Structural color is caused by wavelength-selective scattering of light by microscopic features, such as those on the scales of some insects. The brilliant blue displayed by some male Morpho butterflies is a classic example of this phenomenon. In this paper, experiments used to distinguish structural color from color due to pigmentation are reviewed. A simple electromagnetic model is developed for the structural scattering from Morpho butterfly scales, and the blue color and iridescence normally seen for these butterflies are predicted by this model. The analysis is based on topics usually discussed in courses on electromagnetism and optics and can be used as an example to supplement classroom discussions of these topics.

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Notice, in the model (shown in dark gray), a small section of the lowest lamella has been included that is outside the unit cell to make all of the sections of lamellae in the model the same size, which greatly simplifies the calculations.
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The notation TE (TM) indicates that the electric (magnetic) field of the incident plane wave is transverse to the plane of symmetry of the ridge (x-y plane), which is also the plane of incidence: the plane containing the vector wave number for the incident wave and the normal to the surface of the lamellae. Sometimes, the TE case is indicated by E, , s, or σ (electric field perpendicular to the plane of incidence) and the TM case by H, , p, or π (electric field parallel to the plane of incidence).
28.
For a time-harmonic field with angular frequency ω, a calligraphic letter is used for the time varying quantity, and a letter in the Roman font is used for the corresponding vector phasor; for example, Ei(r,t)=Re[Ei(r)ejωt].
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The superscript sr is used to indicate that this is the “scattered radiated” field: The part of the scattered field that behaves as 1/r, where r is the radial distance from the ridge.
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33.
Because of the many approximations made in estimating the electric field within the lamellae, the analysis is accurate only for obtaining the relative amount of scattering for different wavelengths. Therefore, all plots are presented in the normalized form.
34.
A factor of 1/N has been added before the sum; this factor does not affect the proportionality.
35.
For visible wavelengths (400nmλ700nm), we have 0.09h/λ0.16, and the value of the first sinc function is within the range of 0.73–0.90.
36.
The phase reference for scattering is at the first point (n=1) in the array, and the phases for scattering from all the other points in the array are referenced to this one. In Fig. 10(c) the line that passes through the nth point and is normal to the refracted ray is on a plane of constant phase for the refracted wave. Thus, the distance that should be used in calculating the phase of the refracted wave at point n relative to the phase of the refracted wave at point 1 is dncos(γψ)/cosγ. Similarly, the line that passes through point 1 and is normal to the ray for scattering from the nth point is on a plane of constant phase for the scattered wave. Thus, the distance that should be used in calculating the phase of the scattered wave from the nth point relative to the phase of the scattered wave from point 1 is dncosϕ/cosγ.
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38.
With some additional simplification, namely, omitting the factor k04 and setting γ=0 and km=k0, Eq. (20) becomes comparable to the results for the two-dimensional structure described in Ref. 13.
39.
The small gaps in the curves for |A|2 at angles near ϕ=0° occur because there are no real solutions to the equations in this region.
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