Abstract

The large male tarantula Pamphobeteus antinous is easily recognized at the presence of blue-violet iridescent bristles on some of the segments of its legs and pedipalps. The optical properties of these colored appendages have been measured and the internal geometrical structure of the bristles have been investigated. The coloration is shown to be caused by a curved coaxial multilayer which acts as a “cylindrical Bragg mirror”.

© 2013 OSA

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  29. E. Matijevic, R. H. Ottewill, and M. Kerker, “Light scattering by infinite cylinders, spider fibers,” J. Opt. Soc. Amer.51, 115–116 (1960).
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    [CrossRef]
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  33. O. Deparis, C. Vandenbem, M. Rassart, V. L. Welch, and J.-P. Vigneron, “Color-selecting reflectors inspired from biological periodic multilayer structures,” Opt. Express14 (8), 3547–3555 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  38. J. P. Vigneron, P. Simonis, A. Aiello, A. Bay, D. M. Windsor, J.-F. Colomer, and M. Rassart, “Reverse color sequence in the diffraction of white light by the wing of the male butterfly Pierella luna (Nymphalidae: Satyrinae),” Phys. Rev. E82, 021903 (2010).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  41. J. P. Vigneron, M. Rassart, C. Vandenbem, V. Lousse, O. Deparis, L. P. Biró, D. Dedouaire, A. Cornet, and P. Defrance, “Spectral filtering of visible light by the cuticle of metallic woodboring beetles and microfabrication of a matching bioinspired material,” Phys. Rev. E73, 041905 (2006).
    [CrossRef]
  42. D. P. Gaillot, O. Deparis, V. Welch, B. K. Wagner, J. P. Vigneron, and C. J. Summers, “Composite organic-inorganic butterfly scales: production of photonic structures with atomic layer deposition,” Phys. Rev. E78, 031922 (2008).
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    [CrossRef] [PubMed]

2011

L. P. Biró and J. P. Vigneron, “Photonic nanoarchitectures in butterflies and beetles: valuable sources for bioinspiration,” Laser & Phot. Rev.5, 27–51 (2011).
[CrossRef]

S. Yoshioka and S. Kinoshita, “Direct determination of the refractive index of natural multilayer systems,” Phys. Rev. E83, 051917 (2011).
[CrossRef]

C. E. Finlayson, C. Goddard, E. Papachristodoulou, D. R. E. Snoswell, A. Kontogeorgos, P. Spahn, G. P. Hellmann, O. Hess, and J. J. Baumberg, “Ordering in stretch-tunable polymeric opal fibers,” Opt. Express19(4), 3144–3154 (2011).
[CrossRef] [PubMed]

2010

D. G. Stavenga, M. A. Giraldo, and H. L. Leertouwer, “Butterfly wing colors: glass scales of Graphium sarpedon cause polarized iridescence and enhance blue/green pigment coloration of the wing membrane,” J. Exp. Biol.213, 1731–1739 (2010).
[CrossRef] [PubMed]

J. P. Vigneron, P. Simonis, A. Aiello, A. Bay, D. M. Windsor, J.-F. Colomer, and M. Rassart, “Reverse color sequence in the diffraction of white light by the wing of the male butterfly Pierella luna (Nymphalidae: Satyrinae),” Phys. Rev. E82, 021903 (2010).
[CrossRef]

2009

H. Ghiradella and M. Butler, “Many variations on a few themes: a broader look at iridescent scales (and feathers),” J. Roy. Soc. Interface6, S243–S251 (2009).
[CrossRef]

T. M. Trzeciak and P. Vukusic, “Photonic crystal fiber in the polychaete worm Pherusa sp.,” Phys. Rev. E80, 061908 (2009).
[CrossRef]

J. P. Vigneron, M. Ouedraogo, J.-F. Colomer, and M. Rassart, “Spectral sideband produced by a hemispherical concave multilayer on the African shield-bug Calidea panaethiopica (Scutelleridae),” Phys. Rev. E79, 021907 (2009).
[CrossRef]

M. Rassart, P. Simonis, A. Bay, O. Deparis, and J. P. Vigneron, “Scale coloration change following water absorption in the beetle Hoplia coerulea (Coleoptera),” Phys. Rev. E80, 031910 (2009).
[CrossRef]

E. R. Dufresne, H. Noh, V. Saranathan, S. G. J. Mochrie, H. Cao, and R. O. Prum, “Self-assembly of amorphous biophotonic nanostructures by phase separation,” Soft Matter5, 1792–1795 (2009).
[CrossRef]

A. E. Seago, P. Brady, J. P. Vigneron, and T. D. Schultz, “Gold bugs and beyond: a review of iridescence and structural colour mechanisms in beetles (Coleoptera),” J. R. Soc. Interf.6(Suppl. 2), S165–S184 (2009).
[CrossRef]

A. L. Ingram, A. D. Ball, A. R. Parker, O. Deparis, J. Boulenguez, and S. Berthier, “Characterization of the green iridescence on the chelicerae of the tube web spider, Segestria florentina (Rossi 1790) (Araneae, Segestriidae),” J. Arachnol.37, 68–71 (2009).
[CrossRef]

2008

R. Bertani, C. S. Fukushima, and P. I. da Silva Júnior, “Two new species of Pamphobeteus Pocock, 1901 (Araneae: Mygalomorphae: Theraphosidae) from Brazil, with a new type of stridulatory organ,” Zootaxa1826, 45–58 (2008).

S. Kinoshita, S. Yoshioka, and J. Miyazaki, “Physics of structural colors,” Rep. Prog. Phys.71, 076401 (2008).
[CrossRef]

D. P. Gaillot, O. Deparis, V. Welch, B. K. Wagner, J. P. Vigneron, and C. J. Summers, “Composite organic-inorganic butterfly scales: production of photonic structures with atomic layer deposition,” Phys. Rev. E78, 031922 (2008).
[CrossRef]

2007

M. F. Land, J. Horwood, M. L. M. Lim, and D. Li, “Optics of the ultraviolet reflecting scales of a jumping spider,” Proc. Roy. Soc. B274, 1583–1589 (2007).
[CrossRef]

2006

A. Kienle and R. Hibst, “Light guiding in biological tissue due to scattering,” Phys. Rev. Letters97, 018104 (2006).
[CrossRef]

J. P. Vigneron and V. Lousse, “Variation of a photonic crystal color with the Miller indices of the exposed surface,” Proc. SPIE6128, 61281G1 (2006).

J. P. Vigneron, M. Rassart, C. Vandenbem, V. Lousse, O. Deparis, L. P. Biró, D. Dedouaire, A. Cornet, and P. Defrance, “Spectral filtering of visible light by the cuticle of metallic woodboring beetles and microfabrication of a matching bioinspired material,” Phys. Rev. E73, 041905 (2006).
[CrossRef]

O. Deparis, C. Vandenbem, M. Rassart, V. L. Welch, and J.-P. Vigneron, “Color-selecting reflectors inspired from biological periodic multilayer structures,” Opt. Express14 (8), 3547–3555 (2006).
[CrossRef] [PubMed]

2005

S. Kinoshita and S. Yoshioka, “Structural colors in nature: the role of regularity and irregularity in the structure,” ChemPhysChem6, 1442–1459 (2005).
[CrossRef] [PubMed]

2003

A. R. Parker and D. R. McKenzie, “The cause of 50 million-year-old colour,” Proc. Roy. Soc. Lond. B270 (Suppl 2), S151–S153 (2003).
[CrossRef]

P. Vukusic and J. R. Sambles, “Photonic structures in biology,” Nature424, 852–855 (2003).
[CrossRef] [PubMed]

2001

A. R. Parker, R. C. McPhedran, D. R. McKenzie, L. C. Botten, and N. A. Nicorovici, “Photonic engineering: Aphrodite’s iridescence,” Nature409, 36–37 (2001).
[CrossRef] [PubMed]

1999

M. Srinivasarao, “Nano-optics in the biological world: beetles, butterflies, birds and moths,” Chem. Rev.99(7), 1935–1962 (1999).
[CrossRef]

P. Vukusic, “Quantified interference and diffraction in single Morpho butterfly scales,” Proc. Roy. Soc. Lond. B266 (1427), 1403–1411 (1999).
[CrossRef]

1998

A. R. Parker, D. R. Mc Kenzie, and M. C. J. Large, “Multilayer reflectors in animals using green and gold beetles as contrasting examples,” J. Exp. Biol.201, 1307–1313 (1998).

1991

D. M. Teixeira, G. Luigi, and I. M. Schloemp, “Aves brasileiras como presas de artropodes,” Ararajuba2, 69–74 (1991).

C. S. Kim and C. Yeh, “Scattering of an obliquely incident wave by a multilayered elliptical lossy dielectric cylinder,” Radio Sci.26(5), 1165–1176 (1991).
[CrossRef]

1989

R. D. Dahl and A. M. Granda, “Spectral sensitivities of photoreceptor in the ocelli of the tarantula, Aphonopelma chalcodes (Araneae, Theraphosidae),” J. Arachnol.17, 195–205 (1989).

1973

P. B. Clapham and M. C. Hutley, “Reduction of lens reflexion by the ’moth eye’ principle,” Nature244, 281–282 (1973).
[CrossRef]

1972

M. F. Land, “The physics and biology of animal reflectors,” Prog. Biophys. Mol. Biol.24, 75106 (1972).
[CrossRef]

1969

A. C. Neville and S. Caveney, “Scarabeid beetle exocuticle as an optical analogue of cholesteric liquid crystals,” Biol. Rev.44, 531–562 (1969).
[CrossRef] [PubMed]

1968

A. F. Huxley, “A theoretical treatment of the reflexion of light by multilayer structures,” J. Exp. Biol.48, 227–245 (1968).

1964

L. B. Evans, J. C. Chen, and S. W. Churchill, “Scattering of electromagnetic radiation by infinitely long, hollow, and coated cylinders,” J. Opt. Soc. Amer.54 (8), 1004–1007 (1964).
[CrossRef]

1960

E. Matijevic, R. H. Ottewill, and M. Kerker, “Light scattering by infinite cylinders, spider fibers,” J. Opt. Soc. Amer.51, 115–116 (1960).

1917

Lord Rayleigh, “On the reflection of light from a regularly stratified medium,” Proc. Roy. Soc. Lond. A93, 565–577 (1917).
[CrossRef]

1903

R. I. Pocock, “On some genera and species of South American Aviculariidae,” Ann. Mag. nat. Hist.11(7), 81–115 (1903).
[CrossRef]

Aiello, A.

J. P. Vigneron, P. Simonis, A. Aiello, A. Bay, D. M. Windsor, J.-F. Colomer, and M. Rassart, “Reverse color sequence in the diffraction of white light by the wing of the male butterfly Pierella luna (Nymphalidae: Satyrinae),” Phys. Rev. E82, 021903 (2010).
[CrossRef]

Ball, A. D.

A. L. Ingram, A. D. Ball, A. R. Parker, O. Deparis, J. Boulenguez, and S. Berthier, “Characterization of the green iridescence on the chelicerae of the tube web spider, Segestria florentina (Rossi 1790) (Araneae, Segestriidae),” J. Arachnol.37, 68–71 (2009).
[CrossRef]

Baumberg, J. J.

Bay, A.

J. P. Vigneron, P. Simonis, A. Aiello, A. Bay, D. M. Windsor, J.-F. Colomer, and M. Rassart, “Reverse color sequence in the diffraction of white light by the wing of the male butterfly Pierella luna (Nymphalidae: Satyrinae),” Phys. Rev. E82, 021903 (2010).
[CrossRef]

M. Rassart, P. Simonis, A. Bay, O. Deparis, and J. P. Vigneron, “Scale coloration change following water absorption in the beetle Hoplia coerulea (Coleoptera),” Phys. Rev. E80, 031910 (2009).
[CrossRef]

Bertani, R.

R. Bertani, C. S. Fukushima, and P. I. da Silva Júnior, “Two new species of Pamphobeteus Pocock, 1901 (Araneae: Mygalomorphae: Theraphosidae) from Brazil, with a new type of stridulatory organ,” Zootaxa1826, 45–58 (2008).

Berthier, S.

A. L. Ingram, A. D. Ball, A. R. Parker, O. Deparis, J. Boulenguez, and S. Berthier, “Characterization of the green iridescence on the chelicerae of the tube web spider, Segestria florentina (Rossi 1790) (Araneae, Segestriidae),” J. Arachnol.37, 68–71 (2009).
[CrossRef]

Biró, L. P.

L. P. Biró and J. P. Vigneron, “Photonic nanoarchitectures in butterflies and beetles: valuable sources for bioinspiration,” Laser & Phot. Rev.5, 27–51 (2011).
[CrossRef]

J. P. Vigneron, M. Rassart, C. Vandenbem, V. Lousse, O. Deparis, L. P. Biró, D. Dedouaire, A. Cornet, and P. Defrance, “Spectral filtering of visible light by the cuticle of metallic woodboring beetles and microfabrication of a matching bioinspired material,” Phys. Rev. E73, 041905 (2006).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley and Sons, New York, 1983), pp. 194–219.

Botten, L. C.

A. R. Parker, R. C. McPhedran, D. R. McKenzie, L. C. Botten, and N. A. Nicorovici, “Photonic engineering: Aphrodite’s iridescence,” Nature409, 36–37 (2001).
[CrossRef] [PubMed]

Boulenguez, J.

A. L. Ingram, A. D. Ball, A. R. Parker, O. Deparis, J. Boulenguez, and S. Berthier, “Characterization of the green iridescence on the chelicerae of the tube web spider, Segestria florentina (Rossi 1790) (Araneae, Segestriidae),” J. Arachnol.37, 68–71 (2009).
[CrossRef]

Brady, P.

A. E. Seago, P. Brady, J. P. Vigneron, and T. D. Schultz, “Gold bugs and beyond: a review of iridescence and structural colour mechanisms in beetles (Coleoptera),” J. R. Soc. Interf.6(Suppl. 2), S165–S184 (2009).
[CrossRef]

Breene, R. G.

R. G. Breene, D. A. Dean, J. C. Cokendolpher, and B. H. Reger, “Tarantulas of Texas: Their medical importance, and world-wide bibliography to the Theraphosidae (Araneae),” (American Tarantula Society, South Padre Island, Texas,1996).

Butler, M.

H. Ghiradella and M. Butler, “Many variations on a few themes: a broader look at iridescent scales (and feathers),” J. Roy. Soc. Interface6, S243–S251 (2009).
[CrossRef]

Cao, H.

E. R. Dufresne, H. Noh, V. Saranathan, S. G. J. Mochrie, H. Cao, and R. O. Prum, “Self-assembly of amorphous biophotonic nanostructures by phase separation,” Soft Matter5, 1792–1795 (2009).
[CrossRef]

Caveney, S.

A. C. Neville and S. Caveney, “Scarabeid beetle exocuticle as an optical analogue of cholesteric liquid crystals,” Biol. Rev.44, 531–562 (1969).
[CrossRef] [PubMed]

Chen, J. C.

L. B. Evans, J. C. Chen, and S. W. Churchill, “Scattering of electromagnetic radiation by infinitely long, hollow, and coated cylinders,” J. Opt. Soc. Amer.54 (8), 1004–1007 (1964).
[CrossRef]

Churchill, S. W.

L. B. Evans, J. C. Chen, and S. W. Churchill, “Scattering of electromagnetic radiation by infinitely long, hollow, and coated cylinders,” J. Opt. Soc. Amer.54 (8), 1004–1007 (1964).
[CrossRef]

Clapham, P. B.

P. B. Clapham and M. C. Hutley, “Reduction of lens reflexion by the ’moth eye’ principle,” Nature244, 281–282 (1973).
[CrossRef]

Cokendolpher, J. C.

R. G. Breene, D. A. Dean, J. C. Cokendolpher, and B. H. Reger, “Tarantulas of Texas: Their medical importance, and world-wide bibliography to the Theraphosidae (Araneae),” (American Tarantula Society, South Padre Island, Texas,1996).

Colomer, J.-F.

J. P. Vigneron, P. Simonis, A. Aiello, A. Bay, D. M. Windsor, J.-F. Colomer, and M. Rassart, “Reverse color sequence in the diffraction of white light by the wing of the male butterfly Pierella luna (Nymphalidae: Satyrinae),” Phys. Rev. E82, 021903 (2010).
[CrossRef]

J. P. Vigneron, M. Ouedraogo, J.-F. Colomer, and M. Rassart, “Spectral sideband produced by a hemispherical concave multilayer on the African shield-bug Calidea panaethiopica (Scutelleridae),” Phys. Rev. E79, 021907 (2009).
[CrossRef]

Cornet, A.

J. P. Vigneron, M. Rassart, C. Vandenbem, V. Lousse, O. Deparis, L. P. Biró, D. Dedouaire, A. Cornet, and P. Defrance, “Spectral filtering of visible light by the cuticle of metallic woodboring beetles and microfabrication of a matching bioinspired material,” Phys. Rev. E73, 041905 (2006).
[CrossRef]

da Silva Júnior, P. I.

R. Bertani, C. S. Fukushima, and P. I. da Silva Júnior, “Two new species of Pamphobeteus Pocock, 1901 (Araneae: Mygalomorphae: Theraphosidae) from Brazil, with a new type of stridulatory organ,” Zootaxa1826, 45–58 (2008).

Dahl, R. D.

R. D. Dahl and A. M. Granda, “Spectral sensitivities of photoreceptor in the ocelli of the tarantula, Aphonopelma chalcodes (Araneae, Theraphosidae),” J. Arachnol.17, 195–205 (1989).

Dean, D. A.

R. G. Breene, D. A. Dean, J. C. Cokendolpher, and B. H. Reger, “Tarantulas of Texas: Their medical importance, and world-wide bibliography to the Theraphosidae (Araneae),” (American Tarantula Society, South Padre Island, Texas,1996).

Dedouaire, D.

J. P. Vigneron, M. Rassart, C. Vandenbem, V. Lousse, O. Deparis, L. P. Biró, D. Dedouaire, A. Cornet, and P. Defrance, “Spectral filtering of visible light by the cuticle of metallic woodboring beetles and microfabrication of a matching bioinspired material,” Phys. Rev. E73, 041905 (2006).
[CrossRef]

Defrance, P.

J. P. Vigneron, M. Rassart, C. Vandenbem, V. Lousse, O. Deparis, L. P. Biró, D. Dedouaire, A. Cornet, and P. Defrance, “Spectral filtering of visible light by the cuticle of metallic woodboring beetles and microfabrication of a matching bioinspired material,” Phys. Rev. E73, 041905 (2006).
[CrossRef]

Deparis, O.

M. Rassart, P. Simonis, A. Bay, O. Deparis, and J. P. Vigneron, “Scale coloration change following water absorption in the beetle Hoplia coerulea (Coleoptera),” Phys. Rev. E80, 031910 (2009).
[CrossRef]

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A. E. Seago, P. Brady, J. P. Vigneron, and T. D. Schultz, “Gold bugs and beyond: a review of iridescence and structural colour mechanisms in beetles (Coleoptera),” J. R. Soc. Interf.6(Suppl. 2), S165–S184 (2009).
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Figures (12)

Fig. 1
Fig. 1

(a) The male tarantula Pamphobeteus antinous displays a vivid violet-blue color on the three leg segments closest to its cephalothorax. (b) Blue areas on the dorsal side of the mature male Pamphobeteus antinous. Colored patches appear on the three inner segments of the legs and pedipalps, on the chelicerae and, less visible, on the dorsal cuticle of the thorax. The blue color originates from specialized bristles covering the cuticle. These bristles are roughly parallel, aligned along the length of the spider’s leg segment. (c) Macrophotography of the bristles on the dorsal side of the pedipalp’s femurs, oriented at a small angle to the symmetry plane of the body. (d) Optical microscope view of the blue setae, suggesting a roughly cylindrical shape. At this scale, individual setae are visible and a slight variation of color, from blue to violet is observable. Other, uncolored bristles also appear in the field.

Fig. 2
Fig. 2

(a) The different types of setae, as are revealed by scanning electron microscopy. Most of the setae are asymmetrical in cross section, with one side being cylindrical (A) and the other side flattened and sculpted (B) in a way that recalls the standard ridge-crossrib structure displayed by relatively unspecialized scales in other arthropods. Bristle C shows the sharp extensions typical of an “urticating bristle”, designed to penetrate soft surfaces and produce irritation. (b) The whole cross-section of a blue seta, showing the layered outer cortex that surrounds the structure, the thick homogeneous substrate and the cylindrical cavity, all of which are centered on the axis of the cylinder. (c) Detail of the multilayered structure : a few (around 4) cylindrical sheets are repeated radially. The insert shows details at a larger magnification which suggests that the space between the sheets is essentially empty. (d) On this fractured cross-section, some sheets are protruding in such a way as to show their outer surface. This image also suggests a solid/air interface. (e) This view of the perforated part of the bristle reveals that the multilayer is also present there, providing blue-to-violet iridescent coloration.

Fig. 3
Fig. 3

Sections of the blue setae, viewed with the transmission electron microscope (TEM). The peripheral multilayer as seen (a) through a section at right angle from the seta axis and (b) through a section nearly parallel to the axis. The measurement of the multilayer period on these sections confirm the values obtained from scanning electron microscopy images. The slight opacity of the lighter layers is interpreted as the presence of infiltrated embedding medium between the darker cylindrical chitin sheets.

Fig. 4
Fig. 4

(a) The bristle coloring structure, viewed through a window-like perforation on the cylinder’s surface. The outer surface of the concentric layers is smooth except for random perforations. However, the edges of the sheets are highly structured, laterally, suggesting that the smooth surface hides a fine pattern of hard rods separated by air gaps. (b) An idealized model of the photonic structure suggested by SEM and TEM, with a thick covering layer, a multilayer build from winding chitin rods lying under a thin chitin sheet with binding bridges and a thick substrate. The structure is represented upside down (cover-layer below) in order to reveal the sheet patterning. This model neglects disorder and the cylindrical curvature. (c) The parameters that tune the optical properties of this ideal structure are as follows: h is the thickness of the cover layer, a is the total multilayer period, w is the thickness of the thin binding plate, b is the thickness of the chitin sheet, including the binding plate, c is the width of the chitin bars. r is an artificial lateral period for representing the pattern of rods in a square lattice symmetry.

Fig. 5
Fig. 5

Calculated reflection spectrum (solid line), based on the morphological data obtained by electron microscopy. The structure is the three-dimensional model described in Fig. 4(c). The dashed curve corresponds to the same calculation with all three-dimensional features – bridges between the sheets and the groove between the chitin bars – suppressed. In this case, the spectrum is exactly as one would expect from a one-dimensional multilayer. The red shift is consistent with the increase in the average refractive index.

Fig. 6
Fig. 6

The model’s geometry. The cylindrical fiber is set along the z axis (which is also the cylinder’s axis) and the incident beam (along k⃗in) lies in the plane containing the x axis. Due to conservation laws, the scattered beam (along k⃗out) lies on the surface of a cone and makes the same angle to the xy plane as the incident beam. Once the incidence angle θ is set, the possible emergent directions are described by a single parameter, the azimuthal angle α.

Fig. 7
Fig. 7

The projection of the elements of Fig. 6 in the xy plane, showing the direction of the vector N⃗ bisecting the angle between −k⃗in and k⃗out. This shows that the scattering by the fiber, under the invariance conditions which conserve the norm and the z component of the wave vector, can be seen as a reflection on the fiber surface, from the point where this surface meets the normal N⃗.

Fig. 8
Fig. 8

Dominant fundamental scattered wavelength, for various values of the incidence angle θ, measured from the xy plane, normal to the fiber, and for various azimuthal directions α of the scattered beam in the outgoing wave cone. The iridescence (change of color with viewing direction is maximal for a full reflection in the longitudinal direction of the fiber (α = 180°) and minimal for a tangential, grazing transit (α = 0°). For parameters matching those of the multilayer found on Pamphobeteus antinous, the scattered wavelengths span a blue-to-ultraviolet range.

Fig. 9
Fig. 9

Polar plot of the cylindrical Bragg mirror iridescence. The outgoing wave direction is determined by the angle θ to the xy plane (the same as for the incident wave) and the azimuthal angle α. The black area corresponds to the direction where, for humans, no coloration occurs, because the scattered wavelength is ultraviolet, below 380 nm. The lighter shades area indicate visible light, blue in the central region and violet near the border. The plot is based on Eq. (8).

Fig. 10
Fig. 10

Measured hemispheric reflectance spectrum of a blue area on the spider’s cuticle, under near normal incidence. The distribution of reflected wavelengths peak near 430 nm, due to iridescence. This spectrum integrates contributions from all outgoing directions.

Fig. 11
Fig. 11

Iridescence of the “blue” setae of the spider Pamphobeteus antinous. The wavelength selected by the cylindrical Bragg mirror experience a blue shift when the incidence angle (measured from the normal to the fiber) is increased. The spectra reported are obtained in a longitudinal specular reflection geometry α = 180°. Solid line: θ = 15°; dashed: θ = 30°; dot-dash: θ = 45°; dot-dot-dot-dash: θ = 60°; dotted: θ = 75°.

Fig. 12
Fig. 12

Calculation of the unpolarized reflectance spectrum of a perfect multilayer mirror, avoiding all effects of disorder, for a longitudinal specular reflection geometry, under conditions similar to those in Fig. 11. Solid line: θ = 15°; dashed: θ = 30°; dot-dash: θ = 45°; dot-dot-dot-dash: θ = 60°; dotted: θ = 75°. The structure is assumed flat, with a 220 nm black chitin cover layer above four bilayers (46 nm air and 100 nm black chitin) and a thick black chitin substrate. Black chitin is absorbent and dispersive [19]. Note that the calculated reflectivity is normalized by the incident intensity, while the reflection factor in Fig. 11 is normalized by the diffuse reflection from a white PTFE standard.

Equations (8)

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λ = 2 a n ¯ m
n ¯ = n 1 d 1 + n 2 d 2 d 1 + d 2
k in = ω c ( cos θ , 0 , sin θ )
k out = ω c ( cos θ cos α , cos θ sin α , sin θ )
cos 2 δ = ( k in ) k out ( ω c ) 2 .
cos δ = cos θ sin ( α 2 )
N = ( sin ( α 2 ) , cos ( α 2 ) , 0 )
λ = 2 a ε ¯ 1 + sin 2 ( α 2 ) cos 2 θ m

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