Plasmonic optical antennas (POAs), often constructed from gold or silver nanostructures, can enhance the radiation efficiency of emitters coupled to POAs and are applied in surface-enhanced Raman spectroscopy (SERS) and light-emitting devices. Over the past four decades, radiation enhancement factors (REFs) of POA-emitter systems were considered to be difficult to calculate directly and have been predicted indirectly and approximately, assuming POAs are illuminated by electromagnetic plane waves without emitters. The validity of this approximation remains a significant open problem in SERS theory. Herein, we develop a method based on the rigorous optical reciprocity theorem for accurately calculating the REFs of emitters in nanoparticle-substrate nanogaps for single-molecule SERS and scanning probe-substrate nanogaps for tip-enhanced Raman spectroscopy. We show that the validity of the plane wave approximation breaks down if high-order plasmonic modes are excited. The as-developed method paves the way toward designing high-REF POA nanostructures for luminescence-related devices.
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