Abstract

Many species of butterflies exhibit interesting optical phenomena due to structural color. The physical reason for this color is subwavelength features on the surface of a single scale. The exposed surface of a scale is covered with a ridge structure. The fully three-dimensional, periodic, finite-difference time- domain method is used to create a detailed electromagnetic model of a generic ridge. A novel method for presenting the three-dimensional observed color pattern is developed. Using these tools, the change in color that is a result of varying individual features of the scale is explored. Computational models are developed that are similar to three butterflies: Morpho rhetenor, Troides magellanus, and Ancyluris meliboeus.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Berthier, Iridescences: The Physical Colors of Insects (Springer, 2007).
  2. T. F. Anderson and A. G. Richards, “An electron microscope study of some structural colors of insects,” J. Appl. Phys. 13, 748-758 (1942).
    [CrossRef]
  3. H. Ghiradella, “Structure of iridescent lepidopteran scales: variations on several themes,” Ann. Entomol. Soc. Am. 77, 637-645 (1984).
  4. H. Ghiradella, “Hairs, bristles, and scales,” in Microscopic Anatomy of Invertebrates, W. H. Frederick and L. Michael, eds. (Wiley-Liss, 1998), Vol. 11A, pp. 257-287.
  5. P. Vukusic, J. R. Sambles, and H. Ghiradella, “Optical classification of microstructure in butterfly wing-scales,” Photonics Sci. News 6, 61-68 (2000).
  6. P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wooten, “Quantified interference and diffraction in single Morpho butterfly scales,” Proc. R. Soc. London Ser. B 266, 1403-1411(1999).
    [CrossRef]
  7. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech, 2005).
  8. R. T. Lee and G. S. Smith, “An alternative approach for implementing periodic boundary conditions in the FDTD method using multiple unit cells,” IEEE Trans. Antennas Propag. 54, 698-705 (2006).
    [CrossRef]
  9. R. T. Lee, “A novel technique for incorporating periodic boundaries into the FDTD method and the application to the study of structural color of insects,” Ph.D. thesis (Georgia Institute of Technology, 2009).
  10. L. Plattner, “Optical properties of the scales of Morpho rhetenor butterflies: theoretical and experimental investigation of the backscattering of light in the visible spectrum,” J. R. Soc. Interface 1, 49-59 (2004).
    [CrossRef]
  11. S. Banerjee, J. B. Cole, and T. Yatagai, “Colour characterization of a Morpho butterfly wing-scale using a high accuracy nonstandard finite-difference time-domain method,” Micron 38, 97-103 (2007).
    [CrossRef]
  12. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302-307 (1966).
    [CrossRef]
  13. J. B. Schneider, “Plane waves in FDTD simulations and a nearly perfect total-field/scattered-field boundary,” IEEE Trans. Antennas Propag. 52, 3280-3287 (2004).
    [CrossRef]
  14. J. A. Roden and S. D. Gedney, “Convolutional PML (CPML): an efficient FDTD implementation of the CFS-PML for arbitrary media,” Microw. Opt. Technol. Lett. 27, 334-339 (2000).
    [CrossRef]
  15. S. Kinoshita and S. Yoshioka, “Structural colors in nature: The role of regularity and irregularity in the structure,” Chem. Phys. Chem. 6, 1442-1459 (2005).
    [CrossRef] [PubMed]
  16. “Standard terminology of appearance,” ASTM E 284 08 (ASTM International, 2008).
  17. R. S. Berns, Billmeyer and Saltzman's Principles of Color Technology, 3rd ed. (Wiley, 2000).
  18. “Standard practice for computing the colors of objects by using the CIE system,” ASTM E 308 06 (ASTM International, 2006).
  19. R. A. Potyrailo, H. Ghiradella, A. Vertiatchikh, K. Dovidenko, J. R. Cournoyer, and E. Olson, “Morphobutterfly wing scales demonstrate highly selective vapour response,” Nat. Photon. 1, 123-128 (2007).
    [CrossRef]
  20. S. Berthier, E. Charron, and J. Boulenguez, “Morphological structure and optical properties of the wings of Morphidae,” Insect Sci. 13, 145-158 (2006).
    [CrossRef]
  21. S. Yoshioka and S. Kinoshita, “Wavelength-selective and anisotropic light-diffusing scale on the wing of the Morphobutterfly,” Proc. R. Soc. London Ser. B 271, 581-587 (2004).
    [CrossRef]
  22. B. Gralak, G. Tayeb, and S. Enoch, “Morphobutterflies wings color modeled with lamellar grating theory,” Opt. Express 9, 567-578 (2001).
    [CrossRef] [PubMed]
  23. C. Lawrence, P. Vukusic, and R. Sambles, “Grazing-incidence iridescence from a butterfly wing,” Appl. Opt. 41, 437-441(2002).
    [CrossRef] [PubMed]
  24. J. P. Vigneron, K. Kertesz, Z. Vertesy, M. Rassart, V. Lousse, Z. Balint, and L. P. Biro, “Correlated diffraction and fluorescence in the backscattering iridescence of the male butterfly Troides magellanus (Papilionidae),” Phys. Rev. E 78, 021903(2008).
    [CrossRef]
  25. P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, “Limited-view iridescence in the butterfly Ancyluris meliboeus,” Proc. R. Soc. London Ser. B , 269, 7-14 (2002).
    [CrossRef]
  26. S. Kinoshita, S. Yoshioka, and J. Miyazaki, “Physics of structural colors,” Rep. Prog. Phys. 71, 076401 (2008).
    [CrossRef]

2008

J. P. Vigneron, K. Kertesz, Z. Vertesy, M. Rassart, V. Lousse, Z. Balint, and L. P. Biro, “Correlated diffraction and fluorescence in the backscattering iridescence of the male butterfly Troides magellanus (Papilionidae),” Phys. Rev. E 78, 021903(2008).
[CrossRef]

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

2007

S. Banerjee, J. B. Cole, and T. Yatagai, “Colour characterization of a Morpho butterfly wing-scale using a high accuracy nonstandard finite-difference time-domain method,” Micron 38, 97-103 (2007).
[CrossRef]

R. A. Potyrailo, H. Ghiradella, A. Vertiatchikh, K. Dovidenko, J. R. Cournoyer, and E. Olson, “Morphobutterfly wing scales demonstrate highly selective vapour response,” Nat. Photon. 1, 123-128 (2007).
[CrossRef]

2006

S. Berthier, E. Charron, and J. Boulenguez, “Morphological structure and optical properties of the wings of Morphidae,” Insect Sci. 13, 145-158 (2006).
[CrossRef]

R. T. Lee and G. S. Smith, “An alternative approach for implementing periodic boundary conditions in the FDTD method using multiple unit cells,” IEEE Trans. Antennas Propag. 54, 698-705 (2006).
[CrossRef]

2005

S. Kinoshita and S. Yoshioka, “Structural colors in nature: The role of regularity and irregularity in the structure,” Chem. Phys. Chem. 6, 1442-1459 (2005).
[CrossRef] [PubMed]

2004

J. B. Schneider, “Plane waves in FDTD simulations and a nearly perfect total-field/scattered-field boundary,” IEEE Trans. Antennas Propag. 52, 3280-3287 (2004).
[CrossRef]

S. Yoshioka and S. Kinoshita, “Wavelength-selective and anisotropic light-diffusing scale on the wing of the Morphobutterfly,” Proc. R. Soc. London Ser. B 271, 581-587 (2004).
[CrossRef]

L. Plattner, “Optical properties of the scales of Morpho rhetenor butterflies: theoretical and experimental investigation of the backscattering of light in the visible spectrum,” J. R. Soc. Interface 1, 49-59 (2004).
[CrossRef]

2002

C. Lawrence, P. Vukusic, and R. Sambles, “Grazing-incidence iridescence from a butterfly wing,” Appl. Opt. 41, 437-441(2002).
[CrossRef] [PubMed]

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, “Limited-view iridescence in the butterfly Ancyluris meliboeus,” Proc. R. Soc. London Ser. B , 269, 7-14 (2002).
[CrossRef]

2001

2000

J. A. Roden and S. D. Gedney, “Convolutional PML (CPML): an efficient FDTD implementation of the CFS-PML for arbitrary media,” Microw. Opt. Technol. Lett. 27, 334-339 (2000).
[CrossRef]

P. Vukusic, J. R. Sambles, and H. Ghiradella, “Optical classification of microstructure in butterfly wing-scales,” Photonics Sci. News 6, 61-68 (2000).

1999

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wooten, “Quantified interference and diffraction in single Morpho butterfly scales,” Proc. R. Soc. London Ser. B 266, 1403-1411(1999).
[CrossRef]

1984

H. Ghiradella, “Structure of iridescent lepidopteran scales: variations on several themes,” Ann. Entomol. Soc. Am. 77, 637-645 (1984).

1966

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

1942

T. F. Anderson and A. G. Richards, “An electron microscope study of some structural colors of insects,” J. Appl. Phys. 13, 748-758 (1942).
[CrossRef]

Anderson, T. F.

T. F. Anderson and A. G. Richards, “An electron microscope study of some structural colors of insects,” J. Appl. Phys. 13, 748-758 (1942).
[CrossRef]

Balint, Z.

J. P. Vigneron, K. Kertesz, Z. Vertesy, M. Rassart, V. Lousse, Z. Balint, and L. P. Biro, “Correlated diffraction and fluorescence in the backscattering iridescence of the male butterfly Troides magellanus (Papilionidae),” Phys. Rev. E 78, 021903(2008).
[CrossRef]

Banerjee, S.

S. Banerjee, J. B. Cole, and T. Yatagai, “Colour characterization of a Morpho butterfly wing-scale using a high accuracy nonstandard finite-difference time-domain method,” Micron 38, 97-103 (2007).
[CrossRef]

Berns, R. S.

R. S. Berns, Billmeyer and Saltzman's Principles of Color Technology, 3rd ed. (Wiley, 2000).

Berthier, S.

S. Berthier, E. Charron, and J. Boulenguez, “Morphological structure and optical properties of the wings of Morphidae,” Insect Sci. 13, 145-158 (2006).
[CrossRef]

S. Berthier, Iridescences: The Physical Colors of Insects (Springer, 2007).

Biro, L. P.

J. P. Vigneron, K. Kertesz, Z. Vertesy, M. Rassart, V. Lousse, Z. Balint, and L. P. Biro, “Correlated diffraction and fluorescence in the backscattering iridescence of the male butterfly Troides magellanus (Papilionidae),” Phys. Rev. E 78, 021903(2008).
[CrossRef]

Boulenguez, J.

S. Berthier, E. Charron, and J. Boulenguez, “Morphological structure and optical properties of the wings of Morphidae,” Insect Sci. 13, 145-158 (2006).
[CrossRef]

Charron, E.

S. Berthier, E. Charron, and J. Boulenguez, “Morphological structure and optical properties of the wings of Morphidae,” Insect Sci. 13, 145-158 (2006).
[CrossRef]

Cole, J. B.

S. Banerjee, J. B. Cole, and T. Yatagai, “Colour characterization of a Morpho butterfly wing-scale using a high accuracy nonstandard finite-difference time-domain method,” Micron 38, 97-103 (2007).
[CrossRef]

Cournoyer, J. R.

R. A. Potyrailo, H. Ghiradella, A. Vertiatchikh, K. Dovidenko, J. R. Cournoyer, and E. Olson, “Morphobutterfly wing scales demonstrate highly selective vapour response,” Nat. Photon. 1, 123-128 (2007).
[CrossRef]

Dovidenko, K.

R. A. Potyrailo, H. Ghiradella, A. Vertiatchikh, K. Dovidenko, J. R. Cournoyer, and E. Olson, “Morphobutterfly wing scales demonstrate highly selective vapour response,” Nat. Photon. 1, 123-128 (2007).
[CrossRef]

Enoch, S.

Gedney, S. D.

J. A. Roden and S. D. Gedney, “Convolutional PML (CPML): an efficient FDTD implementation of the CFS-PML for arbitrary media,” Microw. Opt. Technol. Lett. 27, 334-339 (2000).
[CrossRef]

Ghiradella, H.

R. A. Potyrailo, H. Ghiradella, A. Vertiatchikh, K. Dovidenko, J. R. Cournoyer, and E. Olson, “Morphobutterfly wing scales demonstrate highly selective vapour response,” Nat. Photon. 1, 123-128 (2007).
[CrossRef]

P. Vukusic, J. R. Sambles, and H. Ghiradella, “Optical classification of microstructure in butterfly wing-scales,” Photonics Sci. News 6, 61-68 (2000).

H. Ghiradella, “Structure of iridescent lepidopteran scales: variations on several themes,” Ann. Entomol. Soc. Am. 77, 637-645 (1984).

H. Ghiradella, “Hairs, bristles, and scales,” in Microscopic Anatomy of Invertebrates, W. H. Frederick and L. Michael, eds. (Wiley-Liss, 1998), Vol. 11A, pp. 257-287.

Gralak, B.

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech, 2005).

Kertesz, K.

J. P. Vigneron, K. Kertesz, Z. Vertesy, M. Rassart, V. Lousse, Z. Balint, and L. P. Biro, “Correlated diffraction and fluorescence in the backscattering iridescence of the male butterfly Troides magellanus (Papilionidae),” Phys. Rev. E 78, 021903(2008).
[CrossRef]

Kinoshita, S.

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

S. Kinoshita and S. Yoshioka, “Structural colors in nature: The role of regularity and irregularity in the structure,” Chem. Phys. Chem. 6, 1442-1459 (2005).
[CrossRef] [PubMed]

S. Yoshioka and S. Kinoshita, “Wavelength-selective and anisotropic light-diffusing scale on the wing of the Morphobutterfly,” Proc. R. Soc. London Ser. B 271, 581-587 (2004).
[CrossRef]

Lawrence, C.

Lawrence, C. R.

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, “Limited-view iridescence in the butterfly Ancyluris meliboeus,” Proc. R. Soc. London Ser. B , 269, 7-14 (2002).
[CrossRef]

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wooten, “Quantified interference and diffraction in single Morpho butterfly scales,” Proc. R. Soc. London Ser. B 266, 1403-1411(1999).
[CrossRef]

Lee, R. T.

R. T. Lee and G. S. Smith, “An alternative approach for implementing periodic boundary conditions in the FDTD method using multiple unit cells,” IEEE Trans. Antennas Propag. 54, 698-705 (2006).
[CrossRef]

R. T. Lee, “A novel technique for incorporating periodic boundaries into the FDTD method and the application to the study of structural color of insects,” Ph.D. thesis (Georgia Institute of Technology, 2009).

Lousse, V.

J. P. Vigneron, K. Kertesz, Z. Vertesy, M. Rassart, V. Lousse, Z. Balint, and L. P. Biro, “Correlated diffraction and fluorescence in the backscattering iridescence of the male butterfly Troides magellanus (Papilionidae),” Phys. Rev. E 78, 021903(2008).
[CrossRef]

Miyazaki, J.

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

Olson, E.

R. A. Potyrailo, H. Ghiradella, A. Vertiatchikh, K. Dovidenko, J. R. Cournoyer, and E. Olson, “Morphobutterfly wing scales demonstrate highly selective vapour response,” Nat. Photon. 1, 123-128 (2007).
[CrossRef]

Plattner, L.

L. Plattner, “Optical properties of the scales of Morpho rhetenor butterflies: theoretical and experimental investigation of the backscattering of light in the visible spectrum,” J. R. Soc. Interface 1, 49-59 (2004).
[CrossRef]

Potyrailo, R. A.

R. A. Potyrailo, H. Ghiradella, A. Vertiatchikh, K. Dovidenko, J. R. Cournoyer, and E. Olson, “Morphobutterfly wing scales demonstrate highly selective vapour response,” Nat. Photon. 1, 123-128 (2007).
[CrossRef]

Rassart, M.

J. P. Vigneron, K. Kertesz, Z. Vertesy, M. Rassart, V. Lousse, Z. Balint, and L. P. Biro, “Correlated diffraction and fluorescence in the backscattering iridescence of the male butterfly Troides magellanus (Papilionidae),” Phys. Rev. E 78, 021903(2008).
[CrossRef]

Richards, A. G.

T. F. Anderson and A. G. Richards, “An electron microscope study of some structural colors of insects,” J. Appl. Phys. 13, 748-758 (1942).
[CrossRef]

Roden, J. A.

J. A. Roden and S. D. Gedney, “Convolutional PML (CPML): an efficient FDTD implementation of the CFS-PML for arbitrary media,” Microw. Opt. Technol. Lett. 27, 334-339 (2000).
[CrossRef]

Sambles, J. R.

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, “Limited-view iridescence in the butterfly Ancyluris meliboeus,” Proc. R. Soc. London Ser. B , 269, 7-14 (2002).
[CrossRef]

P. Vukusic, J. R. Sambles, and H. Ghiradella, “Optical classification of microstructure in butterfly wing-scales,” Photonics Sci. News 6, 61-68 (2000).

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wooten, “Quantified interference and diffraction in single Morpho butterfly scales,” Proc. R. Soc. London Ser. B 266, 1403-1411(1999).
[CrossRef]

Sambles, R.

Schneider, J. B.

J. B. Schneider, “Plane waves in FDTD simulations and a nearly perfect total-field/scattered-field boundary,” IEEE Trans. Antennas Propag. 52, 3280-3287 (2004).
[CrossRef]

Smith, G. S.

R. T. Lee and G. S. Smith, “An alternative approach for implementing periodic boundary conditions in the FDTD method using multiple unit cells,” IEEE Trans. Antennas Propag. 54, 698-705 (2006).
[CrossRef]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech, 2005).

Tayeb, G.

Vertesy, Z.

J. P. Vigneron, K. Kertesz, Z. Vertesy, M. Rassart, V. Lousse, Z. Balint, and L. P. Biro, “Correlated diffraction and fluorescence in the backscattering iridescence of the male butterfly Troides magellanus (Papilionidae),” Phys. Rev. E 78, 021903(2008).
[CrossRef]

Vertiatchikh, A.

R. A. Potyrailo, H. Ghiradella, A. Vertiatchikh, K. Dovidenko, J. R. Cournoyer, and E. Olson, “Morphobutterfly wing scales demonstrate highly selective vapour response,” Nat. Photon. 1, 123-128 (2007).
[CrossRef]

Vigneron, J. P.

J. P. Vigneron, K. Kertesz, Z. Vertesy, M. Rassart, V. Lousse, Z. Balint, and L. P. Biro, “Correlated diffraction and fluorescence in the backscattering iridescence of the male butterfly Troides magellanus (Papilionidae),” Phys. Rev. E 78, 021903(2008).
[CrossRef]

Vukusic, P.

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, “Limited-view iridescence in the butterfly Ancyluris meliboeus,” Proc. R. Soc. London Ser. B , 269, 7-14 (2002).
[CrossRef]

C. Lawrence, P. Vukusic, and R. Sambles, “Grazing-incidence iridescence from a butterfly wing,” Appl. Opt. 41, 437-441(2002).
[CrossRef] [PubMed]

P. Vukusic, J. R. Sambles, and H. Ghiradella, “Optical classification of microstructure in butterfly wing-scales,” Photonics Sci. News 6, 61-68 (2000).

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wooten, “Quantified interference and diffraction in single Morpho butterfly scales,” Proc. R. Soc. London Ser. B 266, 1403-1411(1999).
[CrossRef]

Wooten, R. J.

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wooten, “Quantified interference and diffraction in single Morpho butterfly scales,” Proc. R. Soc. London Ser. B 266, 1403-1411(1999).
[CrossRef]

Wootton, R. J.

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, “Limited-view iridescence in the butterfly Ancyluris meliboeus,” Proc. R. Soc. London Ser. B , 269, 7-14 (2002).
[CrossRef]

Yatagai, T.

S. Banerjee, J. B. Cole, and T. Yatagai, “Colour characterization of a Morpho butterfly wing-scale using a high accuracy nonstandard finite-difference time-domain method,” Micron 38, 97-103 (2007).
[CrossRef]

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

Yoshioka, S.

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

S. Kinoshita and S. Yoshioka, “Structural colors in nature: The role of regularity and irregularity in the structure,” Chem. Phys. Chem. 6, 1442-1459 (2005).
[CrossRef] [PubMed]

S. Yoshioka and S. Kinoshita, “Wavelength-selective and anisotropic light-diffusing scale on the wing of the Morphobutterfly,” Proc. R. Soc. London Ser. B 271, 581-587 (2004).
[CrossRef]

Ann. Entomol. Soc. Am.

H. Ghiradella, “Structure of iridescent lepidopteran scales: variations on several themes,” Ann. Entomol. Soc. Am. 77, 637-645 (1984).

Appl. Opt.

Chem. Phys. Chem.

S. Kinoshita and S. Yoshioka, “Structural colors in nature: The role of regularity and irregularity in the structure,” Chem. Phys. Chem. 6, 1442-1459 (2005).
[CrossRef] [PubMed]

IEEE Trans. Antennas Propag.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

J. B. Schneider, “Plane waves in FDTD simulations and a nearly perfect total-field/scattered-field boundary,” IEEE Trans. Antennas Propag. 52, 3280-3287 (2004).
[CrossRef]

R. T. Lee and G. S. Smith, “An alternative approach for implementing periodic boundary conditions in the FDTD method using multiple unit cells,” IEEE Trans. Antennas Propag. 54, 698-705 (2006).
[CrossRef]

Insect Sci.

S. Berthier, E. Charron, and J. Boulenguez, “Morphological structure and optical properties of the wings of Morphidae,” Insect Sci. 13, 145-158 (2006).
[CrossRef]

J. Appl. Phys.

T. F. Anderson and A. G. Richards, “An electron microscope study of some structural colors of insects,” J. Appl. Phys. 13, 748-758 (1942).
[CrossRef]

J. R. Soc. Interface

L. Plattner, “Optical properties of the scales of Morpho rhetenor butterflies: theoretical and experimental investigation of the backscattering of light in the visible spectrum,” J. R. Soc. Interface 1, 49-59 (2004).
[CrossRef]

Micron

S. Banerjee, J. B. Cole, and T. Yatagai, “Colour characterization of a Morpho butterfly wing-scale using a high accuracy nonstandard finite-difference time-domain method,” Micron 38, 97-103 (2007).
[CrossRef]

Microw. Opt. Technol. Lett.

J. A. Roden and S. D. Gedney, “Convolutional PML (CPML): an efficient FDTD implementation of the CFS-PML for arbitrary media,” Microw. Opt. Technol. Lett. 27, 334-339 (2000).
[CrossRef]

Nat. Photon.

R. A. Potyrailo, H. Ghiradella, A. Vertiatchikh, K. Dovidenko, J. R. Cournoyer, and E. Olson, “Morphobutterfly wing scales demonstrate highly selective vapour response,” Nat. Photon. 1, 123-128 (2007).
[CrossRef]

Opt. Express

Photonics Sci. News

P. Vukusic, J. R. Sambles, and H. Ghiradella, “Optical classification of microstructure in butterfly wing-scales,” Photonics Sci. News 6, 61-68 (2000).

Phys. Rev. E

J. P. Vigneron, K. Kertesz, Z. Vertesy, M. Rassart, V. Lousse, Z. Balint, and L. P. Biro, “Correlated diffraction and fluorescence in the backscattering iridescence of the male butterfly Troides magellanus (Papilionidae),” Phys. Rev. E 78, 021903(2008).
[CrossRef]

Proc. R. Soc. London Ser. B

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, “Limited-view iridescence in the butterfly Ancyluris meliboeus,” Proc. R. Soc. London Ser. B , 269, 7-14 (2002).
[CrossRef]

S. Yoshioka and S. Kinoshita, “Wavelength-selective and anisotropic light-diffusing scale on the wing of the Morphobutterfly,” Proc. R. Soc. London Ser. B 271, 581-587 (2004).
[CrossRef]

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wooten, “Quantified interference and diffraction in single Morpho butterfly scales,” Proc. R. Soc. London Ser. B 266, 1403-1411(1999).
[CrossRef]

Rep. Prog. Phys.

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

Other

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech, 2005).

R. T. Lee, “A novel technique for incorporating periodic boundaries into the FDTD method and the application to the study of structural color of insects,” Ph.D. thesis (Georgia Institute of Technology, 2009).

S. Berthier, Iridescences: The Physical Colors of Insects (Springer, 2007).

H. Ghiradella, “Hairs, bristles, and scales,” in Microscopic Anatomy of Invertebrates, W. H. Frederick and L. Michael, eds. (Wiley-Liss, 1998), Vol. 11A, pp. 257-287.

“Standard terminology of appearance,” ASTM E 284 08 (ASTM International, 2008).

R. S. Berns, Billmeyer and Saltzman's Principles of Color Technology, 3rd ed. (Wiley, 2000).

“Standard practice for computing the colors of objects by using the CIE system,” ASTM E 308 06 (ASTM International, 2006).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (17)

Fig. 1
Fig. 1

Images of a male Morpho rhetenor butterfly. (a) Photograph of dorsal side (top) of insect. (b) Detail of wing showing scales as viewed under an optical microscope. (c) Cross section of scale showing individual ridges as viewed using a scanning electron microscope. SEM image courtesy S. Kinoshita [[26], p. 13, Fig. 12].

Fig. 2
Fig. 2

Computational model. (a) Portion of a scale showing three ridges. The volume within the black frame is the volume used for the periodic FDTD calculations. (b) Detail of a single ridge showing the individual FDTD cells. (c) Arrangement of the electromagnetic field components within a single FDTD cell.

Fig. 3
Fig. 3

Parameters used to describe the geometry of a periodic cell and the coordinates for a point P in space.

Fig. 4
Fig. 4

Schematic drawing showing elements within an FDTD periodic cell.

Fig. 5
Fig. 5

(a) Geometry for two-dimensional array of ridges with random heights. (b) Equivalent transform surface for obtaining the far-zone scattered field above the array.

Fig. 6
Fig. 6

Comparison of results from an ensemble average of randomized finite models and a periodic model. (a) Far-zone scattering pattern for the ensemble average of 100 simulations with 50 randomly spaced ridges per simulation. (b) Far-zone scattering pattern for the periodic model. (c) Comparison of the reflection coefficients for the ensemble average and the periodic model.

Fig. 7
Fig. 7

Flowchart illustrating the steps used to calculate the observed color using the periodic FDTD method. indicates the Fourier transform, and η is the intrinsic impedance of free space.

Fig. 8
Fig. 8

Illustration for the three-dimensional representation of the observed color as a function of the direction of observation.

Fig. 9
Fig. 9

Observed color as a function of direction for Morpho-like models. For all cases, there are eight lamellae and a base. (a) Aligned lamellae without taper, Y max = 1.0 . (b) Aligned lamellae with the top four lamellae tapered, Y max = 0.30 . (c) Aligned, tapered lamellae plus a cover scale (dielectric slab), Y max = 0.28 . (d)–(f) Same as (a)–(c), but with offset lamellae. (d)  Y max = 0.21 . (e)  Y max = 0.05 . (f)  Y max = 0.22 .

Fig. 10
Fig. 10

Far-zone scattering patterns for the Morpho model shown in Fig. 9a. (a) Pattern in the y–z plane. (b) Pattern in a perpendicular plane that passes through the peak of the beam (angle measured from θ = 20 ° , ϕ = 90 ° ).

Fig. 11
Fig. 11

Power reflection coefficients (a) for structures with aligned lamellae, as in Figs. 9a, 9b, 9c, and (b) for structures with offset lamellae, as in Figs. 9d, 9e, 9f.

Fig. 12
Fig. 12

Observed color as a function of direction for Morpho-like models that include microribs. For both cases, there are eight lamellae with the top four lamellae tapered and a base: (a) aligned lamellae, Y max = 0.26 ; (b) offset lamellae, Y max = 0.05 .

Fig. 13
Fig. 13

Photographs of the dorsal side of a male Troides magellanus butterfly. In both views, the light source is located near the observation point. (a) From most observation directions, the observed color of the lower wings is yellow. (b) When illuminated and viewed near grazing, the color of the lower wings changes abruptly, with a change in angle, to blue.

Fig. 14
Fig. 14

Observed color as a function of direction for Troides magellanus model with six aligned lamellae. The details for the model are the same for all cases, and only the direction of the incident light is changed: (a)  θ i = 40 ° , Y max = 0.05 ; (b)  θ i = 50 ° , Y max = 0.14 ; (c)  θ i = 70 ° , Y max = 1.0 .

Fig. 15
Fig. 15

Power reflection coefficient for Troides magellanus model. The rapid increase in the intensity of the iridescent color is shown by comparing the reflection coefficient for θ i = 40 ° and θ i = 70 ° .

Fig. 16
Fig. 16

Observed color as a function of direction for Ancyluris meliboeus model with six aligned lamellae and a base: (a) without microribs, Y max = 1.0 ; (b) with microribs, Y max = 0.48 .

Fig. 17
Fig. 17

Power reflection coefficient for Ancyluris meliboeus model. The addition of the microribs causes the peak in the reflection coefficient to shift to longer wavelengths.

Tables (1)

Tables Icon

Table 1 Dimensions for Butterfly Models

Equations (7)

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

y p = ( g + h ) / sin α .
× = μ H t ,
× H = σ + ϵ t ,
H z | i , j , k n + 1 / 2 = H z ( i Δ x , j Δ y , k Δ z , ( n + 1 / 2 ) Δ t ) .
H z | i , j , k n + 1 / 2 = H z | i , j , k n 1 / 2 + Δ t μ Δ y ( E x | i , j + 1 / 2 , k n E x | i , j 1 / 2 , k n ) Δ t μ Δ x ( E y | i + 1 / 2 , j , k n E y | i 1 / 2 , j , k n ) .
E i ( r , t ) = G ( t k ^ · r / c ) e ^ ,
X ( θ , ϕ ) = K c λ D 65 ( λ ) R ( λ , θ , ϕ ) x ¯ ( λ ) Δ λ ,

Metrics