F) Photograph of P.sesostris dorsal surface. (F’) Polarized microscope image of P.sesostris scales at 90° azimuth. (F”) Polarized microscope image of P.sesostris scales at 45° azimuth. (F”’) Polarized microscope image of P.sesostris scales at 0° azimuth. Scales bar: (Column 1) 2cm; (column 2, 3, and 4): 50μm.

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The optical microscopic images of the single scale under crossed polarizers reveal their respective polarization-sensitive characteristics (Fig. 1). The scale of butterfly C.excels under crossed polarizers exhibits an identical red color at 90° azimuth and 45° azimuth (Fig. 1(A’) and 1(A”)). However, in the case of the colorful scales of the T.a.kaguya, O.p.poseidon, P.sesostris, M.sulkowsky and A.m.eudaemon butterflies, their hues changed with the azimuth. Under crossed polarizers, the colors of these five scales are dimmed at 90° azimuth and are intense at 45° azimuth (Fig. 1(B’)-1(F’) and Fig. 1(B”)-1(F”)).

Figure 2 presents the anatomical microstructures of the colorful scales of the six species of butterfly. FESEM and TEM images show that each scale contains the ridge structure running parallel to the longitudinal axis of the scale. The distance of adjacent ridges is uniform for specific scale, varying from 0.5μm-2μm for different species. In the case of the butterfly C. excels, the adjacent ridges are connected by cross-ribs, and the upper ridge connects with bottom base film through disorder pillars (Fig. 2(A) and 2(A’)). The tapered ridges with steep multilayer ribs of T.a.kaguya butterfly attach directly to the bottom base film (Fig. 2(B) and 2(B’)). In the case of the M.sulkowskyi and A.m.eudaemon butterflies, the discrete multilayer elements are incorporated into the scale ridge structure (Fig. 2(C) and 2(C’), Fig. 2(D) and 2(D’)). The green scale of the butterfly O.p.poseidon contains two layers, the upper tapered ridge layer and the bottom body-multilayer (Fig. 2(E) and 2(E’)). The scale of butterfly P.sesostris is of the upper two-dimensional ridge layer and the bottom three-dimensional (3D) photonic crystal layer (Fig. 2(F) and 2(F’)).

Fig. 2 FESEM and TEM images and spectra of investigated butterflies. (A) FESEM images of C.excels wing scale. (A’) TEM images of C.excels wing scale. (A”) Absorption spectrum (dotted line) and reflected spectrum (solid line) of C.excels scales (B) FESEM images of T.a.kaguya wing scale. (B’) TEM images of T.a.kaguya wing scale. (B”) Absorption spectrum (dotted line) and reflected spectrum (solid line) of T.a.kaguya scales (C) FESEM images of O.p.poseidon wing scale. (C’) TEM images of O.p.poseidon wing scale. (C”) Absorption spectrum (dotted line) and reflected spectrum (solid line) of O.p.poseidon scales (D) FESEM images of M.sulkowskyi wing scale. (D’) TEM images of M.sulkowskyi wing scale. (D”) Absorption spectrum (dotted line) and reflected spectrum (solid line) of M.sulkowskyi scales (E) FESEM images of A.m.eudaemon wing scale. (E’) TEM images of A.m.eudaemon wing scale. (E”) Absorption spectrum (dotted line) and reflected spectrum (solid line) of A.m.eudaemon scales (F) FESEM images of P.sesostris wing scale. (F’) TEM images of P.sesostris wing scale. (F”) Absorption spectrum (dotted line) and reflected spectrum (solid line) of P.sesostris scales. Scales bar: (Column 1and 2): 1μm.

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The absorption spectra and the reflectance spectra of these six colorful scales are shown in Fig. 2. The wavelengths of the incident lights of both reflectance and absorbance are from 350nm to 800nm. The reflection band of the red scale of butterfly C.excels corresponds to its non-absorption bands, and the reflection and absorption spectra of the yellow scales of butterfly T.a.kaguya are also complementary (Fig. 2(A”) and 2(B”)). However, in the case of the colorful scales of the M.sulkowskyi, A.m.eudaemon, O.p.poseidon, and P.sesostris butterflies, their reflection bands show no complementary relationship with their respective absorption bands (Fig. 2(C”)-2(F”)).

Discussion

Color production mechanisms

The FESEM and TEM images show that all the six colorful scales contain anisotropic ridges, which exhibit diverse forms and different heights. The ridge heights of the colorful scales in O.p.poseidon, M.sulkowskyi, A.m.eudaemon, P.sesostris butterflies are about 2μm, while it is about 0.4μm in the red scale of butterfly C.excels and 5μm in the yellow scale of butterfly T.a.kaguya.

These butterflies achieve the colorful appearances through different mechanisms with their respective micro-architectures and pigments. In the case of the colorful scales of the O.p.poseidon, M.sulkowskyi, A.m.eudaemon, P.sesostris butterflies, there are multilayer or photonic crystal structure in their wing scale microstructures (Fig. 2(C)-2(F) and 2(C’)-2(F’)). Their reflectance spectra bands show little relevance to their absorption (Fig. 2(C”)-2(F”)). According to the typical classification, the blue scales of M.sulkowskyi and A.m.eudaemon butterflies are the Type I scales (ridge-lamellae), having discrete multilayer incorporated into the scale ridges [20]. The interference and diffraction contributes to the blue hue of M.sulkowskyi and A.m.eudaemon butterflies [27]. The green color scale of butterfly O.p.poseidon is the Type II scale (body-lamellae), and the green color results from the interference of bottom multilayer [28]. Butterfly P.sesostris scale is the Type III scale (photonic crystal structure), and the 3D gyroid-type photonic crystal achieve the striking green color [19]. Their striking blue or green hues are structural color, mainly originating from the coherent scattering by the multilayer or photonic crystal elements [27, 28].

For the red scale of C.excels butterfly and the yellow scale of T.a.kaguya butterfly, their reflection band and the absorption band are complementary (Fig. 2(A”) and 2(B”)). Their ridges connect with the bottom disorder pillars or base film, which contributes to the backscattering and diffusion (Fig. 2(A)-2(B) and 2(A”)-2(B”)) [29]. Their pigments absorb the relevant short wavelength, playing the main role in the pigmentary color.

Polarization-sensitive color originating from ridge with reflecting elements

Under crossed polarizers, the wing scale of butterfly C.excels shows the same color at 45° azimuth and at 90° azimuth (Fig. 1). In the wing scales of T.a.kaguya, O.p.poseidon, M.sulkowskyi, A.m.eudaemon, P.sesostris butterflies, their polarization effects are related with the scale azimuth (intense at 45° azimuth and dimmed at 90° azimuth) (Fig. 1(B)-1(F) and 1(B’)-1(F’)). Furthermore, the wing scales of O.p.poseidon, M.sulkowskyi, A.m.eudaemon, P.sesostris butterflies exhibit structural colors and have the same heights of ridges. Considering the commonality of the four structural color scales, we focused on their ridge structures to analyze the polarization-sensitive color.

The ridges of the four structural color scales are diverse, with different periodic reflecting elements. In the case of the wing scale of butterfly O.p.poseidon, the periodic ridge structure is tapered triangular (Fig. 2(C’)). While the ridge structures of blue scales in M.sulkowskyi and A.m.eudaemon butterflies are incorporated with discrete multilayers, whose overall shapes are also triangular (Fig. 2(D’) and 2(E’)). In the green wing scale of butterfly P.sesostris, the ridge structure is comprised of a tapered part and a two dimensional part (Fig. 2(F’)). The polarization conversion is mainly related with ridge structure and not closely related with the forms of reflecting elements, where the three main scale types show a similar polarization effect.

To reveal the relationship between the polarization-dependent spectra and their ridge structures, simulated calculation was conducted with FDTD. The simplified models of the four structural color scales were established (Fig. 3), and parameters of the simplified models are statistically extracted from the FESEM and TEM images (Table 1). In the case of the scale of butterfly P.sesostris, we set equivalent multilayer to replace the bottom gyroid photonic crystal structure, eliminating the influence on polarization from the gyroid structure (which will cause the circularly-polarized light) [18, 19]. Here we set the input light as the p-polarized light and collected the s-polarized reflected light, simulating the effect of the cross-polarizers microscope. The real parts of the RI of chitin and air were set as 1.56 and 1.0, respectively [30]. For simplifying the simulated calculation, we set the imaginary part of the RI is zero. The simulated reflection spectra in Fig. 3 show that when the scales model at 45° azimuth, the reflection bands and peaks are corresponding to the reflection bands of experimental reflection spectra in Fig. 2 (M.sulkowskyi peaks at about 500nm and A.m.eudaemon peaks at about 470nm, and O.p.poseidon and P.sesostris peak at about 550nm).

Fig. 3 Simplified scale models and simulated s-polarization reflected spectra of the butterfly scales with structural color. (A) The simplified M.sulkowskyi scale model is at 45°azimuth. (A’) The simulated s-polarization reflected spectrum of the M.sulkowskyi blue scale. (B) The simplified A.m.eudaemon scale model is at 45°azimuth. (B’) The simulated s-polarization reflected spectrum of the A.m.eudaemon blue scale. (C) The simplified O.p.poseidon scale model is at 45°azimuth. (C’) The simulated s-polarization reflected spectrum of the O.p.poseidon green scale. (D) The simplified P.sesostris scale model is at 45°azimuth. (D’) The simulated s-polarization reflected spectrum of the P.sesostris green scale.

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Table 1. Dimensional parameters of the simplified scale model

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The simulated results show that the scale models utilize ridge structure with reflecting elements to achieve the polarization conversion. When the scales model at 45° azimuth, parts of the p-polarized incident light was reflected by the reflecting elements and converted into s-polarized light by the anisotropic ridges.

The influence of dimensional parameter on polarization conversion

Although the simulated results demonstrate that the polarization-dependent reflection is caused by the ridges with reflecting elements, a deeper analysis is requisite for clarifying the polarization conversion process. In the case of O.p.poseidon and P.sesostris wing scale model, the ridges covered above the multilayer and photonic crystal, where the polarized effect from ridges and the interference from the multilayer or photonic crystal are separated. In the case of the M.sulkowskyi and A.m.eudaemon wing scale model, the discrete multilayer elements are incorporated into the scale ridges, where the polarized effect and interference are simultaneous. Due to the diversity of ridge structures, model simplification is crucial to investigate the influence of dimensional parameters.

The ridge structures in the butterfly scales can be abstracted as a grating structure. Here we established Model-A comprised of an upper rectangular grating and a bottom multilayer, which is simplified from the wing scale structure of butterfly O.p.poseidon, to investigate the influence of grating dimension on polarization conversion (Fig. 4(A)). Previous studies showed that the sub-wavelength grating structure achieved form-birefringence resulted in the polarization conversion of the transmitted light [31]. Therefore, we investigated the polarization conversion process starting from the Model-A with sub-wavelength rectangular grating. The grating period and the height of the sub-wavelength rectangular grating are Λ and h, respectively. The material medium was set as chitin and the model was at 45° or 90°azimuth. The width of chitin, w_chitin_, was set equal to the width of air, w_air, where Λ = w_chitin + w_air. The bottom multilayer was set as 10 layers and the wavelength of the correspondent reflection band center was about 640 nm, the thicknesses of whose chitin and air layers were 0.125 μm. Here, we set the input light as the p-polarized light and collected the s-polarized reflected light. The simulated calculation was focused on Λ and h of the grating (Table 2).

Fig. 4 Simplified Model-A and the simulated s-polarization reflected spectra about the upper rectangular grating with bottom multilayer architecture. (A) The Model-A comprised of upper rectangular grating with bottom multilayer is at 45°azimuth. (B) The influence of h on the s-polarization reflected spectra of Model-A at 90° azimuth. (C) The influence of h on the s-polarization reflected spectra of Model-A at 45°azimuth. (D) The influence of Λ on the s-polarization reflected of Model-A at 45°azimuth.

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Table 2. Dimensional parameters of the rectangular grating of Model-A

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The wavelength of the multilayer reflection center was 640 nm, and the correspondent theoretical phase difference, δ, was estimated according to effective RI theory and birefringence theory (Table 2). In Model-A, the upper rectangular grating acts as form-birefringence, and the RIs in parallel and perpendicular grating orientation ( $n_{/ /}$ and $n_{⊥}$ ), can be calculated by [31]

{\begin{cases} n_{_{/ /}}^{2} = f_{c} n_{c}^{2} + (1 - f_{c}) n_{a i r}^{2} \\ \frac{1}{n_{_{⊥}}^{2}} = \frac{f_{c}}{n_{c}^{2}} + \frac{1 - f_{c}}{n_{a i r}^{2}} \end{cases}

where

n_{/ /}

and

n_{⊥}

are the effective RIs of grating in the parallel and perpendicular grating orientation. n_c (1.56) and n_air (1.00) are the RIs of chitin and air, and f_c is the volume ratio of the chitin.

As for the asymmetric 2D structure (which has two orthogonal gratings), it has primary-grating (whose period is bigger) and subordinate-grating (whose period is smaller), and it will cause the similar phase difference like the 1D grating. In the asymmetric 2D grating structure, the RIs in parallel and perpendicular primary-grating orientation ( $n_{/ /}$ and $n_{⊥}$ ), can be calculated by [32] the Eq. (2)

{\begin{cases} n_{_{/ /}}^{2} = {f^{″}}_{c} n_{c}^{2} + (1 - {f^{″}}_{c}) / (\frac{{f^{'}}_{c}}{n_{c}^{2}} + \frac{1 - {f^{'}}_{c}}{n_{a i r}^{2}}) \\ \frac{1}{n_{_{⊥}}^{2}} = \frac{{f^{″}}_{c}}{n_{c}^{2}} + \frac{1 - {f^{″}}_{c}}{{f^{'}}_{c} n_{c}^{2} + (1 - {f^{'}}_{c}) n_{a i r}^{2}} \end{cases}

where

n_{/ /}

and

n_{⊥}

are the effective RIs of grating in the parallel and perpendicular primary-grating orientation. n_c (1.56) and n_air (1.00) are the RIs of chitin and air, and

{f^{'}}_{c}

is the volume ratio of the chitin in the subordinate-grating, and

{f^{″}}_{c}

is the volume ratio of the chitin in the primary-grating.

The phase difference ( $δ$ ) equation in the case of the Model-A, where the light reflected back by the bottom multilayer passing through the upper grating two times, can be derived from the birefringence theory of the birefringence wafer [33]. Therefore, the phase difference of two component lights, parallel grating polarized light and perpendicular grating polarized light, can be evaluated by Eq. (3),

δ = 2 * \frac{2 π}{λ} (n_{/ /} - n_{⊥}) h

where,

λ

is the wavelength of the light and h is the height of the upper rectangular grating,

n_{/ /}

and

n_{⊥}

are the effective RIs of grating in the parallel and perpendicular grating orientation.

Under crossed polarizers, when the p-polarized incident light illuminates on the Model-A, the s-polarized reflection intensity $I_{R} (s)$ are given by [33],

I_{R} (s) = I_{0} R \sin^{2} (\frac{δ}{2}) \sin (π - 2 θ) \sin (2 θ)

where

I_{0}

is the intensity of incident p-polarized light, and

R

is the reflectance of bottom multilayer of Model-A,

δ

is the phase difference caused by grating,

θ

is the azimuth of Model-A.

According to Eq. (4), when Model-A is at 90° azimuth, $I_{R} (s)$ is zero. To investigate the influence of h on polarization-conversion when Model-A was at 90° azimuth, we fixed Λ as 0.2 μm and varied h from 0.33μm to 2.64μm as shown in Table 2. The simulated results in Fig. 2(B) reconfirms that there is no p-polarized light converting into s-polarized light when the azimuth of Model-A is 90° (Fig. 4(B)). These results are identical with the experimental results in Fig. 1. When Model-A is at 45° azimuth, the s-polarized reflection intensity is decided by the reflectance of bottom multilayer and the polarization conversion caused by the grating. Since the studies about the reflectance influenced by the number of the layers of multilayer have been investigated by lots of researchers [27], here we focused on the investigation on the parameters of the grating.

To investigate the influence of h on polarization-conversion, we fixed Λ as 0.2 μm and varied h from 0.33μm to 2.64μm as shown in Table 2. The simulated reflected spectra show that when h is 1.32μm (the δ is π), the s-polarization component is dominant (Fig. 4(C)). When h is 2.64μm (the δ is 2π), the s-polarization component is small. This simulated results showed that polarization conversion is caused by our sub-wavelength grating, and the bottom multilayer contributed to the reflection band.

To investigate the influence of Λ on polarization conversion, we fixed h as 1.33μm (whose theoretical δ is π) and varied the Λ from 0.2μm to 0.8μm as shown in Table 2. The simulated reflected spectra show that when the Λ is 0.2μm or 0.4μm, the reflected polarization conversion effect is remarkable, while when the Λ is 0.6μm and 0.8μm, the polarization conversion is impeded (Fig. 4(D)). It indicates that when Λ is comparable with the wavelength of visible light, the reflected diffraction order from the grating probably affects the polarization conversion process.

In fact, the distance of adjacent ridges in the butterfly scales is comparable to the wavelength of visible light (Fig. 2). The scales still exhibit a polarization-sensitive color and the simulated results of the respective scale model testify the corresponding polarization dependent reflection, which is different with simulated results of Model-A. To explain the inconsistency of the simulated results, we performed further simulated calculations.

In terms of the butterfly scales, the overall shapes of their ridge structures are triangular, which probably affects the polarization conversion. To investigate the influence of the shape of grating on polarization conversion, we established Model-B comprised an upper triangular grating and a bottom multilayer (Fig. 5(A)). The triangular deep grating exhibits the anti-reflection characteristic, which probably reduces the effect of the reflected diffraction order [34]. In Model-B, the phase difference can be calculated by the integral method based on the Eq. (3),

δ = 2 \int_{0}^{H} \frac{2 π}{λ} (n_{/ /} - n_{⊥}) d_{h}

where,

λ

is the wavelength of the light and H the height of the upper triangular grating,

n_{/ /}

and

n_{⊥}

are the effective RIs of grating in the parallel and perpendicular grating orientation.

Fig. 5 Simplified Model-B and the simulated s-polarization reflected spectra about the upper triangular grating with bottom multilayer architecture. (A) The Model-B comprised of upper triangular grating with bottom multilayer is 45°azimuth. (B) The influence of Λ on the s-polarization reflected spectra. (C) The influence of h on the s-polarization reflected spectra.

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According to the Eq. (5), we set h as 2μm (the theoretical δ is π) and varied the Λ as shown in Table 3. The simulated reflected spectra show that when the Λ varied from 0.4μm to 1.0μm, the Model-B reflects and converts the most of the p-polarized light into s-polarized light (Fig. 5(B)). It indicates that the triangular grating extends the polarization conversion effect from the order of sub-wavelength band to the order of wavelength, while when Λ is much bigger than $λ$ , the polarization conversion is impeded. Then, we investigated influence of h on triangular grating whose Λ was 1μm. We varied h from 2μm to 5μm as shown in Table 3. The results show that when the h is 4μm the s-polarized reflectance spectrum is dominant. It shows that the triangular grating still will achieve form-birefringence, leading to the polarization conversion (Fig. 5(C)). Nevertheless, the theoretical δ estimated by the effective RI theory in Table 3 does not correspond to the simulated results. Because their period is bigger than the wavelength of visible light, the phase difference cannot be effectively estimated by the effective RI theory.

Table 3. Dimensional parameters of the triangular grating of Model-B

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In the case of the M.sulkowskyi wing scale model, whose polarized effect from the ridges and the interference from multilayer are simultaneous, we changed the width of the middle pillar (w_pillar), which will affect the chitin ratio of ridges, to investigate its influence on polarization conversion (Fig. 6(A)). Here,the normal incident was p-polarized light. The results show that when the w_pillar is 0 or 0.3μm, the simulated s-polarized reflectance is less than 10%; while the simulated s-polarized reflection band is outstanding when the w_pillar is 0.15μm (Fig. 6(B)). Therefore, in the case of the ridge-lamellae scale model, the w_pillar that affects the chitin ratio of ridge is a key factor influencing the polarization conversion.

Fig. 6 Influence of w_pillar on simulated s-polarized reflectance spectra (A)The simulated M.sulkowskyi scale model is at 45°azimuth and w_pillar is the width of the middle pillar. (B) The simulated s-polarized reflectance spectra under normal incident p-polarized light.

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As for the Model-M.sulkowskyi, it can be well explained by division calculation. Here, the $h^{m}$ represents the height of the part (whose volume ratio of chitin is $f_{c}^{m}$ ), and the corresponding effective RIs in the parallel and perpendicular grating orientation are $n_{/ /}^{m}$ and $n_{⊥}^{m}$ . Therefore, the phase difference, $δ$ , can be calculated by the Eq. (6)

δ = 2 * \frac{2 π}{λ} [({n^{'}}_{/ /} - {n^{'}}_{⊥}) h^{'} + ({n^{″}}_{/ /} - {n^{″}}_{⊥}) h^{″} + ... + (n_{/ /}^{m} - n_{⊥}^{m}) h^{m}]

According to the parameters in Table 1, we can calculate

δ

based on Eq. (1) and Eq. (6). The calculated results show that

δ \approx 0.3 π

(w_pillar = 0μm),

δ \approx 1.0 π

(w_pillar = 0.15μm),

δ \approx 1.7 π

(w_pillar = 0.3μm). Therefore, the spectra has higher than two others when w_pillar = 0.15μm.

The above simulated polarization-dependent reflection spectra (Fig. 3-6) demonstrate that the grating at 45° azimuth contributes to the polarization conversion, which are identical with the polarization-sensitive color in the butterflies’ wing scales with ridges (Fig. 1). The above simulation shows that the shape, h and Λ of the grating greatly influence the polarization conversion effects. In the case of the sub-wavelength rectangular periodic grating structure with the bottom multilayer, the reflected polarization conversion effect is outstanding and the phase difference of the form-birefringence can be estimated by the effective RI theory. For the comparable wavelength rectangular periodic grating, the polarization conversion effect is probably impeded by the reflected diffraction order. The triangular grating extends the reflected polarization conversion effect to comparable wavelength band from the sub-wavelength band. The wider triangular grating still acts as form-birefringence at the proper height, leading to reflected polarization conversion, which probably explains the polarization-sensitive color of buttefly T.a.kaguya. In the case of the M.sulkowskyi scale model, the chitin ration of ridges greatly influences the polarization conversion.

Conclusion

The polarization-sensitive colors originating from the ridges with diverse reflecting elements in six species of butterfly scales were investigated through experimental measurement and computational simulation. The polarization-sensitive color related with azimuth (intense at 45° scale azimuth and dimmed at 90° scale azimuth) is outstanding in the structural color scales, such as the O.p.poseidon green scales, the M.sulkowskyi blue scales, the A.m.eudaemon blue scales, and the P.sesostris green scales. Periodic ridges with reflecting elements are the structural commonality of these structural color scales, whose reflecting elements, including the discrete multilayer, bottom multilayer, and bottom photonic crystal, mainly determine the scale colors. Anisotropic ridge structure causes the differences of the effective refractive indices in different orientations, and the form-birefringence contributes to the phase differences of different polarized component light. Simulations reveal that the sub-wavelength grating with a bottom multilayer achieves outstanding reflected polarization conversion, and the deep tapered triangular ridge structure extends the reflected polarization conversion effect from the sub-wavelength band to comparable visible wavelength band.

These findings reveal the physical origin of the polarization-sensitive color in butterfly scales with deep ridge structure. Understanding the origin of polarization would help to explain the creation of the polarized signal, which is involved in butterflies’ biological recognition under natural conditions. The deep ridge structure with reflecting elements architecture in scales offers great inspirations for optical materials and devices, and provides an enlightening way to further cultivate the colorful nature.

Acknowledgments

The authors are grateful for the financial support from the National Natural Science Foundation of China (51172141) and the Research Fund for the Doctoral Program of Higher Education (20100073110065 and 20110073120036).

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butterfly	ridge structure				(equivalent) multilayer structure
butterfly	Forms of ridge	d_-ridge/(μm)	w_-ridge/(μm)	h_-ridge /(um)	t_-chitin/(μm)	t_-air/(μm)	λ_-center/(μm)
M.sulkowskyi	discrete multilayer	0.7	0.6	1.9	0.06	0.16	0.47
A.m.eudaemon	oblique multilayer	0.8	0.4	1.8	0.08	0.13	0.50
O. p. poseidon	Triangular	0.52	0.52	1.9	0.11	0.10	0.55
P.sesostris	Tapered part	0.75	0.4	0.8	0.105	0.105	0.54
P.sesostris	2D part	0.75	0.4	2	0.105	0.105	0.54

butterfly	ridge structure				(equivalent) multilayer structure
butterfly	Forms of ridge	d_-ridge/(μm)	w_-ridge/(μm)	h_-ridge /(um)	t_-chitin/(μm)	t_-air/(μm)	λ_-center/(μm)
M.sulkowskyi	discrete multilayer	0.7	0.6	1.9	0.06	0.16	0.47
A.m.eudaemon	oblique multilayer	0.8	0.4	1.8	0.08	0.13	0.50
O. p. poseidon	Triangular	0.52	0.52	1.9	0.11	0.10	0.55
P.sesostris	Tapered part	0.75	0.4	0.8	0.105	0.105	0.54
P.sesostris	2D part	0.75	0.4	2	0.105	0.105	0.54

Polarization-sensitive color in butterfly scales: polarization conversion from ridges with reflecting elements

Abstract

Introduction

Material and method

Butterflies

Morphology characterization

Spectra

Polarization-sensitive characteristics

Results

Discussion

Color production mechanisms

Polarization-sensitive color originating from ridge with reflecting elements

The influence of dimensional parameter on polarization conversion

Conclusion

Acknowledgments

References and links

Cited By

Figures (6)

Tables (3)

Equations (6)

Optics Express

Influence factor	The influence of h			The influence of Λ
Influence factor	*Λ/μm*	*h/μm*	δ	*Λ/μm*	*h/μm*	δ
Dimensional parameters	0.2	0.33	$π / 4$	0.2	1.33	$π$
	0.2	0.66	$π / 2$	0.4	1.33	$π$
	0.2	1.32	$π$	0.6	1.33	$π$
	0.2	2.64	$2 π$	0.8	1.33	$π$

Influence factor	The influence of Λ			The influence of h
Influence factor	Λ/μm	h/μm	δ	Λ/μm	h/μm	δ
	0.4	2.0	$π$	1.0	2.0	$π$
Dimensional parameters	0.6	2.0	$π$	1.0	3.0	$1 .5 π$
	0.8	2.0	$π$	1.0	4.0	$2 π$
	1.0	2.0	$π$	1.0	5.0	$2.5 π$