heat dissipation of metal nanoparticles in the dipole approximation

The dipolar approximation model that describes the heat delivered by a nanoparticle under continuous light irradiation provides a relation in which the dissipated power is proportional to the extinction cross-section. this relation works fairly well for small particles in which all the energy is absorbed, but fails for larger structures due to the non-negligible power scattered in the free space that does not contribute to heat generation. here we show that, if we consider the light-induced dipolar field in the calculation of the dissipated power, we recover the proportionality with the absorption cross-section of the nanoparticle.