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We study the spontaneous emission rate of emitter in a periodically patterned metal or dielectric membrane in the picture of a multimode field of damped Bloch states. For Bloch states in dielectric structures, the approach fully describes the Purcell effect in photonic crystal or spatially coupled cavities with losses. For a metal membrane, the Purcell factor depends on resistive loss at the resonant frequency of surface plasmon polariton (SPP). Analysis of an InP-Au-InP structure indicates that the SPP's Purcell effect can exceed a value of 50 in the ultraviolet. For a plasmonic crystal, we find a position-dependent Purcell enhancement with a mean value similar to the unpatterned membrane.

Analysis of the Purcell effect in photonic and plasmonic crystals with losses