Abstract

The brilliant metallic appearance of two kinds of beetles, the Chrysina aurigans and the Chrysina limbata, is displayed visually as well as from normalized reflection measurements of non polarized visible light under normal incidence. The C. limbata is reflective over the visible spectral wavelength range, with a silver-like aspect, while the golden-like C. aurigans is reflective for wavelengths larger than 525 nm, and with a well defined sequence of minima and maxima depicted in the reflection spectra. Both specimens show selective reflection of circular polarized light with the effect being significantly weaker for the C. limbata. A transfer matrix formalism is applied to approach the main features displayed in the measured reflection spectra, by assuming a chirped multilayer structure with decreasing thicknesses of successive layers through the cuticle of the beetles.

© 2011 OSA

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    [CrossRef]
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2010 (2)

P. Brady and M. Cummings, “Differential response to circularly polarized light by the jewel scarab beetle Chrysina gloriosa,” Am. Nat. 175(5), 614–620 (2010).
[CrossRef] [PubMed]

J. Marshall, “Why are animals colourful? Sex and violence, seeing and signals,” Colour: Design & Creativity 8, 1–8 (2010).

2009 (4)

V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Structural origin of circularly polarized iridescence in jeweled beetles,” Science 325(5939), 449–451 (2009).
[CrossRef] [PubMed]

B. Kohlmann and A. Solís, “New species of Ateuchus and Canthidium (Coleoptera: Scarabaeidae: Scarabaeinae) from Costa Rica,” Zootaxa 2219, 31–37 (2009).

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).
[PubMed]

M. Abbas, F. D’Amico, L. Morresi, N. Pinto, M. Ficcadenti, R. Natali, L. Ottaviano, M. Passacantando, M. Cuccioloni, M. Angeletti, and R. Gunnella, “Structural, electrical, electronic and optical properties of melanin films,” Eur Phys J E Soft Matter 28(3), 285–291 (2009).
[CrossRef] [PubMed]

2008 (2)

T. Lenau and M. Barfoed, “Colours and metallic sheen in beetle shells: a biomimetic search for material structuring principles causing light interference,” Adv. Eng. Mater. 10(4), 299–314 (2008).
[CrossRef]

O. Deparis, M. Rassart, C. Vandenbem, V. Welch, J. P. Vigneron, and S. Lucas, “Structurally tuned iridescent surfaces inspired by nature,” N. J. Phys. 10(1), 013032 (2008).
[CrossRef]

2007 (2)

J. P. Vigneron, J. M. Pasteels, D. M. Windsor, Z. Vértesy, M. Rassart, T. Seldrum, J. Dumont, O. Deparis, V. Lousse, L. P. Biró, D. Ertz, and V. Welch, “Switchable reflector in the Panamanian tortoise beetle Charidotella egregia (Chrysomelidae: Cassidinae),” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(3), 031907 (2007).
[CrossRef] [PubMed]

S. A. Jewell, P. Vukusic, and N. W. Roberts, “Circularly polarized colour reflection from helicoidal structures in the beetle Plusiotis boucardi,” N. J. Phys. 9(4), 99 (2007).
[CrossRef]

2006 (5)

M. Mitov and N. Dessaud, “Going beyond the reflectance limit of cholesteric liquid crystals,” Nat. Mater. 5(5), 361–364 (2006).
[CrossRef] [PubMed]

R. Hegedüs, G. Szél, and G. Horváth, “Imaging polarimetry of the circularly polarizing cuticle of scarab beetles (Coleoptera: Rutelidae, Cetoniidae),” Vision Res. 46(17), 2786–2797 (2006).
[CrossRef] [PubMed]

E. Belamie, G. Mosser, F. Gobeaux, and M. M. Giraud-Guille, “Possible transient liquid crystal phase during the laying out of connective tissues: α-chitin and collagen as models,” J. Phys. Condens. Matter 18(13), S115–S129 (2006).
[CrossRef]

D. H. Goldstein, “Polarization properties of Scarabaeidae,” Appl. Opt. 45(30), 7944–7950 (2006).
[CrossRef] [PubMed]

J. Sánchez-González, A. Díaz-Parralejo, A. L. Ortiz, and F. Guiberteau, “Determination of optical properties in nanostructured thin films using the Swanepoel method,” Appl. Surf. Sci. 252(17), 6013–6017 (2006).
[CrossRef]

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]

L. De Silva, I. Hodgkinson, P. Murray, Q. Wu, M. Arnold, J. Leader, and A. Mcnaughton, “Natural and nanoengineered chiral reflectors: structural color of Manuka beetles and titania coatings,” Electromagnetics 25(5), 391–408 (2005).
[CrossRef]

R. Rengarajan, D. Mittleman, C. Rich, and V. Colvin, “Effect of disorder on the optical properties of colloidal crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(1), 016615 (2005).
[CrossRef] [PubMed]

2004 (1)

A. R. Parker, “A vision for natural photonics,” Philos. Transact. A Math. Phys. Eng. Sci. 362(1825), 2709–2720 (2004).
[CrossRef] [PubMed]

2003 (1)

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(4-6), 349–356 (2003).
[CrossRef]

1999 (2)

J. F. Bertone, P. Jiang, K. S. Hwang, D. M. Mittleman, and V. L. Colvin, “Thickness dependence of the optical properties of ordered silica-air and air-polymer photonic crystals,” Phys. Rev. Lett. 83(2), 300–303 (1999).
[CrossRef]

M. Srinivasarao, “Nano-optics in the biological world: beetles, butterflies, birds, and moths,” Chem. Rev. 99(7), 1935–1962 (1999).
[CrossRef] [PubMed]

1998 (1)

A. R. Parker, D. R. Mckenzie, and M. C. J. Large, “Multilayer reflectors in animals using green and gold beetles as contrasting examples,” J. Exp. Biol. 201(Pt 9), 1307–1313 (1998).
[PubMed]

1996 (1)

1989 (1)

1983 (1)

R. E. Bird, R. L. Hulstrom, and L. J. Lewis, “Terrestrial solar spectra data sets,” Sol. Energy 30(6), 563–573 (1983).
[CrossRef]

1977 (1)

A. C. Neville, “Metallic gold and silver colours in some insect cuticles,” J. Insect Physiol. 23(10), 1267–1274 (1977).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

1971 (1)

S. Caveney, “Cuticle reflectivity and optical activity in scarab beetles: the rôle of uric acid,” Proc. R. Soc. Lond. B Biol. Sci. 178(1051), 205–225 (1971).
[CrossRef] [PubMed]

1969 (1)

A. C. Neville and S. Caveney, “Scarabaeid beetle exocuticle as an optical analogue of cholesteric liquid crystals,” Biol. Rev. Camb. Philos. Soc. 44(4), 531–562 (1969).
[CrossRef] [PubMed]

1911 (1)

A. A. Michelson, “On metallic colouring in birds and insects,” Philos. Mag. 21, 554–567 (1911).

1894 (1)

L. W. Rothschild and K. Jordan, “Six new species of Plusiotis and one new Anoplostethus,” Novit. Zool. 1, 504–507 (1894).

1875 (1)

A. Boucard, “Monographic list of the Coleoptera of the genus Plusiotis of America, North of Panama, with descriptions of several new species,” Proc. Zool. Soc. Lond. 23, 117–125 (1875).

Abbas, M.

M. Abbas, F. D’Amico, L. Morresi, N. Pinto, M. Ficcadenti, R. Natali, L. Ottaviano, M. Passacantando, M. Cuccioloni, M. Angeletti, and R. Gunnella, “Structural, electrical, electronic and optical properties of melanin films,” Eur Phys J E Soft Matter 28(3), 285–291 (2009).
[CrossRef] [PubMed]

Angeletti, M.

M. Abbas, F. D’Amico, L. Morresi, N. Pinto, M. Ficcadenti, R. Natali, L. Ottaviano, M. Passacantando, M. Cuccioloni, M. Angeletti, and R. Gunnella, “Structural, electrical, electronic and optical properties of melanin films,” Eur Phys J E Soft Matter 28(3), 285–291 (2009).
[CrossRef] [PubMed]

Arnold, M.

L. De Silva, I. Hodgkinson, P. Murray, Q. Wu, M. Arnold, J. Leader, and A. Mcnaughton, “Natural and nanoengineered chiral reflectors: structural color of Manuka beetles and titania coatings,” Electromagnetics 25(5), 391–408 (2005).
[CrossRef]

Barfoed, M.

T. Lenau and M. Barfoed, “Colours and metallic sheen in beetle shells: a biomimetic search for material structuring principles causing light interference,” Adv. Eng. Mater. 10(4), 299–314 (2008).
[CrossRef]

Belamie, E.

E. Belamie, G. Mosser, F. Gobeaux, and M. M. Giraud-Guille, “Possible transient liquid crystal phase during the laying out of connective tissues: α-chitin and collagen as models,” J. Phys. Condens. Matter 18(13), S115–S129 (2006).
[CrossRef]

Berthier, S.

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(4-6), 349–356 (2003).
[CrossRef]

Bertone, J. F.

J. F. Bertone, P. Jiang, K. S. Hwang, D. M. Mittleman, and V. L. Colvin, “Thickness dependence of the optical properties of ordered silica-air and air-polymer photonic crystals,” Phys. Rev. Lett. 83(2), 300–303 (1999).
[CrossRef]

Bird, R. E.

R. E. Bird, R. L. Hulstrom, and L. J. Lewis, “Terrestrial solar spectra data sets,” Sol. Energy 30(6), 563–573 (1983).
[CrossRef]

Biró, L. P.

J. P. Vigneron, J. M. Pasteels, D. M. Windsor, Z. Vértesy, M. Rassart, T. Seldrum, J. Dumont, O. Deparis, V. Lousse, L. P. Biró, D. Ertz, and V. Welch, “Switchable reflector in the Panamanian tortoise beetle Charidotella egregia (Chrysomelidae: Cassidinae),” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(3), 031907 (2007).
[CrossRef] [PubMed]

Boucard, A.

A. Boucard, “Monographic list of the Coleoptera of the genus Plusiotis of America, North of Panama, with descriptions of several new species,” Proc. Zool. Soc. Lond. 23, 117–125 (1875).

Boynton, R. M.

Brady, P.

P. Brady and M. Cummings, “Differential response to circularly polarized light by the jewel scarab beetle Chrysina gloriosa,” Am. Nat. 175(5), 614–620 (2010).
[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).
[PubMed]

Caveney, S.

S. Caveney, “Cuticle reflectivity and optical activity in scarab beetles: the rôle of uric acid,” Proc. R. Soc. Lond. B Biol. Sci. 178(1051), 205–225 (1971).
[CrossRef] [PubMed]

A. C. Neville and S. Caveney, “Scarabaeid beetle exocuticle as an optical analogue of cholesteric liquid crystals,” Biol. Rev. Camb. Philos. Soc. 44(4), 531–562 (1969).
[CrossRef] [PubMed]

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(4-6), 349–356 (2003).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Chýlek, P.

Colvin, V.

R. Rengarajan, D. Mittleman, C. Rich, and V. Colvin, “Effect of disorder on the optical properties of colloidal crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(1), 016615 (2005).
[CrossRef] [PubMed]

Colvin, V. L.

J. F. Bertone, P. Jiang, K. S. Hwang, D. M. Mittleman, and V. L. Colvin, “Thickness dependence of the optical properties of ordered silica-air and air-polymer photonic crystals,” Phys. Rev. Lett. 83(2), 300–303 (1999).
[CrossRef]

Crne, M.

V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Structural origin of circularly polarized iridescence in jeweled beetles,” Science 325(5939), 449–451 (2009).
[CrossRef] [PubMed]

Cuccioloni, M.

M. Abbas, F. D’Amico, L. Morresi, N. Pinto, M. Ficcadenti, R. Natali, L. Ottaviano, M. Passacantando, M. Cuccioloni, M. Angeletti, and R. Gunnella, “Structural, electrical, electronic and optical properties of melanin films,” Eur Phys J E Soft Matter 28(3), 285–291 (2009).
[CrossRef] [PubMed]

Cummings, M.

P. Brady and M. Cummings, “Differential response to circularly polarized light by the jewel scarab beetle Chrysina gloriosa,” Am. Nat. 175(5), 614–620 (2010).
[CrossRef] [PubMed]

D’Amico, F.

M. Abbas, F. D’Amico, L. Morresi, N. Pinto, M. Ficcadenti, R. Natali, L. Ottaviano, M. Passacantando, M. Cuccioloni, M. Angeletti, and R. Gunnella, “Structural, electrical, electronic and optical properties of melanin films,” Eur Phys J E Soft Matter 28(3), 285–291 (2009).
[CrossRef] [PubMed]

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(4-6), 349–356 (2003).
[CrossRef]

De Silva, L.

L. De Silva, I. Hodgkinson, P. Murray, Q. Wu, M. Arnold, J. Leader, and A. Mcnaughton, “Natural and nanoengineered chiral reflectors: structural color of Manuka beetles and titania coatings,” Electromagnetics 25(5), 391–408 (2005).
[CrossRef]

Deparis, O.

O. Deparis, M. Rassart, C. Vandenbem, V. Welch, J. P. Vigneron, and S. Lucas, “Structurally tuned iridescent surfaces inspired by nature,” N. J. Phys. 10(1), 013032 (2008).
[CrossRef]

J. P. Vigneron, J. M. Pasteels, D. M. Windsor, Z. Vértesy, M. Rassart, T. Seldrum, J. Dumont, O. Deparis, V. Lousse, L. P. Biró, D. Ertz, and V. Welch, “Switchable reflector in the Panamanian tortoise beetle Charidotella egregia (Chrysomelidae: Cassidinae),” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(3), 031907 (2007).
[CrossRef] [PubMed]

Dessaud, N.

M. Mitov and N. Dessaud, “Going beyond the reflectance limit of cholesteric liquid crystals,” Nat. Mater. 5(5), 361–364 (2006).
[CrossRef] [PubMed]

Díaz-Parralejo, A.

J. Sánchez-González, A. Díaz-Parralejo, A. L. Ortiz, and F. Guiberteau, “Determination of optical properties in nanostructured thin films using the Swanepoel method,” Appl. Surf. Sci. 252(17), 6013–6017 (2006).
[CrossRef]

Dumont, J.

J. P. Vigneron, J. M. Pasteels, D. M. Windsor, Z. Vértesy, M. Rassart, T. Seldrum, J. Dumont, O. Deparis, V. Lousse, L. P. Biró, D. Ertz, and V. Welch, “Switchable reflector in the Panamanian tortoise beetle Charidotella egregia (Chrysomelidae: Cassidinae),” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(3), 031907 (2007).
[CrossRef] [PubMed]

Ertz, D.

J. P. Vigneron, J. M. Pasteels, D. M. Windsor, Z. Vértesy, M. Rassart, T. Seldrum, J. Dumont, O. Deparis, V. Lousse, L. P. Biró, D. Ertz, and V. Welch, “Switchable reflector in the Panamanian tortoise beetle Charidotella egregia (Chrysomelidae: Cassidinae),” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(3), 031907 (2007).
[CrossRef] [PubMed]

Ficcadenti, M.

M. Abbas, F. D’Amico, L. Morresi, N. Pinto, M. Ficcadenti, R. Natali, L. Ottaviano, M. Passacantando, M. Cuccioloni, M. Angeletti, and R. Gunnella, “Structural, electrical, electronic and optical properties of melanin films,” Eur Phys J E Soft Matter 28(3), 285–291 (2009).
[CrossRef] [PubMed]

Giraud-Guille, M. M.

E. Belamie, G. Mosser, F. Gobeaux, and M. M. Giraud-Guille, “Possible transient liquid crystal phase during the laying out of connective tissues: α-chitin and collagen as models,” J. Phys. Condens. Matter 18(13), S115–S129 (2006).
[CrossRef]

Gobeaux, F.

E. Belamie, G. Mosser, F. Gobeaux, and M. M. Giraud-Guille, “Possible transient liquid crystal phase during the laying out of connective tissues: α-chitin and collagen as models,” J. Phys. Condens. Matter 18(13), S115–S129 (2006).
[CrossRef]

Goldstein, D. H.

Guiberteau, F.

J. Sánchez-González, A. Díaz-Parralejo, A. L. Ortiz, and F. Guiberteau, “Determination of optical properties in nanostructured thin films using the Swanepoel method,” Appl. Surf. Sci. 252(17), 6013–6017 (2006).
[CrossRef]

Gunnella, R.

M. Abbas, F. D’Amico, L. Morresi, N. Pinto, M. Ficcadenti, R. Natali, L. Ottaviano, M. Passacantando, M. Cuccioloni, M. Angeletti, and R. Gunnella, “Structural, electrical, electronic and optical properties of melanin films,” Eur Phys J E Soft Matter 28(3), 285–291 (2009).
[CrossRef] [PubMed]

Hegedüs, R.

R. Hegedüs, G. Szél, and G. Horváth, “Imaging polarimetry of the circularly polarizing cuticle of scarab beetles (Coleoptera: Rutelidae, Cetoniidae),” Vision Res. 46(17), 2786–2797 (2006).
[CrossRef] [PubMed]

Hodgkinson, I.

L. De Silva, I. Hodgkinson, P. Murray, Q. Wu, M. Arnold, J. Leader, and A. Mcnaughton, “Natural and nanoengineered chiral reflectors: structural color of Manuka beetles and titania coatings,” Electromagnetics 25(5), 391–408 (2005).
[CrossRef]

Horváth, G.

R. Hegedüs, G. Szél, and G. Horváth, “Imaging polarimetry of the circularly polarizing cuticle of scarab beetles (Coleoptera: Rutelidae, Cetoniidae),” Vision Res. 46(17), 2786–2797 (2006).
[CrossRef] [PubMed]

Hulstrom, R. L.

R. E. Bird, R. L. Hulstrom, and L. J. Lewis, “Terrestrial solar spectra data sets,” Sol. Energy 30(6), 563–573 (1983).
[CrossRef]

Hwang, K. S.

J. F. Bertone, P. Jiang, K. S. Hwang, D. M. Mittleman, and V. L. Colvin, “Thickness dependence of the optical properties of ordered silica-air and air-polymer photonic crystals,” Phys. Rev. Lett. 83(2), 300–303 (1999).
[CrossRef]

Jewell, S. A.

S. A. Jewell, P. Vukusic, and N. W. Roberts, “Circularly polarized colour reflection from helicoidal structures in the beetle Plusiotis boucardi,” N. J. Phys. 9(4), 99 (2007).
[CrossRef]

Jiang, P.

J. F. Bertone, P. Jiang, K. S. Hwang, D. M. Mittleman, and V. L. Colvin, “Thickness dependence of the optical properties of ordered silica-air and air-polymer photonic crystals,” Phys. Rev. Lett. 83(2), 300–303 (1999).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Jordan, K.

L. W. Rothschild and K. Jordan, “Six new species of Plusiotis and one new Anoplostethus,” Novit. Zool. 1, 504–507 (1894).

Kinoshita, S.

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]

Kohlmann, B.

B. Kohlmann and A. Solís, “New species of Ateuchus and Canthidium (Coleoptera: Scarabaeidae: Scarabaeinae) from Costa Rica,” Zootaxa 2219, 31–37 (2009).

Large, M. C. J.

A. R. Parker, D. R. Mckenzie, and M. C. J. Large, “Multilayer reflectors in animals using green and gold beetles as contrasting examples,” J. Exp. Biol. 201(Pt 9), 1307–1313 (1998).
[PubMed]

Leader, J.

L. De Silva, I. Hodgkinson, P. Murray, Q. Wu, M. Arnold, J. Leader, and A. Mcnaughton, “Natural and nanoengineered chiral reflectors: structural color of Manuka beetles and titania coatings,” Electromagnetics 25(5), 391–408 (2005).
[CrossRef]

Lenau, T.

T. Lenau and M. Barfoed, “Colours and metallic sheen in beetle shells: a biomimetic search for material structuring principles causing light interference,” Adv. Eng. Mater. 10(4), 299–314 (2008).
[CrossRef]

Lewis, L. J.

R. E. Bird, R. L. Hulstrom, and L. J. Lewis, “Terrestrial solar spectra data sets,” Sol. Energy 30(6), 563–573 (1983).
[CrossRef]

Lousse, V.

J. P. Vigneron, J. M. Pasteels, D. M. Windsor, Z. Vértesy, M. Rassart, T. Seldrum, J. Dumont, O. Deparis, V. Lousse, L. P. Biró, D. Ertz, and V. Welch, “Switchable reflector in the Panamanian tortoise beetle Charidotella egregia (Chrysomelidae: Cassidinae),” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(3), 031907 (2007).
[CrossRef] [PubMed]

Lucas, S.

O. Deparis, M. Rassart, C. Vandenbem, V. Welch, J. P. Vigneron, and S. Lucas, “Structurally tuned iridescent surfaces inspired by nature,” N. J. Phys. 10(1), 013032 (2008).
[CrossRef]

Marshall, J.

J. Marshall, “Why are animals colourful? Sex and violence, seeing and signals,” Colour: Design & Creativity 8, 1–8 (2010).

Mckenzie, D. R.

A. R. Parker, D. R. Mckenzie, and M. C. J. Large, “Multilayer reflectors in animals using green and gold beetles as contrasting examples,” J. Exp. Biol. 201(Pt 9), 1307–1313 (1998).
[PubMed]

Mcnaughton, A.

L. De Silva, I. Hodgkinson, P. Murray, Q. Wu, M. Arnold, J. Leader, and A. Mcnaughton, “Natural and nanoengineered chiral reflectors: structural color of Manuka beetles and titania coatings,” Electromagnetics 25(5), 391–408 (2005).
[CrossRef]

Michelson, A. A.

A. A. Michelson, “On metallic colouring in birds and insects,” Philos. Mag. 21, 554–567 (1911).

Mitov, M.

M. Mitov and N. Dessaud, “Going beyond the reflectance limit of cholesteric liquid crystals,” Nat. Mater. 5(5), 361–364 (2006).
[CrossRef] [PubMed]

Mittleman, D.

R. Rengarajan, D. Mittleman, C. Rich, and V. Colvin, “Effect of disorder on the optical properties of colloidal crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(1), 016615 (2005).
[CrossRef] [PubMed]

Mittleman, D. M.

J. F. Bertone, P. Jiang, K. S. Hwang, D. M. Mittleman, and V. L. Colvin, “Thickness dependence of the optical properties of ordered silica-air and air-polymer photonic crystals,” Phys. Rev. Lett. 83(2), 300–303 (1999).
[CrossRef]

Morresi, L.

M. Abbas, F. D’Amico, L. Morresi, N. Pinto, M. Ficcadenti, R. Natali, L. Ottaviano, M. Passacantando, M. Cuccioloni, M. Angeletti, and R. Gunnella, “Structural, electrical, electronic and optical properties of melanin films,” Eur Phys J E Soft Matter 28(3), 285–291 (2009).
[CrossRef] [PubMed]

Mosser, G.

E. Belamie, G. Mosser, F. Gobeaux, and M. M. Giraud-Guille, “Possible transient liquid crystal phase during the laying out of connective tissues: α-chitin and collagen as models,” J. Phys. Condens. Matter 18(13), S115–S129 (2006).
[CrossRef]

Murray, P.

L. De Silva, I. Hodgkinson, P. Murray, Q. Wu, M. Arnold, J. Leader, and A. Mcnaughton, “Natural and nanoengineered chiral reflectors: structural color of Manuka beetles and titania coatings,” Electromagnetics 25(5), 391–408 (2005).
[CrossRef]

Natali, R.

M. Abbas, F. D’Amico, L. Morresi, N. Pinto, M. Ficcadenti, R. Natali, L. Ottaviano, M. Passacantando, M. Cuccioloni, M. Angeletti, and R. Gunnella, “Structural, electrical, electronic and optical properties of melanin films,” Eur Phys J E Soft Matter 28(3), 285–291 (2009).
[CrossRef] [PubMed]

Neville, A. C.

A. C. Neville, “Metallic gold and silver colours in some insect cuticles,” J. Insect Physiol. 23(10), 1267–1274 (1977).
[CrossRef]

A. C. Neville and S. Caveney, “Scarabaeid beetle exocuticle as an optical analogue of cholesteric liquid crystals,” Biol. Rev. Camb. Philos. Soc. 44(4), 531–562 (1969).
[CrossRef] [PubMed]

Ortiz, A. L.

J. Sánchez-González, A. Díaz-Parralejo, A. L. Ortiz, and F. Guiberteau, “Determination of optical properties in nanostructured thin films using the Swanepoel method,” Appl. Surf. Sci. 252(17), 6013–6017 (2006).
[CrossRef]

Ottaviano, L.

M. Abbas, F. D’Amico, L. Morresi, N. Pinto, M. Ficcadenti, R. Natali, L. Ottaviano, M. Passacantando, M. Cuccioloni, M. Angeletti, and R. Gunnella, “Structural, electrical, electronic and optical properties of melanin films,” Eur Phys J E Soft Matter 28(3), 285–291 (2009).
[CrossRef] [PubMed]

Park, J. O.

V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Structural origin of circularly polarized iridescence in jeweled beetles,” Science 325(5939), 449–451 (2009).
[CrossRef] [PubMed]

Parker, A. R.

A. R. Parker, “A vision for natural photonics,” Philos. Transact. A Math. Phys. Eng. Sci. 362(1825), 2709–2720 (2004).
[CrossRef] [PubMed]

A. R. Parker, D. R. Mckenzie, and M. C. J. Large, “Multilayer reflectors in animals using green and gold beetles as contrasting examples,” J. Exp. Biol. 201(Pt 9), 1307–1313 (1998).
[PubMed]

Passacantando, M.

M. Abbas, F. D’Amico, L. Morresi, N. Pinto, M. Ficcadenti, R. Natali, L. Ottaviano, M. Passacantando, M. Cuccioloni, M. Angeletti, and R. Gunnella, “Structural, electrical, electronic and optical properties of melanin films,” Eur Phys J E Soft Matter 28(3), 285–291 (2009).
[CrossRef] [PubMed]

Pasteels, J. M.

J. P. Vigneron, J. M. Pasteels, D. M. Windsor, Z. Vértesy, M. Rassart, T. Seldrum, J. Dumont, O. Deparis, V. Lousse, L. P. Biró, D. Ertz, and V. Welch, “Switchable reflector in the Panamanian tortoise beetle Charidotella egregia (Chrysomelidae: Cassidinae),” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(3), 031907 (2007).
[CrossRef] [PubMed]

Pinto, N.

M. Abbas, F. D’Amico, L. Morresi, N. Pinto, M. Ficcadenti, R. Natali, L. Ottaviano, M. Passacantando, M. Cuccioloni, M. Angeletti, and R. Gunnella, “Structural, electrical, electronic and optical properties of melanin films,” Eur Phys J E Soft Matter 28(3), 285–291 (2009).
[CrossRef] [PubMed]

Rassart, M.

O. Deparis, M. Rassart, C. Vandenbem, V. Welch, J. P. Vigneron, and S. Lucas, “Structurally tuned iridescent surfaces inspired by nature,” N. J. Phys. 10(1), 013032 (2008).
[CrossRef]

J. P. Vigneron, J. M. Pasteels, D. M. Windsor, Z. Vértesy, M. Rassart, T. Seldrum, J. Dumont, O. Deparis, V. Lousse, L. P. Biró, D. Ertz, and V. Welch, “Switchable reflector in the Panamanian tortoise beetle Charidotella egregia (Chrysomelidae: Cassidinae),” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(3), 031907 (2007).
[CrossRef] [PubMed]

Rengarajan, R.

R. Rengarajan, D. Mittleman, C. Rich, and V. Colvin, “Effect of disorder on the optical properties of colloidal crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(1), 016615 (2005).
[CrossRef] [PubMed]

Rich, C.

R. Rengarajan, D. Mittleman, C. Rich, and V. Colvin, “Effect of disorder on the optical properties of colloidal crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(1), 016615 (2005).
[CrossRef] [PubMed]

Roberts, N. W.

S. A. Jewell, P. Vukusic, and N. W. Roberts, “Circularly polarized colour reflection from helicoidal structures in the beetle Plusiotis boucardi,” N. J. Phys. 9(4), 99 (2007).
[CrossRef]

Rothschild, L. W.

L. W. Rothschild and K. Jordan, “Six new species of Plusiotis and one new Anoplostethus,” Novit. Zool. 1, 504–507 (1894).

Sánchez-González, J.

J. Sánchez-González, A. Díaz-Parralejo, A. L. Ortiz, and F. Guiberteau, “Determination of optical properties in nanostructured thin films using the Swanepoel method,” Appl. Surf. Sci. 252(17), 6013–6017 (2006).
[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(Suppl 2), S165–S184 (2009).
[PubMed]

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(Suppl 2), S165–S184 (2009).
[PubMed]

Seldrum, T.

J. P. Vigneron, J. M. Pasteels, D. M. Windsor, Z. Vértesy, M. Rassart, T. Seldrum, J. Dumont, O. Deparis, V. Lousse, L. P. Biró, D. Ertz, and V. Welch, “Switchable reflector in the Panamanian tortoise beetle Charidotella egregia (Chrysomelidae: Cassidinae),” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(3), 031907 (2007).
[CrossRef] [PubMed]

Sharma, V.

V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Structural origin of circularly polarized iridescence in jeweled beetles,” Science 325(5939), 449–451 (2009).
[CrossRef] [PubMed]

Solís, A.

B. Kohlmann and A. Solís, “New species of Ateuchus and Canthidium (Coleoptera: Scarabaeidae: Scarabaeinae) from Costa Rica,” Zootaxa 2219, 31–37 (2009).

Srinivasarao, M.

V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Structural origin of circularly polarized iridescence in jeweled beetles,” Science 325(5939), 449–451 (2009).
[CrossRef] [PubMed]

M. Srinivasarao, “Nano-optics in the biological world: beetles, butterflies, birds, and moths,” Chem. Rev. 99(7), 1935–1962 (1999).
[CrossRef] [PubMed]

Szél, G.

R. Hegedüs, G. Szél, and G. Horváth, “Imaging polarimetry of the circularly polarizing cuticle of scarab beetles (Coleoptera: Rutelidae, Cetoniidae),” Vision Res. 46(17), 2786–2797 (2006).
[CrossRef] [PubMed]

Vandenbem, C.

O. Deparis, M. Rassart, C. Vandenbem, V. Welch, J. P. Vigneron, and S. Lucas, “Structurally tuned iridescent surfaces inspired by nature,” N. J. Phys. 10(1), 013032 (2008).
[CrossRef]

Vértesy, Z.

J. P. Vigneron, J. M. Pasteels, D. M. Windsor, Z. Vértesy, M. Rassart, T. Seldrum, J. Dumont, O. Deparis, V. Lousse, L. P. Biró, D. Ertz, and V. Welch, “Switchable reflector in the Panamanian tortoise beetle Charidotella egregia (Chrysomelidae: Cassidinae),” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(3), 031907 (2007).
[CrossRef] [PubMed]

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(Suppl 2), S165–S184 (2009).
[PubMed]

O. Deparis, M. Rassart, C. Vandenbem, V. Welch, J. P. Vigneron, and S. Lucas, “Structurally tuned iridescent surfaces inspired by nature,” N. J. Phys. 10(1), 013032 (2008).
[CrossRef]

J. P. Vigneron, J. M. Pasteels, D. M. Windsor, Z. Vértesy, M. Rassart, T. Seldrum, J. Dumont, O. Deparis, V. Lousse, L. P. Biró, D. Ertz, and V. Welch, “Switchable reflector in the Panamanian tortoise beetle Charidotella egregia (Chrysomelidae: Cassidinae),” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(3), 031907 (2007).
[CrossRef] [PubMed]

Vukusic, P.

S. A. Jewell, P. Vukusic, and N. W. Roberts, “Circularly polarized colour reflection from helicoidal structures in the beetle Plusiotis boucardi,” N. J. Phys. 9(4), 99 (2007).
[CrossRef]

Welch, V.

O. Deparis, M. Rassart, C. Vandenbem, V. Welch, J. P. Vigneron, and S. Lucas, “Structurally tuned iridescent surfaces inspired by nature,” N. J. Phys. 10(1), 013032 (2008).
[CrossRef]

J. P. Vigneron, J. M. Pasteels, D. M. Windsor, Z. Vértesy, M. Rassart, T. Seldrum, J. Dumont, O. Deparis, V. Lousse, L. P. Biró, D. Ertz, and V. Welch, “Switchable reflector in the Panamanian tortoise beetle Charidotella egregia (Chrysomelidae: Cassidinae),” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(3), 031907 (2007).
[CrossRef] [PubMed]

Windsor, D. M.

J. P. Vigneron, J. M. Pasteels, D. M. Windsor, Z. Vértesy, M. Rassart, T. Seldrum, J. Dumont, O. Deparis, V. Lousse, L. P. Biró, D. Ertz, and V. Welch, “Switchable reflector in the Panamanian tortoise beetle Charidotella egregia (Chrysomelidae: Cassidinae),” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(3), 031907 (2007).
[CrossRef] [PubMed]

Wu, Q.

L. De Silva, I. Hodgkinson, P. Murray, Q. Wu, M. Arnold, J. Leader, and A. Mcnaughton, “Natural and nanoengineered chiral reflectors: structural color of Manuka beetles and titania coatings,” Electromagnetics 25(5), 391–408 (2005).
[CrossRef]

Yoshioka, S.

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]

Zhan, J.

Adv. Eng. Mater. (1)

T. Lenau and M. Barfoed, “Colours and metallic sheen in beetle shells: a biomimetic search for material structuring principles causing light interference,” Adv. Eng. Mater. 10(4), 299–314 (2008).
[CrossRef]

Am. Nat. (1)

P. Brady and M. Cummings, “Differential response to circularly polarized light by the jewel scarab beetle Chrysina gloriosa,” Am. Nat. 175(5), 614–620 (2010).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Surf. Sci. (1)

J. Sánchez-González, A. Díaz-Parralejo, A. L. Ortiz, and F. Guiberteau, “Determination of optical properties in nanostructured thin films using the Swanepoel method,” Appl. Surf. Sci. 252(17), 6013–6017 (2006).
[CrossRef]

Biol. Rev. Camb. Philos. Soc. (1)

A. C. Neville and S. Caveney, “Scarabaeid beetle exocuticle as an optical analogue of cholesteric liquid crystals,” Biol. Rev. Camb. Philos. Soc. 44(4), 531–562 (1969).
[CrossRef] [PubMed]

Chem. Rev. (1)

M. Srinivasarao, “Nano-optics in the biological world: beetles, butterflies, birds, and moths,” Chem. Rev. 99(7), 1935–1962 (1999).
[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]

Colour: Design & Creativity (1)

J. Marshall, “Why are animals colourful? Sex and violence, seeing and signals,” Colour: Design & Creativity 8, 1–8 (2010).

Electromagnetics (1)

L. De Silva, I. Hodgkinson, P. Murray, Q. Wu, M. Arnold, J. Leader, and A. Mcnaughton, “Natural and nanoengineered chiral reflectors: structural color of Manuka beetles and titania coatings,” Electromagnetics 25(5), 391–408 (2005).
[CrossRef]

Eur Phys J E Soft Matter (1)

M. Abbas, F. D’Amico, L. Morresi, N. Pinto, M. Ficcadenti, R. Natali, L. Ottaviano, M. Passacantando, M. Cuccioloni, M. Angeletti, and R. Gunnella, “Structural, electrical, electronic and optical properties of melanin films,” Eur Phys J E Soft Matter 28(3), 285–291 (2009).
[CrossRef] [PubMed]

J. Exp. Biol. (1)

A. R. Parker, D. R. Mckenzie, and M. C. J. Large, “Multilayer reflectors in animals using green and gold beetles as contrasting examples,” J. Exp. Biol. 201(Pt 9), 1307–1313 (1998).
[PubMed]

J. Insect Physiol. (1)

A. C. Neville, “Metallic gold and silver colours in some insect cuticles,” J. Insect Physiol. 23(10), 1267–1274 (1977).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Phys. Condens. Matter (1)

E. Belamie, G. Mosser, F. Gobeaux, and M. M. Giraud-Guille, “Possible transient liquid crystal phase during the laying out of connective tissues: α-chitin and collagen as models,” J. Phys. Condens. Matter 18(13), S115–S129 (2006).
[CrossRef]

J. R. Soc. Interface (1)

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).
[PubMed]

N. J. Phys. (2)

O. Deparis, M. Rassart, C. Vandenbem, V. Welch, J. P. Vigneron, and S. Lucas, “Structurally tuned iridescent surfaces inspired by nature,” N. J. Phys. 10(1), 013032 (2008).
[CrossRef]

S. A. Jewell, P. Vukusic, and N. W. Roberts, “Circularly polarized colour reflection from helicoidal structures in the beetle Plusiotis boucardi,” N. J. Phys. 9(4), 99 (2007).
[CrossRef]

Nat. Mater. (1)

M. Mitov and N. Dessaud, “Going beyond the reflectance limit of cholesteric liquid crystals,” Nat. Mater. 5(5), 361–364 (2006).
[CrossRef] [PubMed]

Novit. Zool. (1)

L. W. Rothschild and K. Jordan, “Six new species of Plusiotis and one new Anoplostethus,” Novit. Zool. 1, 504–507 (1894).

Opt. Commun. (1)

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(4-6), 349–356 (2003).
[CrossRef]

Philos. Mag. (1)

A. A. Michelson, “On metallic colouring in birds and insects,” Philos. Mag. 21, 554–567 (1911).

Philos. Transact. A Math. Phys. Eng. Sci. (1)

A. R. Parker, “A vision for natural photonics,” Philos. Transact. A Math. Phys. Eng. Sci. 362(1825), 2709–2720 (2004).
[CrossRef] [PubMed]

Phys. Rev. B (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

R. Rengarajan, D. Mittleman, C. Rich, and V. Colvin, “Effect of disorder on the optical properties of colloidal crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(1), 016615 (2005).
[CrossRef] [PubMed]

J. P. Vigneron, J. M. Pasteels, D. M. Windsor, Z. Vértesy, M. Rassart, T. Seldrum, J. Dumont, O. Deparis, V. Lousse, L. P. Biró, D. Ertz, and V. Welch, “Switchable reflector in the Panamanian tortoise beetle Charidotella egregia (Chrysomelidae: Cassidinae),” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(3), 031907 (2007).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

J. F. Bertone, P. Jiang, K. S. Hwang, D. M. Mittleman, and V. L. Colvin, “Thickness dependence of the optical properties of ordered silica-air and air-polymer photonic crystals,” Phys. Rev. Lett. 83(2), 300–303 (1999).
[CrossRef]

Proc. R. Soc. Lond. B Biol. Sci. (1)

S. Caveney, “Cuticle reflectivity and optical activity in scarab beetles: the rôle of uric acid,” Proc. R. Soc. Lond. B Biol. Sci. 178(1051), 205–225 (1971).
[CrossRef] [PubMed]

Proc. Zool. Soc. Lond. (1)

A. Boucard, “Monographic list of the Coleoptera of the genus Plusiotis of America, North of Panama, with descriptions of several new species,” Proc. Zool. Soc. Lond. 23, 117–125 (1875).

Science (1)

V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Structural origin of circularly polarized iridescence in jeweled beetles,” Science 325(5939), 449–451 (2009).
[CrossRef] [PubMed]

Sol. Energy (1)

R. E. Bird, R. L. Hulstrom, and L. J. Lewis, “Terrestrial solar spectra data sets,” Sol. Energy 30(6), 563–573 (1983).
[CrossRef]

Vision Res. (1)

R. Hegedüs, G. Szél, and G. Horváth, “Imaging polarimetry of the circularly polarizing cuticle of scarab beetles (Coleoptera: Rutelidae, Cetoniidae),” Vision Res. 46(17), 2786–2797 (2006).
[CrossRef] [PubMed]

Zootaxa (1)

B. Kohlmann and A. Solís, “New species of Ateuchus and Canthidium (Coleoptera: Scarabaeidae: Scarabaeinae) from Costa Rica,” Zootaxa 2219, 31–37 (2009).

Other (4)

V. C. Smith and J. Pokorny, “Color matching and color discrimination,” in The Science of Color, S. K. Shevell, ed. (Elsevier, 2003) pp.103–148.

H. A. Macleod, Thin Film Optical Filters (Institute of Physics Publishing, 2002).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

G. A. Niklasson, “Optical properties of inhomogeneous two-component materials,” in Materials Science for Solar Energy Conversion Systems, C. G. Granqvist, ed. (Pergamon, 1991) pp.7–43.

Supplementary Material (1)

» Media 1: AVI (11850 KB)     

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Figures (10)

Fig. 1
Fig. 1

Pictures of the Chrysina aurigans (left) and the Chrysina limbata (right) beetle specimens displaying their brilliant golden- and silver-like appearance, respectively.

Fig. 2
Fig. 2

Device used to carry out the direct reflectance measurements under normal incidence of non-polarized light on the elytron of a beetle. The allowed displacements and rotations of the probe holder allow us to focus the beam on the beetle’s elytron perpendicularly, as shown in Media 1.

Fig. 3
Fig. 3

Reflection spectra of C. aurigans beetle when illuminating an area of its head or a rear section with non-polarized radiation under near normal illumination. The reflectivity spectrum of gold, evaluated from its optical constants taken from the literature [8], and the eye sensitivity curve are included in the figure.

Fig. 4
Fig. 4

Reflection spectra from the C. aurigans and C. limbata beetle’s dorsal elytra. They are consistent with the color observed under white light illumination. Both show sequences of maxima and minima, as explained in the text.

Fig. 5
Fig. 5

Spectral dependence of the average refractive index of chitin, evaluated from the curves reported by Berthier et al. [10].

Fig. 9
Fig. 9

Smoothed reflection spectra of chirped multilayer structures with linearly decreasing values in the thickness of the sequence of layers, and low contrast between the refractive indices of successive layers. The number of layers is 68 for both cases: (a) C. aurigans, and (b) C. limbata. The larger and lower thicknesses values were set as indicated in the text. The blue thin solid lines correspond to reflection measurements.

Fig. 6
Fig. 6

Chromaticity diagram of the International Commission on Illumination, showing the coordinates (x,y) obtained from the reflection spectra reported in Fig. 4, and by assuming the solar irradiance spectrum AM1.5.

Fig. 7
Fig. 7

Reflection spectra of a multilayer consisting of ten stacks of high (n1 = 1.70) and low (n2 = 1.40) refractive index materials, with corresponding thicknesses of 100 and 121 nm. Two different incidence angles (θo) have been considered, as indicated in the figure.

Fig. 8
Fig. 8

Broad band reflection spectrum displayed for a chirped multilayer structure with a high contrast in the refractive index of successive layers ( n 2 / n 1 = 1.25 ). The total number of layers considered is 82, thickness and low refractive index of the top layer d1max = 138 nm and n1 = 1.40 respectively, thickness and high refractive index of the next layer d2max = 113 nm and n2 = 1.75 respectively, with a total thickness for the chirped structure of 7.5 μm.

Fig. 10
Fig. 10

Experimental set up used to measure the reflection of circularly polarized light: A- He-Ne tunable laser, B- linear polarizer, C- 45° beam splitter, D- λ/4 wave crystal, E- lens, F- sample, G- analyzer, and H- sensor.

Tables (1)

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Table 1 Reflection of Light from the Beetle’s Elytra When Illuminating with Circularly Polarized Light of Wavelength 543 nm a

Equations (2)

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R = λ 1 λ 2 R b ( λ ) I S ( λ ) d λ λ 1 λ 2 I S ( λ ) d λ ,
ε ¯ = 1 D i = 1 N d i ε i ,

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