Abstract

Disordered structures producing a non-iridescent color impression have been shown to feature a spherically shaped Fourier transform of their refractive-index distribution. We determine the direction and efficiency of scattering from thin films made from such structures with the help of the Ewald sphere construction which follows from first-order scattering approximation. This way we present a simple geometrical argument why these structures are well suited for creating short wavelength colors like blue but are hindered from producing long wavelength colors like red. We also numerically synthesize a model structure dedicated to produce a sharp spherical shell in reciprocal space. The reflectivity of this structure as predicted by the first-order approximation is compared to direct electromagnetic simulations. The results indicate the Ewald sphere construction to constitute a simple geometrical tool that can be used to describe and to explain important spectral and directional features of the reflectivity. It is shown that total internal reflection in the film in combination with directed scattering can be used to obtain long wavelength structural colors.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (1)

M. Iwata, M. Teshima, T. Seki, S. Yoshioka, and Y. Takeoka, “Bio-Inspired Bright Structurally Colored Colloidal Amorphous Array Enhanced by Controlling Thickness and Black Background,” Adv. Mater. 29(26), 1605050 (2017).
[Crossref] [PubMed]

2016 (2)

H. Huang, C.-P. Huang, C. Zhang, X.-H. Hong, X.-J. Zhang, Y.-Q. Qin, and Y.-Y. Zhu, “From Ewald sphere to Ewald shell in nonlinear optics,” Sci. Rep. 6(1), 29365 (2016).
[Crossref] [PubMed]

A. Kawamura, M. Kohri, G. Morimoto, Y. Nannichi, T. Taniguchi, and K. Kishikawa, “Full-Color Biomimetic Photonic Materials with Iridescent and Non-Iridescent Structural Colors,” Sci. Rep. 6(1), 33984 (2016).
[Crossref] [PubMed]

2015 (2)

Y. Zhang, B. Dong, A. Chen, X. Liu, L. Shi, and J. Zi, “Using Cuttlefish Ink as an Additive to Produce -Non-iridescent Structural Colors of High Color Visibility,” Adv. Mater. 27(32), 4719–4724 (2015).
[Crossref] [PubMed]

M. Teshima, T. Seki, R. Kawano, S. Takeuchi, S. Yoshioka, and Y. Takeoka, “Preparation of structurally colored, monodisperse spherical assemblies composed of black and white colloidal particles using a micro-flow-focusing device,” J. Mater. Chem. C Mater. Opt. Electron. Devices 3(4), 769–777 (2015).
[Crossref]

2014 (5)

D. Ge, L. Yang, G. Wu, and S. Yang, “Angle-independent colours from spray coated quasi-amorphous arrays of nanoparticles: combination of constructive interference and Rayleigh scattering,” J. Mater. Chem. C Mater. Opt. Electron. Devices 2(22), 4395–4400 (2014).
[Crossref]

J.-G. Park, S.-H. Kim, S. Magkiriadou, T. M. Choi, Y.-S. Kim, and V. N. Manoharan, “Full-Spectrum Photonic Pigments with Non-iridescent Structural Colors through Colloidal Assembly,” Angew. Chem. Int. Ed. Engl. 53(11), 2899–2903 (2014).
[Crossref] [PubMed]

C. H. Lim, H. Kang, and S.-H. Kim, “Colloidal Assembly in Leidenfrost Drops for Noniridescent Structural Color Pigments,” Langmuir 30(28), 8350–8356 (2014).
[Crossref] [PubMed]

S. Magkiriadou, J.-G. Park, Y.-S. Kim, and V. N. Manoharan, “Absence of red structural color in photonic glasses, bird feathers, and certain beetles,” Phys. Rev. E 90(6), 062302 (2014).
[Crossref] [PubMed]

B. D. Wilts, K. Michielsen, H. De Raedt, and D. G. Stavenga, “Sparkling feather reflections of a bird-of-paradise explained by finite-difference time-domain modeling,” Proc. Natl. Acad. Sci. U.S.A. 111(12), 4363–4368 (2014).
[Crossref] [PubMed]

2013 (2)

J. Tinbergen, B. D. Wilts, and D. G. Stavenga, “Spectral tuning of Amazon parrot feather coloration by psittacofulvin pigments and spongy structures,” J. Exp. Biol. 216(23), 4358–4364 (2013).
[Crossref] [PubMed]

Y. Takeoka, S. Yoshioka, A. Takano, S. Arai, K. Nueangnoraj, H. Nishihara, M. Teshima, Y. Ohtsuka, and T. Seki, “Production of Colored Pigments with Amorphous Arrays of Black and White Colloidal Particles,” Angew. Chem. Int. Ed. Engl. 52(28), 7261–7265 (2013).
[Crossref] [PubMed]

2012 (5)

S. Vignolini, P. J. Rudall, A. V. Rowland, A. Reed, E. Moyroud, R. B. Faden, J. J. Baumberg, B. J. Glover, and U. Steiner, “Pointillist structural color in Pollia fruit,” Proc. Natl. Acad. Sci. U.S.A. 109(39), 15712–15715 (2012).
[Crossref] [PubMed]

V. Saranathan, J. D. Forster, H. Noh, S.-F. Liew, S. G. J. Mochrie, H. Cao, E. R. Dufresne, and R. O. Prum, “Structure and optical function of amorphous photonic nanostructures from avian feather barbs: a comparative small angle X-ray scattering (SAXS) analysis of 230 bird species,” J. R. Soc. Interface 9(75), 2563–2580 (2012).
[Crossref] [PubMed]

L. D’Alba, L. Kieffer, and M. D. Shawkey, “Relative contributions of pigments and biophotonic nanostructures to natural color production: a case study in budgerigar (Melopsittacus undulatus) feathers,” J. Exp. Biol. 215(8), 1272–1277 (2012).
[Crossref] [PubMed]

B. D. Wilts, K. Michielsen, J. Kuipers, H. De Raedt, and D. G. Stavenga, “Brilliant camouflage: photonic crystals in the diamond weevil, Entimus imperialis,” Proc. Biol. Sci. 279(1738), 2524–2530 (2012).
[Crossref] [PubMed]

S. Magkiriadou, J.-G. Park, Y.-S. Kim, and V. N. Manoharan, “Disordered packings of core-shell particles with angle-independent structural colors,” Opt. Mater. Express 2(10), 1343–1352 (2012).
[Crossref]

2011 (5)

S.-H. Kim, S. Y. Lee, S.-M. Yang, and G.-R. Yi, “Self-assembled colloidal structures for photonics,” NPG Asia Mater. 3(1), 25–33 (2011).
[Crossref]

H. L. Leertouwer, B. D. Wilts, and D. G. Stavenga, “Refractive index and dispersion of butterfly chitin and bird keratin measured by polarizing interference microscopy,” Opt. Express 19(24), 24061–24066 (2011).
[Crossref] [PubMed]

E. Shevtsova, C. Hansson, D. H. Janzen, and J. Kjærandsen, “Stable structural color patterns displayed on transparent insect wings,” Proc. Natl. Acad. Sci. U.S.A. 108(2), 668–673 (2011).
[Crossref] [PubMed]

D. G. Stavenga, J. Tinbergen, H. L. Leertouwer, and B. D. Wilts, “Kingfisher feathers-colouration by pigments, spongy nanostructures and thin films,” J. Exp. Biol. 214(23), 3960–3967 (2011).
[Crossref] [PubMed]

G. E. Schröder-Turk, S. Wickham, H. Averdunk, F. Brink, J. D. Fitz Gerald, L. Poladian, M. C. J. Large, and S. T. Hyde, “The chiral structure of porous chitin within the wing-scales of Callophrys rubi,” J. Struct. Biol. 174(2), 290–295 (2011).
[Crossref] [PubMed]

2010 (7)

H. Noh, S. F. Liew, V. Saranathan, S. G. J. Mochrie, R. O. Prum, E. R. Dufresne, and H. Cao, “How Noniridescent Colors Are Generated by Quasi-ordered Structures of Bird Feathers,” Adv. Mater. 22(26-27), 2871–2880 (2010).
[Crossref] [PubMed]

H. Noh, S. F. Liew, V. Saranathan, R. O. Prum, S. G. J. Mochrie, E. R. Dufresne, and H. Cao, “Double scattering of light from Biophotonic Nanostructures with short-range order,” Opt. Express 18(11), 11942–11948 (2010).
[Crossref] [PubMed]

V. Saranathan, C. O. Osuji, S. G. J. Mochrie, H. Noh, S. Narayanan, A. Sandy, E. R. Dufresne, and R. O. Prum, “Structure, function, and self-assembly of single network gyroid (I4132) photonic crystals in butterfly wing scales,” Proc. Natl. Acad. Sci. U.S.A. 107(26), 11676–11681 (2010).
[Crossref] [PubMed]

P. D. García, R. Sapienza, and C. López, “Photonic Glasses: A Step Beyond White Paint,” Adv. Mater. 22(1), 12–19 (2010).
[Crossref] [PubMed]

J. D. Forster, H. Noh, S. F. Liew, V. Saranathan, C. F. Schreck, L. Yang, J.-G. Park, R. O. Prum, S. G. J. Mochrie, C. S. O’Hern, H. Cao, and E. R. Dufresne, “Biomimetic Isotropic Nanostructures for Structural Coloration,” Adv. Mater. 22(26-27), 2939–2944 (2010).
[Crossref] [PubMed]

I. Lee, D. Kim, J. Kal, H. Baek, D. Kwak, D. Go, E. Kim, C. Kang, J. Chung, Y. Jang, S. Ji, J. Joo, and Y. Kang, “Quasi-Amorphous Colloidal Structures for Electrically Tunable Full-Color Photonic Pixels with Angle-Independency,” Adv. Mater. 22(44), 4973–4977 (2010).
[Crossref] [PubMed]

T. D. Gerke and R. Piestun, “Aperiodic volume optics,” Nat. Photonics 4, 188–193 (2010).

2009 (4)

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 80(1), 051903 (2009).
[Crossref] [PubMed]

L. M. Mäthger, E. J. Denton, N. J. Marshall, and R. T. Hanlon, “Mechanisms and behavioural functions of structural coloration in cephalopods,” J. R. Soc. Interface 6(Suppl 2), S149–S163 (2009).
[Crossref] [PubMed]

M. D. Shawkey, N. I. Morehouse, and P. Vukusic, “A protean palette: colour materials and mixing in birds and butterflies,” J. R. Soc. Interface 6(Suppl 2), S221–S231 (2009).
[Crossref] [PubMed]

A. E. Seago, P. Brady, J.-P. Vigneron, and T. D. Schultz, “Gold bugs and beyond: a review of iridescence and structural colour mechanisms in beetles (Coleoptera),” J. R. Soc. Interface 6(Suppl 2), S165–S184 (2009).
[Crossref] [PubMed]

2008 (2)

2007 (2)

P. Vukusic, B. Hallam, and J. Noyes, “Brilliant Whiteness in Ultrathin Beetle Scales,” Science 315(5810), 348 (2007).
[Crossref] [PubMed]

P. D. García, R. Sapienza, Á. Blanco, and C. López, “Photonic Glass: A Novel Random Material for Light,” Adv. Mater. 19(18), 2597–2602 (2007).
[Crossref]

2006 (3)

M. D. Shawkey and G. E. Hill, “Significance of a basal melanin layer to production of non-iridescent structural plumage color: evidence from an amelanotic Steller’s jay (Cyanocitta stelleri),” J. Exp. Biol. 209(7), 1245–1250 (2006).
[Crossref] [PubMed]

J. P. Vigneron, J.-F. Colomer, M. Rassart, A. L. Ingram, and V. Lousse, “Structural origin of the colored reflections from the black-billed magpie feathers,” Phys. Rev. E 73(2), 021914 (2006).
[Crossref] [PubMed]

R. O. Prum, T. Quinn, and R. H. Torres, “Anatomically diverse butterfly scales all produce structural colours by coherent scattering,” J. Exp. Biol. 209(4), 748–765 (2006).
[Crossref] [PubMed]

2005 (3)

S. Kinoshita and S. Yoshioka, “Structural Colors in Nature: The Role of Regularity and Irregularity in the Structure,” ChemPhysChem 6(8), 1442–1459 (2005).
[Crossref] [PubMed]

J. P. Vigneron, J.-F. Colomer, N. Vigneron, and V. Lousse, “Natural layer-by-layer photonic structure in the squamae of Hoplia coerulea (Coleoptera),” Phys. Rev. E 72(1), 061904 (2005).
[Crossref] [PubMed]

M. D. Shawkey and G. E. Hill, “Carotenoids need structural colours to shine,” Biol. Lett. 1(2), 121–124 (2005).
[Crossref] [PubMed]

2004 (1)

R. O. Prum and R. H. Torres, “Structural colouration of mammalian skin: convergent evolution of coherently scattering dermal collagen arrays,” J. Exp. Biol. 207(12), 2157–2172 (2004).
[Crossref] [PubMed]

2003 (3)

R. O. Prum and R. Torres, “Structural colouration of avian skin: convergent evolution of coherently scattering dermal collagen arrays,” J. Exp. Biol. 206(14), 2409–2429 (2003).
[Crossref] [PubMed]

P. Vukusic and J. R. Sambles, “Photonic structures in biology,” Nature 424(6950), 852–855 (2003).
[Crossref] [PubMed]

R. O. Prum and R. H. Torres, “A Fourier Tool for the Analysis of Coherent Light Scattering by Bio-Optical Nanostructures,” Integr. Comp. Biol. 43(4), 591–602 (2003).
[Crossref] [PubMed]

2000 (1)

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404(6779), 740–743 (2000).
[Crossref] [PubMed]

1999 (1)

R. O. Prum, R. Torres, S. Williamson, and J. Dyck, “Two-dimensional Fourier analysis of the spongy medullary keratin of structurally coloured feather barbs,” Proc. Biol. Sci. 266(1414), 13–22 (1999).
[Crossref]

1998 (1)

R. O. Prum, R. H. Torres, S. Williamson, and J. Dyck, “Coherent light scattering by blue feather barbs,” Nature 396(6706), 28–29 (1998).
[Crossref]

1981 (1)

R. P. Porter, “Determination of structure of weak scatterers from holographic images,” Opt. Commun. 39(6), 362–364 (1981).
[Crossref]

Arai, S.

Y. Takeoka, S. Yoshioka, A. Takano, S. Arai, K. Nueangnoraj, H. Nishihara, M. Teshima, Y. Ohtsuka, and T. Seki, “Production of Colored Pigments with Amorphous Arrays of Black and White Colloidal Particles,” Angew. Chem. Int. Ed. Engl. 52(28), 7261–7265 (2013).
[Crossref] [PubMed]

Averdunk, H.

G. E. Schröder-Turk, S. Wickham, H. Averdunk, F. Brink, J. D. Fitz Gerald, L. Poladian, M. C. J. Large, and S. T. Hyde, “The chiral structure of porous chitin within the wing-scales of Callophrys rubi,” J. Struct. Biol. 174(2), 290–295 (2011).
[Crossref] [PubMed]

Baek, H.

I. Lee, D. Kim, J. Kal, H. Baek, D. Kwak, D. Go, E. Kim, C. Kang, J. Chung, Y. Jang, S. Ji, J. Joo, and Y. Kang, “Quasi-Amorphous Colloidal Structures for Electrically Tunable Full-Color Photonic Pixels with Angle-Independency,” Adv. Mater. 22(44), 4973–4977 (2010).
[Crossref] [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 80(1), 051903 (2009).
[Crossref] [PubMed]

Baumberg, J. J.

S. Vignolini, P. J. Rudall, A. V. Rowland, A. Reed, E. Moyroud, R. B. Faden, J. J. Baumberg, B. J. Glover, and U. Steiner, “Pointillist structural color in Pollia fruit,” Proc. Natl. Acad. Sci. U.S.A. 109(39), 15712–15715 (2012).
[Crossref] [PubMed]

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404(6779), 740–743 (2000).
[Crossref] [PubMed]

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 80(1), 051903 (2009).
[Crossref] [PubMed]

Blanco, Á.

P. D. García, R. Sapienza, Á. Blanco, and C. López, “Photonic Glass: A Novel Random Material for Light,” Adv. Mater. 19(18), 2597–2602 (2007).
[Crossref]

Brady, P.

A. E. Seago, P. Brady, J.-P. Vigneron, and T. D. Schultz, “Gold bugs and beyond: a review of iridescence and structural colour mechanisms in beetles (Coleoptera),” J. R. Soc. Interface 6(Suppl 2), S165–S184 (2009).
[Crossref] [PubMed]

Brink, F.

G. E. Schröder-Turk, S. Wickham, H. Averdunk, F. Brink, J. D. Fitz Gerald, L. Poladian, M. C. J. Large, and S. T. Hyde, “The chiral structure of porous chitin within the wing-scales of Callophrys rubi,” J. Struct. Biol. 174(2), 290–295 (2011).
[Crossref] [PubMed]

Cao, H.

V. Saranathan, J. D. Forster, H. Noh, S.-F. Liew, S. G. J. Mochrie, H. Cao, E. R. Dufresne, and R. O. Prum, “Structure and optical function of amorphous photonic nanostructures from avian feather barbs: a comparative small angle X-ray scattering (SAXS) analysis of 230 bird species,” J. R. Soc. Interface 9(75), 2563–2580 (2012).
[Crossref] [PubMed]

H. Noh, S. F. Liew, V. Saranathan, S. G. J. Mochrie, R. O. Prum, E. R. Dufresne, and H. Cao, “How Noniridescent Colors Are Generated by Quasi-ordered Structures of Bird Feathers,” Adv. Mater. 22(26-27), 2871–2880 (2010).
[Crossref] [PubMed]

J. D. Forster, H. Noh, S. F. Liew, V. Saranathan, C. F. Schreck, L. Yang, J.-G. Park, R. O. Prum, S. G. J. Mochrie, C. S. O’Hern, H. Cao, and E. R. Dufresne, “Biomimetic Isotropic Nanostructures for Structural Coloration,” Adv. Mater. 22(26-27), 2939–2944 (2010).
[Crossref] [PubMed]

H. Noh, S. F. Liew, V. Saranathan, R. O. Prum, S. G. J. Mochrie, E. R. Dufresne, and H. Cao, “Double scattering of light from Biophotonic Nanostructures with short-range order,” Opt. Express 18(11), 11942–11948 (2010).
[Crossref] [PubMed]

Chao, C.-H.

Charlton, M. D. B.

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404(6779), 740–743 (2000).
[Crossref] [PubMed]

Chen, A.

Y. Zhang, B. Dong, A. Chen, X. Liu, L. Shi, and J. Zi, “Using Cuttlefish Ink as an Additive to Produce -Non-iridescent Structural Colors of High Color Visibility,” Adv. Mater. 27(32), 4719–4724 (2015).
[Crossref] [PubMed]

Chi, J.-Y.

Choi, T. M.

J.-G. Park, S.-H. Kim, S. Magkiriadou, T. M. Choi, Y.-S. Kim, and V. N. Manoharan, “Full-Spectrum Photonic Pigments with Non-iridescent Structural Colors through Colloidal Assembly,” Angew. Chem. Int. Ed. Engl. 53(11), 2899–2903 (2014).
[Crossref] [PubMed]

Chung, J.

I. Lee, D. Kim, J. Kal, H. Baek, D. Kwak, D. Go, E. Kim, C. Kang, J. Chung, Y. Jang, S. Ji, J. Joo, and Y. Kang, “Quasi-Amorphous Colloidal Structures for Electrically Tunable Full-Color Photonic Pixels with Angle-Independency,” Adv. Mater. 22(44), 4973–4977 (2010).
[Crossref] [PubMed]

Colomer, J.-F.

J. P. Vigneron, J.-F. Colomer, M. Rassart, A. L. Ingram, and V. Lousse, “Structural origin of the colored reflections from the black-billed magpie feathers,” Phys. Rev. E 73(2), 021914 (2006).
[Crossref] [PubMed]

J. P. Vigneron, J.-F. Colomer, N. Vigneron, and V. Lousse, “Natural layer-by-layer photonic structure in the squamae of Hoplia coerulea (Coleoptera),” Phys. Rev. E 72(1), 061904 (2005).
[Crossref] [PubMed]

D’Alba, L.

L. D’Alba, L. Kieffer, and M. D. Shawkey, “Relative contributions of pigments and biophotonic nanostructures to natural color production: a case study in budgerigar (Melopsittacus undulatus) feathers,” J. Exp. Biol. 215(8), 1272–1277 (2012).
[Crossref] [PubMed]

De Raedt, H.

B. D. Wilts, K. Michielsen, H. De Raedt, and D. G. Stavenga, “Sparkling feather reflections of a bird-of-paradise explained by finite-difference time-domain modeling,” Proc. Natl. Acad. Sci. U.S.A. 111(12), 4363–4368 (2014).
[Crossref] [PubMed]

B. D. Wilts, K. Michielsen, J. Kuipers, H. De Raedt, and D. G. Stavenga, “Brilliant camouflage: photonic crystals in the diamond weevil, Entimus imperialis,” Proc. Biol. Sci. 279(1738), 2524–2530 (2012).
[Crossref] [PubMed]

Denton, E. J.

L. M. Mäthger, E. J. Denton, N. J. Marshall, and R. T. Hanlon, “Mechanisms and behavioural functions of structural coloration in cephalopods,” J. R. Soc. Interface 6(Suppl 2), S149–S163 (2009).
[Crossref] [PubMed]

Dong, B.

Y. Zhang, B. Dong, A. Chen, X. Liu, L. Shi, and J. Zi, “Using Cuttlefish Ink as an Additive to Produce -Non-iridescent Structural Colors of High Color Visibility,” Adv. Mater. 27(32), 4719–4724 (2015).
[Crossref] [PubMed]

Dufresne, E. R.

V. Saranathan, J. D. Forster, H. Noh, S.-F. Liew, S. G. J. Mochrie, H. Cao, E. R. Dufresne, and R. O. Prum, “Structure and optical function of amorphous photonic nanostructures from avian feather barbs: a comparative small angle X-ray scattering (SAXS) analysis of 230 bird species,” J. R. Soc. Interface 9(75), 2563–2580 (2012).
[Crossref] [PubMed]

H. Noh, S. F. Liew, V. Saranathan, S. G. J. Mochrie, R. O. Prum, E. R. Dufresne, and H. Cao, “How Noniridescent Colors Are Generated by Quasi-ordered Structures of Bird Feathers,” Adv. Mater. 22(26-27), 2871–2880 (2010).
[Crossref] [PubMed]

J. D. Forster, H. Noh, S. F. Liew, V. Saranathan, C. F. Schreck, L. Yang, J.-G. Park, R. O. Prum, S. G. J. Mochrie, C. S. O’Hern, H. Cao, and E. R. Dufresne, “Biomimetic Isotropic Nanostructures for Structural Coloration,” Adv. Mater. 22(26-27), 2939–2944 (2010).
[Crossref] [PubMed]

V. Saranathan, C. O. Osuji, S. G. J. Mochrie, H. Noh, S. Narayanan, A. Sandy, E. R. Dufresne, and R. O. Prum, “Structure, function, and self-assembly of single network gyroid (I4132) photonic crystals in butterfly wing scales,” Proc. Natl. Acad. Sci. U.S.A. 107(26), 11676–11681 (2010).
[Crossref] [PubMed]

H. Noh, S. F. Liew, V. Saranathan, R. O. Prum, S. G. J. Mochrie, E. R. Dufresne, and H. Cao, “Double scattering of light from Biophotonic Nanostructures with short-range order,” Opt. Express 18(11), 11942–11948 (2010).
[Crossref] [PubMed]

Dyck, J.

R. O. Prum, R. Torres, S. Williamson, and J. Dyck, “Two-dimensional Fourier analysis of the spongy medullary keratin of structurally coloured feather barbs,” Proc. Biol. Sci. 266(1414), 13–22 (1999).
[Crossref]

R. O. Prum, R. H. Torres, S. Williamson, and J. Dyck, “Coherent light scattering by blue feather barbs,” Nature 396(6706), 28–29 (1998).
[Crossref]

Faden, R. B.

S. Vignolini, P. J. Rudall, A. V. Rowland, A. Reed, E. Moyroud, R. B. Faden, J. J. Baumberg, B. J. Glover, and U. Steiner, “Pointillist structural color in Pollia fruit,” Proc. Natl. Acad. Sci. U.S.A. 109(39), 15712–15715 (2012).
[Crossref] [PubMed]

Fitz Gerald, J. D.

G. E. Schröder-Turk, S. Wickham, H. Averdunk, F. Brink, J. D. Fitz Gerald, L. Poladian, M. C. J. Large, and S. T. Hyde, “The chiral structure of porous chitin within the wing-scales of Callophrys rubi,” J. Struct. Biol. 174(2), 290–295 (2011).
[Crossref] [PubMed]

Forster, J. D.

V. Saranathan, J. D. Forster, H. Noh, S.-F. Liew, S. G. J. Mochrie, H. Cao, E. R. Dufresne, and R. O. Prum, “Structure and optical function of amorphous photonic nanostructures from avian feather barbs: a comparative small angle X-ray scattering (SAXS) analysis of 230 bird species,” J. R. Soc. Interface 9(75), 2563–2580 (2012).
[Crossref] [PubMed]

J. D. Forster, H. Noh, S. F. Liew, V. Saranathan, C. F. Schreck, L. Yang, J.-G. Park, R. O. Prum, S. G. J. Mochrie, C. S. O’Hern, H. Cao, and E. R. Dufresne, “Biomimetic Isotropic Nanostructures for Structural Coloration,” Adv. Mater. 22(26-27), 2939–2944 (2010).
[Crossref] [PubMed]

García, P. D.

P. D. García, R. Sapienza, and C. López, “Photonic Glasses: A Step Beyond White Paint,” Adv. Mater. 22(1), 12–19 (2010).
[Crossref] [PubMed]

P. D. García, R. Sapienza, Á. Blanco, and C. López, “Photonic Glass: A Novel Random Material for Light,” Adv. Mater. 19(18), 2597–2602 (2007).
[Crossref]

Ge, D.

D. Ge, L. Yang, G. Wu, and S. Yang, “Angle-independent colours from spray coated quasi-amorphous arrays of nanoparticles: combination of constructive interference and Rayleigh scattering,” J. Mater. Chem. C Mater. Opt. Electron. Devices 2(22), 4395–4400 (2014).
[Crossref]

Gerke, T. D.

T. D. Gerke and R. Piestun, “Aperiodic volume optics,” Nat. Photonics 4, 188–193 (2010).

Glover, B. J.

S. Vignolini, P. J. Rudall, A. V. Rowland, A. Reed, E. Moyroud, R. B. Faden, J. J. Baumberg, B. J. Glover, and U. Steiner, “Pointillist structural color in Pollia fruit,” Proc. Natl. Acad. Sci. U.S.A. 109(39), 15712–15715 (2012).
[Crossref] [PubMed]

Go, D.

I. Lee, D. Kim, J. Kal, H. Baek, D. Kwak, D. Go, E. Kim, C. Kang, J. Chung, Y. Jang, S. Ji, J. Joo, and Y. Kang, “Quasi-Amorphous Colloidal Structures for Electrically Tunable Full-Color Photonic Pixels with Angle-Independency,” Adv. Mater. 22(44), 4973–4977 (2010).
[Crossref] [PubMed]

Hallam, B.

P. Vukusic, B. Hallam, and J. Noyes, “Brilliant Whiteness in Ultrathin Beetle Scales,” Science 315(5810), 348 (2007).
[Crossref] [PubMed]

Hanlon, R. T.

L. M. Mäthger, E. J. Denton, N. J. Marshall, and R. T. Hanlon, “Mechanisms and behavioural functions of structural coloration in cephalopods,” J. R. Soc. Interface 6(Suppl 2), S149–S163 (2009).
[Crossref] [PubMed]

Hansson, C.

E. Shevtsova, C. Hansson, D. H. Janzen, and J. Kjærandsen, “Stable structural color patterns displayed on transparent insect wings,” Proc. Natl. Acad. Sci. U.S.A. 108(2), 668–673 (2011).
[Crossref] [PubMed]

Hill, G. E.

M. D. Shawkey and G. E. Hill, “Significance of a basal melanin layer to production of non-iridescent structural plumage color: evidence from an amelanotic Steller’s jay (Cyanocitta stelleri),” J. Exp. Biol. 209(7), 1245–1250 (2006).
[Crossref] [PubMed]

M. D. Shawkey and G. E. Hill, “Carotenoids need structural colours to shine,” Biol. Lett. 1(2), 121–124 (2005).
[Crossref] [PubMed]

Hong, X.-H.

H. Huang, C.-P. Huang, C. Zhang, X.-H. Hong, X.-J. Zhang, Y.-Q. Qin, and Y.-Y. Zhu, “From Ewald sphere to Ewald shell in nonlinear optics,” Sci. Rep. 6(1), 29365 (2016).
[Crossref] [PubMed]

Hsueh, H.-T.

Huang, C.-P.

H. Huang, C.-P. Huang, C. Zhang, X.-H. Hong, X.-J. Zhang, Y.-Q. Qin, and Y.-Y. Zhu, “From Ewald sphere to Ewald shell in nonlinear optics,” Sci. Rep. 6(1), 29365 (2016).
[Crossref] [PubMed]

Huang, H.

H. Huang, C.-P. Huang, C. Zhang, X.-H. Hong, X.-J. Zhang, Y.-Q. Qin, and Y.-Y. Zhu, “From Ewald sphere to Ewald shell in nonlinear optics,” Sci. Rep. 6(1), 29365 (2016).
[Crossref] [PubMed]

Hyde, S. T.

G. E. Schröder-Turk, S. Wickham, H. Averdunk, F. Brink, J. D. Fitz Gerald, L. Poladian, M. C. J. Large, and S. T. Hyde, “The chiral structure of porous chitin within the wing-scales of Callophrys rubi,” J. Struct. Biol. 174(2), 290–295 (2011).
[Crossref] [PubMed]

Ingram, A. L.

J. P. Vigneron, J.-F. Colomer, M. Rassart, A. L. Ingram, and V. Lousse, “Structural origin of the colored reflections from the black-billed magpie feathers,” Phys. Rev. E 73(2), 021914 (2006).
[Crossref] [PubMed]

Iwata, M.

M. Iwata, M. Teshima, T. Seki, S. Yoshioka, and Y. Takeoka, “Bio-Inspired Bright Structurally Colored Colloidal Amorphous Array Enhanced by Controlling Thickness and Black Background,” Adv. Mater. 29(26), 1605050 (2017).
[Crossref] [PubMed]

Jang, Y.

I. Lee, D. Kim, J. Kal, H. Baek, D. Kwak, D. Go, E. Kim, C. Kang, J. Chung, Y. Jang, S. Ji, J. Joo, and Y. Kang, “Quasi-Amorphous Colloidal Structures for Electrically Tunable Full-Color Photonic Pixels with Angle-Independency,” Adv. Mater. 22(44), 4973–4977 (2010).
[Crossref] [PubMed]

Janzen, D. H.

E. Shevtsova, C. Hansson, D. H. Janzen, and J. Kjærandsen, “Stable structural color patterns displayed on transparent insect wings,” Proc. Natl. Acad. Sci. U.S.A. 108(2), 668–673 (2011).
[Crossref] [PubMed]

Ji, S.

I. Lee, D. Kim, J. Kal, H. Baek, D. Kwak, D. Go, E. Kim, C. Kang, J. Chung, Y. Jang, S. Ji, J. Joo, and Y. Kang, “Quasi-Amorphous Colloidal Structures for Electrically Tunable Full-Color Photonic Pixels with Angle-Independency,” Adv. Mater. 22(44), 4973–4977 (2010).
[Crossref] [PubMed]

Joo, J.

I. Lee, D. Kim, J. Kal, H. Baek, D. Kwak, D. Go, E. Kim, C. Kang, J. Chung, Y. Jang, S. Ji, J. Joo, and Y. Kang, “Quasi-Amorphous Colloidal Structures for Electrically Tunable Full-Color Photonic Pixels with Angle-Independency,” Adv. Mater. 22(44), 4973–4977 (2010).
[Crossref] [PubMed]

Kal, J.

I. Lee, D. Kim, J. Kal, H. Baek, D. Kwak, D. Go, E. Kim, C. Kang, J. Chung, Y. Jang, S. Ji, J. Joo, and Y. Kang, “Quasi-Amorphous Colloidal Structures for Electrically Tunable Full-Color Photonic Pixels with Angle-Independency,” Adv. Mater. 22(44), 4973–4977 (2010).
[Crossref] [PubMed]

Kang, C.

I. Lee, D. Kim, J. Kal, H. Baek, D. Kwak, D. Go, E. Kim, C. Kang, J. Chung, Y. Jang, S. Ji, J. Joo, and Y. Kang, “Quasi-Amorphous Colloidal Structures for Electrically Tunable Full-Color Photonic Pixels with Angle-Independency,” Adv. Mater. 22(44), 4973–4977 (2010).
[Crossref] [PubMed]

Kang, H.

C. H. Lim, H. Kang, and S.-H. Kim, “Colloidal Assembly in Leidenfrost Drops for Noniridescent Structural Color Pigments,” Langmuir 30(28), 8350–8356 (2014).
[Crossref] [PubMed]

Kang, Y.

I. Lee, D. Kim, J. Kal, H. Baek, D. Kwak, D. Go, E. Kim, C. Kang, J. Chung, Y. Jang, S. Ji, J. Joo, and Y. Kang, “Quasi-Amorphous Colloidal Structures for Electrically Tunable Full-Color Photonic Pixels with Angle-Independency,” Adv. Mater. 22(44), 4973–4977 (2010).
[Crossref] [PubMed]

Kawamura, A.

A. Kawamura, M. Kohri, G. Morimoto, Y. Nannichi, T. Taniguchi, and K. Kishikawa, “Full-Color Biomimetic Photonic Materials with Iridescent and Non-Iridescent Structural Colors,” Sci. Rep. 6(1), 33984 (2016).
[Crossref] [PubMed]

Kawano, R.

M. Teshima, T. Seki, R. Kawano, S. Takeuchi, S. Yoshioka, and Y. Takeoka, “Preparation of structurally colored, monodisperse spherical assemblies composed of black and white colloidal particles using a micro-flow-focusing device,” J. Mater. Chem. C Mater. Opt. Electron. Devices 3(4), 769–777 (2015).
[Crossref]

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 80(1), 051903 (2009).
[Crossref] [PubMed]

Kieffer, L.

L. D’Alba, L. Kieffer, and M. D. Shawkey, “Relative contributions of pigments and biophotonic nanostructures to natural color production: a case study in budgerigar (Melopsittacus undulatus) feathers,” J. Exp. Biol. 215(8), 1272–1277 (2012).
[Crossref] [PubMed]

Kim, D.

I. Lee, D. Kim, J. Kal, H. Baek, D. Kwak, D. Go, E. Kim, C. Kang, J. Chung, Y. Jang, S. Ji, J. Joo, and Y. Kang, “Quasi-Amorphous Colloidal Structures for Electrically Tunable Full-Color Photonic Pixels with Angle-Independency,” Adv. Mater. 22(44), 4973–4977 (2010).
[Crossref] [PubMed]

Kim, E.

I. Lee, D. Kim, J. Kal, H. Baek, D. Kwak, D. Go, E. Kim, C. Kang, J. Chung, Y. Jang, S. Ji, J. Joo, and Y. Kang, “Quasi-Amorphous Colloidal Structures for Electrically Tunable Full-Color Photonic Pixels with Angle-Independency,” Adv. Mater. 22(44), 4973–4977 (2010).
[Crossref] [PubMed]

Kim, S.-H.

C. H. Lim, H. Kang, and S.-H. Kim, “Colloidal Assembly in Leidenfrost Drops for Noniridescent Structural Color Pigments,” Langmuir 30(28), 8350–8356 (2014).
[Crossref] [PubMed]

J.-G. Park, S.-H. Kim, S. Magkiriadou, T. M. Choi, Y.-S. Kim, and V. N. Manoharan, “Full-Spectrum Photonic Pigments with Non-iridescent Structural Colors through Colloidal Assembly,” Angew. Chem. Int. Ed. Engl. 53(11), 2899–2903 (2014).
[Crossref] [PubMed]

S.-H. Kim, S. Y. Lee, S.-M. Yang, and G.-R. Yi, “Self-assembled colloidal structures for photonics,” NPG Asia Mater. 3(1), 25–33 (2011).
[Crossref]

Kim, Y.-S.

S. Magkiriadou, J.-G. Park, Y.-S. Kim, and V. N. Manoharan, “Absence of red structural color in photonic glasses, bird feathers, and certain beetles,” Phys. Rev. E 90(6), 062302 (2014).
[Crossref] [PubMed]

J.-G. Park, S.-H. Kim, S. Magkiriadou, T. M. Choi, Y.-S. Kim, and V. N. Manoharan, “Full-Spectrum Photonic Pigments with Non-iridescent Structural Colors through Colloidal Assembly,” Angew. Chem. Int. Ed. Engl. 53(11), 2899–2903 (2014).
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Adv. Mater. (7)

H. Noh, S. F. Liew, V. Saranathan, S. G. J. Mochrie, R. O. Prum, E. R. Dufresne, and H. Cao, “How Noniridescent Colors Are Generated by Quasi-ordered Structures of Bird Feathers,” Adv. Mater. 22(26-27), 2871–2880 (2010).
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P. D. García, R. Sapienza, Á. Blanco, and C. López, “Photonic Glass: A Novel Random Material for Light,” Adv. Mater. 19(18), 2597–2602 (2007).
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P. D. García, R. Sapienza, and C. López, “Photonic Glasses: A Step Beyond White Paint,” Adv. Mater. 22(1), 12–19 (2010).
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I. Lee, D. Kim, J. Kal, H. Baek, D. Kwak, D. Go, E. Kim, C. Kang, J. Chung, Y. Jang, S. Ji, J. Joo, and Y. Kang, “Quasi-Amorphous Colloidal Structures for Electrically Tunable Full-Color Photonic Pixels with Angle-Independency,” Adv. Mater. 22(44), 4973–4977 (2010).
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Y. Zhang, B. Dong, A. Chen, X. Liu, L. Shi, and J. Zi, “Using Cuttlefish Ink as an Additive to Produce -Non-iridescent Structural Colors of High Color Visibility,” Adv. Mater. 27(32), 4719–4724 (2015).
[Crossref] [PubMed]

M. Iwata, M. Teshima, T. Seki, S. Yoshioka, and Y. Takeoka, “Bio-Inspired Bright Structurally Colored Colloidal Amorphous Array Enhanced by Controlling Thickness and Black Background,” Adv. Mater. 29(26), 1605050 (2017).
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J. D. Forster, H. Noh, S. F. Liew, V. Saranathan, C. F. Schreck, L. Yang, J.-G. Park, R. O. Prum, S. G. J. Mochrie, C. S. O’Hern, H. Cao, and E. R. Dufresne, “Biomimetic Isotropic Nanostructures for Structural Coloration,” Adv. Mater. 22(26-27), 2939–2944 (2010).
[Crossref] [PubMed]

Angew. Chem. Int. Ed. Engl. (2)

Y. Takeoka, S. Yoshioka, A. Takano, S. Arai, K. Nueangnoraj, H. Nishihara, M. Teshima, Y. Ohtsuka, and T. Seki, “Production of Colored Pigments with Amorphous Arrays of Black and White Colloidal Particles,” Angew. Chem. Int. Ed. Engl. 52(28), 7261–7265 (2013).
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J.-G. Park, S.-H. Kim, S. Magkiriadou, T. M. Choi, Y.-S. Kim, and V. N. Manoharan, “Full-Spectrum Photonic Pigments with Non-iridescent Structural Colors through Colloidal Assembly,” Angew. Chem. Int. Ed. Engl. 53(11), 2899–2903 (2014).
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Biol. Lett. (1)

M. D. Shawkey and G. E. Hill, “Carotenoids need structural colours to shine,” Biol. Lett. 1(2), 121–124 (2005).
[Crossref] [PubMed]

ChemPhysChem (1)

S. Kinoshita and S. Yoshioka, “Structural Colors in Nature: The Role of Regularity and Irregularity in the Structure,” ChemPhysChem 6(8), 1442–1459 (2005).
[Crossref] [PubMed]

Integr. Comp. Biol. (1)

R. O. Prum and R. H. Torres, “A Fourier Tool for the Analysis of Coherent Light Scattering by Bio-Optical Nanostructures,” Integr. Comp. Biol. 43(4), 591–602 (2003).
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Figures (7)

Fig. 1
Fig. 1 Ewald sphere application for the example of a Bragg mirror with a low refractive index contrast and incident waves with two different wavelengths indicated by the arrow color. The incident wave vectors k0 and k0’ are indicated by the solid arrow, the scattered wave vector k1’ corresponds to the dashed arrow. The left short-wavelength case is off Bragg resonance while the right long-wavelength case shows a k-vector for which Bragg reflection occurs. In the reciprocal space, the Ewald sphere overlaps with the non-zero Fourier-transform spots in which case light is scattered back in the corresponding direction (right) or it does not overlap with the spots in which case no scattering is observed and all light is transmitted (left).
Fig. 2
Fig. 2 2D cut through the Ewald sphere construction for the scattering from a structure with a spherical shell shaped Fourier transform. (a) Short wavelength, leading to forward scattering, (b) intermediate wavelength, leading to perpendicular scattering, (c) long wavelength, leading to backscattering and (d) very long wavelength, leading to no scattering. Solid arrows indicate the wave vectors of the incident waves; dashed arrows indicate wave vectors of scattered waves.
Fig. 3
Fig. 3 Schematic 2D representation of the scattering in a film as a function of wavelength. The film is structured in such a way that its Fourier transform is a spherical shell (not shown here, see Fig. 2). Short wavelengths (shown as blue) are scattered in a forward direction. Intermediate wavelengths (orange) are backscattered in a large angle. Due to their scattering angle they may be reflected at the film surface. Also, their probability for a second scattering event is high due to a long propagation path inside the structure. Long wavelengths (red) are directly scattered back and very long wavelengths (infrared, shown as black) are not scattered at all and will be transmitted into the downward direction.
Fig. 4
Fig. 4 3 × 3 × 3 μm3 excerpt from the model structure made by an overlap of 10,000 sinusoidal gratings with 220 nm period. The refractive-index distribution in the structure is scaled such that its standard deviation is σ=0.025. The shown refractive-index range is limited to 1.45 to 1.55 in order to make the structure more distinguishable, the full refractive-index range considered in the calculation is from 1.40 to 1.60.
Fig. 5
Fig. 5 Inset: Cut through the spatial spectral density of the Fourier transform of the 3 × 3 × 3 µm3 refractive index perturbation shown in Fig. 4. The plane k z =0 is shown. Main panel: Average of the spatial spectral density as a function of the distance to the origin of the reciprocal space.
Fig. 6
Fig. 6 (a) Schematic of the simulated volume. (b) FIT-simulated reflectivity spectrum of the model structure with 40 µm thickness, a mean refractive index of 1.5 and a refractive-index standard deviation of σ=0.025 (black curve). In comparison to that, the first-order approximation calculated without (blue curve) and with (red curve) interface reflections (Fresnel reflection as well as total internal reflection) taken into account are shown. The incident wave impinges normally onto the film from the top. (c) Scattering angle for first-order scattering with respect to the normal for a scattering structure that exhibits a perfect spherical shell in k-space with radius K=0.0286 nm 1 . The horizontal, dashed lines mark the 90 degree angle and the angle of total internal reflection at the film-air interface.
Fig. 7
Fig. 7 Absolute value squared of the Fourier transform of the scattered fields at certain wavelengths calculated in an (x,y)-plane above the structure and encoded in color; red corresponds to large values and dark blue to zero. We obtained the squared amplitude by Fourier transforming the fields Ex, Ey, Ez and subsequently calculating A 2 ( k x , k y )= | F{ E x } | 2 + | F{ E y } | 2 + | F{ E z } | 2 , where F denotes the two-dimensional Fourier transform in the (x,y)-plane. k-vectors parallel to the film surface mark the maximum spatial frequency which is indicated by the white circle. The red point in the center represents the incident and the Fresnel-reflected wave which are propagating normally to the film interface and therefore correspond to a spatial frequency of zero in the (kx,ky)-plane. The shown wavelengths are (a) 465 nm, (b) 645 nm, (c) 665 nm and (d) 750 nm, selected to lie, respectively, in the second-order scattering peak, in the conical reflection regime, at the reflectivity edge, and in the scattering-free spectral regime (cf. Figure 6(b)). At the bottom right for each case the corresponding Ewald sphere construction is shown schematically.

Equations (2)

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n ^ f(r)= n 0 i=1 N sin( γ i r+ ϕ i )
R= R af + T af k 2 ε ^ 2 ( 4π ) 2 l 2 ε ¯ 2 halfofsphere| k 1 |=k | F l ( k 1 k 0 ) | 2 [ T fa s ( e 0 e 1 s ) 2 + T fa p ( e 0 e 1 p ) 2 ] d 2 k 1 ,

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