Comment on “Theoretical study of single molecule fluorescence in a metallic nanocavity” [Appl. Phys. Lett. 80, 315 (2002)]

In a recent letter, Enderlein, reported enhanced single molecule fluorescence in a nanometric metal-coated dielectric bead. The enhancement of the fluorescence can be more than one order of magnitude for a thin silver coating layer down to 5 nm. They have used the standard numerical method for the calculations, but the size-dependent dielectric function for the thin silver layer was not included in the calculations. It is well known that the dielectric function of a small metal particle will become size dependent when the size of the metal particle is much smaller than the electron mean-free path of the bulk metal. The electron mean-free path for bulk silver is about 57 nm, which is one order of magnitude more than the thickness of the silver coating layer in Ref. 1. In this case, surface-electron collisions will give a dominating contribution to the damping mechanism of the plasmon response of the silver shell rather than electronelectron collisions. The larger damping as a result of more frequent electron-surface collisions diminishes drastically the field enhancement inside the nanocavity of the silver shell. Hence, the results in Ref. 1 will not be reliable. Except for the electron-electron collision with a frequency in metal nanostructures, the electron-surface collision frequency in the simple Drude theory is =VF / x̄, where VF is the Fermi velocity and x̄ is the electron mean path of the electron-surface collision. For complex metal nanostructures, the exact value of x̄ is not obviously determined. For a spherical metal nanoshell, Averrit et al. just simply took the shell thickness as the value of x̄. But the tangential path can be larger than the shell thickness. In order to calculate x̄, we use the following mathematical description. A random electron free path x of the electron-surface collision can be either a line connecting the inner surface and the outer surface of the shell, or a line with two ends on the outer surface only. For the former case, x=r2 cos − r1−r2 sin2 sin r1 /r2 , and for the latter case x =2r2 cos sin r1 /r2 , where is the angle between x and the radius at the end on the outer surface, r1 and r2 are the radii of the inner and outer surfaces of the shell, respectively. Then, x̄ can be calculated,