The Quenching of Molecular Fluorescence Through the Interaction with Rough Surfaces.

A classical theoretical calculation is presented for the effect rough surface structure has on the lifetime of an excited fluorescing molecule in the vicinity of the surface. The exact classical dyadic Green function technique is used to calculate the inverse lifetime of a fluorescing molecule, which is modelled as a simple oscillating point dipole. Since the rough surface effects are completely described by the scattering part of the dyadic Green function, an exact inhomogeneous integral equation is derived for the rough surface Green function. The integral equation is solved by using a perturbative expansion technique for small surface roughness. The first modification to the inverse lifetime is shown to correspond to the second order of the small roughness parameter. Detailed expressions for the second order Green function and its effects on the fluorescent lifetime of a molcular dipole oriented perpendicularly to the average surface of a cylindrically symmetric periodically rough interface are presented and numerically analyzed, using Monte Carlo integration techniques, for several parameters of the molecule-metal substrate system. Specifically, the lifetime's functional dependence on the molecular-substrate separation distance for fixed emission wavelength, and its dependence on emission energy for fixed molecular distance are presented. Furthermore, the second order Green function's dependence on grating periodicity for fixed wavelength and separation distance is demonstrated.