Control of the applicability of the dipole approximation for gold nanoparticles
Advanced Studies in Biology
Gold nanoparticles are widely used for biomedical applications such as cancer therapy, drug delivery and high resolution imaging of biological tissues (spectroscopy, Surface Enhanced Raman spectroscopy, fluorescence...). The specific interaction of light with metallic nanoparticles produces an enhancement of the local field which is used as a nanometric probe of molecules, but also as a nanometric heater for drug delivery or for the necrosis of diseased cells. This interaction is commonly introduced through the polarisability of a dipole subject to the local electromagnetic field. The dipole approximation is also used to explain the resonance of the interaction between light and metallic nanoparticles in undergraduate courses. The validity of this approximation commonly relates the radius of the particle R to the illumination wavelength l0 through inequality R << l0. Nevertheless this condition is inaccurate and insufficiently precise to be operational in practice. We propose to precise the criterion of validity of the dipole approximation and therefore to deduce the maximum radius of a metallic nanoparticle that could be considered as a dipole, as a function of the tolerance on the relative error between the rigorous solution and the dipole approximation. A general law is deduced for gold nanoparticles.