Abstract

On the wing of the moth Trichoplusia orichalcea a prominent, apparently highly reflective, golden spot can be seen. Scales from this area of the wing exhibit a regular microstructure resembling a submicrometer herringbone pattern. We show that a diffraction process from this structure is responsible for the observed optical properties, such as directionality, brightness variations, polarization, and color.

© 1995 Optical Society of America

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References

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  1. T. F. Anderson, A. G. Richards, “An electron microscope study of some structural colors of insects,” J. Appl. Phys. 13, 748–758 (1942).
    [CrossRef]
  2. C. H. Greenwalt, W. Brandt, D. D. Friel, “Iridescent colors of hummingbird feathers,” J. Opt. Soc. Am. 50, 1005–1013 (1960).
    [CrossRef]
  3. D. Mossakowski, “Reflection measurements used in the analysis of structural colours of beetles,” J. Microsc. 116, 351–364 (1979).
    [CrossRef]
  4. H. Ghiradella, “Light and color on the wing: Structural colors in butterflies and moths,” Appl. Opt. 30, 4392–3500 (1991).
    [CrossRef]
  5. M. F. Land, “The physics and biology of animal reflectors,” Prog. Biophys. 24, 75–106 (1972).
    [CrossRef]
  6. 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).
    [CrossRef]
  7. R. Petit, The Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980), p. 10.
  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]

1991 (1)

H. Ghiradella, “Light and color on the wing: Structural colors in butterflies and moths,” Appl. Opt. 30, 4392–3500 (1991).
[CrossRef]

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. Entomol. Ser. A 49, 149–154 (1975).
[CrossRef]

1972 (2)

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]

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

1960 (1)

1942 (1)

T. F. Anderson, A. G. Richards, “An electron microscope study of some structural colors of insects,” J. Appl. Phys. 13, 748–758 (1942).
[CrossRef]

Anderson, T. F.

T. F. Anderson, A. G. Richards, “An electron microscope study of some structural colors of insects,” J. Appl. Phys. 13, 748–758 (1942).
[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]

Brandt, W.

Friel, D. D.

Ghiradella, H.

H. Ghiradella, “Light and color on the wing: Structural colors in butterflies and moths,” Appl. Opt. 30, 4392–3500 (1991).
[CrossRef]

Greenwalt, C. H.

Land, M. F.

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

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).
[CrossRef]

Mossakowski, D.

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

Petit, R.

R. Petit, The Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980), p. 10.

Richards, A. G.

T. F. Anderson, A. G. Richards, “An electron microscope study of some structural colors of insects,” J. Appl. Phys. 13, 748–758 (1942).
[CrossRef]

Silver, S.

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

Appl. Opt. (1)

H. Ghiradella, “Light and color on the wing: Structural colors in butterflies and moths,” Appl. Opt. 30, 4392–3500 (1991).
[CrossRef]

J. Appl. Phys. (1)

T. F. Anderson, A. G. Richards, “An electron microscope study of some structural colors of insects,” J. Appl. Phys. 13, 748–758 (1942).
[CrossRef]

J. Entomol. Ser. A (1)

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).
[CrossRef]

J. Microsc. (1)

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

J. Opt. Soc. Am. (1)

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)

R. Petit, The Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980), p. 10.

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

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Figures (8)

Fig. 1
Fig. 1

SEM micrographs of the scales of the highly reflective wing patch of Trichoplusia orichalcea: (a) Micrograph showing a top view of part of a scale. The vertical lines are raised ridges spaced 1.6 μm apart (represented by the solid bar) and they are connected with a herringbone pattern of microribs spaced 140 nm apart. (b) Oblique view of a wing scale. The solid bar represents a length of 0.5 μm. The broken, diagonal bar in (a) indicates the relative direction of the view presented in this micrograph.

Fig. 2
Fig. 2

Schematic outline of the simplified wing diffracting structure. Line CC represents a valley between the raised ridges shown in Fig. 1(a). Numbers 1–5 represent planes of the wing scale. Distance d is the height of a microrib above the plane of the wing scale in the z direction, and h is the width of a microrib along the y axis. If the depression of line CC were ignored, planes 5 and 6 would correspond to the plane of the wing scale.

Fig. 3
Fig. 3

Schematic diagram of the experimental layout showing the mounted wing (W), which can be rotated about the y and z axes, the monochromator (M), the photomultiplier (P), the tungsten lamp (T), the collimating telescope (C), polarizers (P1 and P2), and the collecting lens (L).

Fig. 4
Fig. 4

Angular spread of the diffracted beam: (a) Experimental measurement for line CC oriented vertically for 0° (0) and −90° (90) rotations, in the plane of the wing, for both s(S) and p(P) polarizations. The wavelength is 550 nm. (b) Calculated angular spread for line CC oriented vertically for 0° (0) and 90° (90) rotations and both s(S) and p(P) polarizations. The wavelength is 550 nm.

Fig. 5
Fig. 5

Dependence of the diffracted power and the diffraction efficiency on the wing orientation (rotation in the plane of the wing. Rotation angle of 0° for line CC oriented vertically. (a) Measured dependence for s-polarized incident light at angles of incidence of 30°, 45°, and 60° and a wavelength of 550 nm. The units on the y axis are the photomultiplier output normalized to a direct reading without reflection from the moth wing. However, because the light-collecting efficiency may differ between the collimated direct beam and the diffracted beam, the units should be regarded as arbitrary (au). They can, however, be used for comparisons with Figs. 5(a), 5(b), and 6(a). (b) Measured dependence for p-polarized incident light under the same conditions as for (a). (c) Calculated dependence of the diffraction efficiency under the same conditions as for (a) and (b).

Fig. 6
Fig. 6

Measured and calculated spectral distributions of diffracted light: (a) Measured distributions for s- (solid curves) and p-polarized (dashed curves) incident light at rotation angles of 0°, −30°, −60°, and −90°, indicated by the numbers in parentheses. The angle of incidence is 60°. (b) Calculated distributions for the same rotation angles shown in (a) for s-polarized light (S30, S0, S60, and S90) and for p-polarized light (P30, P0, P60, and P90).

Fig. 7
Fig. 7

Calculated dependence of the diffraction efficiency for s-and p-polarized incident light for angle of incidence θi. The diffraction angle is equal to θi, the wavelength is 550 nm, and the rotation angle is 90°.

Fig. 8
Fig. 8

Calculated influence of variations in parameter values: (a) On the diffraction efficiency for line CC oriented vertically for a variation equal to (PP0/P0) 100. Parameters changed are the spatial period of the pattern (2h + f) (solid curve), the fraction of area taken up by planes 5 and 6 [f/(2h + f)] (dashed curve), the height of the microribs (d) (dotted curve), and the depression of the center of a strip (ϕd) (dotted–dashed curve). The wavelength is 550 nm, and the angle of incidence is 60°. (b) On the diffraction efficiency for the wing rotated by 90° in its own plane. The curves are identified as in (a).

Equations (12)

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E ( P ) = A k ˆ d × S [ n ˆ × E η k ˆ d × ( n ˆ × H ) ] × exp [ i k ( k ˆ d k ˆ i ) · r ] d S ,
H i , d = 1 η k ˆ i , d × E i , d .
u ˆ 1 = ( + cos ϕ b , + sin ϕ b , 0 ) , ν ˆ 1 = ( cos β sin ϕ b , + cos β cos ϕ b , 1 cos 2 β ) ,
u ˆ 2 = u ˆ 1 , ν ˆ 2 = ( + cos β sin ϕ b , cos β cos ϕ b , 1 cos 2 β ) ,
u ˆ 3 = ( + cos ϕ b , sin ϕ b , 0 ) , ν ˆ 3 = ( + cos β sin ϕ b , + cos β cos ϕ b , 1 cos 2 β ) ,
u ˆ 4 = u ˆ 3 , ν ˆ 4 = ( cos β sin ϕ b , cos β cos ϕ b , 1 cos 2 β ) ,
n ˆ j = u ˆ j × ν ˆ j , j = 1 , , 4 , n ˆ 5 = n ˆ 6 = ( 0 , 0 , 1 ) .
[ n j x n j z ] = [ cos ϕ d ± sin ϕ d sin ϕ d cos ϕ d ] [ n j x n j z ] , j = 1 , , 6 ,
[ n j x n j z ] = [ cos ϕ r sin ϕ r sin ϕ r cos ϕ r ] [ n j x n j z ] , j = 1 , , 6 .
r p q = [ x , y , z p q n j x n j z ( x x p ) n j y n j z ( y y q ) ] ,
E ( P ) = A j = 1 6 k ˆ d × [ ( n ˆ j × E j ) η k ˆ d × ( n ˆ j × H j ) ] × p , q exp [ i k ( k ˆ d k ˆ i ) · r p q ] d x d y .
exp [ i k ( k ˆ d k ˆ i ) · r p q ] d x d y = l w ( exp ( i θ 1 ) 1 θ 1 ) ( exp ( i θ 2 ) 1 θ 2 ) exp ( i θ 3 ) ,

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