We provide a momentum space formulation for thermal emission from photonic crystals and corroborate Kirchhoff's law for periodic structures. This formalism allows us to calculate the optical coherence in the far and near fields of photonic crystals. Calculations in the far field show that the exchange of momentum between a linear grating and the surface polaritons can significantly decrease the coherence length for the grating compared to that of a flat surface. Considerations in the near field of photonic crystals show that, unlike observations of flat surfaces, the electric energy density does not necessarily decrease as 1/z³ for a distance z from the surface.
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Sang Eon Han (2009) studied this question.
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