Note that one or two layers of melanin rods are buried in the surface keratin layer. The lattice constants for the blue, green, and yellow barbules are ≈140, 150, and 165 nm, respectively. In the brown barbule the lattice structure is less regular, with the lattice constants of ≈150 and 185 nm along the directions parallel and perpendicular to the cortex surface, respectively. The number of periods is ≈9–12 for the blue and green barbules, ≈6 for the yellow barbule, and ≈4 for the brown barbule.

In Fig. 2A we show the measured reflectance by using a microspectrophotometer for differently colored barbules at normal incidence with the electric vector parallel to the melanin rods (E polarization). The reflectance spectra for the blue and green barbules show a number of features distinct from those of the yellow and brown barbules. The blue and green barbules have a narrower width of the main peaks with the peak positions located into the blue and green wavelengths, respectively. For the yellow barbule, the main peak ranges from the green to the orange wavelength and from the green to the red wavelength for the brown barbule, indicating that the yellow and brown colors are mixed colors. In addition, a side peak appears at the blue wavelength in the yellow and brown barbules.

To confirm that coloration in peacock feathers is produced structurally, barbules were immersed into glycerin (refractive index, 1.47) to fill the air holes. The infiltration of glycerin reduces the refractive index contrast and increases the average refractive index of the system. All peak positions in the reflectance spectra for the glycerin-infiltrated barbules shift to the longer wavelengths (Fig. 2B). This fact, together with the iridescent phenomenon, indicates that coloration in peacock feathers is caused by structural colors, instead of pigmentation.

For a 2D photonic crystal, reflectance spectra for E and H (with the electric vector perpendicular to the melanin rods) polarizations should be different. The measured reflectance spectra for two polarizations show that there is only a small difference in the peak position (Fig. 2C). Other colored barbules exhibit the same feature, indicating that coloration in peacock feathers is not altered by polarization.

To explore the origin of coloration in peacock feathers, we calculated the photonic band structure of an infinite 2D photonic crystal by a plane-wave expansion method (15), shown in Fig. 3. The structural parameters for this photonic crystal are taken from the measurements, i.e., r_rod/a = 0.4 and r_air/a = 0.25, where r_rod and r_air are the radii of the melanin rods and air holes, respectively, and a is the lattice constant. The refractive indices of keratin and melanin are taken to be 1.54 (20) and 2.0 (5), respectively. This 2D photonic crystal does not exhibit a complete photonic bandgap. However, a partial photonic bandgap for both E and H polarizations exists along the Γ–X direction. The difference between the midgap frequencies of two polarizations is rather small, confirming the experimental observation (Fig. 2C). It is known that a strong reflection is expected for frequencies within the partial photonic bandgap along the Γ–X direction (19). The partial photonic bandgap is hence the cause of color production. It should be mentioned that the partial photonic bandgap shifts to a higher frequency range with the increasing angle of incidence, leading to iridescent colors.

Note that the midgap frequency scales inversely with the lattice constant. Thus the color strategy in peacock feathers is very simple: the variation of the lattice constant results in different colors. In fact, using the lattice constants for differently colored barbules, the resultant midgap wavelengths match well with the main peak positions observed in the experiment.

To confirm the predictions from the photonic band structure, we calculated the reflectance spectra of generic 2D photonic crystals with a finite number of periods by a transfer matrix method (16), shown in Fig. 4. The lattice constant and the number of periods in differently colored barbules are taken from the measurements. For melanin an imaginary refractive index of 0.01 is introduced to take into account light absorption. The calculated reflectance spectra correctly reproduce the main features of the experiment. Importantly, the predicted peak positions are in good agreement with the experimental observations, although there are some differences in shapes. Note that within the partial photonic bandgap the reflectance decreases and the peak width increases with the decreasing number of periods.

On both sides of the main peaks, the reflectance spectra show some oscillations, due to the Fabry-Perot interference because there are two interfaces in the finite photonic crystal. It is more distinct on the lower wavelength side than on the higher wavelength side. For a photonic crystal consisting of dielectric rods without touching each other, it is the opposite case. The calculated side peaks at the blue wavelength in the yellow and brown barbules agree well with the experimental observations. It should be mentioned that the side peak intensity is more enhanced with the decreasing number of periods. For photonic crystal with a large number of periods, the effect of the partial photonic bandgap is dominant. However, with the decreasing number of periods side peaks also play a role in coloration, giving rise to an additional color.