Surface enhanced fluorescence: a classic electromagnetic approach

The fluorescence enhancement by a single Noble metal sphere is separated into excitation/absorption enhancement and the emission quantum yield enhancement. Incorporating the classical model of molecular spontaneous emission into the excitation/absorption transition, the excitation enhancement is calculated rigorously by electrodynamics in the frequency domain. The final formula for the excitation enhancement contains two parts: the primary field enhancement calculated from the Mie theory, and a derating factor due to the backscattering field from the molecule. When compared against a simplified model that only involves the primary Mie theory field calculation, this more rigorous model indicates that the excitation enhancement near the surface of the sphere is quenched severely due to the back-scattering field from the molecule. The degree of quenching depends in part on the bandwidth of the illumination because the presence of the sphere induces a red-shift in the absorption frequency of the molecule and at the same time broadens its spectrum. Monochromatic narrow band illumination at the molecule's original (unperturbed) resonant frequency yields large quenching. For the more realistic broadband illumination scenario, we calculate the final enhancement by integrating over the excitation/absorption spectrum. The numerical results indicate that the resonant illumination scenario overestimates the quenching and therefore would underestimate the total excitation enhancement if the illumination has a broader bandwidth than the molecule. Combining the excitation model with the exact Electrodynamical theory for emission, the complete realistic model demonstrates that there is a potential for significant fluorescence enhancement only for the case of a low quantum yield molecule close to the surface of the sphere. General expressions of the fluorescence enhancement for arbitrarily-shaped metal antennas are derived. The finite difference time domain method is utilized for analyzing these complicated antenna structures. We calculate the total excitation enhancement for the two-sphere dimer. Although the enhancement is greater in this case than for the single sphere, because of the derating effects the total enhancement can never reach the local field enhancement. In general, placing molecules very close to a plasmonic antenna surface yields poor enhancement because the local field is strongly affected by the molecular self-interaction with the metal antenna.