Using either quasistatic approximation or exact Mie expansion, we characterize the localized surface plasmons supported by a metallic spherical nanoparticle. We estimate the quality factor

Metallic nanoparticles support localized surface plasmonpolaritons (SPP) strongly confined at the metal surface ensuring efficient electromagnetic coupling with neighbouring materials, offering a variety of applications such as surface-enhanced spectroscopies [

In this context, we propose to determine the quality factors and effective volumes of localized SPPs supported by a metallic nanosphere. Indeed, these quantities are useful parameters to understand and evaluate the coupling mechanisms between dipolar emitters and plasmonic nanostructures [

In Section

We first characterize the dipolar mode of a spherical particle. For sphere radius

The dipolar polarisability presents a simple shape near the resonance if the metallic dielectric constant follows Drude model [

The dipolar response can be described by either the extinction efficiency

As an example, we consider a

Although Drude model qualitatively explains the shape of the resonance, a more representative value of the quality factor can only be determined using tabulated data for the dielectric constant of the metal [

Extinction efficiency for the dipolar resonance calculated keeping only the dipolar mode (

Coupling rate of a dipolar emitter to a dipolar particle expresses for very short emitter-particle distances

Unlike here, usual definition of the mode effective volume does not include the emitter position. For instance, in case of cavity quantum electrodynamics (cQED) applications, it can be expressed as

If the excitation field is generated by a dipolar emitter (fluorescent molecules, quantum dots,…), it cannot be considered uniform anymore and the dipolar approximation fails. One needs therefore to consider the coupling strength to high-order modes (Figure

(a) Dipolar and (b) quadrupolar mode profiles of a

The

For a Drude metal, the

It is now a simple matter to generalize the dipolar mode analysis reported in the previous section to all the particle modes. The

The quality factor associated with the

Figure

(a) Extinction efficiency of a

Last, we express the

Effective volume of the dipole (

Finally, it is worthwhile to note that mode effective volume is generally defined independently on the particle-emitter distance so that it gives an estimation of the mode extension. This is done by evaluating the maximum effective volume available and for a random emitter orientation. In case of localized SPP, this is achieved for contact (

Normalized effective volume

Note that mode effective volume is generally defined by its energy confinement

Purcell factor quantifies the coupling strength between a quantum emitter and a (plasmon) mode but lacks information on the coupling efficiency as compared to all the other emitter relaxation channels. For the sake of clarity, it has to be mentioned that coupling strength to one SPP mode corresponds to the total emission decay rate induced by this coupling. It does not permit to distinguish radiative (

Coupling efficiency into the dipolar (

We explicitly determined the effective volumes for all the SPP modes supported by a metallic nanosphere. Their quality factor is also approximated in the quasistatic case or calculated using exact Mie expansion. Rather low-quality factors ranging from 10 to 100 can be achieved, associated with extremely confined effective volume of nanometric dimensions. This results in high

In this appendix, we derive the expression of mode quality factor and effective volume for a spherical particle embedded in homogeneous background of optical index

The

Considering a Drude metal, we achieve a simple approximated expression for

The total coupling strength of a dipolar emitter to the spherical metallic particle, embedded in

This work is supported by the Agence Nationale de la Recherche (ANR) under Grants Plastips (ANR-09-BLAN-0049-01), Fenopti