Reverse color sequence in the diffraction of white light by the wing of the male butterfly Pierella luna (Nymphalidae: Satyrinae)

The butterfly Pierella luna (Nymphalidae) shows an intriguing rainbow iridescence effect: the forewings of the male, when illuminated along the axis from the body to the wing tip, decompose a white light beam as a diffraction grating would do. Violet light, however, emerges along a grazing angle, near the wing surface, while the other colors, from blue to red, exit respectively at angles progressively closer to the direction perpendicular to the wing plane. This sequence is the reverse of the usual decomposition of light by a grating with a periodicity parallel to the wing surface. It is shown that this effect is produced by a macroscopic deformation of the entire scale, which curls in such a way that it forms a “vertical” grating, perpendicular to the wing surface, and functions in transmission instead of reflection.

Figure 1

(Color online) The male butterfly Pierella luna, subject of the present study, at rest on the ground. ©Steve Collins, reproduced with permission.

Figure 2

(Color online) The male butterfly Pierella luna shows, under most illumination angles, an inconspicuous brown color that closely matches the colors of the forest floor. However, under very specific illumination and viewing angles, rainbow iridescence appears in the central portion of the forewing, the area inside the dashed line in the lower view.

Figure 3

(Color online) Male and female Pierella luna butterflies viewed at different angles. The male is behind the female. The illumination is $45°$ from the normal, and originates from a point opposite to the viewer. As we lower our angle of view with a fixed light source, the delineated area on the forewing of the male butterfly displays a rainbow of iridescence, covering nearly the entire human spectrum: in positions (a), (b), (c), (d), and (e), red, yellow, green, cyan, and blue are perceived, respectively. The female lacks iridescence.

Figure 4

Spectral distribution of the light measured from the iridescent portion of the wing of the male butterfly Pierella luna at various viewing angles $\varphi$ (emergence angle measured from the vertical). The illumination source (oriented toward the wing tip at $45°$) and the probe are opposite with regard to the vertical, in the measurement plane.

Figure 5

(Color online) This figure shows the three types of scales found on the dorsal surface of male Pierella luna forewings. Type (1) (see insert) lies flat against the wing membrane in the normal, noniridescent portion of the wing; type (2) found in the iridescent portion of the wing is curled, with the distal end protruding high above the wing surface; type (3) is a narrow tube, also protruding high above the wing surface. The zone occupied by curled scales (c) is sharply delineated (as indicated by the solid line) from that occupied by flat scales (f). Those parts of the wings that are not iridescent (including the ventral sides) bear resemblance to the (f) areas. On the lower part of the figure, a light-microscope grazing angle view shows that the iridescence originates from the curled scales of type (2). The tubular scales-type (3)-appear dark.

Figure 6

Scanning electron microscope image of a curled scale of a male Pierella luna, showing its structure. The ribs (vertical structures shown in the lower portion of the figure) and the cross-ribs (horizontal) are attached directly to the scale basal membrane. We note the absence of any other structure (often referred to as a “pepper-pot”) between the net of ribs and cross-ribs and the basal membrane. The distance between the cross-ribs is small, on the average, 440 nm (corrected for a perspective effect on the SEM picture

Figure 7

(Color online) Configuration of an upright grating that functions in transmission. The angle of incidence $\theta$ is measured from the vertical to the basal plane, i. e. from the grating plane. The angle of emergence $\varphi$ is measured from the same direction. The picture shows a lateral view of the transversely curled scales (type 2) that alternate with the narrow, longitudinally curled scales (type 3).

Figure 8

(Color online) (Color online). Angular distribution of the light intensity emergent from a collection of about $10000$ pointlike scatterers disposed on a surface following an average scale shape (as shown in the insert). The distance between the scatterers, in the rows along the curved direction, is 440 nm, while the distance between rows, in the perpendicular direction is $1.3\mu \text{m}$. The angular distribution of intensities is obtained as the interference of all waves emitted by the scatterers, in the first Born approximation. From the geometric point of view, this model is more realistic than the “vertical” planar grating model from Fig. 7. It also predicts a reverse ordering of the color emergences and better explains the angular range spanned by the diffracted beams.