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I was curious about simulating opals, and after some research, found that their amazing colors come from diffraction gratings.

Although, it seems to be different from the gratings caused by what is usually depicted as a sawtooth-shaped surface. Along with the geometry being composed differently, it appears that sub-wavelength spheres can cause interference effects, whereas normal grating distances appear to be necessarily greater than a specific wavelength to cause an effect.

Maybe I wasn't searching with the correct terms, but can anyone point me in the correct direction for understanding this effect?

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The spherical particles in an opal act as a volume diffraction grating or Bragg grating, only if 1) they are stacked in a quasicrystalline fashion, forming uniformly spaced layers; and 2) if they have a uniform size on the order of a wavelength of light (or whatever wave they are going to diffract), and 3) if they have a refractive index that differs from the medium between the particles.

The search terms you'll find most useful for this are "Bragg gratings" and "volume holographic gratings". There is also a lot of relevant information to be found under the general heading of X-ray diffraction and crystallography.

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