Abstract

Natural photonic structures exhibit remarkable color effects such as metallic appearance and iridescence. A rigorous study of the electromagnetic response of such complex structures requires to accurately determine some of their relevant optical parameters, such as the refractive indices of the materials involved. In this paper, we apply different heuristic optimization strategies to retrieve the real and imaginary parts of the refractive index of the materials comprising natural multilayer systems. Through some examples, we compare the performances of the inversion methods proposed and show that these kinds of algorithms have a great potential as a tool to investigate natural photonic structures.

© 2013 Optical Society of America

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2012

H. Arwin, R. Magnusson, J. Landin, and K. Jarrendahl, “Chirality-induced polarization effects in the cuticle of scarab beetles: 100 years after Michelson,” Philos. Mag. 92(12), 1583–1599 (2012).
[CrossRef]

D. Macías, P.-M. Adam, V. Ruiz-Cortés, R. Rodríguez-Oliveros, and J. A. Sánchez-Gil, “Heuristic optimization for the design of plasmonic nanowires with specific resonant and scattering properties,” Opt. Express 20, 13146–13163 (2012).
[CrossRef]

2011

A. Tassadit, D. Macías, J. A. Sánchez-Gil, P.-M. Adam, and R. Rodriguez-Oliveros, “Metal nanostars: Stochastic optimization of resonant scattering properties,” Superlattices Microstruct. 49, 288–293 (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, 24061–24066 (2011).
[CrossRef]

S. Yoshioka and S. Kinoshita, “Direct determination of the refractive index of natural multilayer systems,” Phys. Rev. E 83, 051917 (2011).
[CrossRef]

D. G. Stavenga, B. D. Wilts, H. L. Leertouwer, and T. Hariyama, “Polarized iridescence of the multilayered elytra of the Japanese jewel beetle, Chrysochroa fulgidissima,” Philos. Trans. R. Soc. Biol. Sci. 366, 709–723 (2011).
[CrossRef]

2010

A. Luna, D. Skigin, M. Inchaussandague, and A. Roig Alsina, “Structural color in beetles of South America,” Proc. SPIE 7782, 778205 (2010).
[CrossRef]

K. R. Thomas, M. Kolle, H. M. Whitney, B. J. Glover, and U. Steiner, “Function of blue iridescence in tropical understorey plants,” J. R. Soc. Interface 7, 1699–1707 (2010).
[CrossRef]

2009

P. Vukusic and D. G. Stavenga, “Physical methods for investigating structural colours in biological systems,” J. R. Soc. Interface 6, S133–S148 (2009).
[CrossRef]

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, S165–S184 (2009).
[CrossRef]

2008

D. Macías and A. Vial, “Optimal design of plasmonic nanostructures for plasmon-interference assisted lithography,” Appl. Phys. B 93, 159–163 (2008).
[CrossRef]

D. Barchiesi, D. Macas, L. Belmar-Letellier, D. van Labeke, M. Lamy de la Chapelle, T. Toury, E. Kremer, L. Moreau, and T. Grosges, “Plasmonics: influence of the intermediate (or stick) layer on the efficiency of sensors,” Appl. Phys. B 93, 177–181 (2008).
[CrossRef]

2007

R. Poli, J. Kennedy, and T. Blackwell, “Particle swarm optimization: an overview,” Swarm Intell. 1, 33–57 (2007).
[CrossRef]

J. A. Noyes, P. Vukusic, and I. R. Hooper, “Experimental method for reliably establishing the refractive index of buprestid beetle exocuticle,” Opt. Express 15, 4351–4357 (2007).
[CrossRef]

M. F. Land, J. Horwood, M. L. M. Lim, and D. Li, “Optics of the ultraviolet reflecting scales of a jumping spider,” Proc. R. Soc. B 274, 1583–1589 (2007).
[CrossRef]

S. Berthier, J. Boulenguez, and Z. Bálint, “Multiscaled polarization effects in Suneve coronata (Lepidoptera) and other insects: application to anti-counterfeiting of banknotes,” App. Phys. A 86, 123–130 (2007).
[CrossRef]

2006

J. P. Vigneron, M. Rassart, C. Vandenbem, V. Lousse, O. Deparis, L. P. Birø, D. Dedouaire, A. Cornet, and P. Defrance, “Spectral filtering of visible light by the cuticle of metallic woodboring beetles and microfabrication of a matching bioinspired material,” Phys. Rev. E 73, 041905 (2006).
[CrossRef]

D. Macías, G. Olague, and E. R. Méndez, “Inverse scattering with far-field intensity data: random surfaces that belong to a well-defined statistical class,” Waves Random Complex Media 16, 545–560 (2006).
[CrossRef]

2005

A. Vial, A. S. Grimault, D. Macías, D. Barchiesi, and M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion: application to the modelling of extinction spectra with the FDTD method,” Phys. Rev. B 71, 085416 (2005).
[CrossRef]

2004

D. Macías, A. Vial, and D. Barchiesi, “Application of evolution strategies for the solution of an inverse problem in near-field optics,” J. Opt. Soc. Am. A 21, 1465–1471 (2004).
[CrossRef]

J. Robinson and Y. Rahmat-Samii, “Particle swarm optimization in electromagnetics,” IEEE Trans. Antennas Propag. 52, 397–407 (2004).
[CrossRef]

2003

S. Berthier, E. Charron, and A. Da Silva, “Determination of the cuticle index of the scales of the iridescent butterfly Morpho menelaus,” Opt. Commun. 228, 349–356 (2003).
[CrossRef]

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

2002

K. Miyamoto and A. Kosaku, “Cuticular microstructures and their relationship to structural color in the Shieldbug Poecilocoris lewisi distant,” Forma 17, 155–167 (2002).

2000

A. Parker, “515 million years of structural colour,” J. Opt. A 2, R15–R28 (2000).
[CrossRef]

1999

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, “Quantified interference and diffraction in single Morphobutterfly scales,” Proc. R. Soc. Lond. B 266, 1403–1411(1999).
[CrossRef]

1997

A. B. Djurišic, J. M. Elazar, and A. D. Rakic, “Modeling the optical constants of solids using acceptance-probability-controlled simulated annealing with adaptive move generation procedure,” Phys. Rev. E 55, 4797–4803 (1997).
[CrossRef]

1985

T. D. Schultz and M. A. Rankin, “The ultrastructure of the epicuticular interference reflectors of tiger beetles (Cicindela),” J. Exp. Biol. 117, 87–110 (1985).

Adam, P.-M.

D. Macías, P.-M. Adam, V. Ruiz-Cortés, R. Rodríguez-Oliveros, and J. A. Sánchez-Gil, “Heuristic optimization for the design of plasmonic nanowires with specific resonant and scattering properties,” Opt. Express 20, 13146–13163 (2012).
[CrossRef]

A. Tassadit, D. Macías, J. A. Sánchez-Gil, P.-M. Adam, and R. Rodriguez-Oliveros, “Metal nanostars: Stochastic optimization of resonant scattering properties,” Superlattices Microstruct. 49, 288–293 (2011).
[CrossRef]

Arwin, H.

H. Arwin, R. Magnusson, J. Landin, and K. Jarrendahl, “Chirality-induced polarization effects in the cuticle of scarab beetles: 100 years after Michelson,” Philos. Mag. 92(12), 1583–1599 (2012).
[CrossRef]

Bálint, Z.

S. Berthier, J. Boulenguez, and Z. Bálint, “Multiscaled polarization effects in Suneve coronata (Lepidoptera) and other insects: application to anti-counterfeiting of banknotes,” App. Phys. A 86, 123–130 (2007).
[CrossRef]

Barchiesi, D.

D. Barchiesi, D. Macas, L. Belmar-Letellier, D. van Labeke, M. Lamy de la Chapelle, T. Toury, E. Kremer, L. Moreau, and T. Grosges, “Plasmonics: influence of the intermediate (or stick) layer on the efficiency of sensors,” Appl. Phys. B 93, 177–181 (2008).
[CrossRef]

A. Vial, A. S. Grimault, D. Macías, D. Barchiesi, and M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion: application to the modelling of extinction spectra with the FDTD method,” Phys. Rev. B 71, 085416 (2005).
[CrossRef]

D. Macías, A. Vial, and D. Barchiesi, “Application of evolution strategies for the solution of an inverse problem in near-field optics,” J. Opt. Soc. Am. A 21, 1465–1471 (2004).
[CrossRef]

Belmar-Letellier, L.

D. Barchiesi, D. Macas, L. Belmar-Letellier, D. van Labeke, M. Lamy de la Chapelle, T. Toury, E. Kremer, L. Moreau, and T. Grosges, “Plasmonics: influence of the intermediate (or stick) layer on the efficiency of sensors,” Appl. Phys. B 93, 177–181 (2008).
[CrossRef]

Berthier, S.

S. Berthier, J. Boulenguez, and Z. Bálint, “Multiscaled polarization effects in Suneve coronata (Lepidoptera) and other insects: application to anti-counterfeiting of banknotes,” App. Phys. A 86, 123–130 (2007).
[CrossRef]

S. Berthier, E. Charron, and A. Da Silva, “Determination of the cuticle index of the scales of the iridescent butterfly Morpho menelaus,” Opt. Commun. 228, 349–356 (2003).
[CrossRef]

S. Berthier, Iridescences, the Physical Colours of Insects (Springer Science+Business Media, LLC, 2007).

Beyer, H. G.

H. G. Beyer, The Theory of Evolution Strategies (Springer, 2001).

Birø, L. P.

J. P. Vigneron, M. Rassart, C. Vandenbem, V. Lousse, O. Deparis, L. P. Birø, D. Dedouaire, A. Cornet, and P. Defrance, “Spectral filtering of visible light by the cuticle of metallic woodboring beetles and microfabrication of a matching bioinspired material,” Phys. Rev. E 73, 041905 (2006).
[CrossRef]

Blackwell, T.

R. Poli, J. Kennedy, and T. Blackwell, “Particle swarm optimization: an overview,” Swarm Intell. 1, 33–57 (2007).
[CrossRef]

Boulenguez, J.

S. Berthier, J. Boulenguez, and Z. Bálint, “Multiscaled polarization effects in Suneve coronata (Lepidoptera) and other insects: application to anti-counterfeiting of banknotes,” App. Phys. A 86, 123–130 (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, S165–S184 (2009).
[CrossRef]

Charron, E.

S. Berthier, E. Charron, and A. Da Silva, “Determination of the cuticle index of the scales of the iridescent butterfly Morpho menelaus,” Opt. Commun. 228, 349–356 (2003).
[CrossRef]

Cornet, A.

J. P. Vigneron, M. Rassart, C. Vandenbem, V. Lousse, O. Deparis, L. P. Birø, D. Dedouaire, A. Cornet, and P. Defrance, “Spectral filtering of visible light by the cuticle of metallic woodboring beetles and microfabrication of a matching bioinspired material,” Phys. Rev. E 73, 041905 (2006).
[CrossRef]

Da Silva, A.

S. Berthier, E. Charron, and A. Da Silva, “Determination of the cuticle index of the scales of the iridescent butterfly Morpho menelaus,” Opt. Commun. 228, 349–356 (2003).
[CrossRef]

Dedouaire, D.

J. P. Vigneron, M. Rassart, C. Vandenbem, V. Lousse, O. Deparis, L. P. Birø, D. Dedouaire, A. Cornet, and P. Defrance, “Spectral filtering of visible light by the cuticle of metallic woodboring beetles and microfabrication of a matching bioinspired material,” Phys. Rev. E 73, 041905 (2006).
[CrossRef]

Defrance, P.

J. P. Vigneron, M. Rassart, C. Vandenbem, V. Lousse, O. Deparis, L. P. Birø, D. Dedouaire, A. Cornet, and P. Defrance, “Spectral filtering of visible light by the cuticle of metallic woodboring beetles and microfabrication of a matching bioinspired material,” Phys. Rev. E 73, 041905 (2006).
[CrossRef]

Deparis, O.

J. P. Vigneron, M. Rassart, C. Vandenbem, V. Lousse, O. Deparis, L. P. Birø, D. Dedouaire, A. Cornet, and P. Defrance, “Spectral filtering of visible light by the cuticle of metallic woodboring beetles and microfabrication of a matching bioinspired material,” Phys. Rev. E 73, 041905 (2006).
[CrossRef]

Djurišic, A. B.

A. B. Djurišic, J. M. Elazar, and A. D. Rakic, “Modeling the optical constants of solids using acceptance-probability-controlled simulated annealing with adaptive move generation procedure,” Phys. Rev. E 55, 4797–4803 (1997).
[CrossRef]

Eberhart, R. C.

R. C. Eberhart and J. Kennedy, “A new optimizer using particle swarm theory,” in Proceedings of the Sixth International Symposium on Micro Machine and Human Science (IEEE, 1995), pp. 39–43.

Elazar, J. M.

A. B. Djurišic, J. M. Elazar, and A. D. Rakic, “Modeling the optical constants of solids using acceptance-probability-controlled simulated annealing with adaptive move generation procedure,” Phys. Rev. E 55, 4797–4803 (1997).
[CrossRef]

Fox, H. M.

H. M. Fox and G. Vevers, The Nature of Animal Colours(Sidgwick and Jackson, 1960).

Glover, B. J.

K. R. Thomas, M. Kolle, H. M. Whitney, B. J. Glover, and U. Steiner, “Function of blue iridescence in tropical understorey plants,” J. R. Soc. Interface 7, 1699–1707 (2010).
[CrossRef]

Grimault, A. S.

A. Vial, A. S. Grimault, D. Macías, D. Barchiesi, and M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion: application to the modelling of extinction spectra with the FDTD method,” Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Grosges, T.

D. Barchiesi, D. Macas, L. Belmar-Letellier, D. van Labeke, M. Lamy de la Chapelle, T. Toury, E. Kremer, L. Moreau, and T. Grosges, “Plasmonics: influence of the intermediate (or stick) layer on the efficiency of sensors,” Appl. Phys. B 93, 177–181 (2008).
[CrossRef]

Hariyama, T.

D. G. Stavenga, B. D. Wilts, H. L. Leertouwer, and T. Hariyama, “Polarized iridescence of the multilayered elytra of the Japanese jewel beetle, Chrysochroa fulgidissima,” Philos. Trans. R. Soc. Biol. Sci. 366, 709–723 (2011).
[CrossRef]

Holland, J. H.

J. H. Holland, Adaptation in Natural and Artificial Systems (University of Michigan, 1975).

Hooper, I. R.

Horwood, J.

M. F. Land, J. Horwood, M. L. M. Lim, and D. Li, “Optics of the ultraviolet reflecting scales of a jumping spider,” Proc. R. Soc. B 274, 1583–1589 (2007).
[CrossRef]

Inchaussandague, M.

A. Luna, D. Skigin, M. Inchaussandague, and A. Roig Alsina, “Structural color in beetles of South America,” Proc. SPIE 7782, 778205 (2010).
[CrossRef]

Jarrendahl, K.

H. Arwin, R. Magnusson, J. Landin, and K. Jarrendahl, “Chirality-induced polarization effects in the cuticle of scarab beetles: 100 years after Michelson,” Philos. Mag. 92(12), 1583–1599 (2012).
[CrossRef]

Kennedy, J.

R. Poli, J. Kennedy, and T. Blackwell, “Particle swarm optimization: an overview,” Swarm Intell. 1, 33–57 (2007).
[CrossRef]

R. C. Eberhart and J. Kennedy, “A new optimizer using particle swarm theory,” in Proceedings of the Sixth International Symposium on Micro Machine and Human Science (IEEE, 1995), pp. 39–43.

Kinoshita, S.

S. Yoshioka and S. Kinoshita, “Direct determination of the refractive index of natural multilayer systems,” Phys. Rev. E 83, 051917 (2011).
[CrossRef]

S. Kinoshita, Structural Colors in the Realm of Nature (World Scientific, 2008).

Kolle, M.

K. R. Thomas, M. Kolle, H. M. Whitney, B. J. Glover, and U. Steiner, “Function of blue iridescence in tropical understorey plants,” J. R. Soc. Interface 7, 1699–1707 (2010).
[CrossRef]

Kosaku, A.

K. Miyamoto and A. Kosaku, “Cuticular microstructures and their relationship to structural color in the Shieldbug Poecilocoris lewisi distant,” Forma 17, 155–167 (2002).

Kremer, E.

D. Barchiesi, D. Macas, L. Belmar-Letellier, D. van Labeke, M. Lamy de la Chapelle, T. Toury, E. Kremer, L. Moreau, and T. Grosges, “Plasmonics: influence of the intermediate (or stick) layer on the efficiency of sensors,” Appl. Phys. B 93, 177–181 (2008).
[CrossRef]

Lamy de la Chapelle, M.

D. Barchiesi, D. Macas, L. Belmar-Letellier, D. van Labeke, M. Lamy de la Chapelle, T. Toury, E. Kremer, L. Moreau, and T. Grosges, “Plasmonics: influence of the intermediate (or stick) layer on the efficiency of sensors,” Appl. Phys. B 93, 177–181 (2008).
[CrossRef]

A. Vial, A. S. Grimault, D. Macías, D. Barchiesi, and M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion: application to the modelling of extinction spectra with the FDTD method,” Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Land, M. F.

M. F. Land, J. Horwood, M. L. M. Lim, and D. Li, “Optics of the ultraviolet reflecting scales of a jumping spider,” Proc. R. Soc. B 274, 1583–1589 (2007).
[CrossRef]

Landin, J.

H. Arwin, R. Magnusson, J. Landin, and K. Jarrendahl, “Chirality-induced polarization effects in the cuticle of scarab beetles: 100 years after Michelson,” Philos. Mag. 92(12), 1583–1599 (2012).
[CrossRef]

Lawrence, C. R.

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, “Quantified interference and diffraction in single Morphobutterfly scales,” Proc. R. Soc. Lond. B 266, 1403–1411(1999).
[CrossRef]

Leertouwer, H. L.

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, 24061–24066 (2011).
[CrossRef]

D. G. Stavenga, B. D. Wilts, H. L. Leertouwer, and T. Hariyama, “Polarized iridescence of the multilayered elytra of the Japanese jewel beetle, Chrysochroa fulgidissima,” Philos. Trans. R. Soc. Biol. Sci. 366, 709–723 (2011).
[CrossRef]

Li, D.

M. F. Land, J. Horwood, M. L. M. Lim, and D. Li, “Optics of the ultraviolet reflecting scales of a jumping spider,” Proc. R. Soc. B 274, 1583–1589 (2007).
[CrossRef]

Lim, M. L. M.

M. F. Land, J. Horwood, M. L. M. Lim, and D. Li, “Optics of the ultraviolet reflecting scales of a jumping spider,” Proc. R. Soc. B 274, 1583–1589 (2007).
[CrossRef]

Lousse, V.

J. P. Vigneron, M. Rassart, C. Vandenbem, V. Lousse, O. Deparis, L. P. Birø, D. Dedouaire, A. Cornet, and P. Defrance, “Spectral filtering of visible light by the cuticle of metallic woodboring beetles and microfabrication of a matching bioinspired material,” Phys. Rev. E 73, 041905 (2006).
[CrossRef]

Luna, A.

A. Luna, D. Skigin, M. Inchaussandague, and A. Roig Alsina, “Structural color in beetles of South America,” Proc. SPIE 7782, 778205 (2010).
[CrossRef]

Macas, D.

D. Barchiesi, D. Macas, L. Belmar-Letellier, D. van Labeke, M. Lamy de la Chapelle, T. Toury, E. Kremer, L. Moreau, and T. Grosges, “Plasmonics: influence of the intermediate (or stick) layer on the efficiency of sensors,” Appl. Phys. B 93, 177–181 (2008).
[CrossRef]

Macías, D.

D. Macías, P.-M. Adam, V. Ruiz-Cortés, R. Rodríguez-Oliveros, and J. A. Sánchez-Gil, “Heuristic optimization for the design of plasmonic nanowires with specific resonant and scattering properties,” Opt. Express 20, 13146–13163 (2012).
[CrossRef]

A. Tassadit, D. Macías, J. A. Sánchez-Gil, P.-M. Adam, and R. Rodriguez-Oliveros, “Metal nanostars: Stochastic optimization of resonant scattering properties,” Superlattices Microstruct. 49, 288–293 (2011).
[CrossRef]

D. Macías and A. Vial, “Optimal design of plasmonic nanostructures for plasmon-interference assisted lithography,” Appl. Phys. B 93, 159–163 (2008).
[CrossRef]

D. Macías, G. Olague, and E. R. Méndez, “Inverse scattering with far-field intensity data: random surfaces that belong to a well-defined statistical class,” Waves Random Complex Media 16, 545–560 (2006).
[CrossRef]

A. Vial, A. S. Grimault, D. Macías, D. Barchiesi, and M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion: application to the modelling of extinction spectra with the FDTD method,” Phys. Rev. B 71, 085416 (2005).
[CrossRef]

D. Macías, A. Vial, and D. Barchiesi, “Application of evolution strategies for the solution of an inverse problem in near-field optics,” J. Opt. Soc. Am. A 21, 1465–1471 (2004).
[CrossRef]

Magnusson, R.

H. Arwin, R. Magnusson, J. Landin, and K. Jarrendahl, “Chirality-induced polarization effects in the cuticle of scarab beetles: 100 years after Michelson,” Philos. Mag. 92(12), 1583–1599 (2012).
[CrossRef]

Méndez, E. R.

D. Macías, G. Olague, and E. R. Méndez, “Inverse scattering with far-field intensity data: random surfaces that belong to a well-defined statistical class,” Waves Random Complex Media 16, 545–560 (2006).
[CrossRef]

Miyamoto, K.

K. Miyamoto and A. Kosaku, “Cuticular microstructures and their relationship to structural color in the Shieldbug Poecilocoris lewisi distant,” Forma 17, 155–167 (2002).

Moreau, L.

D. Barchiesi, D. Macas, L. Belmar-Letellier, D. van Labeke, M. Lamy de la Chapelle, T. Toury, E. Kremer, L. Moreau, and T. Grosges, “Plasmonics: influence of the intermediate (or stick) layer on the efficiency of sensors,” Appl. Phys. B 93, 177–181 (2008).
[CrossRef]

Noyes, J. A.

Olague, G.

D. Macías, G. Olague, and E. R. Méndez, “Inverse scattering with far-field intensity data: random surfaces that belong to a well-defined statistical class,” Waves Random Complex Media 16, 545–560 (2006).
[CrossRef]

Parker, A.

A. Parker, “515 million years of structural colour,” J. Opt. A 2, R15–R28 (2000).
[CrossRef]

Poli, R.

R. Poli, J. Kennedy, and T. Blackwell, “Particle swarm optimization: an overview,” Swarm Intell. 1, 33–57 (2007).
[CrossRef]

Rahmat-Samii, Y.

J. Robinson and Y. Rahmat-Samii, “Particle swarm optimization in electromagnetics,” IEEE Trans. Antennas Propag. 52, 397–407 (2004).
[CrossRef]

Rakic, A. D.

A. B. Djurišic, J. M. Elazar, and A. D. Rakic, “Modeling the optical constants of solids using acceptance-probability-controlled simulated annealing with adaptive move generation procedure,” Phys. Rev. E 55, 4797–4803 (1997).
[CrossRef]

Rankin, M. A.

T. D. Schultz and M. A. Rankin, “The ultrastructure of the epicuticular interference reflectors of tiger beetles (Cicindela),” J. Exp. Biol. 117, 87–110 (1985).

Rassart, M.

J. P. Vigneron, M. Rassart, C. Vandenbem, V. Lousse, O. Deparis, L. P. Birø, D. Dedouaire, A. Cornet, and P. Defrance, “Spectral filtering of visible light by the cuticle of metallic woodboring beetles and microfabrication of a matching bioinspired material,” Phys. Rev. E 73, 041905 (2006).
[CrossRef]

Robinson, J.

J. Robinson and Y. Rahmat-Samii, “Particle swarm optimization in electromagnetics,” IEEE Trans. Antennas Propag. 52, 397–407 (2004).
[CrossRef]

Rodriguez-Oliveros, R.

A. Tassadit, D. Macías, J. A. Sánchez-Gil, P.-M. Adam, and R. Rodriguez-Oliveros, “Metal nanostars: Stochastic optimization of resonant scattering properties,” Superlattices Microstruct. 49, 288–293 (2011).
[CrossRef]

Rodríguez-Oliveros, R.

Roig Alsina, A.

A. Luna, D. Skigin, M. Inchaussandague, and A. Roig Alsina, “Structural color in beetles of South America,” Proc. SPIE 7782, 778205 (2010).
[CrossRef]

Ruiz-Cortés, V.

Sambles, J. R.

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

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, “Quantified interference and diffraction in single Morphobutterfly scales,” Proc. R. Soc. Lond. B 266, 1403–1411(1999).
[CrossRef]

Sánchez-Gil, J. A.

D. Macías, P.-M. Adam, V. Ruiz-Cortés, R. Rodríguez-Oliveros, and J. A. Sánchez-Gil, “Heuristic optimization for the design of plasmonic nanowires with specific resonant and scattering properties,” Opt. Express 20, 13146–13163 (2012).
[CrossRef]

A. Tassadit, D. Macías, J. A. Sánchez-Gil, P.-M. Adam, and R. Rodriguez-Oliveros, “Metal nanostars: Stochastic optimization of resonant scattering properties,” Superlattices Microstruct. 49, 288–293 (2011).
[CrossRef]

Schultz, T. D.

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, S165–S184 (2009).
[CrossRef]

T. D. Schultz and M. A. Rankin, “The ultrastructure of the epicuticular interference reflectors of tiger beetles (Cicindela),” J. Exp. Biol. 117, 87–110 (1985).

Schwefel, H.-P.

H.-P. Schwefel, Evolution and Optimum Seeking (Wiley-Interscience, 1995).

Seago, A. E.

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, S165–S184 (2009).
[CrossRef]

Skigin, D.

A. Luna, D. Skigin, M. Inchaussandague, and A. Roig Alsina, “Structural color in beetles of South America,” Proc. SPIE 7782, 778205 (2010).
[CrossRef]

Stavenga, D. G.

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, 24061–24066 (2011).
[CrossRef]

D. G. Stavenga, B. D. Wilts, H. L. Leertouwer, and T. Hariyama, “Polarized iridescence of the multilayered elytra of the Japanese jewel beetle, Chrysochroa fulgidissima,” Philos. Trans. R. Soc. Biol. Sci. 366, 709–723 (2011).
[CrossRef]

P. Vukusic and D. G. Stavenga, “Physical methods for investigating structural colours in biological systems,” J. R. Soc. Interface 6, S133–S148 (2009).
[CrossRef]

Steiner, U.

K. R. Thomas, M. Kolle, H. M. Whitney, B. J. Glover, and U. Steiner, “Function of blue iridescence in tropical understorey plants,” J. R. Soc. Interface 7, 1699–1707 (2010).
[CrossRef]

Tassadit, A.

A. Tassadit, D. Macías, J. A. Sánchez-Gil, P.-M. Adam, and R. Rodriguez-Oliveros, “Metal nanostars: Stochastic optimization of resonant scattering properties,” Superlattices Microstruct. 49, 288–293 (2011).
[CrossRef]

Thomas, K. R.

K. R. Thomas, M. Kolle, H. M. Whitney, B. J. Glover, and U. Steiner, “Function of blue iridescence in tropical understorey plants,” J. R. Soc. Interface 7, 1699–1707 (2010).
[CrossRef]

Toury, T.

D. Barchiesi, D. Macas, L. Belmar-Letellier, D. van Labeke, M. Lamy de la Chapelle, T. Toury, E. Kremer, L. Moreau, and T. Grosges, “Plasmonics: influence of the intermediate (or stick) layer on the efficiency of sensors,” Appl. Phys. B 93, 177–181 (2008).
[CrossRef]

van Labeke, D.

D. Barchiesi, D. Macas, L. Belmar-Letellier, D. van Labeke, M. Lamy de la Chapelle, T. Toury, E. Kremer, L. Moreau, and T. Grosges, “Plasmonics: influence of the intermediate (or stick) layer on the efficiency of sensors,” Appl. Phys. B 93, 177–181 (2008).
[CrossRef]

Vandenbem, C.

J. P. Vigneron, M. Rassart, C. Vandenbem, V. Lousse, O. Deparis, L. P. Birø, D. Dedouaire, A. Cornet, and P. Defrance, “Spectral filtering of visible light by the cuticle of metallic woodboring beetles and microfabrication of a matching bioinspired material,” Phys. Rev. E 73, 041905 (2006).
[CrossRef]

Vevers, G.

H. M. Fox and G. Vevers, The Nature of Animal Colours(Sidgwick and Jackson, 1960).

Vial, A.

D. Macías and A. Vial, “Optimal design of plasmonic nanostructures for plasmon-interference assisted lithography,” Appl. Phys. B 93, 159–163 (2008).
[CrossRef]

A. Vial, A. S. Grimault, D. Macías, D. Barchiesi, and M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion: application to the modelling of extinction spectra with the FDTD method,” Phys. Rev. B 71, 085416 (2005).
[CrossRef]

D. Macías, A. Vial, and D. Barchiesi, “Application of evolution strategies for the solution of an inverse problem in near-field optics,” J. Opt. Soc. Am. A 21, 1465–1471 (2004).
[CrossRef]

Vigneron, J. P.

J. P. Vigneron, M. Rassart, C. Vandenbem, V. Lousse, O. Deparis, L. P. Birø, D. Dedouaire, A. Cornet, and P. Defrance, “Spectral filtering of visible light by the cuticle of metallic woodboring beetles and microfabrication of a matching bioinspired material,” Phys. Rev. E 73, 041905 (2006).
[CrossRef]

Vigneron, J.-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, S165–S184 (2009).
[CrossRef]

Vukusic, P.

P. Vukusic and D. G. Stavenga, “Physical methods for investigating structural colours in biological systems,” J. R. Soc. Interface 6, S133–S148 (2009).
[CrossRef]

J. A. Noyes, P. Vukusic, and I. R. Hooper, “Experimental method for reliably establishing the refractive index of buprestid beetle exocuticle,” Opt. Express 15, 4351–4357 (2007).
[CrossRef]

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

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, “Quantified interference and diffraction in single Morphobutterfly scales,” Proc. R. Soc. Lond. B 266, 1403–1411(1999).
[CrossRef]

Whitney, H. M.

K. R. Thomas, M. Kolle, H. M. Whitney, B. J. Glover, and U. Steiner, “Function of blue iridescence in tropical understorey plants,” J. R. Soc. Interface 7, 1699–1707 (2010).
[CrossRef]

Wilts, B. D.

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, 24061–24066 (2011).
[CrossRef]

D. G. Stavenga, B. D. Wilts, H. L. Leertouwer, and T. Hariyama, “Polarized iridescence of the multilayered elytra of the Japanese jewel beetle, Chrysochroa fulgidissima,” Philos. Trans. R. Soc. Biol. Sci. 366, 709–723 (2011).
[CrossRef]

Wootton, R. J.

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, “Quantified interference and diffraction in single Morphobutterfly scales,” Proc. R. Soc. Lond. B 266, 1403–1411(1999).
[CrossRef]

Yariv, A.

P. Yeh and A. Yariv, Optical Waves in Crystals (Wiley, 1984).

Yeh, P.

P. Yeh and A. Yariv, Optical Waves in Crystals (Wiley, 1984).

Yoshioka, S.

S. Yoshioka and S. Kinoshita, “Direct determination of the refractive index of natural multilayer systems,” Phys. Rev. E 83, 051917 (2011).
[CrossRef]

App. Phys. A

S. Berthier, J. Boulenguez, and Z. Bálint, “Multiscaled polarization effects in Suneve coronata (Lepidoptera) and other insects: application to anti-counterfeiting of banknotes,” App. Phys. A 86, 123–130 (2007).
[CrossRef]

Appl. Phys. B

D. Macías and A. Vial, “Optimal design of plasmonic nanostructures for plasmon-interference assisted lithography,” Appl. Phys. B 93, 159–163 (2008).
[CrossRef]

D. Barchiesi, D. Macas, L. Belmar-Letellier, D. van Labeke, M. Lamy de la Chapelle, T. Toury, E. Kremer, L. Moreau, and T. Grosges, “Plasmonics: influence of the intermediate (or stick) layer on the efficiency of sensors,” Appl. Phys. B 93, 177–181 (2008).
[CrossRef]

Forma

K. Miyamoto and A. Kosaku, “Cuticular microstructures and their relationship to structural color in the Shieldbug Poecilocoris lewisi distant,” Forma 17, 155–167 (2002).

IEEE Trans. Antennas Propag.

J. Robinson and Y. Rahmat-Samii, “Particle swarm optimization in electromagnetics,” IEEE Trans. Antennas Propag. 52, 397–407 (2004).
[CrossRef]

J. Exp. Biol.

T. D. Schultz and M. A. Rankin, “The ultrastructure of the epicuticular interference reflectors of tiger beetles (Cicindela),” J. Exp. Biol. 117, 87–110 (1985).

J. Opt. A

A. Parker, “515 million years of structural colour,” J. Opt. A 2, R15–R28 (2000).
[CrossRef]

J. Opt. Soc. Am. A

J. R. Soc. Interface

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, S165–S184 (2009).
[CrossRef]

P. Vukusic and D. G. Stavenga, “Physical methods for investigating structural colours in biological systems,” J. R. Soc. Interface 6, S133–S148 (2009).
[CrossRef]

K. R. Thomas, M. Kolle, H. M. Whitney, B. J. Glover, and U. Steiner, “Function of blue iridescence in tropical understorey plants,” J. R. Soc. Interface 7, 1699–1707 (2010).
[CrossRef]

Nature

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

Opt. Commun.

S. Berthier, E. Charron, and A. Da Silva, “Determination of the cuticle index of the scales of the iridescent butterfly Morpho menelaus,” Opt. Commun. 228, 349–356 (2003).
[CrossRef]

Opt. Express

Philos. Mag.

H. Arwin, R. Magnusson, J. Landin, and K. Jarrendahl, “Chirality-induced polarization effects in the cuticle of scarab beetles: 100 years after Michelson,” Philos. Mag. 92(12), 1583–1599 (2012).
[CrossRef]

Philos. Trans. R. Soc. Biol. Sci.

D. G. Stavenga, B. D. Wilts, H. L. Leertouwer, and T. Hariyama, “Polarized iridescence of the multilayered elytra of the Japanese jewel beetle, Chrysochroa fulgidissima,” Philos. Trans. R. Soc. Biol. Sci. 366, 709–723 (2011).
[CrossRef]

Phys. Rev. B

A. Vial, A. S. Grimault, D. Macías, D. Barchiesi, and M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion: application to the modelling of extinction spectra with the FDTD method,” Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Phys. Rev. E

A. B. Djurišic, J. M. Elazar, and A. D. Rakic, “Modeling the optical constants of solids using acceptance-probability-controlled simulated annealing with adaptive move generation procedure,” Phys. Rev. E 55, 4797–4803 (1997).
[CrossRef]

S. Yoshioka and S. Kinoshita, “Direct determination of the refractive index of natural multilayer systems,” Phys. Rev. E 83, 051917 (2011).
[CrossRef]

J. P. Vigneron, M. Rassart, C. Vandenbem, V. Lousse, O. Deparis, L. P. Birø, D. Dedouaire, A. Cornet, and P. Defrance, “Spectral filtering of visible light by the cuticle of metallic woodboring beetles and microfabrication of a matching bioinspired material,” Phys. Rev. E 73, 041905 (2006).
[CrossRef]

Proc. R. Soc. B

M. F. Land, J. Horwood, M. L. M. Lim, and D. Li, “Optics of the ultraviolet reflecting scales of a jumping spider,” Proc. R. Soc. B 274, 1583–1589 (2007).
[CrossRef]

Proc. R. Soc. Lond. B

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, “Quantified interference and diffraction in single Morphobutterfly scales,” Proc. R. Soc. Lond. B 266, 1403–1411(1999).
[CrossRef]

Proc. SPIE

A. Luna, D. Skigin, M. Inchaussandague, and A. Roig Alsina, “Structural color in beetles of South America,” Proc. SPIE 7782, 778205 (2010).
[CrossRef]

Superlattices Microstruct.

A. Tassadit, D. Macías, J. A. Sánchez-Gil, P.-M. Adam, and R. Rodriguez-Oliveros, “Metal nanostars: Stochastic optimization of resonant scattering properties,” Superlattices Microstruct. 49, 288–293 (2011).
[CrossRef]

Swarm Intell.

R. Poli, J. Kennedy, and T. Blackwell, “Particle swarm optimization: an overview,” Swarm Intell. 1, 33–57 (2007).
[CrossRef]

Waves Random Complex Media

D. Macías, G. Olague, and E. R. Méndez, “Inverse scattering with far-field intensity data: random surfaces that belong to a well-defined statistical class,” Waves Random Complex Media 16, 545–560 (2006).
[CrossRef]

Other

S. Berthier, Iridescences, the Physical Colours of Insects (Springer Science+Business Media, LLC, 2007).

S. Kinoshita, Structural Colors in the Realm of Nature (World Scientific, 2008).

H. M. Fox and G. Vevers, The Nature of Animal Colours(Sidgwick and Jackson, 1960).

P. Yeh and A. Yariv, Optical Waves in Crystals (Wiley, 1984).

H. G. Beyer, The Theory of Evolution Strategies (Springer, 2001).

R. C. Eberhart and J. Kennedy, “A new optimizer using particle swarm theory,” in Proceedings of the Sixth International Symposium on Micro Machine and Human Science (IEEE, 1995), pp. 39–43.

J. H. Holland, Adaptation in Natural and Artificial Systems (University of Michigan, 1975).

H.-P. Schwefel, Evolution and Optimum Seeking (Wiley-Interscience, 1995).

ImageJ is a public domain, Java-based image processing program, http://rsbweb.nih.gov/ij/ .

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Figures (7)

Fig. 1.
Fig. 1.

Scheme of the inversion procedure proposed to retrieve the relevant parameters of biological microstructures.

Fig. 2.
Fig. 2.

Scheme of the planar periodic multilayer model.

Fig. 3.
Fig. 3.

Target and optimized reflectance spectra from a bilayer periodic structure with nine periods, layers’ thicknesses d1=60nm, d2=100nm, and dielectric constants ϵ1=2.3829+i0.434 and ϵ2=2.8215+i0.1008, for different angles of incidence. The incidence medium is air and the dielectric constant of the substrate is (ϵ1+ϵ2)/2.

Fig. 4.
Fig. 4.

Histograms of the retrieved values of the real and imaginary parts of ϵ1 corresponding to the same structure of Fig. 2, for the three inversion schemes: (a)–(b) ES(μ/ρ+λ); (c)–(d) ES(μ/ρ,λ); (e)–(f) PSO. In each figure the converged results for both polarization modes and for the four incidence angles considered (0°, 30°, 45°, and 60°) are included.

Fig. 5.
Fig. 5.

Histograms of the retrieved values of the real and imaginary parts of ϵ2 corresponding to the same structure of Fig. 4, for the three inversion schemes: (a)–(b) ES(μ/ρ+λ); (c)–(d) ES(μ/ρ,λ); (e)–(f) PSO. In each figure, the converged results for both polarization modes and for the four incidence angles considered (0°, 30°, 45°, and 60°) are included.

Fig. 6.
Fig. 6.

(a) View of the dorsal side of a Ceroglossus suturalis specimen. (b) SEM image of a transversal cut of the cuticle. Inset: TEM image of the multilayer structure.

Fig. 7.
Fig. 7.

Specular reflectance spectra of the Ceroglossus suturalis beetle for an incidence angle of 15° and s polarization. The red solid line corresponds to the experimental measurement; the blue stars, the black circles, and the green triangles correspond to the ES(μ/ρ+λ), ES(μ/ρ,λ) strategies and PSO, respectively.

Tables (3)

Tables Icon

Table 1. Relative Success (percentage) of the Different Strategies for the Retrieval of the Real and Imaginary Parts of the Dielectric Functions of Both Materials that Comprise the Multilayer System for the Numerically Generated Example

Tables Icon

Table 2. Real and Imaginary Parts of the Retrieved Dielectric Functions of Both Materials that Comprise the Multilayer System in the Ceroglossus suturalis Beetle

Tables Icon

Table 3. Percentage of Occurence of Each Solution for the Different Strategies

Equations (3)

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

f(pT)=Iexp(λ)Ithe(λ|pT)22,
xm,ig+1=xm,ig+Δtvm,i,
vm,i=wvm,i+c1U1(pbestm,ixm,i)+c2U2(gbestixm,i),

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