Abstract

It is well known that the wing scales of butterflies and moths have elaborated microstructures that cause various optical effects. structural colors occur when the microstructures have a size comparable with the wavelength of light. On the other hand, the wing scales of some species are structurally modified at a size much larger size than the light wavelength. Here we show for the Madagascan sunset moth that not only the microstructures but also the large-size modifications can play an important role in scale coloration. The wing of the sunset moth shows a striking iridescence that is caused by the air-cuticle multilayer structure inside the wing scales. Further, the scale itself is highly curved from its root to distal end. Owing to this strong curvature, a deep groove structure is formed between adjacent two rows of the regularly arranged scales. We find that this groove structure together with multilayer optical interference produces an unusual optical effect through an inter-scale reflection mechanism; the wing color changes depending on light polarization. A model is proposed that quantitatively describes this color change.

© 2007 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. W. Lippert and K. Gentil, "Uber lamellare Feinstrukturen bei den SchillerSchuppen der Schmetterlinge vom Urania- und Morpho- Typ," Z. Morph. Okol. Tiere 48, 115-122 (1959).
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    [CrossRef]
  16. S. Yoshioka and S. Kinoshita, "Effect of macroscopic structure in iridescent color of the peacock feather," Forma 17, 169-181 (2002).
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    [CrossRef]
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    [CrossRef] [PubMed]

2006

S. Berthier, E. Charron, and J. Boulenguez, "Morphological structure and optical properties of the wings of Morphidae," Insect Science 13,145-157 (2006).
[CrossRef]

S. Yoshioka and S. Kinoshita, "Single-scale spectroscopy of structurally colored butterflies: measurements of quantified reflectance and transmittance," J. Opt. Soc. Am. A,  23, 134-141 (2006).
[CrossRef]

2005

S. Kinoshita and S. Yoshioka, "Structural colors in Nature: the role of regularity and irregularity in the structure," ChemPhysChem 6,1442-1459 (2005).
[CrossRef] [PubMed]

2004

S. Yoshioka and S. Kinoshita, "Wavelength-selective and anisotropic light-diffusing scale on the wing of the Morpho butterfly," Proc. R. Soc. Lond. B 271, 581-587 (2004).
[CrossRef]

R. Hegedus and G. Horvath, "Polarizational colors could help polarization-dependent color vision systems to discriminate between shiny and matt surfaces, but cannot unambiguously code surface orientation," Vision Research 44, 2337-2348 (2004).
[CrossRef] [PubMed]

2003

A. Sweeney, C. Jiggins, and S. Johnsen, "Polarized light as a butterfly mating signal," Nature 423, 31 (2003).
[CrossRef] [PubMed]

P. Vukusic and J. R. Sambles, "Photonic structures in biology," Nature 424,852-855 (2003).
[CrossRef] [PubMed]

L. P. Biró, Zs. Bálint, K. Kertész, Z. Vértesy, G. I. Márk, Z. E. Horváth, J. Balázs, D. Méhn, I. Kiricsi, V. Lousse, J. -P. Vigneron, "Role of photonic-crystal-type structures in the thermal regulation of a Lycaenid butterfly sister species pair," Phys. Rev. E 67, 021907 (2003).
[CrossRef]

2002

S. Kinoshita, S. Yoshioka, and K. Kawagoe, "Mechanisms of structural color in theMorpho butterfly: cooperation of regularity and irregularity in an iridescent scale," Proc. R. Soc. Lond. B 269,1417-1421 (2002).
[CrossRef]

S. Yoshioka and S. Kinoshita, "Effect of macroscopic structure in iridescent color of the peacock feather," Forma 17, 169-181 (2002).

2001

A. Kelber, C. Thunell, and K. Ariwaka, "Polarization-dependent color vision in Papilio butterflies," J. Exp. Biol. 204, 2469-2480 (2001).
[PubMed]

2000

P. Vukusic, J. R. Sambles, and C. R. Lawrence, "Color mixing in scales of a butterfly," Nature 404, 457 (2000).
[CrossRef] [PubMed]

A. R. Parker, "515 million years of structural color," J. Opt. A: Pure Appl. Opt. 2,R15-R28 (2000).
[CrossRef]

1999

M. Srinivasarao, "Nano-optics in the biological world: beetles, butterflies, birds, and moths," Chem. Rev. 99,1935-1961 (1999).
[CrossRef]

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, "Quantified interference and diffraction in single Morpho butterfly scales," Proc. R. Soc. Lond. B 266,1403-1411 (1999).
[CrossRef]

1998

A. R. Parker, D. R. Mckenzie, and S. T. Ahyong, "A unique form of light reflector and the evolution of signaling in Ovalipes (Crustacea: Decapoda: Portunidae)," Proc. R. Soc. Lond. B 265, 861-867 (1998).
[CrossRef]

1991

1975

R. B. Morris, "Iridescence from diffraction structures in the wing scales of Callophrys rubi, the Green Hairstreak," J. Ent. (A) 49,149-154 (1975).

1959

W. Lippert and K. Gentil, "Uber lamellare Feinstrukturen bei den SchillerSchuppen der Schmetterlinge vom Urania- und Morpho- Typ," Z. Morph. Okol. Tiere 48, 115-122 (1959).
[CrossRef]

1927

C. W. Mason, "Structural colors in insects. II," J. Phys. Chem. 31, 321-354 (1927).
[CrossRef]

Ahyong, S. T.

A. R. Parker, D. R. Mckenzie, and S. T. Ahyong, "A unique form of light reflector and the evolution of signaling in Ovalipes (Crustacea: Decapoda: Portunidae)," Proc. R. Soc. Lond. B 265, 861-867 (1998).
[CrossRef]

Ariwaka, K.

A. Kelber, C. Thunell, and K. Ariwaka, "Polarization-dependent color vision in Papilio butterflies," J. Exp. Biol. 204, 2469-2480 (2001).
[PubMed]

Balázs, J.

L. P. Biró, Zs. Bálint, K. Kertész, Z. Vértesy, G. I. Márk, Z. E. Horváth, J. Balázs, D. Méhn, I. Kiricsi, V. Lousse, J. -P. Vigneron, "Role of photonic-crystal-type structures in the thermal regulation of a Lycaenid butterfly sister species pair," Phys. Rev. E 67, 021907 (2003).
[CrossRef]

Bálint, Zs.

L. P. Biró, Zs. Bálint, K. Kertész, Z. Vértesy, G. I. Márk, Z. E. Horváth, J. Balázs, D. Méhn, I. Kiricsi, V. Lousse, J. -P. Vigneron, "Role of photonic-crystal-type structures in the thermal regulation of a Lycaenid butterfly sister species pair," Phys. Rev. E 67, 021907 (2003).
[CrossRef]

Berthier, S.

S. Berthier, E. Charron, and J. Boulenguez, "Morphological structure and optical properties of the wings of Morphidae," Insect Science 13,145-157 (2006).
[CrossRef]

Biró, L. P.

L. P. Biró, Zs. Bálint, K. Kertész, Z. Vértesy, G. I. Márk, Z. E. Horváth, J. Balázs, D. Méhn, I. Kiricsi, V. Lousse, J. -P. Vigneron, "Role of photonic-crystal-type structures in the thermal regulation of a Lycaenid butterfly sister species pair," Phys. Rev. E 67, 021907 (2003).
[CrossRef]

Boulenguez, J.

S. Berthier, E. Charron, and J. Boulenguez, "Morphological structure and optical properties of the wings of Morphidae," Insect Science 13,145-157 (2006).
[CrossRef]

Charron, E.

S. Berthier, E. Charron, and J. Boulenguez, "Morphological structure and optical properties of the wings of Morphidae," Insect Science 13,145-157 (2006).
[CrossRef]

Gentil, K.

W. Lippert and K. Gentil, "Uber lamellare Feinstrukturen bei den SchillerSchuppen der Schmetterlinge vom Urania- und Morpho- Typ," Z. Morph. Okol. Tiere 48, 115-122 (1959).
[CrossRef]

Ghiradella, H.

Horváth, Z. E.

L. P. Biró, Zs. Bálint, K. Kertész, Z. Vértesy, G. I. Márk, Z. E. Horváth, J. Balázs, D. Méhn, I. Kiricsi, V. Lousse, J. -P. Vigneron, "Role of photonic-crystal-type structures in the thermal regulation of a Lycaenid butterfly sister species pair," Phys. Rev. E 67, 021907 (2003).
[CrossRef]

Jiggins, C.

A. Sweeney, C. Jiggins, and S. Johnsen, "Polarized light as a butterfly mating signal," Nature 423, 31 (2003).
[CrossRef] [PubMed]

Johnsen, S.

A. Sweeney, C. Jiggins, and S. Johnsen, "Polarized light as a butterfly mating signal," Nature 423, 31 (2003).
[CrossRef] [PubMed]

Kawagoe, K.

S. Kinoshita, S. Yoshioka, and K. Kawagoe, "Mechanisms of structural color in theMorpho butterfly: cooperation of regularity and irregularity in an iridescent scale," Proc. R. Soc. Lond. B 269,1417-1421 (2002).
[CrossRef]

Kelber, A.

A. Kelber, C. Thunell, and K. Ariwaka, "Polarization-dependent color vision in Papilio butterflies," J. Exp. Biol. 204, 2469-2480 (2001).
[PubMed]

Kertész, K.

L. P. Biró, Zs. Bálint, K. Kertész, Z. Vértesy, G. I. Márk, Z. E. Horváth, J. Balázs, D. Méhn, I. Kiricsi, V. Lousse, J. -P. Vigneron, "Role of photonic-crystal-type structures in the thermal regulation of a Lycaenid butterfly sister species pair," Phys. Rev. E 67, 021907 (2003).
[CrossRef]

Kinoshita, S.

S. Yoshioka and S. Kinoshita, "Single-scale spectroscopy of structurally colored butterflies: measurements of quantified reflectance and transmittance," J. Opt. Soc. Am. A,  23, 134-141 (2006).
[CrossRef]

S. Kinoshita and S. Yoshioka, "Structural colors in Nature: the role of regularity and irregularity in the structure," ChemPhysChem 6,1442-1459 (2005).
[CrossRef] [PubMed]

S. Yoshioka and S. Kinoshita, "Wavelength-selective and anisotropic light-diffusing scale on the wing of the Morpho butterfly," Proc. R. Soc. Lond. B 271, 581-587 (2004).
[CrossRef]

S. Yoshioka and S. Kinoshita, "Effect of macroscopic structure in iridescent color of the peacock feather," Forma 17, 169-181 (2002).

S. Kinoshita, S. Yoshioka, and K. Kawagoe, "Mechanisms of structural color in theMorpho butterfly: cooperation of regularity and irregularity in an iridescent scale," Proc. R. Soc. Lond. B 269,1417-1421 (2002).
[CrossRef]

Kiricsi, I.

L. P. Biró, Zs. Bálint, K. Kertész, Z. Vértesy, G. I. Márk, Z. E. Horváth, J. Balázs, D. Méhn, I. Kiricsi, V. Lousse, J. -P. Vigneron, "Role of photonic-crystal-type structures in the thermal regulation of a Lycaenid butterfly sister species pair," Phys. Rev. E 67, 021907 (2003).
[CrossRef]

Lawrence, C. R.

P. Vukusic, J. R. Sambles, and C. R. Lawrence, "Color mixing in scales of a butterfly," Nature 404, 457 (2000).
[CrossRef] [PubMed]

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, "Quantified interference and diffraction in single Morpho butterfly scales," Proc. R. Soc. Lond. B 266,1403-1411 (1999).
[CrossRef]

Lippert, W.

W. Lippert and K. Gentil, "Uber lamellare Feinstrukturen bei den SchillerSchuppen der Schmetterlinge vom Urania- und Morpho- Typ," Z. Morph. Okol. Tiere 48, 115-122 (1959).
[CrossRef]

Lousse, V.

L. P. Biró, Zs. Bálint, K. Kertész, Z. Vértesy, G. I. Márk, Z. E. Horváth, J. Balázs, D. Méhn, I. Kiricsi, V. Lousse, J. -P. Vigneron, "Role of photonic-crystal-type structures in the thermal regulation of a Lycaenid butterfly sister species pair," Phys. Rev. E 67, 021907 (2003).
[CrossRef]

Márk, G. I.

L. P. Biró, Zs. Bálint, K. Kertész, Z. Vértesy, G. I. Márk, Z. E. Horváth, J. Balázs, D. Méhn, I. Kiricsi, V. Lousse, J. -P. Vigneron, "Role of photonic-crystal-type structures in the thermal regulation of a Lycaenid butterfly sister species pair," Phys. Rev. E 67, 021907 (2003).
[CrossRef]

Mason, C. W.

C. W. Mason, "Structural colors in insects. II," J. Phys. Chem. 31, 321-354 (1927).
[CrossRef]

Mckenzie, D. R.

A. R. Parker, D. R. Mckenzie, and S. T. Ahyong, "A unique form of light reflector and the evolution of signaling in Ovalipes (Crustacea: Decapoda: Portunidae)," Proc. R. Soc. Lond. B 265, 861-867 (1998).
[CrossRef]

Méhn, D.

L. P. Biró, Zs. Bálint, K. Kertész, Z. Vértesy, G. I. Márk, Z. E. Horváth, J. Balázs, D. Méhn, I. Kiricsi, V. Lousse, J. -P. Vigneron, "Role of photonic-crystal-type structures in the thermal regulation of a Lycaenid butterfly sister species pair," Phys. Rev. E 67, 021907 (2003).
[CrossRef]

Morris, R. B.

R. B. Morris, "Iridescence from diffraction structures in the wing scales of Callophrys rubi, the Green Hairstreak," J. Ent. (A) 49,149-154 (1975).

Parker, A. R.

A. R. Parker, "515 million years of structural color," J. Opt. A: Pure Appl. Opt. 2,R15-R28 (2000).
[CrossRef]

A. R. Parker, D. R. Mckenzie, and S. T. Ahyong, "A unique form of light reflector and the evolution of signaling in Ovalipes (Crustacea: Decapoda: Portunidae)," Proc. R. Soc. Lond. B 265, 861-867 (1998).
[CrossRef]

Sambles, J. R.

P. Vukusic and J. R. Sambles, "Photonic structures in biology," Nature 424,852-855 (2003).
[CrossRef] [PubMed]

P. Vukusic, J. R. Sambles, and C. R. Lawrence, "Color mixing in scales of a butterfly," Nature 404, 457 (2000).
[CrossRef] [PubMed]

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, "Quantified interference and diffraction in single Morpho butterfly scales," Proc. R. Soc. Lond. B 266,1403-1411 (1999).
[CrossRef]

Srinivasarao, M.

M. Srinivasarao, "Nano-optics in the biological world: beetles, butterflies, birds, and moths," Chem. Rev. 99,1935-1961 (1999).
[CrossRef]

Sweeney, A.

A. Sweeney, C. Jiggins, and S. Johnsen, "Polarized light as a butterfly mating signal," Nature 423, 31 (2003).
[CrossRef] [PubMed]

Thunell, C.

A. Kelber, C. Thunell, and K. Ariwaka, "Polarization-dependent color vision in Papilio butterflies," J. Exp. Biol. 204, 2469-2480 (2001).
[PubMed]

Vértesy, Z.

L. P. Biró, Zs. Bálint, K. Kertész, Z. Vértesy, G. I. Márk, Z. E. Horváth, J. Balázs, D. Méhn, I. Kiricsi, V. Lousse, J. -P. Vigneron, "Role of photonic-crystal-type structures in the thermal regulation of a Lycaenid butterfly sister species pair," Phys. Rev. E 67, 021907 (2003).
[CrossRef]

Vigneron, J. -P.

L. P. Biró, Zs. Bálint, K. Kertész, Z. Vértesy, G. I. Márk, Z. E. Horváth, J. Balázs, D. Méhn, I. Kiricsi, V. Lousse, J. -P. Vigneron, "Role of photonic-crystal-type structures in the thermal regulation of a Lycaenid butterfly sister species pair," Phys. Rev. E 67, 021907 (2003).
[CrossRef]

Vukusic, P.

P. Vukusic and J. R. Sambles, "Photonic structures in biology," Nature 424,852-855 (2003).
[CrossRef] [PubMed]

P. Vukusic, J. R. Sambles, and C. R. Lawrence, "Color mixing in scales of a butterfly," Nature 404, 457 (2000).
[CrossRef] [PubMed]

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, "Quantified interference and diffraction in single Morpho butterfly scales," Proc. R. Soc. Lond. B 266,1403-1411 (1999).
[CrossRef]

Wootton, R. J.

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, "Quantified interference and diffraction in single Morpho butterfly scales," Proc. R. Soc. Lond. B 266,1403-1411 (1999).
[CrossRef]

Yoshioka, S.

S. Yoshioka and S. Kinoshita, "Single-scale spectroscopy of structurally colored butterflies: measurements of quantified reflectance and transmittance," J. Opt. Soc. Am. A,  23, 134-141 (2006).
[CrossRef]

S. Kinoshita and S. Yoshioka, "Structural colors in Nature: the role of regularity and irregularity in the structure," ChemPhysChem 6,1442-1459 (2005).
[CrossRef] [PubMed]

S. Yoshioka and S. Kinoshita, "Wavelength-selective and anisotropic light-diffusing scale on the wing of the Morpho butterfly," Proc. R. Soc. Lond. B 271, 581-587 (2004).
[CrossRef]

S. Yoshioka and S. Kinoshita, "Effect of macroscopic structure in iridescent color of the peacock feather," Forma 17, 169-181 (2002).

S. Kinoshita, S. Yoshioka, and K. Kawagoe, "Mechanisms of structural color in theMorpho butterfly: cooperation of regularity and irregularity in an iridescent scale," Proc. R. Soc. Lond. B 269,1417-1421 (2002).
[CrossRef]

Appl. Opt.

Chem. Rev.

M. Srinivasarao, "Nano-optics in the biological world: beetles, butterflies, birds, and moths," Chem. Rev. 99,1935-1961 (1999).
[CrossRef]

ChemPhysChem

S. Kinoshita and S. Yoshioka, "Structural colors in Nature: the role of regularity and irregularity in the structure," ChemPhysChem 6,1442-1459 (2005).
[CrossRef] [PubMed]

Forma

S. Yoshioka and S. Kinoshita, "Effect of macroscopic structure in iridescent color of the peacock feather," Forma 17, 169-181 (2002).

Insect Science

S. Berthier, E. Charron, and J. Boulenguez, "Morphological structure and optical properties of the wings of Morphidae," Insect Science 13,145-157 (2006).
[CrossRef]

J. Ent. (A)

R. B. Morris, "Iridescence from diffraction structures in the wing scales of Callophrys rubi, the Green Hairstreak," J. Ent. (A) 49,149-154 (1975).

J. Exp. Biol.

A. Kelber, C. Thunell, and K. Ariwaka, "Polarization-dependent color vision in Papilio butterflies," J. Exp. Biol. 204, 2469-2480 (2001).
[PubMed]

J. Opt. A: Pure Appl. Opt.

A. R. Parker, "515 million years of structural color," J. Opt. A: Pure Appl. Opt. 2,R15-R28 (2000).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. Chem.

C. W. Mason, "Structural colors in insects. II," J. Phys. Chem. 31, 321-354 (1927).
[CrossRef]

Nature

P. Vukusic and J. R. Sambles, "Photonic structures in biology," Nature 424,852-855 (2003).
[CrossRef] [PubMed]

P. Vukusic, J. R. Sambles, and C. R. Lawrence, "Color mixing in scales of a butterfly," Nature 404, 457 (2000).
[CrossRef] [PubMed]

A. Sweeney, C. Jiggins, and S. Johnsen, "Polarized light as a butterfly mating signal," Nature 423, 31 (2003).
[CrossRef] [PubMed]

Phys. Rev. E

L. P. Biró, Zs. Bálint, K. Kertész, Z. Vértesy, G. I. Márk, Z. E. Horváth, J. Balázs, D. Méhn, I. Kiricsi, V. Lousse, J. -P. Vigneron, "Role of photonic-crystal-type structures in the thermal regulation of a Lycaenid butterfly sister species pair," Phys. Rev. E 67, 021907 (2003).
[CrossRef]

Proc. R. Soc. Lond. B

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, "Quantified interference and diffraction in single Morpho butterfly scales," Proc. R. Soc. Lond. B 266,1403-1411 (1999).
[CrossRef]

S. Kinoshita, S. Yoshioka, and K. Kawagoe, "Mechanisms of structural color in theMorpho butterfly: cooperation of regularity and irregularity in an iridescent scale," Proc. R. Soc. Lond. B 269,1417-1421 (2002).
[CrossRef]

A. R. Parker, D. R. Mckenzie, and S. T. Ahyong, "A unique form of light reflector and the evolution of signaling in Ovalipes (Crustacea: Decapoda: Portunidae)," Proc. R. Soc. Lond. B 265, 861-867 (1998).
[CrossRef]

S. Yoshioka and S. Kinoshita, "Wavelength-selective and anisotropic light-diffusing scale on the wing of the Morpho butterfly," Proc. R. Soc. Lond. B 271, 581-587 (2004).
[CrossRef]

Vision Research

R. Hegedus and G. Horvath, "Polarizational colors could help polarization-dependent color vision systems to discriminate between shiny and matt surfaces, but cannot unambiguously code surface orientation," Vision Research 44, 2337-2348 (2004).
[CrossRef] [PubMed]

Z. Morph. Okol. Tiere

W. Lippert and K. Gentil, "Uber lamellare Feinstrukturen bei den SchillerSchuppen der Schmetterlinge vom Urania- und Morpho- Typ," Z. Morph. Okol. Tiere 48, 115-122 (1959).
[CrossRef]

Other

H. F. Nijhout, The development and evolution of butterfly wing patterns (Smithonian Institution Press, Washington, 1991).

H. Ghiradella, "Hairs, bristles, and scales," in Microscopic anatomy of invertebrates, 11A: Insecta, M. Locke ed. (Wiley-Liss, New York, 1998), pp. 257-287.

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Figures (8)

Fig. 1.
Fig. 1.

Ventral side of the wing of the Madagascan sunset moth.

Fig. 2.
Fig. 2.

Experimental setup for the measurement of the polarization dependence of the reflectance spectrum. Unpolarized white light from a Xe lamp is focused on the sample after the spot size is controlled by an aperture to be several mm2. The light reflected into 8° from the incident light beam is collected by a lens and focused on one end of an optical fiber, which guides the light into a spectrometer. The reflected light passes through a polarizer and also a quartz-made depolarizer that nullifies the polarization dependence of the spectrometer.

Fig. 3.
Fig. 3.

Structure of the wing scales and their arrangement. (a) Microscopic image of a longitudinal cross-section of the hind wing. The upper surface corresponds to the ventral side of the red-purplish area and the lower to the dorsal side of the black hairy part. Scale bar: 300 μm. (b) Scanning electron microscopic image of the upper surface of the scale. Scale bar: 12 μm. (c) Transmission electron microscopic (TEM) images of the longitudinal cross-section of the scale. The center shows an assembled TEM image showing the whole curvature of the scale. The centeral black part is a part of the metal grid upon which the cross-sectioned sample was placed. Note that the longitudinal cross-sections of two scales are seen because they laterally overlapped. The surrounding eight TEM images under higher magnification show an alternate air-cuticle multilayer structure. Scale bar: 2 μm.

Fig. 4.
Fig. 4.

Polarization dependence of the red purplish part of the ventral hind wing and a schematic illustration of the reflection mechanism. (a) and (b): Polarization-dependent images of the scale arrangement taken with the same exposure time. White arrows show the analyzing direction of the reflected light, while the illuminating light is unpolarized. The right upper black area corresponds to the wing area of the black patch. Scale bar: 200 μ of the scales (purplish red arrow) and the other path is the dual reflection between adjacent scales (yellow arrows). (d) and (e): Wing-color change depending on the analyzer direction, indicated by white arrows, under unpolarized light illumination. Scale bar: 3 mm

Fig. 5.
Fig. 5.

Experimentally determined reflectance of the wing and a schematic illustration of multilayer optical interference. (a) Reflectance of the wing for two analyzing directions of the reflected light under the illumination of unpolarized light. The black and grey lines show the results for s- and p-polarization, respectively, and the broken line is the difference of the two. The accompanying letters, s, p and s-p, indicate the polarization. The experimental setup for this measurement is shown in Fig. 2. (b) A schematic illustration of multilayer optical interference. The parameters nc (na ), dc (da ), and θc (θa ) are a refractive index, a thickness, and a refraction angle in the cuticle layer (the air spacing), respectively.

Fig. 6.
Fig. 6.

Optical model for the surface structure of the curved scales. It consists of laterally arranged arcs of 90°. The angles θref and θarc are defined as the angles from the direction normal to the plane of the arranged arcs, which is depicted by the dashed-dotted line in the left arc.

Fig. 7.
Fig. 7.

Reflectance of the multilayer system and of the wing of the moth. (a) Reflectance determined by the transfer matrix method for the multilayer system which is assumed to consist of 6 cuticle layers and 5 air gaps with thicknesses of 170 and 130 nm, respectively. A refractive index 1.55 is used for the cuticle layer. Black and broken lines show the calculated reflectance for s- and p- polarizations under 45 ° incidence, respectively, and the grey line is the reflectance under normal incidence. (b) The polarization dependence in the reflectance of the wing. The spectra are calculated according to Eq. (1) with A=0.35 by using the reflectance shown in (a). Black and grey lines are the results for R s(λ) and R p(λ), respectively and the broken line shows the difference of the two.

Fig. 8.
Fig. 8.

Reflectance of the multilayer system with irregularities and of the wing of the moth. (a) Reflectance calculated by a theoretical model containing the irregular aspects of the multilayer structure. The complex refractive index and the distribution of the layer thickness are assumed. See the text for detail. Black and broken lines are the reflectance of 45° incident light for s- and p- polarizations. The grey line is the result for normal incidence. (b) Polarization dependence of the reflectance of the wing. The spectra are calculated according to Eq. (1) with A=0.35 by using the reflectance shown in (a). Black and grey lines are the results for R s(λ) and R p(λ), respectively, and the broken line shows the difference of the two.

Equations (1)

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R i ( λ ) R 0 ( λ ) + A R i 45 2 ( λ ) .

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