Numerical Calculations of Radiative and Non-Radiative Relaxation of Molecules Near Metal Particles

The dependence of the radiative emission and the nonradiative (energy transfer to the metal) relaxation rates of a molecule near a small metal particle on the molecule-to-particle distance and on the molecular orientation is calculated using a numerical solution of the Maxwell equations for a model that described the metal as a dispersive dielectric particle and the molecule as an oscillating point dipole. The emission rate is obtained by evaluating the total oscillating dipole in the system, while the nonradiative rate is inferred from the rate of heat production on the particle. For the distance dependence of the nonradiative rate we find, in agreement with experimental observations, marked deviation from the prediction of the standard theory of fluorescence resonance energy transfer (FRET). In departure from previous interpretations, we find that electromagnetic retardation is the main source of this deviation at large molecule–particle separations. The radiative emission rate reflects the total dipole induced in the molecule–particle system, and its behavior as a function of distance and orientation stems mostly from the magnitude of the oscillating polarization on the metal particle (which, at resonance, is strongly affected by plasmon excitation), and from the way this polarization combines with the molecular dipole to form the total system dipole.