What is a photonic bandgap?
Similar to the energy-gap for electrons in a semiconductor, photonic crystals exhibit an energy-gap for photons. This means that photons, whose energy (and thus frequency) is in a certain region, are not allowed to exist inside the photonic crystal. This region is called a bandgap, because by convention, the allowed energy values with respect to the wave number are expressed in terms of bands in a photonic crystal. So if there are forbidden energies, there are no energy-bands in that region and a bandgap occurs.