Abstract

Scales on the wings of certain insects, such as Trichoplusia orichalcea, exhibit a surface microstructure resembling a fine diffraction grating. Diffraction of incident light by this structure is responsible for many of the optical properties of the wings of this moth, such as the metallic yellow color and the almost-specular reflection and polarization properties of the scattered radiation. It is shown that by the use of null ellipsometry the polarization characteristics can be used to obtain the optical constants of the scale material. Theoretical considerations and suitable experimental conditions are discussed and evaluated.

© 1996 Optical Society of America

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References

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  1. H. Ghiradella, “Light and color on the wing: structural colors in butterflies and moths,” Appl. Opt. 30, 3492–3500 (1991).
    [CrossRef] [PubMed]
  2. 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]
  3. 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]
  4. S. Silver, Microwave Antenna Theory and Design (McGraw-Hill, New York, 1947), p. 161.
  5. R. Guenter, Modern Optics (Wiley, New York, 1990), pp. 124–128.
  6. D. Mossakowski, “Reflection measurements used in the analysis of structural colors of beetles,” J. Microscopy 116, 351–364 (1979).
    [CrossRef]
  7. M. F. Land, “The physics and biology of animal reflectors,” Prog. Biophys. 24, 75–106 (1972).
    [CrossRef]
  8. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1989), pp. 153–169.
  9. D. H. Loescher, R. J. Detry, M. J. Clauser, “Least squares analysis of the film-substrate problem in ellipsometry,” J. Opt. Soc. Am. 61, 1230–1235 (1971).
    [CrossRef]

1995 (1)

1991 (1)

1979 (1)

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

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]

1971 (1)

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]

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1989), pp. 153–169.

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]

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1989), pp. 153–169.

Brink, D. J.

Clauser, M. J.

Detry, R. J.

Ghiradella, H.

Guenter, R.

R. Guenter, Modern Optics (Wiley, New York, 1990), pp. 124–128.

Land, M. F.

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

Lee, M. E.

Loescher, D. H.

Möller, A.

Mossakowski, D.

D. Mossakowski, “Reflection measurements used in the analysis of structural colors of beetles,” J. Microscopy 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. (2)

J. Microscopy (1)

D. Mossakowski, “Reflection measurements used in the analysis of structural colors of beetles,” J. Microscopy 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 (3)

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1989), pp. 153–169.

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

R. Guenter, Modern Optics (Wiley, New York, 1990), pp. 124–128.

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Figures (5)

Fig. 1
Fig. 1

(a) Scanning electron microscope micrograph showing a top view of part of a scale from Trichoplusia orichalcea. The broad white vertical lines are raised ridges spaced 1.6 μm apart (horizontal length marker). These ridges are connected with a herringbone pattern of microribs spaced by 140 nm. The microribs are approximately 65 nm high, and the center of the herringbone pattern is depressed by approximately 200 nm below the level of the ridges. (b) Oblique view of a wing scale. The scale is not viewed at 90° to the raised ridges, but along the inclined line drawn in (a). Consequently the length marker is now 2.0 μm instead of 1.6 μm.

Fig. 2
Fig. 2

Schematic layout of the experimental setup: A1–A3, circular apertures; A4, slit aperture; L1–L3, lenses; P, polarizer; A, analyzer; C, quarter-wave plate; BS, beam splitter; PMT, photomultiplier; W, ellipsometer table with the mounted wing.

Fig. 3
Fig. 3

Angular dependence of scattered intensity at normal incidence for vertically [electric field parallel to raised ridges in Fig. 1(a)] and horizontally polarized light.

Fig. 4
Fig. 4

(a) Ellipsometer transmission (photomultiplier signal) versus analyzer and polarizer angle. The wavelengths is 488 nm, and the angle of incidence is 50°. (b) Ellipsometer transmission versus analyzer and polarizer angle. The wavelength is 633 nm, and the angle of incidence is 50°.

Fig. 5
Fig. 5

(a) Measured ellipsometer null angle Δ versus angle of incidence for 488 and 633 nm. The solid and the dashed curves represent calculated values when the subsurface structure of the scales is included or ignored, respectively. (b) Measured ellipsometer null angle Ψ versus angle of incidence for 488 and 633 nm. The solid and the dashed curves represent calculated values when the subsurface structure of the scales is included or ignored, respectively.

Tables (1)

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Table 1 Calculated N and Q Values by Depression Angle

Equations (12)

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( r P r S ) j = tan Ψ j exp ( i Δ j ) ,
Q = j ( Ψ j - Ψ j δ Ψ j ) + ( Δ j - Δ j δ Δ j ) 2 ,
E D = A k ^ d × S [ n ^ × E - η k ^ d × ( n ^ × H ) ] × exp [ i k ( k ^ d - k ^ i ) · r ] d S ,
E k = ( E k + E k - ) ,
M I = 1 C [ A B B A ] S , P ,             M T = [ exp ( i δ ) 0 0 exp ( - i δ ) ] ,
A S = N k cos ϕ k + N l cos ϕ l , A P = N l cos ϕ k + N k cos ϕ l ,
B S = N k cos ϕ k - N l cos ϕ l , B P = N l cos ϕ k - N k cos ϕ l , C = 2 N k cos ϕ k , δ = 2 π N k cos ϕ k d k / λ 0 .
( E 0 + E 0 - ) S , P = M I ( 0 , 1 ) M T ( 1 ) M I ( 1 , 2 ) M I ( k , l ) ( E l + E l - ) S , P = [ a b c d ] S , P ( E l + E l - ) S , P .
r S , P = E 0 - ( s , p ) E 0 + ( s , p ) = c S , P a S , P .
r P , S = B P , S A P , S .
C μ v = j A μ j A v j δ j 2 ,
σ μ = ( Γ μ μ ) 1 / 2 ,             Γ = C - 1 .

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