Nanostructured materials like graded refractive index (GRIN) structures in moth eyes have inspired the design of novel antireflective coatings. Such structures are more flexible than uniform coatings, but applications have been mainly limited to broadband antireflection in solar cells and LEDs. Here we show that cylindrical pigment granules in two bird species (Polyplectron bicalcaratum and Patagioenas fasciata) form a GRIN that suppresses interference and expands the range of colors produced by a multilayer. These results demonstrate that a GRIN structure can function like a pigment (i.e. through selective, independent wavelength blocking) to generate unique colors and may inspire the design of novel antireflective and structurally colored coatings.
© 2014 Optical Society of America
Multilayers produce structural colors through constructive interference of light beams reflecting at different interfaces. The reflectance of such structures is determined by the number of layers, refractive index (RI) contrast between layers, thicknesses of individual layers, and the polarization and angle of incident light . Reflectance maxima (λmax) for a simple 2-layer stack can be determined using the Bragg-Snell diffraction equation :2]. Achieving more saturated colors requires either an increase in the number of layers  or narrowband reduction of reflection at an interface.
Controlling reflection at the interface between two materials differing in RI is important for a wide variety of industrial applications like solar cells [3,4] and LED light extraction . One common control mechanism is a thin-film coating with quarter-wavelength thickness and a RI of , where n0 and nsub are the RIs of the ambient material and substrate, respectively . However, no materials that form films have RIs less than ~1.4, limiting the flexibility of this method . Alternatively, materials could be structured to produce a graded refractive index (GRIN), in which RI varies gradually and consistently throughout the nanostructure. Because Fresnel reflection depends on RI contrast at an interface, such incremental steps in RI can strongly reduce reflection, as in the antireflecting bumps on the surface of moth eyes . Inspired by these natural structures, researchers have recently achieved RIs approaching that of air (n = 1.00), strongly reducing Fresnel reflection over a range of wavelengths and incident angles .
Birds have evolved diverse photonic structures (e.g., multilayers, photonic crystals, thin films) [9,10] from relatively few materials (keratin, melanin and air) . Despite this material limitation, the often non-planar shapes of melanin-containing organelles (melanosomes) might produce a GRIN (e.g., see ), potentially reducing interference and enhancing color. Here, we test this hypothesis in two bird species: the grey peacock-pheasant (Polyplectron bicalcaratum) and the band-tailed pigeon (Patagioenas fasciata). Using a combination of electron microscopy, reflectance spectrometry, focused ion beam (FIB) milling, and optical modeling, we show that iridescent color is caused by interference from a composite structure consisting of a uniform keratin layer and a monolayer of cylindrical melanosomes. Structural analyses and optical simulations suggest that melanosomes enhance color by forming a GRIN to reduce reflection at the cortex-melanosome interface and produce a broader gamut of colors than is possible with a non-GRIN structure.
2.1 Morphological analysis
We obtained untreated feathers from private sellers and museum collections (Patagioenas fasciata: University of Akron Ornithological Collection #1050; Polyplectron bicalcaratum: Field Museum of Natural History, David Willard curator). Peacock-pheasants have numerous iridescent eyespots on their tail and body and we analyzed a contour feather eyespot (Fig. 1(a)). Band-tailed pigeons are generally drab brown except for a yellow iridescent patch on their necks, thus we plucked a feather from this region (Fig. 1(d)). We used TEM to image transverse cross-sections of feathers barbules following the protocol in Shawkey et al. . From the resulting TEM images, we used ImageJ  to measure melanosome diameter (dmel) and keratin cortex thickness (dker) thickness at haphazardly chosen locations along the exposed surface of a barbule. To confirm that melanosomes were surrounded by air as previously suggested , we used a dual-beam FIB (Nova Nano-lab 200, FEI, Hillsboro, OR, USA) at an operating voltage of 30kV and a current of 0.8 nA to ablate the entire cortex and leave the underlying melanosomes intact.
2.2 Spectral analysis
We measured angle-resolved spectra (from 10 to 70° in 5° increments) at two incident light polarizations (s: E-field parallel to surface; p: E-field perpendicular to surface) using a linear grid polarizer (Thorlabs, Newton, NJ, USA) placed between the light source and feather. We mounted feathers so that the reflecting structures (barbules) were oriented perpendicular to the incident light on a lab-made goniometer. From the measured curves, we calculated the location (λmax) and amplitude of reflectance peaks (Rmax) using the R package pavo .
2.3 Optical modeling
To understand the structural color mechanism, we compared the match between measured and predicted reflectance spectra for two different structural models based on previous studies and TEM measurements: 1) a keratin thin film over a melanosome layer with a GRIN ; and 2) a keratin thin film over a melanosome monolayer and amorphous melanosome substrate . For model 1 we calculated RI as a function of vertical position by dividing the melanosome layer into vertical slices and homogenizing their refractive indices according to the proportions of melanin and air. Based on similar equations in for spheres , the refractive index as a function of depth into the cylinder (z) is:Fig. 1(f)). For model 2, we used a molecular dynamics, collision-based simulation algorithm to generate random melanosome packing configurations  similar to those observed in feathers. To evaluate the match between real and simulated structures, we compared radial distribution functions for the simulated and empirical structures using the x and y coordinates of between 20 and 60 melanosomes per barbule measured from TEM images.
We used the transfer matrix method  implemented in an R script to compute reflectance spectra for model 1. To calculate reflectance for model 2 and validate the GRIN method in model 1, we used the finite difference time domain method (FDTD) implemented in Meep . We used published values for the refractive index of melanin (nmel = 2.00) [20,21] and keratin (nker = 1.56) . The extinction coefficient of avian melanin has not been empirically determined, thus we used a value for a melanin-like material in beetles (kmel = 0.1 at 400 nm) .
2.4 Colorspace analyses
To compare the range of colors produced by GRIN and uniform layers, we converted calculated spectra (without melanin absorption) to Commission Internationale de Eclairage (CIE) xyY coordinates following Dong et al.  using 1931 CIE color-matching functions obtained from the Color and Vision Research Laboratory. We also converted spectra to xyz coordinates using information on the visual physiology of birds. Unlike humans, birds have a fourth UV-sensitive color-sensitive cone in their retina allowing for perception of a broader range of colors (reviewed in ). To compare simulated spectra in this avian colorspace, we first computed quantum catches for each cone as , where qi is the amount of light captured by cone i, R is the reflectance at a given wavelength and S is the cone sensitivity . We then converted these qi values into 3D xyz coordinates using published equations .
Peak locations depend on optical thickness (nd) of a nanostructure. Thus, to control for difference in n for GRIN and uniform layers of melanin, we calculated an adjusted melanin layer thickness (dadj) to give equivalent optical thicknesses for the graded and uniform index structures:, where n1 = 1.59 and n2 = 2.00.
3.1 Feather nanostructure
In both species, melanosomes formed a loosely-packed monolayer at the edges of barbules (Fig. 1(b), 1(e)) and were surrounded by air (Fig. 1(c)), consistent with previous findings . FFTs of barbule cross-sections showed weak 2D positional ordering of melanosomes (insets in Fig. 1(b), 1(e)). The cylindrical shape of melanosomes produced a GRIN, as indicated by variation in electron density with position as shown in Fig. 1(f). The diameters of melanosomes (dmel) were 145 nm (95% confidence interval, CI: 136-162 nm) and 156 nm (CI: 141-177), and the average keratin cortex thicknesses (dker) were 242 nm (CI: 222-257 nm) and 155 nm (CI: 138-179 nm) in Polyplectron and Patagioenas, respectively.
3.2 Spectral analysis
Reflectance spectra measured at near-normal incidence (10°) for p- and s-polarized incident light were similar, suggesting that the observed orientational disorder of melanosomes in Fig. 1(c) eliminates the linear polarization expected for light scattering from parallel cylinders . There was a good match between the measured and predicted reflectance spectra based on the best-fitting GRIN model (Fig. 2(a), 2(c)). Different levels of kmel (from 0 - 0.3) had only a minor effect on spectral shape; specifically, the small peaks near 350 nm decreased in amplitude relative to the overall spectrum.
Feather color was strongly iridescent in both species and reflectance became more linearly polarized with incident angle (Fig. 3(a), 2(c)). Different levels of kmel (from 0 - 0.3) had only a minor effect on spectral shape; specifically, the small peaks near 350 nm decreased in amplitude relative to the overall spectrum.
3.3. Antireflection mechanism
To explore the potential antireflection properties of the GRIN layer formed by melanosomes, we simulated reflectance at a keratin-air interface with and without an adjacent GRIN layer. Figure 4(a) shows reflectance as a function of reduced frequency dmel/λ (for comparison of reflectance at different thicknesses and wavelengths) with and without melanin absorption, revealing strong antireflection at multiple frequencies compared to a bare keratin interface (R < 0.05% versus 4.8%). Similar antireflection can also be achieved with a uniform layer, but optical simulations revealed that the GRIN layer functions over a broader range of RIs (R < 0.01% for n = 1.78 - 1.87 compared to 1.24 - 1.26 for a non-GRIN layer) and the optimal RI was 1.82 compared to 1.25 for a uniform layer, impossible to achieve with available film-forming materials .
Next, to understand the link between antireflection at the cortex-GRIN layer interface and color of the composite structure, we simulated reflectance at a reduced frequency of 1.24 but with a finite upper keratin cortex varying in thickness. This frequency was chosen because its antireflection properties were similar for absorbing and non-absorbing cases (arrow in Fig. 4(a)). Figure 4(b) shows that, compared to a uniform layer of melanin, reflectance of a nanostructure with a GRIN layer varies only slightly with phase thickness, , around a mean value of 4.8%. This weak relationship between R and δ indicates that antireflection at the keratin-melanosome interface suppresses interference at specific wavelengths, and that this effect is largely independent of cortex thickness. Thus, color produced by these structures is flexible and maintains constant light transmission over a given wavelength range.
3.4. Colorspace analysis
Reflectance simulations for the GRIN and uniform melanin layers over a range of parameter combinations for dmel and dker (both varying from 50 to 450 nm in 10-nm increments) indicated that the range of theoretical colors for a uniform layer is limited relative to a GRIN layer. Figure 5(a) shows that the GRIN layer produces more colors extending further toward the edges of the CIE color gamut (i.e. pure, monochromatic colors). We found a similar pattern for analyses of spectra in avian 3D colorspace (Fig. 5(b)). The color gamut shown in Fig. 5 is for simulations without melanin absorption (kmel = 0) because we wanted to investigate the independent effects of nanostructure on color production. Additional simulations including a wavelength-dependent extinction coefficient for melanin  and keratin  produced similar results (i.e. more colors were possible with a GRIN layer).
The limited range of colors produced by a layered structure with uniform RI can be understood with wave impedance theory . For a 2-layer stack of non-absorbing uniform layers, a reflectance peak will reach a maximum when the layer thicknesses are λ/2 (high RI) and λ/4 (low RI) and a minimum when the layer thicknesses are λ/4 (low RI) and λ/2 (high RI). The amplitude of the peak is a function of the RI of the layer (n), ambient medium (n0) and substrate (nsub):Fig. 5(a), outsets).
Recent studies on similar structures in closely related rock pigeons and mourning doves indicate that only the cortex is involved in coloration [29,30]. Nakamura et al.  suggested this was due to melanosome disorder or size variation. An alternative hypothesis is that the large melanosomes in these species may strongly scatter light in the forward direction, decoupling the optical effects of the cortex and melanosome layers. Consistent with this hypothesis, our simulations for absorbing melanosomes show decreasing variation in reflectance with wavelength at large diameters (d/λ > 3; Fig. 4(a)), suggesting that large melanosomes play a minimal role in producing interference colors.
Previous morphological data  for the two species analyzed here fall within the confidence intervals of our measurements for the peacock-pheasant (dmel = 148 nm, dker = 245 nm) but not the pigeon (dmel = 192 nm, dker = 111 nm). This latter disagreement could be due to the fact that we analyzed a different part of the feather barbule (curved, exposed regions compared to flat sides obscured by adjacent barbules in Durrer ) or morphological variation between individuals. Interestingly, the total thickness (dmel + dker) of the composite structures were comparable (303 nm in Durrer compared to 311 nm here), thus the predicted peak locations would be similar.
Similar interference suppression to that shown in Fig. 4(b) has recently been described in artificial materials using nanocone arrays . However, our results differ because the change in RI at the cortex-melanosome interface is abrupt rather than gradual, the melanosome layer has a finite thickness, and the interference reduction is over a narrower range of wavelengths, facilitating more subtle variations in color (Fig. 5(a)). These results suggest a possible route to engineered solar cells with flexible structural colors that maintain constant light transmission over a target wavelength range [32,33].
Color-producing nanostructures in birds likely develop by self-assembly of basic feather materials , therefore nanostructural diversity may be driven by variation in basic parameters controlling the self-assembly process. Comparing our morphological results to those of highly ordered photonic crystals in peacocks  provides an opportunity to explore potential traits involved in development of disordered and ordered nanostructures. Large colloidal particles like melanosomes typically aggregate into disordered structures unless there is a long-range interaction force stabilizing them . The presence of air between melanosomes observed in Fig. 1(c) likely reduces short-range order (Fig. 1(b), 1(e) insets) and, at the same time, provides a strong RI contrast for saturated colors (Fig. 5(a)). Understanding the development of a keratin cortex over a porous network of melanosomes may also give insight into the design of suspended polymer membranes for applications in pressure sensing  or nanofiltration .
We have described a composite nanostructure in birds that likely causes suppression of interference and therefore reduction in the secondary reflectance peaks produced by multilayer reflectors. Melanosomes provide a strong RI contrast similar to other natural structures , highlighting a largely unexplored gamut of natural materials for novel antireflective and structural color applications. We expect these results will inspire the biomimetic design of non-hazardous and cost-effective LEDs, solar cells, and color displays.
We thank L. D’Alba, M. Xiao, D. Fechyr-Lippens, R. Maia, M. Blastrom, B. Hsiung, J. Peteya and an anonymous reviewer for helpful comments and discussion on earlier versions of this manuscript. A. Avishai provided methodological insight and performed FIB-SEM analysis. This work was supported by grants HFSP RGY0083 and AFOSR FA9550-09-1-0159 (both to M.D.S.).
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