Antireflection-enhanced color by a natural graded refractive index ( GRIN ) structure

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 OCIS codes: (310.1210) Antireflection coatings; (310.6860) Thin films, optical properties; (330.1690) Color; (160.1435) Biomaterials. References and links 1. S. 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Introduction
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 [1].Reflectance maxima (λ max ) for a simple 2-layer stack can be determined using the Bragg-Snell diffraction equation [1]: where n and d are the RIs and thicknesses of the two layers, m is the diffraction order, and θ is the incident angle of light.Because numerous wavelengths fulfill the condition for diffraction (i.e.multiple values of m), reflectance spectra produced by such structures are often multipeaked in visible wavelengths.Newton first observed that the series of colors produced by thin films of increasing thickness were not monochromatic but "compound," and thus unsaturated [2].Achieving more saturated colors requires either an increase in the number of layers [1] 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 [4].One common control mechanism is a thin-film coating with quarter-wavelength thickness and a RI of n 0 n sub , where n 0 and n sub are the RIs of the ambient material and substrate, respectively [5].However, no materials that form films have RIs less than ~1.4,limiting the flexibility of this method [6].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 [7].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 [8].
Birds have evolved diverse photonic structures (e.g., multilayers, photonic crystals, thin films) [9,10] from relatively few materials (keratin, melanin and air) [10].Despite this material limitation, the often non-planar shapes of melanin-containing organelles (melanosomes) might produce a GRIN (e.g., see [11]), 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.

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. [12].From the resulting TEM images, we used ImageJ [13] to measure melanosome diameter (d mel ) and keratin cortex thickness (d ker ) thickness at haphazardly chosen locations along the exposed surface of a barbule.To confirm that melanosomes were surrounded by air as previously suggested [9], 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.

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 (λ max ) and amplitude of reflectance peaks (R max ) using the R package pavo [14].

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 [15]; and 2) a keratin thin film over a melanosome monolayer and amorphous melanosome substrate [16].
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 [15], the refractive index as a function of depth into the cylinder (z) is: where n air = 1.00, n mel = 2.00, r is the melanosome radius and Θ is the ratio of melanosome diameter to space between melanosomes (Θ = 0 refers to melanosomes with infinite space between them and Θ = 1 to close-packed melanosomes).We determined Θ ≈0.75 from TEM measurements.There was a good match between predicted n(z) and empirical variation in average grey value with position along the z-axis through a melanosome monolayer (Fig. 1(f)).For model 2, we used a molecular dynamics, collision-based simulation algorithm to generate random melanosome packing configurations [17] 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 [18] 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 [19].We used published values for the refractive index of melanin (n mel = 2.00) [20,21] and keratin (n ker = 1.56) [22].The extinction coefficient of avian melanin has not been empirically determined, thus we used a value for a melanin-like material in beetles (k mel = 0.1 at 400 nm) [23].

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. [16] 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 [24]).To compare simulated spectra in this avian colorspace, we first computed quantum catches for each cone as , where q i is the amount of light captured by cone i, R is the reflectance at a given wavelength and S is the cone sensitivity [24].We then converted these q i values into 3D xyz coordinates using published equations [25].
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 (d adj ) to give equivalent optical thicknesses for the graded and uniform index structures:, ( ) where n 1 = 1.59 and n 2 = 2.00.

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 [9].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

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 [26].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 k mel (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), 3(c)), consistent with thin-film optical theory [27] and simulated reflectance data (Fig. 3(b), 3(d)).Angle-resolved results were similar for both species, thus only those for the peacock-pheasant are presented here.

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 d mel /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 filmforming materials [6].
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, δ = 2π n ker d ker + n mel d mel ( ) / λ , 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.

Colorspace analysis
Reflectance simulations for the GRIN and uniform melanin layers over a range of parameter combinations for d mel and d ker (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 (k mel = 0) because we wanted to investigate the independent effects of nanostructure on color production.Additional simulations including a wavelength-dependent extinction coefficient for melanin [23] and keratin [22] 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 [28].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 (n 0 ) and substrate (n sub ): Thus, for a uniform stack of keratin (n = 1.56) and melanin (n = 2.00), the amplitude of a reflectance peak can vary from 17.4 -36.0%, giving a maximum peak height ratio of 2.07.By comparison, peak values for the GRIN layer ranged from ~5 to 25% (maximum peak height ratio ~5), producing greater variation in spectral shape and thus more saturated colors (Fig. 5(a), outsets).

Discussion
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. [29] 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 [9] for the two species analyzed here fall within the confidence intervals of our measurements for the peacock-pheasant (d mel = 148 nm, d ker = 245 nm) but not the pigeon (d mel = 192 nm, d ker = 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 [9]) or morphological variation between individuals.Interestingly, the total thickness (d mel + d ker ) 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 [31].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 [34], 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 [21] 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 [35].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 [36] or nanofiltration [37].
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 [16], 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.

Fig. 1 .
Fig. 1.Color and nanostructure of iridescent feathers.(a,d) Optical images of iridescent feathers from the grey peacock-pheasant (a) and band-tailed pigeon (d).(b,e) TEM images of feather barbule cross-sections; lower insets are FFTs of pictured regions.(c) SEM longitudinal view of melanosomes, with labels indicating melanosomes (m), keratin channels (k) and air spaces (a).(f) Measured average grey value (dashed line) versus z for the boxed region shown in (e) along with refractive index n(z) versus z (solid line) calculated with Eq. (2).(g) Schematic diagram of GRIN model.All scale bars are 500 nm.

Fig. 2 .
Fig. 2. Match between measured and modeled reflectance spectra in the peacock-pheasant (a,b) and pigeon (c,d).Lines show empirical (solid, y-axis) and predicted reflectance (dashed, secondary y-axis) for candidate optical models.(a,c) Model 1: cortex and graded index melanosome layer.(b,d) Model 2: amorphous melanosome nanostructure.Values used in calculations: n mel = 2.00, n air = 1.00, k mel = 0.1, and n ker = 1.56.All models have air as the substrate.Amplitudes of the spectra were adjusted to allow for easier comparison.

Fig. 3 .
Fig. 3. Measured and calculated changes in reflectance with incident angle for grey peacockpheasant feathers.False color maps showing measured (a,c) and calculated (b,d) reflectance versus wavelength and incident angle (blue: minimum, red: maximum).Upper panels are results for light polarized perpendicular to melanosomes (p-polarization) and lower panels are with light polarized parallel to melanosomes (s-polarization).Schematic shows optical setup (white rectangle: feather surface, black arrows: light direction, vertical dashed line: surface normal).

Fig. 4 .
Fig. 4. Antireflection and interference suppression by a GRIN structure.(a) Reflectance versus reduced frequency (d mel /λ) for a GRIN layer under bulk keratin (n ker = 1.56) both without (solid line) and with absorption (dashed line, k mel = 0.1).Horizontal green line is reflectance calculated for a bare keratin-air interface (R = 4.8%).(b) Reflectance versus phase thickness δ at d mel /λ = 1.24 (marked by vertical arrow in (a)) for a GRIN (pink) and uniform (black) composite structure varying in cortex thickness (d ker ).Note the log scale for the y-axis.

Fig. 5 .
Fig. 5. Colorspace expansion by a GRIN layer.(a) Calculated spectra in CIE colorspace for different combinations of d ker and d mel .Lines are minimum convex polygons enclosing spectra (solid: GRIN, dashed: uniform).Outsets show extreme spectra corresponding to indicated points for GRIN (dark lines, closed circles) and equivalent uniform layers (light lines, open circles) with similar optical thickness and optimized for minimal reflectance (i.e.n ker d ker = λ/4); vertical arrows correspond to d mel /λ = 1.24 as in Fig. 4(a).(b) Calculated spectra in avian tetrahedral colorspace (pink: GRIN, black: uniform) with vertices corresponding to long-(red), medium-(green), short-(blue) and UV-sensitive cones (violet) in a bird retina.Absorption by melanin was neglected in order to highlight the independent effects of nanostructure on color, and for comparison with Eq. (3) calculations.