  We introduce a numerical framework for calculating decay rate contributions
when excited two-level quantum emitters are located near layered plasmonic
nanostructures, particularly emphasizing the case of plasmonic nanostructures
atop metal substrates where three decay channels exist: free space radiation,
Ohmic losses, and excitation of surface plasmon polaritons (SPPs). The
calculation of decay rate contributions is based on Huygen's equivalence
principle together with a near-field to far-field transformation of the local
electric field, thereby allowing us to discern the part of the electromagnetic
field associated with free propagating waves rather than SPPs. The methodology
is applied to the case of an emitter inside and near a gap-plasmon resonator,
emphasizing strong position and orientation dependencies of the total decay
rate, contributions of different decay channels, radiation patterns, and
directivity of SPP excitation.
