Abstract

When illuminated and viewed along certain well-defined directions, segments on the wings of the butterfly Cynandra opis shows a striking violet-blue to blue-green. We quantify the spectral and the directional properties of these areas of the wings of the insect. Electron microscopy shows that wing scales from these iridescent regions of the wings contain two gratinglike microstructures crossed at right angles. Application of the diffraction theory, as formulated by the Stratton–Silver–Chu integral, to the microstructure can explain all the important features observed experimentally.

© 1999 Optical Society of America

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References

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  1. R. B. Morris, “Iridescence from diffraction structures in the wing scales of Callophrys rubi, the green hairstreak,” J. Enbtomol. Ser. A 49, 149–154 (1975).
  2. H. Ghiradella, “Light and color on the wing: structural colors in butterflies and moths,” Appl. Opt. 30, 3492–3500 (1991).
    [CrossRef] [PubMed]
  3. D. J. Brink, J. E. Smit, M. E. Lee, A. Möller, “Optical diffraction by the microstructure of the wing of a moth,” Appl. Opt. 34, 6049–6057 (1995).
    [CrossRef] [PubMed]
  4. D. J. Brink, M. E. Lee, “Ellipsometry of diffractive insect reflectors,” Appl. Opt. 35, 1950–1955 (1996).
    [CrossRef] [PubMed]
  5. M. F. Land, “The physics and biology of animal reflectors,” Prog. Biophys. 24, 75–106 (1972).
    [CrossRef]
  6. D. J. Brink, M. E. Lee, “Thin-film biological reflectors: optical characterization of the Chrysiridia croesus moth,” Appl. Opt. 37, 4213–4217 (1998).
    [CrossRef]
  7. D. Mossakowski, “Reflection measurements used in the analysis of structural colours of beetles,” J. Microsc. 116, 351–364 (1979).
    [CrossRef]
  8. S. Silver, Microwave Antenna Theory and Design (McGraw-Hill, New York, 1947), p. 161.
  9. R. M. A. Azzam, N. M. Bashara, “Polarization characteristics of scattered radiation from a diffraction grating by ellipsometry with application to surface roughness,” Phys. Rev. B 5, 4721–4729 (1972).
    [CrossRef]
  10. E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, 1987), pp. 426, 428, 531.

1998 (1)

1996 (1)

1995 (1)

1991 (1)

1979 (1)

D. Mossakowski, “Reflection measurements used in the analysis of structural colours of beetles,” J. Microsc. 116, 351–364 (1979).
[CrossRef]

1975 (1)

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

1972 (2)

M. F. Land, “The physics and biology of animal reflectors,” Prog. Biophys. 24, 75–106 (1972).
[CrossRef]

R. M. A. Azzam, N. M. Bashara, “Polarization characteristics of scattered radiation from a diffraction grating by ellipsometry with application to surface roughness,” Phys. Rev. B 5, 4721–4729 (1972).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, “Polarization characteristics of scattered radiation from a diffraction grating by ellipsometry with application to surface roughness,” Phys. Rev. B 5, 4721–4729 (1972).
[CrossRef]

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, “Polarization characteristics of scattered radiation from a diffraction grating by ellipsometry with application to surface roughness,” Phys. Rev. B 5, 4721–4729 (1972).
[CrossRef]

Brink, D. J.

Ghiradella, H.

Hecht, E.

E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, 1987), pp. 426, 428, 531.

Land, M. F.

M. F. Land, “The physics and biology of animal reflectors,” Prog. Biophys. 24, 75–106 (1972).
[CrossRef]

Lee, M. E.

Möller, A.

Morris, R. B.

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

Mossakowski, D.

D. Mossakowski, “Reflection measurements used in the analysis of structural colours of beetles,” J. Microsc. 116, 351–364 (1979).
[CrossRef]

Silver, S.

S. Silver, Microwave Antenna Theory and Design (McGraw-Hill, New York, 1947), p. 161.

Smit, J. E.

Appl. Opt. (4)

J. Enbtomol. Ser. A (1)

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

J. Microsc. (1)

D. Mossakowski, “Reflection measurements used in the analysis of structural colours of beetles,” J. Microsc. 116, 351–364 (1979).
[CrossRef]

Phys. Rev. B (1)

R. M. A. Azzam, N. M. Bashara, “Polarization characteristics of scattered radiation from a diffraction grating by ellipsometry with application to surface roughness,” Phys. Rev. B 5, 4721–4729 (1972).
[CrossRef]

Prog. Biophys. (1)

M. F. Land, “The physics and biology of animal reflectors,” Prog. Biophys. 24, 75–106 (1972).
[CrossRef]

Other (2)

E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, 1987), pp. 426, 428, 531.

S. Silver, Microwave Antenna Theory and Design (McGraw-Hill, New York, 1947), p. 161.

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Figures (9)

Fig. 1
Fig. 1

(a) SEM micrograph of iridescent wing scales. The white length bar (lower left corner) indicates 10 µm. The ridges (planes 1) are parallel to a line from A to A′. Wing scales are stacked in such a way that the bases of the scales are hidden. The base of the wing scales face toward the front of the wing itself (right side of the micrograph). Note that the slightly lighter scale near the center is atypical. The ribs are more visible than normal, and all spacing is slightly larger. Calculations (and measurements) refer to the more numerous normal scales. (b) SEM micrograph under higher magnification. Ridges (planes 1) are parallel to a line from A to A′. Microribs are just visible on them. The set of ribs underneath the ridges and at right angles to them are planes 2. The white length bar indicates 5 µm.

Fig. 2
Fig. 2

(a) Simplified sketch of the diffracting structure showing planes 1 and 2. The angle between the X and the X′ axes is θ R . In the sketch θ R has a negative value. (b) Top view of the experimental layout. Line AA′ indicates the top edge of a wing scale. It is the same as line AA′ in Figs. 1(a) and 1(b). WL is the tungsten white-light source, and P 1 and P 2 are polarizers used to select either S-(transmission directions vertical, i.e., out of the page) or P-type (transmission directions horizontal, i.e., in the plane of the page) diffraction. M is a small mirror to allow almost equal incident and diffraction angles. L1 and L2 are lenses to collect diffracted light and to focus it onto the entrance slit of the monochromator MC. A slit aperture is placed in front of L1 to limit the reception angle of diffracted light. The inset shows a front view of the sample, which can be rotated around axes CC′ and XX′.

Fig. 3
Fig. 3

Calculated diffraction efficiency of the microribs on planes 1. The intensity scale is in arbitrary units, but it starts from zero.

Fig. 4
Fig. 4

Calculated spectra for θ R = -90° and light incident from the left. A perfect diffracting structure is assumed. Angles of incidence are shown, and diffraction angles are 5° smaller.

Fig. 5
Fig. 5

Experimentally observed spectra of wing scales oriented at θ R = -90°. Diffraction is dominated by planes 1. Angles of incidence are shown, and diffraction angles are 5° smaller.

Fig. 6
Fig. 6

Calculated spectra under the same conditions as Figs. 4 and 5, but with random variations in grating spacing (d 1) included.

Fig. 7
Fig. 7

Experimentally observed spectra for wing scales at θ R = 0° [orientation close to that shown in Figs. 1(a) and 2] and light incident from the left. Diffraction is dominated by planes 2. Angles of incidence are shown, and diffraction angles are 5° smaller.

Fig. 8
Fig. 8

Calculated spectra under the same conditions as Fig. 7. Random variations in d 2 are included.

Fig. 9
Fig. 9

Experimentally observed diffracted signal at 440 nm and at an angle of incidence ϕ i = 35°. The rotation angle θ R is varied from -90° to 0°.

Tables (3)

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Table 1 Parameter Values Used for Calculating Spectraa

Tables Icon

Table 2 Wavelengths for Different Diffraction Orders Calculated with Grating Formula (13) for Planes 1

Tables Icon

Table 3 Wavelengths for Different Diffraction Orders Calculated with Grating Formula (13) for Planes 2

Equations (16)

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|S1|=H1·pˆ1×kˆi/sˆ1·pˆ1×kˆi,
S1Y=|S1|p1X/p1X2+p1Y21/2.
S1S=S1Y-d1cos ϕi/cosθ1-ϕi
S2S=S2X-d2cos ϕi/cosθ2-ϕi
S2X=|S2|p2Y/p2X2+p2Y21/2,
nˆ1=0, -sin θ1, cos θ1,  nˆ2=-sin θ2, 0, cos θ2
ET=Akˆd×Snˆ×E-ηkˆd×nˆ×H×expikkˆd-kˆi·rdS,
Hi,d=1η kˆi,d×Ei,d.
ET=E1+E2,
EjP=Akˆd×nˆj×Ej-ηkˆd×nˆj×HjmnexpiΔK · rdxdy,
rm=x, y, z1m-x-xmn1x/n1z
rn=x, y, -y-ynn1y/n1z
 expiΔK·rmdxdy=-expia11-expia12×expia13-1×expia14/b1ΔKx,
 expiΔK·rndxdy=-expia21-expia22×expia23-1×expia24/b2ΔKy,
LC=1.22λ/θFULL,
dsin ϕi+sin ϕd=mλ,

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