## Abstract

When illuminated and viewed along certain well-defined directions,
segments on the wings of the butterfly *Cynandra opis* shows a
striking violet-blue to blue-green. We quantify the spectral and
the directional properties of these areas of the wings of the
insect. Electron microscopy shows that wing scales from these
iridescent regions of the wings contain two gratinglike microstructures
crossed at right angles. Application of the diffraction theory, as
formulated by the Stratton–Silver–Chu integral, to the microstructure
can explain all the important features observed
experimentally.

© 1999 Optical Society of America

Full Article |

PDF Article
### Equations (16)

Equations on this page are rendered with MathJax. Learn more.

(1)
$$|{\mathbf{S}}_{1}|=\left[{\mathbf{H}}_{1}\xb7\left({\stackrel{\u02c6}{p}}_{1}\times {\stackrel{\u02c6}{k}}_{i}\right)\right]/\left[{\stackrel{\u02c6}{s}}_{1}\xb7\left({\stackrel{\u02c6}{p}}_{1}\times {\stackrel{\u02c6}{k}}_{i}\right)\right],$$
(2)
$${\mathbf{S}}_{1Y\prime}=|{\mathbf{S}}_{1}|{p}_{1X\prime}/{\left({p}_{1X\prime}^{2}+{p}_{1Y\prime}^{2}\right)}^{1/2}.$$
(3)
$${S}_{1S}=\left({S}_{1Y\prime}-{d}_{1}\right)cos{\mathrm{\varphi}}_{i}/cos\left({\mathrm{\theta}}_{1}-{\mathrm{\varphi}}_{i}\right)$$
(4)
$${S}_{2S}=\left({S}_{2X\prime}-{d}_{2}\right)cos{\mathrm{\varphi}}_{i}/cos\left({\mathrm{\theta}}_{2}-{\mathrm{\varphi}}_{i}\right)$$
(5)
$${S}_{2X\prime}=|{\mathbf{S}}_{2}|{p}_{2Y\prime}/{\left({p}_{2X\prime}^{2}+{p}_{2Y\prime}^{2}\right)}^{1/2},$$
(6)
$${\stackrel{\u02c6}{n}}_{1}^{\prime}=\left[0,-sin{\mathrm{\theta}}_{1},cos{\mathrm{\theta}}_{1}\right],{\stackrel{\u02c6}{n}}_{2}^{\prime}=\left[-sin{\mathrm{\theta}}_{2},0,cos{\mathrm{\theta}}_{2}\right]$$
(7)
$${\mathbf{E}}_{\mathbf{T}}=A{\stackrel{\u02c6}{k}}_{d}\times \underset{S}{\iint}\left[\stackrel{\u02c6}{n}\times \mathbf{E}-\mathrm{\eta}{\stackrel{\u02c6}{k}}_{d}\times \left(\stackrel{\u02c6}{n}\times \mathbf{H}\right)\right]\times exp\left[\mathit{ik}\left({\stackrel{\u02c6}{k}}_{d}-{\stackrel{\u02c6}{k}}_{i}\right)\xb7\mathbf{r}\right]\mathrm{d}S,$$
(8)
$${\mathbf{H}}_{i,d}=\frac{1}{\mathrm{\eta}}{\stackrel{\u02c6}{k}}_{i,d}\times {\mathbf{E}}_{i,d}.$$
(9)
$${\mathbf{E}}_{T}={\mathbf{E}}_{1}+{\mathbf{E}}_{2},$$
(10)
$${\mathbf{E}}_{j}\left(P\right)=A\left[{\stackrel{\u02c6}{k}}_{d}\times \left({\stackrel{\u02c6}{n}}_{j}\times {\mathbf{E}}_{j}\right)-\mathrm{\eta}{\stackrel{\u02c6}{k}}_{d}\times \left({\stackrel{\u02c6}{n}}_{j}\times {\mathbf{H}}_{j}\right)\right]\sum _{m\left(n\right)}\iint exp\left[i\mathrm{\Delta}\mathbf{K}\prime \xb7\mathbf{r}\prime \right]\mathrm{d}x\prime \mathrm{d}y\prime ,$$
(11)
$${\mathbf{r}}_{m}^{\prime}=\left[x\prime ,y\prime ,{z}_{1m}-\left(x\prime -{x}_{m}^{\prime}\right){n}_{1x}/{n}_{1z}\right]$$
(12)
$${\mathbf{r}}_{n}^{\prime}=\left[\mathbf{x}\prime ,y\prime ,-\left(y\prime -{y}_{n}^{\prime}\right){n}_{1y}/{n}_{1z}\right]$$
(13)
$$\iint exp\left[i\mathrm{\Delta}\mathbf{K}\prime \xb7{\mathbf{r}}_{m}^{\prime}\right]\mathrm{d}x\prime \mathrm{d}y\prime =-\left[exp\left({\mathit{ia}}_{11}\right)-exp\left({\mathit{ia}}_{12}\right)\right]\times \left[exp\left({\mathit{ia}}_{13}-1\right)\right]\times exp\left({\mathit{ia}}_{14}\right)/\left({b}_{1}\mathrm{\Delta}{K}_{x}^{\prime}\right),$$
(14)
$$\iint exp\left[i\mathrm{\Delta}\mathbf{K}\prime \xb7{\mathbf{r}}_{n}^{\prime}\right]\mathrm{d}x\prime \mathrm{d}y\prime =-\left[exp\left({\mathit{ia}}_{21}\right)-exp\left({\mathit{ia}}_{22}\right)\right]\times \left[exp\left({\mathit{ia}}_{23}-1\right)\right]\times exp\left({\mathit{ia}}_{24}\right)/\left({b}_{2}\mathrm{\Delta}{K}_{y}^{\prime}\right),$$
(15)
$${L}_{C}=1.22\mathrm{\lambda}/{\mathrm{\theta}}_{\mathrm{FULL}},$$
(16)
$$d\left(sin{\mathrm{\varphi}}_{i}+sin{\mathrm{\varphi}}_{d}\right)=m\mathrm{\lambda},$$