This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

The non-radiative coupling of a molecule to a metallic spherical particle is approximated by a sum involving particle quasistatic polarizabilities. We demonstrate that energy transfer from molecule to particle satisfies the optical theorem if size effects corrections are properly introduced into the quasistatic polarizabilities. We hope that this simplified model gives valuable information on the coupling mechanism between molecule and metallic nanos-tructures available for,

The interaction between molecules and metallic particles has been extensively studied since the pioneer work of Gersten and Nitzan in the 1980s [

The electromagnetic coupling of a single molecule to a metallic particle is classically described as the interaction of the molecule dipole transition moment with a sphere of radius _{S}_{0} and _{B}_{B}ω/c

Using Mie formulation, we recently achieved an exact expression of the molecule normalized non-radiative decay rate, ^{NR}/γ_{0}. This involves the Mie scattering coefficients _{n}_{n}_{n}_{n}_{n}, B_{n}^{th}_{n}|^{2} correspond to the scattering emitted light of the coupled molecule–particle system, also through the ^{th}

We are now interested in the optical theorem verification when the quasistatic form of the decay rates are considered instead of the exact Mie expansion given above. We start from the approximated non-radiative rates, deduced from expressions (_{B}z_{0} _{n}^{th}

Resonances occur at frequencies _{n}_{S}

Physically, when the metallic particle is illuminated with a non-uniform electric field wave ^{n}^{th}

For instance, only the dipole moment ^{(1)} = 4_{0}_{B}α_{1}

Nevertheless, _{S}_{n}_{ext}_{ext}_{abs}_{sca}_{ext}_{abs}_{sca}_{ext}_{B}Im_{1}). This last relation is no more valuable for a non absorbing particle (_{abs}_{1}) = 0) since then _{ext}_{sca}

This can be overcome taking into account the particle finite size. An exact expression of the particle dipolar polarizability can be obtained for regular shapes [_{ext}_{abs}_{sca}_{1} by an effective polarizability

A close inspection of relations (^{th}

The non-radiative coupling expressions are now modified, by analogy with the dipolar case [

In conclusion, we obtain a simple expression for the non-radiative coupling rate of an excited molecule to a metallic spherical particle. The retardation effects are pertubatively introduced into the quasistatic polarizabilities. In this formulation, we achieve a consistent simplified model for which the energy conservation, or equivalently the optical theorem, is satisfied.

Gérard Colas des Francs acknowledges Alexandre Bouhelier, Jean-Claude Weeber and Alain Dereux for stimulating discussions on this topic and Pierre Bramant for careful reading of the manuscript. GCF is also grateful to the guest editors, Karl Greulich and Herbert Schneckenburger, for their invitation to submit this communication. This work is financially supported by the Agence Nationale de la Recherche (ANR), under grant ANTARES (PNANO 07-51).

Molecule-particle geometry. The molecule dipole moment _{0} from the particle center.

Multipolar mode cross-sections definition and optical theorem. An incident plane wave _{inc}^{th}_{n}_{ext}_{ext}_{0})_{0} _{0}

Non–radiative coupling in function of molecule-particle surface distance _{0} _{B}^{−3}) at very short distances.