Abstract

We investigate the physical mechanism for color production by isotropic nanostructures with short-range order in bird feather barbs. While the primary peak in optical scattering spectra results from constructive interference of singly-scattered light, many species exhibit secondary peaks with distinct characteristic. Our experimental and numerical studies show that these secondary peaks result from double scattering of light by the correlated structures. Without an analog in periodic or random structures, such a phenomenon is unique for short-range ordered structures, and has been widely used by nature for non-iridescent structural coloration.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
  4. A. R. Parker, R. C. McPhedran, D. R. McKenzie, L. C. Botten, and N. P. Nicorovici, “Photonic engineering: Aphrodite’s iridescence,” Nature 409, 36–37 (2001).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  8. R. O. Prum, R. H. Torres, S. Williamson, and J. Dyck, “Coherent light scattering by blue feather barbs,” Nature 396, 28–29 (1998).
    [CrossRef]
  9. D. Osorio, and A. D. Ham, “Spectral reflectance and directional properties of structural coloration in bird plumage,” J. Exp. Biol. 205, 2017–2027 (2002).
    [PubMed]
  10. M. D. Shawkey, V. Saranathan, H. Pálsdóttir, J. Crum, M. H. Ellisman, M. Auer, and R. O. Prum, “Electron tomography, three-dimensional Fourier analysis and colour prediction of a three-dimensional amorphous biophotonic nanostructure,” J. R. Soc. Interface 6, S213–S220 (2009).
    [PubMed]
  11. E. R. Dufresne, H. Noh, V. Saranathan, S. G. J. Mochrie, H. Cao, and R. O. Prum, “Self-assembly of amorphous biophotonic nanostructures by phase separation,” Soft Matter 5, 1792 (2009).
    [CrossRef]
  12. A. S. Barreira, G. Garcia, D. A. Lijtmaer, S. C. Lougheed, and P. L. Tubaro, “Blue males and green females: Sexual dichromatism in the Blue dacnis (Dacnis cayania) and the Swallow tanager (Tersina viridis),” Ornitol. Neotrop. 19, 441–450 (2008).
  13. J. Dyck, “Structural Colors,” Proc. Int. Orthnithol. Congr. 16, 426–437 (1976).
  14. H. Noh, “Optical Properties of Nanostructures: from Random to Periodic,” PhD thesis (Northwestern Univ., Evanston, 2009)
  15. Source code can be downloaded at http://local.wasp.uwa.edu.au/pbourke/geometry
  16. P. Vukusic, and R. J. Sambles, “Shedding light on butterfly wings,” Proc. SPIE 4438, 85–95 (2001).
    [CrossRef]
  17. K. Kertész, Z. Bálint, Z. Vértesy, G. I. Márk, V. Lousse, J. P. Vigneron, M. Rassart, and L. P. Biró, “Gleaming and dull surface textures from photonic-crystal-type nanostructures in the butterfly Cyanophrys remus,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 021922 (2006).
    [CrossRef]
  18. D. G. Stavenga, H. L. Leertouwer, P. Pirih, and M. F. Wehling, “Imaging scatterometry of butterfly wing scales,” Opt. Express 17, 193–202 (2009).
    [CrossRef] [PubMed]
  19. G. I. Márk, Z. Vértesy, K. Kertész, Z. Bálint, and L. P. Biró, “Order-disorder effects in structure and color relation of photonic-crystal-type nanostructures in butterfly wing scales,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80, 051903 (2009).
    [CrossRef]

2009

M. D. Shawkey, V. Saranathan, H. Pálsdóttir, J. Crum, M. H. Ellisman, M. Auer, and R. O. Prum, “Electron tomography, three-dimensional Fourier analysis and colour prediction of a three-dimensional amorphous biophotonic nanostructure,” J. R. Soc. Interface 6, S213–S220 (2009).
[PubMed]

E. R. Dufresne, H. Noh, V. Saranathan, S. G. J. Mochrie, H. Cao, and R. O. Prum, “Self-assembly of amorphous biophotonic nanostructures by phase separation,” Soft Matter 5, 1792 (2009).
[CrossRef]

G. I. Márk, Z. Vértesy, K. Kertész, Z. Bálint, and L. P. Biró, “Order-disorder effects in structure and color relation of photonic-crystal-type nanostructures in butterfly wing scales,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80, 051903 (2009).
[CrossRef]

D. G. Stavenga, H. L. Leertouwer, P. Pirih, and M. F. Wehling, “Imaging scatterometry of butterfly wing scales,” Opt. Express 17, 193–202 (2009).
[CrossRef] [PubMed]

2008

A. S. Barreira, G. Garcia, D. A. Lijtmaer, S. C. Lougheed, and P. L. Tubaro, “Blue males and green females: Sexual dichromatism in the Blue dacnis (Dacnis cayania) and the Swallow tanager (Tersina viridis),” Ornitol. Neotrop. 19, 441–450 (2008).

S. Kinoshita, S. Yoshioka, and J. Miyazaki, “Physics of structural colors,” Rep. Prog. Phys. 71, 076401 (2008).
[CrossRef]

2006

K. Kertész, Z. Bálint, Z. Vértesy, G. I. Márk, V. Lousse, J. P. Vigneron, M. Rassart, and L. P. Biró, “Gleaming and dull surface textures from photonic-crystal-type nanostructures in the butterfly Cyanophrys remus,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 021922 (2006).
[CrossRef]

2002

D. Osorio, and A. D. Ham, “Spectral reflectance and directional properties of structural coloration in bird plumage,” J. Exp. Biol. 205, 2017–2027 (2002).
[PubMed]

2001

P. Vukusic, and R. J. Sambles, “Shedding light on butterfly wings,” Proc. SPIE 4438, 85–95 (2001).
[CrossRef]

A. R. Parker, R. C. McPhedran, D. R. McKenzie, L. C. Botten, and N. P. Nicorovici, “Photonic engineering: Aphrodite’s iridescence,” Nature 409, 36–37 (2001).
[CrossRef] [PubMed]

2000

P. Vukusic, J. R. Sambles, and C. R. Lawrence, “Structural colour: Colour mixing in wing scales of a butterfly,” Nature 404, 457 (2000).
[CrossRef] [PubMed]

1998

R. O. Prum, R. H. Torres, S. Williamson, and J. Dyck, “Coherent light scattering by blue feather barbs,” Nature 396, 28–29 (1998).
[CrossRef]

1976

J. Dyck, “Structural Colors,” Proc. Int. Orthnithol. Congr. 16, 426–437 (1976).

1971

J. Dyck, “Structure and colour-production of the blue barbs of Agapornis roseicollis and Cotinga maynana,” Z. Zellforsch. 115, 17–29 (1971).
[CrossRef] [PubMed]

Auer, M.

M. D. Shawkey, V. Saranathan, H. Pálsdóttir, J. Crum, M. H. Ellisman, M. Auer, and R. O. Prum, “Electron tomography, three-dimensional Fourier analysis and colour prediction of a three-dimensional amorphous biophotonic nanostructure,” J. R. Soc. Interface 6, S213–S220 (2009).
[PubMed]

Bálint, Z.

G. I. Márk, Z. Vértesy, K. Kertész, Z. Bálint, and L. P. Biró, “Order-disorder effects in structure and color relation of photonic-crystal-type nanostructures in butterfly wing scales,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80, 051903 (2009).
[CrossRef]

K. Kertész, Z. Bálint, Z. Vértesy, G. I. Márk, V. Lousse, J. P. Vigneron, M. Rassart, and L. P. Biró, “Gleaming and dull surface textures from photonic-crystal-type nanostructures in the butterfly Cyanophrys remus,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 021922 (2006).
[CrossRef]

Barreira, A. S.

A. S. Barreira, G. Garcia, D. A. Lijtmaer, S. C. Lougheed, and P. L. Tubaro, “Blue males and green females: Sexual dichromatism in the Blue dacnis (Dacnis cayania) and the Swallow tanager (Tersina viridis),” Ornitol. Neotrop. 19, 441–450 (2008).

Biró, L. P.

G. I. Márk, Z. Vértesy, K. Kertész, Z. Bálint, and L. P. Biró, “Order-disorder effects in structure and color relation of photonic-crystal-type nanostructures in butterfly wing scales,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80, 051903 (2009).
[CrossRef]

K. Kertész, Z. Bálint, Z. Vértesy, G. I. Márk, V. Lousse, J. P. Vigneron, M. Rassart, and L. P. Biró, “Gleaming and dull surface textures from photonic-crystal-type nanostructures in the butterfly Cyanophrys remus,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 021922 (2006).
[CrossRef]

Botten, L. C.

A. R. Parker, R. C. McPhedran, D. R. McKenzie, L. C. Botten, and N. P. Nicorovici, “Photonic engineering: Aphrodite’s iridescence,” Nature 409, 36–37 (2001).
[CrossRef] [PubMed]

Cao, H.

E. R. Dufresne, H. Noh, V. Saranathan, S. G. J. Mochrie, H. Cao, and R. O. Prum, “Self-assembly of amorphous biophotonic nanostructures by phase separation,” Soft Matter 5, 1792 (2009).
[CrossRef]

Crum, J.

M. D. Shawkey, V. Saranathan, H. Pálsdóttir, J. Crum, M. H. Ellisman, M. Auer, and R. O. Prum, “Electron tomography, three-dimensional Fourier analysis and colour prediction of a three-dimensional amorphous biophotonic nanostructure,” J. R. Soc. Interface 6, S213–S220 (2009).
[PubMed]

Dufresne, E. R.

E. R. Dufresne, H. Noh, V. Saranathan, S. G. J. Mochrie, H. Cao, and R. O. Prum, “Self-assembly of amorphous biophotonic nanostructures by phase separation,” Soft Matter 5, 1792 (2009).
[CrossRef]

Dyck, J.

R. O. Prum, R. H. Torres, S. Williamson, and J. Dyck, “Coherent light scattering by blue feather barbs,” Nature 396, 28–29 (1998).
[CrossRef]

J. Dyck, “Structural Colors,” Proc. Int. Orthnithol. Congr. 16, 426–437 (1976).

J. Dyck, “Structure and colour-production of the blue barbs of Agapornis roseicollis and Cotinga maynana,” Z. Zellforsch. 115, 17–29 (1971).
[CrossRef] [PubMed]

Ellisman, M. H.

M. D. Shawkey, V. Saranathan, H. Pálsdóttir, J. Crum, M. H. Ellisman, M. Auer, and R. O. Prum, “Electron tomography, three-dimensional Fourier analysis and colour prediction of a three-dimensional amorphous biophotonic nanostructure,” J. R. Soc. Interface 6, S213–S220 (2009).
[PubMed]

Garcia, G.

A. S. Barreira, G. Garcia, D. A. Lijtmaer, S. C. Lougheed, and P. L. Tubaro, “Blue males and green females: Sexual dichromatism in the Blue dacnis (Dacnis cayania) and the Swallow tanager (Tersina viridis),” Ornitol. Neotrop. 19, 441–450 (2008).

Ham, A. D.

D. Osorio, and A. D. Ham, “Spectral reflectance and directional properties of structural coloration in bird plumage,” J. Exp. Biol. 205, 2017–2027 (2002).
[PubMed]

Kertész, K.

G. I. Márk, Z. Vértesy, K. Kertész, Z. Bálint, and L. P. Biró, “Order-disorder effects in structure and color relation of photonic-crystal-type nanostructures in butterfly wing scales,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80, 051903 (2009).
[CrossRef]

K. Kertész, Z. Bálint, Z. Vértesy, G. I. Márk, V. Lousse, J. P. Vigneron, M. Rassart, and L. P. Biró, “Gleaming and dull surface textures from photonic-crystal-type nanostructures in the butterfly Cyanophrys remus,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 021922 (2006).
[CrossRef]

Kinoshita, S.

S. Kinoshita, S. Yoshioka, and J. Miyazaki, “Physics of structural colors,” Rep. Prog. Phys. 71, 076401 (2008).
[CrossRef]

Lawrence, C. R.

P. Vukusic, J. R. Sambles, and C. R. Lawrence, “Structural colour: Colour mixing in wing scales of a butterfly,” Nature 404, 457 (2000).
[CrossRef] [PubMed]

Leertouwer, H. L.

Lijtmaer, D. A.

A. S. Barreira, G. Garcia, D. A. Lijtmaer, S. C. Lougheed, and P. L. Tubaro, “Blue males and green females: Sexual dichromatism in the Blue dacnis (Dacnis cayania) and the Swallow tanager (Tersina viridis),” Ornitol. Neotrop. 19, 441–450 (2008).

Lougheed, S. C.

A. S. Barreira, G. Garcia, D. A. Lijtmaer, S. C. Lougheed, and P. L. Tubaro, “Blue males and green females: Sexual dichromatism in the Blue dacnis (Dacnis cayania) and the Swallow tanager (Tersina viridis),” Ornitol. Neotrop. 19, 441–450 (2008).

Lousse, V.

K. Kertész, Z. Bálint, Z. Vértesy, G. I. Márk, V. Lousse, J. P. Vigneron, M. Rassart, and L. P. Biró, “Gleaming and dull surface textures from photonic-crystal-type nanostructures in the butterfly Cyanophrys remus,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 021922 (2006).
[CrossRef]

Márk, G. I.

G. I. Márk, Z. Vértesy, K. Kertész, Z. Bálint, and L. P. Biró, “Order-disorder effects in structure and color relation of photonic-crystal-type nanostructures in butterfly wing scales,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80, 051903 (2009).
[CrossRef]

K. Kertész, Z. Bálint, Z. Vértesy, G. I. Márk, V. Lousse, J. P. Vigneron, M. Rassart, and L. P. Biró, “Gleaming and dull surface textures from photonic-crystal-type nanostructures in the butterfly Cyanophrys remus,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 021922 (2006).
[CrossRef]

McKenzie, D. R.

A. R. Parker, R. C. McPhedran, D. R. McKenzie, L. C. Botten, and N. P. Nicorovici, “Photonic engineering: Aphrodite’s iridescence,” Nature 409, 36–37 (2001).
[CrossRef] [PubMed]

McPhedran, R. C.

A. R. Parker, R. C. McPhedran, D. R. McKenzie, L. C. Botten, and N. P. Nicorovici, “Photonic engineering: Aphrodite’s iridescence,” Nature 409, 36–37 (2001).
[CrossRef] [PubMed]

Miyazaki, J.

S. Kinoshita, S. Yoshioka, and J. Miyazaki, “Physics of structural colors,” Rep. Prog. Phys. 71, 076401 (2008).
[CrossRef]

Mochrie, S. G. J.

E. R. Dufresne, H. Noh, V. Saranathan, S. G. J. Mochrie, H. Cao, and R. O. Prum, “Self-assembly of amorphous biophotonic nanostructures by phase separation,” Soft Matter 5, 1792 (2009).
[CrossRef]

Nicorovici, N. P.

A. R. Parker, R. C. McPhedran, D. R. McKenzie, L. C. Botten, and N. P. Nicorovici, “Photonic engineering: Aphrodite’s iridescence,” Nature 409, 36–37 (2001).
[CrossRef] [PubMed]

Noh, H.

E. R. Dufresne, H. Noh, V. Saranathan, S. G. J. Mochrie, H. Cao, and R. O. Prum, “Self-assembly of amorphous biophotonic nanostructures by phase separation,” Soft Matter 5, 1792 (2009).
[CrossRef]

Osorio, D.

D. Osorio, and A. D. Ham, “Spectral reflectance and directional properties of structural coloration in bird plumage,” J. Exp. Biol. 205, 2017–2027 (2002).
[PubMed]

Pálsdóttir, H.

M. D. Shawkey, V. Saranathan, H. Pálsdóttir, J. Crum, M. H. Ellisman, M. Auer, and R. O. Prum, “Electron tomography, three-dimensional Fourier analysis and colour prediction of a three-dimensional amorphous biophotonic nanostructure,” J. R. Soc. Interface 6, S213–S220 (2009).
[PubMed]

Parker, A. R.

A. R. Parker, R. C. McPhedran, D. R. McKenzie, L. C. Botten, and N. P. Nicorovici, “Photonic engineering: Aphrodite’s iridescence,” Nature 409, 36–37 (2001).
[CrossRef] [PubMed]

Pirih, P.

Prum, R. O.

E. R. Dufresne, H. Noh, V. Saranathan, S. G. J. Mochrie, H. Cao, and R. O. Prum, “Self-assembly of amorphous biophotonic nanostructures by phase separation,” Soft Matter 5, 1792 (2009).
[CrossRef]

M. D. Shawkey, V. Saranathan, H. Pálsdóttir, J. Crum, M. H. Ellisman, M. Auer, and R. O. Prum, “Electron tomography, three-dimensional Fourier analysis and colour prediction of a three-dimensional amorphous biophotonic nanostructure,” J. R. Soc. Interface 6, S213–S220 (2009).
[PubMed]

R. O. Prum, R. H. Torres, S. Williamson, and J. Dyck, “Coherent light scattering by blue feather barbs,” Nature 396, 28–29 (1998).
[CrossRef]

Rassart, M.

K. Kertész, Z. Bálint, Z. Vértesy, G. I. Márk, V. Lousse, J. P. Vigneron, M. Rassart, and L. P. Biró, “Gleaming and dull surface textures from photonic-crystal-type nanostructures in the butterfly Cyanophrys remus,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 021922 (2006).
[CrossRef]

Sambles, J. R.

P. Vukusic, J. R. Sambles, and C. R. Lawrence, “Structural colour: Colour mixing in wing scales of a butterfly,” Nature 404, 457 (2000).
[CrossRef] [PubMed]

Sambles, R. J.

P. Vukusic, and R. J. Sambles, “Shedding light on butterfly wings,” Proc. SPIE 4438, 85–95 (2001).
[CrossRef]

Saranathan, V.

M. D. Shawkey, V. Saranathan, H. Pálsdóttir, J. Crum, M. H. Ellisman, M. Auer, and R. O. Prum, “Electron tomography, three-dimensional Fourier analysis and colour prediction of a three-dimensional amorphous biophotonic nanostructure,” J. R. Soc. Interface 6, S213–S220 (2009).
[PubMed]

E. R. Dufresne, H. Noh, V. Saranathan, S. G. J. Mochrie, H. Cao, and R. O. Prum, “Self-assembly of amorphous biophotonic nanostructures by phase separation,” Soft Matter 5, 1792 (2009).
[CrossRef]

Shawkey, M. D.

M. D. Shawkey, V. Saranathan, H. Pálsdóttir, J. Crum, M. H. Ellisman, M. Auer, and R. O. Prum, “Electron tomography, three-dimensional Fourier analysis and colour prediction of a three-dimensional amorphous biophotonic nanostructure,” J. R. Soc. Interface 6, S213–S220 (2009).
[PubMed]

Stavenga, D. G.

Torres, R. H.

R. O. Prum, R. H. Torres, S. Williamson, and J. Dyck, “Coherent light scattering by blue feather barbs,” Nature 396, 28–29 (1998).
[CrossRef]

Tubaro, P. L.

A. S. Barreira, G. Garcia, D. A. Lijtmaer, S. C. Lougheed, and P. L. Tubaro, “Blue males and green females: Sexual dichromatism in the Blue dacnis (Dacnis cayania) and the Swallow tanager (Tersina viridis),” Ornitol. Neotrop. 19, 441–450 (2008).

Vértesy, Z.

G. I. Márk, Z. Vértesy, K. Kertész, Z. Bálint, and L. P. Biró, “Order-disorder effects in structure and color relation of photonic-crystal-type nanostructures in butterfly wing scales,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80, 051903 (2009).
[CrossRef]

K. Kertész, Z. Bálint, Z. Vértesy, G. I. Márk, V. Lousse, J. P. Vigneron, M. Rassart, and L. P. Biró, “Gleaming and dull surface textures from photonic-crystal-type nanostructures in the butterfly Cyanophrys remus,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 021922 (2006).
[CrossRef]

Vigneron, J. P.

K. Kertész, Z. Bálint, Z. Vértesy, G. I. Márk, V. Lousse, J. P. Vigneron, M. Rassart, and L. P. Biró, “Gleaming and dull surface textures from photonic-crystal-type nanostructures in the butterfly Cyanophrys remus,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 021922 (2006).
[CrossRef]

Vukusic, P.

P. Vukusic, and R. J. Sambles, “Shedding light on butterfly wings,” Proc. SPIE 4438, 85–95 (2001).
[CrossRef]

P. Vukusic, J. R. Sambles, and C. R. Lawrence, “Structural colour: Colour mixing in wing scales of a butterfly,” Nature 404, 457 (2000).
[CrossRef] [PubMed]

Wehling, M. F.

Williamson, S.

R. O. Prum, R. H. Torres, S. Williamson, and J. Dyck, “Coherent light scattering by blue feather barbs,” Nature 396, 28–29 (1998).
[CrossRef]

Yoshioka, S.

S. Kinoshita, S. Yoshioka, and J. Miyazaki, “Physics of structural colors,” Rep. Prog. Phys. 71, 076401 (2008).
[CrossRef]

J. Exp. Biol.

D. Osorio, and A. D. Ham, “Spectral reflectance and directional properties of structural coloration in bird plumage,” J. Exp. Biol. 205, 2017–2027 (2002).
[PubMed]

J. R. Soc. Interface

M. D. Shawkey, V. Saranathan, H. Pálsdóttir, J. Crum, M. H. Ellisman, M. Auer, and R. O. Prum, “Electron tomography, three-dimensional Fourier analysis and colour prediction of a three-dimensional amorphous biophotonic nanostructure,” J. R. Soc. Interface 6, S213–S220 (2009).
[PubMed]

Nature

P. Vukusic, J. R. Sambles, and C. R. Lawrence, “Structural colour: Colour mixing in wing scales of a butterfly,” Nature 404, 457 (2000).
[CrossRef] [PubMed]

A. R. Parker, R. C. McPhedran, D. R. McKenzie, L. C. Botten, and N. P. Nicorovici, “Photonic engineering: Aphrodite’s iridescence,” Nature 409, 36–37 (2001).
[CrossRef] [PubMed]

R. O. Prum, R. H. Torres, S. Williamson, and J. Dyck, “Coherent light scattering by blue feather barbs,” Nature 396, 28–29 (1998).
[CrossRef]

Opt. Express

Ornitol. Neotrop.

A. S. Barreira, G. Garcia, D. A. Lijtmaer, S. C. Lougheed, and P. L. Tubaro, “Blue males and green females: Sexual dichromatism in the Blue dacnis (Dacnis cayania) and the Swallow tanager (Tersina viridis),” Ornitol. Neotrop. 19, 441–450 (2008).

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

K. Kertész, Z. Bálint, Z. Vértesy, G. I. Márk, V. Lousse, J. P. Vigneron, M. Rassart, and L. P. Biró, “Gleaming and dull surface textures from photonic-crystal-type nanostructures in the butterfly Cyanophrys remus,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 021922 (2006).
[CrossRef]

G. I. Márk, Z. Vértesy, K. Kertész, Z. Bálint, and L. P. Biró, “Order-disorder effects in structure and color relation of photonic-crystal-type nanostructures in butterfly wing scales,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80, 051903 (2009).
[CrossRef]

Proc. Int. Orthnithol. Congr.

J. Dyck, “Structural Colors,” Proc. Int. Orthnithol. Congr. 16, 426–437 (1976).

Proc. SPIE

P. Vukusic, and R. J. Sambles, “Shedding light on butterfly wings,” Proc. SPIE 4438, 85–95 (2001).
[CrossRef]

Rep. Prog. Phys.

S. Kinoshita, S. Yoshioka, and J. Miyazaki, “Physics of structural colors,” Rep. Prog. Phys. 71, 076401 (2008).
[CrossRef]

Soft Matter

E. R. Dufresne, H. Noh, V. Saranathan, S. G. J. Mochrie, H. Cao, and R. O. Prum, “Self-assembly of amorphous biophotonic nanostructures by phase separation,” Soft Matter 5, 1792 (2009).
[CrossRef]

Z. Zellforsch.

J. Dyck, “Structure and colour-production of the blue barbs of Agapornis roseicollis and Cotinga maynana,” Z. Zellforsch. 115, 17–29 (1971).
[CrossRef] [PubMed]

Other

H. Ghiradella, “Hairs, Bristles and Scales” in Microscopic Anatomy of Invertebrates, edited by M. Locke (Wiley-Liss, New York, 1998), Vol. 11A, 257–287.

R. O. Prum, “Anatomy, Physics, and Evolution of Structural Colors” in Bird coloration, (Harvard University Press, Boston, 2006), Vol. 1, 295–353.

C. V. Raman, “The Origin of the Colours in the Plumage of Birds,” Proc. Ind. Acad. Sci. (A) 1, 1–7 (1934)

H. Noh, “Optical Properties of Nanostructures: from Random to Periodic,” PhD thesis (Northwestern Univ., Evanston, 2009)

Source code can be downloaded at http://local.wasp.uwa.edu.au/pbourke/geometry

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Figures (4)

Fig. 1.
Fig. 1.

(a) Coracias benghalensis (Indian Roller) whose wing feather color was studied by Raman in the 1930s. Photo credit to Pascal Rapin (reproduced with permission) (b) Scanning electron micrograph of the feather barbs showing channel-type nanostructures with β-keratin rods and air channels. The scale bar = 500nm. Inset: small-angle X-ray scattering (SAXS) pattern of the feather barbs that exhibits a ring. The scale bar = 0.05 nm-1

Fig. 2.
Fig. 2.

(a) Azimuthal average of SAXS intensity (blue dashed line) in comparison to nearly backscattered light intensity at normal incidence (black solid line) plotted as a function of the magnitude of spatial vector q. The optical scattering spectrum has a secondary peak. (b) Scattered light intensity of co-polarization (black solid line) and cross-polarization (blue dashed line) as a function of wavelength. The linearly polarized white light is incident at normal, ϕ = 0°. The detector collects the scattered light at an angle of θ = 10° from the surface normal. The polarization direction of the incident light is parallel to the scattering plane that is formed by the surface normal and detector. Similar results are obtained when the polarization of incident light is perpendicular to the scattering plane.

Fig. 3.
Fig. 3.

(a) Inset: a schematic showing the white light incident on the feather barb at an angle ϕ from the surface normal is scattered or reflected to a direction of angle θ from the incident beam. In the specular reflection measurement, θ = 2ϕ. Main panel: Wavelengths of the primary (squares) and secondary (circles) peaks in optical scattering spectra (solid symbols) and specular reflection spectra (open symbols) as a function of θ. The top horizontal axis represents the incident angle ϕ in the specular reflection measurement. (b) q values for the primary peak (squares, solid line) and secondary peak (circles, dashed line) as a function of scattering angle θ. The discrete symbols represent experimental data and the lines calculations. Inset: single scattering diagram.

Fig. 4.
Fig. 4.

(a) Two representative diagrams of double scattering. Light is scattered successively from k i to k m , and then to k o . q 1 = k m - k i and q 2 = k o - k m are spatial vectors of the structure. The angle θm between -k i and k o is the same in the two diagrams. The single scattering angles α 1 and α 2 are smaller than 90° in the upper diagram and larger than 90° in the lower diagram. (b) Calculated double scattering spectra for different scattering angles θ when the incident angle ϕ is fixed at 0°. The values of θ are marked next to the curves.

Equations (1)

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q = 2 k cos ( θ m / 2 ) ,

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