Opals: Natural Band Gaps for Photons
Periodic objects reflect incident waves when the wavelength and interplanar spacing satisfy Bragg's Law. Under these conditions waves do not penetrate very far and are reflected from the object. Usually this happens for X-rays in crystals, but crystals can also diffract electrons creating a similar effect. In semiconductors diffraction dominates whole ranges of electron energies and creates a band gap. Electrons with energy in the band gap are forbidden inside the semiconductor crystal. In fact that is why a semiconductor does not conduct.
Bragg's law applies to any wave in any periodic object. There are many
naturally occurring materials which have much longer periods that the
atomic dimensions of crystals. The gemstone opal is one of these and on
the left an electron micrograph is shown of some Hungarian opal:
underneath some surface debris can be seen a close packed array of
silica spheres whose diameters are a fraction of a micron.
The lattice spacing of spheres is exactly right to diffract visible
light and the bright colours of the gemstone result from Bragg
reflection of incident light.