Royal Society Publishing

Gyroid cuticular structures in butterfly wing scales: biological photonic crystals

K Michielsen, D.G Stavenga
Published 6 January 2008.DOI: 10.1098/rsif.2007.1065

Article Figures & Data

Figures

  • Figure 1
    Figure 1

    (a–c) Unit cells of the P, D and G nodal surfaces constructed from equations (2.2)–(2.4), respectively, with t=0. These surfaces divide the cubic structure into two regions forming two continuous interpenetrating networks in the system. (d–f) Skeletal graphs for one of the two distinct networks formed by the P, D and G nodal surfaces. The skeletal graphs show the connectivity of the channels in the network. In the P-, D- and G-structures, these channels are six-, four- and threefold connected, respectively.

  • Figure 2
    Figure 2

    SEM micrograph showing a longitudinal view of a fractured scale of P. sesostris. (Reproduced with permission from Ghiradella (1994).) Scale bar, 1 μm.

  • Figure 3
    Figure 3

    (a) TEM micrograph showing a cross section through the scale of P. sesostris. (Reproduced with permission from Vukusic & Sambles (2003).) The numbers indicate various domains in the cuticle crystal. The vertical lines indicate the position of the grain boundaries. Scale bar, 2.5 μm. (b) Computer-simulated projections for a G-structure with t=−0.3 (equations (2.4) and (4.1)). The projections are generated from sections with a thickness of 0.15a (a denotes the length of the cubic unit cell) along the directions: 1, [1 2 3]; 2, [1 1 11]; 3, Embedded Image; 4, [4 9 12]; 5, Embedded Image; 6, [2 4 9]; 7, Embedded Image; 8, [7 7 10]. The chitin (cuticle) structures appear black in both the micrograph and the simulation.

  • Figure 4
    Figure 4

    (a–c) Gyroid structure (eight unit cells) constructed from equations (2.4) and (4.1). For t=0.0, −0.3 and −1.0, the cuticle volume fractions are 0.50, 0.40 and 0.17, respectively. (d–f) Projections of the gyroid structures along the direction [0 0 1]. For t=0.0, −0.3 and −1.0, the circular holes have a diameter of approximately a/4, a/3 and a/2, respectively.

  • Figure 5
    Figure 5

    (a) TEM micrograph showing a transverse section through a green scale of C. rubi. (Reproduced with permission from Ghiradella & Radigan (1976).) The numbers indicate various domains in the cuticle crystal. The vertical line indicates the position of the grain boundary. Scale bar, 1 μm. (b) Computer-simulated projections for a G-structure with t=−1.0 (equations (2.4) and (4.1)). The projections are generated from sections with a thickness of 0.2a (a denotes the length of the cubic unit cell) along the directions: 1, Embedded Image; 2, [0 3 10]. The chitin (cuticle) structures appear black in both the micrograph and the simulation.

  • Figure 6
    Figure 6

    (a) TEM micrograph showing a longitudinal section through a green scale of C. rubi. (Reproduced with permission from Ghiradella & Radigan (1976).) The numbers indicate various domains in the cuticle crystal. The vertical lines indicate the position of the grain boundaries. Scale bar, 1 μm. (b) Computer-simulated projections for a G-structure with t=−1.0 (equations (2.4) and (4.1)). The projections are generated from sections with a thickness of 0.2a (a denotes the length of the cubic unit cell) along the directions: 1, [0 3 5]; 2, [2 7 9]; 3, Embedded Image. The chitin (cuticle) structures appear black in both the micrograph and the simulation.

  • Figure 7
    Figure 7

    TEM micrograph of whole mount of C. rubi scale. (Reproduced with permission from Ghiradella & Radigan (1976).) Scale bar, 1 μm.

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