Recently we covered Bloch's theorem and its application to the motion of electrons in a periodic potential, i.e. our crystal lattice of ions. The theorem however is not strictly contained to crystal structures, as it only discussed the translationally invariant Hamiltonians and the resulting form of wavefunctions.
An electromagnetic analogue of the above behaviour is found in optical nanostructures which exhibit a periodic potential, due to a periodic dielectric of the material. The behaviour of the EM field in the structure is found to mirror that of the electrons in the crystal structure.
Although we haven't yet covered it, the greatest similarity is between the Bloch treatment of semi-conductors and this photonic crystal. Analogous to the semi-conductor, forbidden energy zones or wavelength band gaps are formed. This gives rise to a range of behaviours such as inhibition of spontaneous emission and and high reflecting omni-directional mirrors.
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