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Purcell effect refers to the case when a quantum emitter couples to a resonant ambient (scatterer, cavity, antenna, antenna array, etc.). Therefore, the surface-enhanced Raman scattering (SERS) -- enhancement of the Raman emission by a patterned/textured plasmonic surface – is, in fact, essentially the same effect. In this talk, we compare the Purcell effect in SERS with that observed in the plasmon-enhanced fluorescence (PEF). In PEF the Purcell effect is a commonplace, whereas in SERS it is not yet recognized by the majority of experts. The reason why it is so is simple: In PEF the Purcell factor is a measurable decrease of the fluorescence lifetime. Meanwhile, in SERS, the enhanced power of the Raman signal is also measurable, however, how the decay rate of the excited Raman states is enhanced in SERS is not directly observed. Moreover, in PEF, the spectrum of the pumping radiation is far from the plasmon resonance band, whereas, in SERS, the pumping radiation resonates with the surface plasmon. Therefore, in PEF, the gain in the fluorescence is solely due to the radiative Purcell factor (RPF), whereas, in SERS, the Purcell effect is accompanied by the local field intensity enhancement (LFIE) of the source wave. This combination of the two seemingly different effects created a mess in the literature on the electromagnetic gain in SERS. This situation becomes apparent when one discusses the equivalence of the LFIE and the RPF. In the approximate model of SERS (this model reduces the action of the plasmonic substrate to a quasistatic action of an ellipsoidal plasmonic protrusion on which the reference molecule is located), the equivalence between LFIE and RPF can be analytically proved by averaging of both LFIE and RPF over all possible positions of a molecule on the protrusion surface. In the analytical model developed by M. Stockman, this equivalence is absent and these two effects appear different, although both factors are expressed through the same dyadic Green function. In the present work, we prove the fundamental equivalence between LFIE and RPF for arbitrary molecule locations in any electromagnetically reciprocal environments. The identity of these two factors (and the effects) was not evident from the theory of M. Stockman, because he did not average the LFIE and RPF factors over all possible directions of the molecule dipole moment and the source local field vector. After this averaging (which is a commonplace in SERS), these factors match exactly, because, basically, they refer to the same underlying physics. Such identity explains the huge values of the Raman gain in the advanced SERS schemes and opens new doors in the enhancement of both photo-fluorescence and luminescence. It is important for all applications where the Purcell effect potentially combines with the local field enhancement.
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