Abstract

This paper presents a computational adaptive mesh refinement technique for designing photonic nanostructures with a specific perceived color. This inverse design method can be used for any color-based application of photonic structures, including pigment-free paints, anticounterfeiting materials, and reflective displays. The adaptive mesh refinement technique is efficient, and results are returned within seconds or minutes on a laptop computer, eliminating the need for cluster computing. This search method can be used for any well-characterized photonic structure and can even be adapted to accommodate fabrication constraints. In this work, the adaptive mesh search is applied to 1D, 2D, and 3D photonic structures, and the resulting designs are satisfactory matches with the desired colors.

© 2017 Optical Society of America

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References

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2016 (4)

Y. Fu, C. A. Tippets, E. U. Donev, and R. Lopez, “Structural colors: from natural to artificial systems,” Wiley Interdiscip. Rev. 8, 758–775 (2016).
[Crossref]

H. Nam, K. Song, D. Ha, and T. Kim, “Inkjet printing based mono-layered photonic crystal patterning for anti-counterfeiting structural colors,” Sci. Rep. 6, 30885 (2016).
[Crossref]

M. Sarollahi, S. J. Bauman, J. Mishler, and J. B. Herzog, “Calculation of reflectivity spectra for semi-infinite two-dimensional photonic crystals,” J. Nanophoton. 10, 046012 (2016).
[Crossref]

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, 33984 (2016).
[Crossref]

2015 (1)

2014 (3)

2013 (2)

H. S. Lee, T. S. Shim, H. Hwang, S.-M. Yang, and S.-H. Kim, “Colloidal photonic crystals toward structural color palettes for security materials,” Chem. Mater. 25, 2684–2690 (2013).
[Crossref]

F. Schenk, B. D. Wilts, and D. G. Stavenga, “The Japanese jewel beetle: a painter’s challenge,” Bioinspiration Biomimetics 8, 045002 (2013).
[Crossref]

2010 (2)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

C. I. Aguirre, E. Reguera, and A. Stein, “Colloidal photonic crystal pigments with low angle dependence,” ACS Appl. Mater. Interfaces 2, 3257–3262 (2010).
[Crossref]

2007 (2)

A. C. Arsenault, D. P. Puzzo, I. Manners, and G. A. Ozin, “Photonic-crystal full-colour displays,” Nat. Photonics 1, 468–472 (2007).
[Crossref]

A. Rudzinski, “Analytic expressions for electromagnetic field envelopes in a 1D photonic crystal,” Acta Phys. Pol. A 111, 323–333 (2007).
[Crossref]

2006 (1)

M. N. Vouvakis, Z. Cendes, and J.-F. Lee, “A FEM domain decomposition method for photonic and electromagnetic band gap structures,” IEEE Trans. Antennas Propag. 54, 721–733 (2006).
[Crossref]

2005 (2)

A. Rudzinski, A. Tyszka-Zawadzka, and P. Szczepanski, “Simple model of the density of states in 1D photonic crystal,” Proc. SPIE 5950, 59501A (2005).
[Crossref]

G. Sharma, W. Wu, and E. N. Dalal, “The ciede2000 color-difference formula: implementation notes, supplementary test data, and mathematical observations,” Color Res. Appl. 30, 21–30 (2005).
[Crossref]

2004 (1)

P. Jiang and M. J. McFarland, “Large-scale fabrication of wafer-size colloidal crystals, macroporous polymers and nanocomposites by spin-coating,” J. Am. Chem. Soc. 126, 13778–13786 (2004).
[Crossref]

2002 (1)

M. Kaliteevski, J. M. Martinez, D. Cassagne, and J. Albert, “Disorder-induced modification of the transmission of light in a two-dimensional photonic crystal,” Phys. Rev. B 66, 113101 (2002).
[Crossref]

2001 (1)

Y. Xia, B. Gates, and Z.-Y. Li, “Self-assembly approaches to three-dimensional photonic crystals,” Adv. Mater. 13, 409–413 (2001).
[Crossref]

2000 (1)

A. Ward and J. Pendry, “A program for calculating photonic band structures, Green’s functions and transmission/reflection coefficients using a non-orthogonal FDTD method,” Comput. Phys. Commun. 128, 590–621 (2000).
[Crossref]

1962 (1)

C. E. Helm and L. R. Tucker, “Individual differences in the structure of color-perception,” Am. J. Psychol. 75, 437–444 (1962).
[Crossref]

1931 (1)

T. Smith and J. Guild, “The C.I.E. colorimetric standards and their use,” Trans. Opt. Soc. 33, 73–134 (1931).
[Crossref]

Aguirre, C. I.

C. I. Aguirre, E. Reguera, and A. Stein, “Colloidal photonic crystal pigments with low angle dependence,” ACS Appl. Mater. Interfaces 2, 3257–3262 (2010).
[Crossref]

Albert, J.

M. Kaliteevski, J. M. Martinez, D. Cassagne, and J. Albert, “Disorder-induced modification of the transmission of light in a two-dimensional photonic crystal,” Phys. Rev. B 66, 113101 (2002).
[Crossref]

Andkjær, J.

Arsenault, A. C.

A. C. Arsenault, D. P. Puzzo, I. Manners, and G. A. Ozin, “Photonic-crystal full-colour displays,” Nat. Photonics 1, 468–472 (2007).
[Crossref]

Bauman, S. J.

M. Sarollahi, S. J. Bauman, J. Mishler, and J. B. Herzog, “Calculation of reflectivity spectra for semi-infinite two-dimensional photonic crystals,” J. Nanophoton. 10, 046012 (2016).
[Crossref]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

Busch, K.

K. Busch, S. Lölkes, R. B. Wehrspohn, and H. Föll, Photonic Crystals: Advances in Design, Fabrication, and Characterization (Wiley, 2006).

Carter, W. C.

T. Sarathi and W. C. Carter, “Multilayer photonic bandgap” (Wolfram Demonstrations Project), http://demonstrations.wolfram.com/MultilayerPhotonicBandgap/ .

Cassagne, D.

M. Kaliteevski, J. M. Martinez, D. Cassagne, and J. Albert, “Disorder-induced modification of the transmission of light in a two-dimensional photonic crystal,” Phys. Rev. B 66, 113101 (2002).
[Crossref]

Cendes, Z.

M. N. Vouvakis, Z. Cendes, and J.-F. Lee, “A FEM domain decomposition method for photonic and electromagnetic band gap structures,” IEEE Trans. Antennas Propag. 54, 721–733 (2006).
[Crossref]

Dalal, E. N.

G. Sharma, W. Wu, and E. N. Dalal, “The ciede2000 color-difference formula: implementation notes, supplementary test data, and mathematical observations,” Color Res. Appl. 30, 21–30 (2005).
[Crossref]

Donev, E. U.

Y. Fu, C. A. Tippets, E. U. Donev, and R. Lopez, “Structural colors: from natural to artificial systems,” Wiley Interdiscip. Rev. 8, 758–775 (2016).
[Crossref]

Föll, H.

K. Busch, S. Lölkes, R. B. Wehrspohn, and H. Föll, Photonic Crystals: Advances in Design, Fabrication, and Characterization (Wiley, 2006).

Friis, K. S.

Fu, Y.

Y. Fu, C. A. Tippets, E. U. Donev, and R. Lopez, “Structural colors: from natural to artificial systems,” Wiley Interdiscip. Rev. 8, 758–775 (2016).
[Crossref]

Gates, B.

Y. Xia, B. Gates, and Z.-Y. Li, “Self-assembly approaches to three-dimensional photonic crystals,” Adv. Mater. 13, 409–413 (2001).
[Crossref]

Guild, J.

T. Smith and J. Guild, “The C.I.E. colorimetric standards and their use,” Trans. Opt. Soc. 33, 73–134 (1931).
[Crossref]

Ha, D.

H. Nam, K. Song, D. Ha, and T. Kim, “Inkjet printing based mono-layered photonic crystal patterning for anti-counterfeiting structural colors,” Sci. Rep. 6, 30885 (2016).
[Crossref]

Helm, C. E.

C. E. Helm and L. R. Tucker, “Individual differences in the structure of color-perception,” Am. J. Psychol. 75, 437–444 (1962).
[Crossref]

Herzog, J. B.

M. Sarollahi, S. J. Bauman, J. Mishler, and J. B. Herzog, “Calculation of reflectivity spectra for semi-infinite two-dimensional photonic crystals,” J. Nanophoton. 10, 046012 (2016).
[Crossref]

Hiemenz, P. C.

P. C. Hiemenz and R. Rajagopalan, Principles of Colloid and Surface Chemistry (Marcel Dekker, 1986), Vol. 188.

Hwang, H.

H. S. Lee, T. S. Shim, H. Hwang, S.-M. Yang, and S.-H. Kim, “Colloidal photonic crystals toward structural color palettes for security materials,” Chem. Mater. 25, 2684–2690 (2013).
[Crossref]

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

Jiang, P.

P. Jiang and M. J. McFarland, “Large-scale fabrication of wafer-size colloidal crystals, macroporous polymers and nanocomposites by spin-coating,” J. Am. Chem. Soc. 126, 13778–13786 (2004).
[Crossref]

Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Johansen, V. E.

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Kaliteevski, M.

M. Kaliteevski, J. M. Martinez, D. Cassagne, and J. Albert, “Disorder-induced modification of the transmission of light in a two-dimensional photonic crystal,” Phys. Rev. B 66, 113101 (2002).
[Crossref]

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, 33984 (2016).
[Crossref]

Kim, S.-H.

H. S. Lee, T. S. Shim, H. Hwang, S.-M. Yang, and S.-H. Kim, “Colloidal photonic crystals toward structural color palettes for security materials,” Chem. Mater. 25, 2684–2690 (2013).
[Crossref]

Kim, T.

H. Nam, K. Song, D. Ha, and T. Kim, “Inkjet printing based mono-layered photonic crystal patterning for anti-counterfeiting structural colors,” Sci. Rep. 6, 30885 (2016).
[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, 062302 (2014).
[Crossref]

Kishikawa, K.

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, 33984 (2016).
[Crossref]

Kohri, M.

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, 33984 (2016).
[Crossref]

Lee, H. S.

H. S. Lee, T. S. Shim, H. Hwang, S.-M. Yang, and S.-H. Kim, “Colloidal photonic crystals toward structural color palettes for security materials,” Chem. Mater. 25, 2684–2690 (2013).
[Crossref]

Lee, J.-F.

M. N. Vouvakis, Z. Cendes, and J.-F. Lee, “A FEM domain decomposition method for photonic and electromagnetic band gap structures,” IEEE Trans. Antennas Propag. 54, 721–733 (2006).
[Crossref]

Li, Z.-Y.

Y. Xia, B. Gates, and Z.-Y. Li, “Self-assembly approaches to three-dimensional photonic crystals,” Adv. Mater. 13, 409–413 (2001).
[Crossref]

Lölkes, S.

K. Busch, S. Lölkes, R. B. Wehrspohn, and H. Föll, Photonic Crystals: Advances in Design, Fabrication, and Characterization (Wiley, 2006).

Lopez, R.

Y. Fu, C. A. Tippets, E. U. Donev, and R. Lopez, “Structural colors: from natural to artificial systems,” Wiley Interdiscip. Rev. 8, 758–775 (2016).
[Crossref]

Mafi, A.

Magkiriadou, 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, 062302 (2014).
[Crossref]

S. Magkiriadou, “Structural color from colloidal glasses,” Ph.D. thesis (Harvard University, 2014).

Manners, I.

A. C. Arsenault, D. P. Puzzo, I. Manners, and G. A. Ozin, “Photonic-crystal full-colour displays,” Nat. Photonics 1, 468–472 (2007).
[Crossref]

Manoharan, V. N.

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, 062302 (2014).
[Crossref]

Martinez, J. M.

M. Kaliteevski, J. M. Martinez, D. Cassagne, and J. Albert, “Disorder-induced modification of the transmission of light in a two-dimensional photonic crystal,” Phys. Rev. B 66, 113101 (2002).
[Crossref]

McFarland, M. J.

P. Jiang and M. J. McFarland, “Large-scale fabrication of wafer-size colloidal crystals, macroporous polymers and nanocomposites by spin-coating,” J. Am. Chem. Soc. 126, 13778–13786 (2004).
[Crossref]

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Mishler, J.

M. Sarollahi, S. J. Bauman, J. Mishler, and J. B. Herzog, “Calculation of reflectivity spectra for semi-infinite two-dimensional photonic crystals,” J. Nanophoton. 10, 046012 (2016).
[Crossref]

Morimoto, G.

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, 33984 (2016).
[Crossref]

Nam, H.

H. Nam, K. Song, D. Ha, and T. Kim, “Inkjet printing based mono-layered photonic crystal patterning for anti-counterfeiting structural colors,” Sci. Rep. 6, 30885 (2016).
[Crossref]

Nannichi, Y.

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, 33984 (2016).
[Crossref]

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

Ozin, G. A.

A. C. Arsenault, D. P. Puzzo, I. Manners, and G. A. Ozin, “Photonic-crystal full-colour displays,” Nat. Photonics 1, 468–472 (2007).
[Crossref]

Park, J.-G.

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, 062302 (2014).
[Crossref]

Pendry, J.

A. Ward and J. Pendry, “A program for calculating photonic band structures, Green’s functions and transmission/reflection coefficients using a non-orthogonal FDTD method,” Comput. Phys. Commun. 128, 590–621 (2000).
[Crossref]

Prum, R. O.

R. O. Prum and R. H. Torres, “Fourier blues: structural coloration of biological tissues,” in Excursions in Harmonic Analysis (Springer, 2013), Vol. 2, pp. 401–421.

Puzzo, D. P.

A. C. Arsenault, D. P. Puzzo, I. Manners, and G. A. Ozin, “Photonic-crystal full-colour displays,” Nat. Photonics 1, 468–472 (2007).
[Crossref]

Rajagopalan, R.

P. C. Hiemenz and R. Rajagopalan, Principles of Colloid and Surface Chemistry (Marcel Dekker, 1986), Vol. 188.

Reguera, E.

C. I. Aguirre, E. Reguera, and A. Stein, “Colloidal photonic crystal pigments with low angle dependence,” ACS Appl. Mater. Interfaces 2, 3257–3262 (2010).
[Crossref]

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

Rudzinski, A.

A. Rudzinski, “Analytic expressions for electromagnetic field envelopes in a 1D photonic crystal,” Acta Phys. Pol. A 111, 323–333 (2007).
[Crossref]

A. Rudzinski, A. Tyszka-Zawadzka, and P. Szczepanski, “Simple model of the density of states in 1D photonic crystal,” Proc. SPIE 5950, 59501A (2005).
[Crossref]

Sarathi, T.

T. Sarathi and W. C. Carter, “Multilayer photonic bandgap” (Wolfram Demonstrations Project), http://demonstrations.wolfram.com/MultilayerPhotonicBandgap/ .

Sarollahi, M.

M. Sarollahi, S. J. Bauman, J. Mishler, and J. B. Herzog, “Calculation of reflectivity spectra for semi-infinite two-dimensional photonic crystals,” J. Nanophoton. 10, 046012 (2016).
[Crossref]

Schenk, F.

F. Schenk, B. D. Wilts, and D. G. Stavenga, “The Japanese jewel beetle: a painter’s challenge,” Bioinspiration Biomimetics 8, 045002 (2013).
[Crossref]

Sharma, G.

G. Sharma, W. Wu, and E. N. Dalal, “The ciede2000 color-difference formula: implementation notes, supplementary test data, and mathematical observations,” Color Res. Appl. 30, 21–30 (2005).
[Crossref]

Shim, T. S.

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H. Nam, K. Song, D. Ha, and T. Kim, “Inkjet printing based mono-layered photonic crystal patterning for anti-counterfeiting structural colors,” Sci. Rep. 6, 30885 (2016).
[Crossref]

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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, 33984 (2016).
[Crossref]

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Y. Fu, C. A. Tippets, E. U. Donev, and R. Lopez, “Structural colors: from natural to artificial systems,” Wiley Interdiscip. Rev. 8, 758–775 (2016).
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R. O. Prum and R. H. Torres, “Fourier blues: structural coloration of biological tissues,” in Excursions in Harmonic Analysis (Springer, 2013), Vol. 2, pp. 401–421.

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ACS Appl. Mater. Interfaces (1)

C. I. Aguirre, E. Reguera, and A. Stein, “Colloidal photonic crystal pigments with low angle dependence,” ACS Appl. Mater. Interfaces 2, 3257–3262 (2010).
[Crossref]

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A. Rudzinski, “Analytic expressions for electromagnetic field envelopes in a 1D photonic crystal,” Acta Phys. Pol. A 111, 323–333 (2007).
[Crossref]

Adv. Mater. (1)

Y. Xia, B. Gates, and Z.-Y. Li, “Self-assembly approaches to three-dimensional photonic crystals,” Adv. Mater. 13, 409–413 (2001).
[Crossref]

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C. E. Helm and L. R. Tucker, “Individual differences in the structure of color-perception,” Am. J. Psychol. 75, 437–444 (1962).
[Crossref]

Bioinspiration Biomimetics (1)

F. Schenk, B. D. Wilts, and D. G. Stavenga, “The Japanese jewel beetle: a painter’s challenge,” Bioinspiration Biomimetics 8, 045002 (2013).
[Crossref]

Chem. Mater. (1)

H. S. Lee, T. S. Shim, H. Hwang, S.-M. Yang, and S.-H. Kim, “Colloidal photonic crystals toward structural color palettes for security materials,” Chem. Mater. 25, 2684–2690 (2013).
[Crossref]

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G. Sharma, W. Wu, and E. N. Dalal, “The ciede2000 color-difference formula: implementation notes, supplementary test data, and mathematical observations,” Color Res. Appl. 30, 21–30 (2005).
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[Crossref]

Proc. SPIE (1)

A. Rudzinski, A. Tyszka-Zawadzka, and P. Szczepanski, “Simple model of the density of states in 1D photonic crystal,” Proc. SPIE 5950, 59501A (2005).
[Crossref]

Sci. Rep. (2)

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, 33984 (2016).
[Crossref]

H. Nam, K. Song, D. Ha, and T. Kim, “Inkjet printing based mono-layered photonic crystal patterning for anti-counterfeiting structural colors,” Sci. Rep. 6, 30885 (2016).
[Crossref]

Trans. Opt. Soc. (1)

T. Smith and J. Guild, “The C.I.E. colorimetric standards and their use,” Trans. Opt. Soc. 33, 73–134 (1931).
[Crossref]

Wiley Interdiscip. Rev. (1)

Y. Fu, C. A. Tippets, E. U. Donev, and R. Lopez, “Structural colors: from natural to artificial systems,” Wiley Interdiscip. Rev. 8, 758–775 (2016).
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K. Busch, S. Lölkes, R. B. Wehrspohn, and H. Föll, Photonic Crystals: Advances in Design, Fabrication, and Characterization (Wiley, 2006).

T. Sarathi and W. C. Carter, “Multilayer photonic bandgap” (Wolfram Demonstrations Project), http://demonstrations.wolfram.com/MultilayerPhotonicBandgap/ .

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R. O. Prum and R. H. Torres, “Fourier blues: structural coloration of biological tissues,” in Excursions in Harmonic Analysis (Springer, 2013), Vol. 2, pp. 401–421.

S. Magkiriadou, “Structural color from colloidal glasses,” Ph.D. thesis (Harvard University, 2014).

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Figures (13)

Fig. 1.
Fig. 1.

Schematic of four different photonic structures: (a) 1D stack, (b) 2D lattice, (c) 3D glass, (d) a biological structure, in this case a Morpho butterfly wing.

Fig. 2.
Fig. 2.

Plot of the three CIE color-matching functions, spanning the range of visible wavelengths.

Fig. 3.
Fig. 3.

(a) Schematic of the three orthogonal axes of the L*a*b* color space, the space in which CIE ΔE* color distance is measured. (b) Dartboard representation of CIE ΔE* color distance, with example colors at distances of ΔE*=0.05, 0.10, and 0.15 given for the primary colors blue, yellow, and red.

Fig. 4.
Fig. 4.

Comparison between (a) a computed continuous parameter space, showing smooth gradations between neighboring colors, and (b) a theoretical discontinuous parameter space. All parameter spaces used in the methods presented are assumed to be continuous.

Fig. 5.
Fig. 5.

Each plot shows two reflectance spectra that represent the same perceived XYZ color. It is evident that similarity of two spectrum functions is a poor metric for similarity of the colors they represent.

Fig. 6.
Fig. 6.

Visualization of the adaptive mesh algorithm on a two-dimensional parameter space. The steps are as follows: (a) Iteration 1: combinations of parameters are selected in 50 nm increments across the whole parameter space, creating a mesh. (b) Spectrum and perceived color calculations are performed for each combination of parameters. The three mesh points with the smallest ΔE* from the desired color are selected. (c) Iteration 2: new 3×3 meshes are calculated around each of these chosen points, with a resolution of 25 nm. (d) Again, the three mesh points with the smallest ΔE* from the desired color are selected. (e) Iteration 3: these three points are used as the center of 3×3 meshes with a resolution of 12.5 nm. (f) After the desired number of iterations, a set of chosen color matches is returned. n.b. the actual algorithm chooses 10 points from each iteration rather than three.

Fig. 7.
Fig. 7.

Full parameter space for a five-layer crystal made of alternating PMMA and air layers, with refractive indices of 1.49 and 1, respectively. Within this space, there are at least three separate 1D geometries with similar green colors.

Fig. 8.
Fig. 8.

(a) Table of color matches for a desired color after 10 iterations. (b) Averaged convergence of 20 randomly generated colors, ending with an average ΔE* of 0.013. (c) Matched dimensions after three iterations for XYZ color (X=0.37,Y=0.19,Z=0.08), showing four distinct pairs of parameters with a ΔE* less than 0.05.

Fig. 9.
Fig. 9.

Results for a 2D hexagonal lattice made of silicon and drilled air holes, with refractive indices of 3.88 and 1.0. The colors are notably more muted than for the 1D geometry.

Fig. 10.
Fig. 10.

(a) Initial color photograph of a swallowtail butterfly wing. (b) Reduced six-color image. (c) 2D photonic crystal results without constraints applied, where a is the lattice constant and r is the air hole radius. (d) Results with a constraint of no feature smaller than 250 nm. The constraint leads to poorer color matches, but most are still within the acceptable range of a ΔE* less than or equal to 0.06.

Fig. 11.
Fig. 11.

Results from a photonic glass made of PMMA spheres in a water matrix (refractive indices of 1.49 and 1.33), viewed through air. The square cross-sections are meant to be schematic, as the system is semi-ordered. The colors created by this system again are duller than in the 1D case, due to the increased complexity of the system.

Fig. 12.
Fig. 12.

Artificial peacock feather was designed for 3D photonic glasses made of PMMA spheres in water. The pale tan color match had the greatest color distance by a factor of two, demonstrating the challenge of producing pale structural colors.

Fig. 13.
Fig. 13.

(a) Measured ΔE* color distance between colors calculated from a reflectance spectrum and (b) color captured by a digital camera.

Tables (1)

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Table 1. Results for 1D, 2D, and 3D Geometries

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

X=λS(λ)I(λ)x¯(λ)dλ,
Y=λS(λ)I(λ)y¯(λ)dλ,
Z=λS(λ)I(λ)z¯(λ)dλ.