Abstract

The Troides magellanus butterfly exhibits a specialized iridescence that is visible only when its hind wings are both illuminated and viewed at near-grazing incidence. The effect is due to the presence of a constrained bigrating structure in its wing scales that has been previously observed in only one other species of butterfly (Ancyluris meliboeus). However, whereas the Ancyluris presents wide-angle flickering iridescence, the Troides butterfly uses pigmentary coloration at all but a narrow tailored range of angles, producing a characteristic effect.

© 2002 Optical Society of America

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References

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  1. P. Vukusic, J. R. Sambles, C. R. Lawrence, “Colour mixing in wing scales of a butterfly,” Nature (London) 404, 457 (2000).
    [CrossRef]
  2. R. B. Morris, “Iridescence from diffraction structures in the wing scales of Callophrys rubi, the Green Hairstreak,” J. Entomol. Ser. A 49, 149–154 (1975).
  3. P. Vukusic, J. R. Sambles, C. R. Lawrence, R. J. Wootton, “Quantified interference and diffraction in single Morpho butterfly scales,” Proc. R. Soc. London Ser. B 266, 1403–1411 (1999).
    [CrossRef]
  4. R. B. Hwang, S. T. Peng, “Performance evaluation of a bigrating as a beam splitter,” Appl. Opt. 36, 2011–2018 (1997).
    [CrossRef] [PubMed]
  5. J. B. Harris, T. W. Preist, J. R. Sambles, R. N. Thorpe, R. A. Watts, “Optical response of bigratings,” J. Opt. Soc. Am. A 13, 2041–2049 (1996).
    [CrossRef]
  6. S. A. Khan, D. N. Qu, R. E. Burge, “Experimental analysis of diffraction by wavelength-sized metallic gratings in the microwave region,” Opt. Eng. 32, 3249–3253 (1993).
    [CrossRef]
  7. K. Hirayama, E. N. Glytsis, T. K. Gaylord, “Rigorous electromagnetic analysis of diffraction by finite-number-of-periods gratings,” J. Opt. Soc. Am. A 14, 907–917 (1997).
    [CrossRef]
  8. C. R. Lawrence, A. S. Treen, “Polarisation conversion at a textured surface,” IEE Proc. Microwave Antennas Propag. 146, 241–246 (1999).
    [CrossRef]
  9. M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), p. 402.
  10. N. W. Ashcroft, N. D. Mermin, Solid State Physics (Saunders, Philadelphia, Pa., 1976), Chap. 4.
  11. P. Vukusic, J. R. Sambles, C. R. Lawrence, R. J. Wotton, “Structural colour: now you see it—now you don’t,” Nature (London) 410, 36–36 (2001).
    [CrossRef]

2001

P. Vukusic, J. R. Sambles, C. R. Lawrence, R. J. Wotton, “Structural colour: now you see it—now you don’t,” Nature (London) 410, 36–36 (2001).
[CrossRef]

2000

P. Vukusic, J. R. Sambles, C. R. Lawrence, “Colour mixing in wing scales of a butterfly,” Nature (London) 404, 457 (2000).
[CrossRef]

1999

C. R. Lawrence, A. S. Treen, “Polarisation conversion at a textured surface,” IEE Proc. Microwave Antennas Propag. 146, 241–246 (1999).
[CrossRef]

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

1997

1996

1993

S. A. Khan, D. N. Qu, R. E. Burge, “Experimental analysis of diffraction by wavelength-sized metallic gratings in the microwave region,” Opt. Eng. 32, 3249–3253 (1993).
[CrossRef]

1975

R. B. Morris, “Iridescence from diffraction structures in the wing scales of Callophrys rubi, the Green Hairstreak,” J. Entomol. Ser. A 49, 149–154 (1975).

Ashcroft, N. W.

N. W. Ashcroft, N. D. Mermin, Solid State Physics (Saunders, Philadelphia, Pa., 1976), Chap. 4.

Born, M.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), p. 402.

Burge, R. E.

S. A. Khan, D. N. Qu, R. E. Burge, “Experimental analysis of diffraction by wavelength-sized metallic gratings in the microwave region,” Opt. Eng. 32, 3249–3253 (1993).
[CrossRef]

Gaylord, T. K.

Glytsis, E. N.

Harris, J. B.

Hirayama, K.

Hwang, R. B.

Khan, S. A.

S. A. Khan, D. N. Qu, R. E. Burge, “Experimental analysis of diffraction by wavelength-sized metallic gratings in the microwave region,” Opt. Eng. 32, 3249–3253 (1993).
[CrossRef]

Lawrence, C. R.

P. Vukusic, J. R. Sambles, C. R. Lawrence, R. J. Wotton, “Structural colour: now you see it—now you don’t,” Nature (London) 410, 36–36 (2001).
[CrossRef]

P. Vukusic, J. R. Sambles, C. R. Lawrence, “Colour mixing in wing scales of a butterfly,” Nature (London) 404, 457 (2000).
[CrossRef]

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

C. R. Lawrence, A. S. Treen, “Polarisation conversion at a textured surface,” IEE Proc. Microwave Antennas Propag. 146, 241–246 (1999).
[CrossRef]

Mermin, N. D.

N. W. Ashcroft, N. D. Mermin, Solid State Physics (Saunders, Philadelphia, Pa., 1976), Chap. 4.

Morris, R. B.

R. B. Morris, “Iridescence from diffraction structures in the wing scales of Callophrys rubi, the Green Hairstreak,” J. Entomol. Ser. A 49, 149–154 (1975).

Peng, S. T.

Preist, T. W.

Qu, D. N.

S. A. Khan, D. N. Qu, R. E. Burge, “Experimental analysis of diffraction by wavelength-sized metallic gratings in the microwave region,” Opt. Eng. 32, 3249–3253 (1993).
[CrossRef]

Sambles, J. R.

P. Vukusic, J. R. Sambles, C. R. Lawrence, R. J. Wotton, “Structural colour: now you see it—now you don’t,” Nature (London) 410, 36–36 (2001).
[CrossRef]

P. Vukusic, J. R. Sambles, C. R. Lawrence, “Colour mixing in wing scales of a butterfly,” Nature (London) 404, 457 (2000).
[CrossRef]

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

J. B. Harris, T. W. Preist, J. R. Sambles, R. N. Thorpe, R. A. Watts, “Optical response of bigratings,” J. Opt. Soc. Am. A 13, 2041–2049 (1996).
[CrossRef]

Thorpe, R. N.

Treen, A. S.

C. R. Lawrence, A. S. Treen, “Polarisation conversion at a textured surface,” IEE Proc. Microwave Antennas Propag. 146, 241–246 (1999).
[CrossRef]

Vukusic, P.

P. Vukusic, J. R. Sambles, C. R. Lawrence, R. J. Wotton, “Structural colour: now you see it—now you don’t,” Nature (London) 410, 36–36 (2001).
[CrossRef]

P. Vukusic, J. R. Sambles, C. R. Lawrence, “Colour mixing in wing scales of a butterfly,” Nature (London) 404, 457 (2000).
[CrossRef]

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

Watts, R. A.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), p. 402.

Wootton, R. J.

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

Wotton, R. J.

P. Vukusic, J. R. Sambles, C. R. Lawrence, R. J. Wotton, “Structural colour: now you see it—now you don’t,” Nature (London) 410, 36–36 (2001).
[CrossRef]

Appl. Opt.

IEE Proc. Microwave Antennas Propag.

C. R. Lawrence, A. S. Treen, “Polarisation conversion at a textured surface,” IEE Proc. Microwave Antennas Propag. 146, 241–246 (1999).
[CrossRef]

J. Entomol. Ser. A

R. B. Morris, “Iridescence from diffraction structures in the wing scales of Callophrys rubi, the Green Hairstreak,” J. Entomol. Ser. A 49, 149–154 (1975).

J. Opt. Soc. Am. A

Nature (London)

P. Vukusic, J. R. Sambles, C. R. Lawrence, “Colour mixing in wing scales of a butterfly,” Nature (London) 404, 457 (2000).
[CrossRef]

P. Vukusic, J. R. Sambles, C. R. Lawrence, R. J. Wotton, “Structural colour: now you see it—now you don’t,” Nature (London) 410, 36–36 (2001).
[CrossRef]

Opt. Eng.

S. A. Khan, D. N. Qu, R. E. Burge, “Experimental analysis of diffraction by wavelength-sized metallic gratings in the microwave region,” Opt. Eng. 32, 3249–3253 (1993).
[CrossRef]

Proc. R. Soc. London Ser. B

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

Other

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), p. 402.

N. W. Ashcroft, N. D. Mermin, Solid State Physics (Saunders, Philadelphia, Pa., 1976), Chap. 4.

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Figures (11)

Fig. 1
Fig. 1

Schematic of the roof tile arrangement of scales on the butterfly’s wings. The arrow points toward the tip of the hind wing, running parallel to the scale ridges, and is repeated in Figs. 2 4 and Fig. 7.

Fig. 2
Fig. 2

SEM image of the surface of a typical butterfly wing (T. magellanus), with an arrow pointing toward the tip of the hind wing (see Fig. 1). Scale bar is ∼150 µm long.

Fig. 3
Fig. 3

SEM image of the end of a wing scale, revealing surface ridges. The scale bar represents a distance of ∼30 µm.

Fig. 4
Fig. 4

Side view of ridges presented in Fig. 3, revealing flanges that branch from the ridges. Scale bar is ∼1.5 µm long.

Fig. 5
Fig. 5

Schematic of sample orientation in the integrating sphere. Top view illustrates the orientation of multilayer plates with regard to +θ. Incident light that is not absorbed by the sample is reflected from the interior of the sphere until it leaves by a second aperture. The intensity of this light is measured to produce a measure of the total sample reflectivity (specular and diffuse).

Fig. 6
Fig. 6

Reflectivity ratios obtained from the spectrometer. Each data set was normalized to the reflectivity obtained at normal incidence (i.e., θ = 0).

Fig. 7
Fig. 7

Definitions of axes and periodicities. The SEM image is of the broken end of a ridge, illustrating the sloping plates. The black circles on the schematic diagram illustrate the two periodic structures that form a lattice of diffracting elements. The white arrow points toward the tip of the hind wing (see Fig. 1).

Fig. 8
Fig. 8

Momentum-space diagram for infinite lattice of diffractors (i.e., an unrestricted bigrating). Because the photon momentum cannot change during the diffraction process, the incident and diffracted vectors must be of equal length. Hence, for a specific incident angle (θl), only one wavelength can undergo a (-1, -1) scattering process.

Fig. 9
Fig. 9

As per Fig. 8, but for the restricted bigrating of the T. magellanus. The points are now elongated in the y direction, and more solutions are possible for a given incident angle. By utilizing different wavelength photons (i.e., vectors of different lengths), we can meet the diffraction conditions by following different paths from one point to another.

Fig. 10
Fig. 10

Calculated relative scattering efficiencies for 100-period (solid curve) and 7-period (dashed curve) gratings. Note the spread in diffracted wavelengths for the restricted grating.

Fig. 11
Fig. 11

Prediction of the wavelengths diffracted from the T. magellanus bigrating as a function of incident angle. The shaded region contains the solutions to the diffraction equations; see text for details.

Equations (1)

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ϕ=sin2N kph d/2/sin2kph d)/2.

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