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

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Abstract

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

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Figures (5)

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: nmel = 2.00, nair = 1.00, kmel = 0.1, and nker = 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 peacock-pheasant 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 (dmel/λ) for a GRIN layer under bulk keratin (nker = 1.56) both without (solid line) and with absorption (dashed line, kmel = 0.1). Horizontal green line is reflectance calculated for a bare keratin-air interface (R = 4.8%). (b) Reflectance versus phase thickness δ at dmel/λ = 1.24 (marked by vertical arrow in (a)) for a GRIN (pink) and uniform (black) composite structure varying in cortex thickness (dker). 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 dker and dmel. 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. nkerdker = λ/4); vertical arrows correspond to dmel/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.

Equations (3)

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(m1/2 ) λ max =2( d 1 n 1 2 sin 2 θ + d 2 n 2 2 sin 2 θ )
n(z)= n air + Θ r ( n mel n air ) z 2 2zr
R= [ ( n 2 n 0 n sub )/( n 2 + n 0 n sub ) ] 2
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