Energy breathing of nanoparticles

The paper considers the energy exchange process of the electromagnetic wave with a spherical metal nanoparticle. Based on the account of the temporal dependencies of electric and magnetic fields, the author presents an analytical dependence of the energy flow passing through the spherical surface. It is shown that the electromagnetic energy, localized in metal nanoparticles, is not a stationary value and periodically varies with time. A consequence of the energy nonstationarity is a nonradiating exit of the electromagnetic energy out of the nanoparticle. During the time equal to the period of wave oscillations, the electromagnetic energy is penetrating twice into the particle and quits it twice. The particle warms up because of the difference in the incoming and outgoing energies. Such “energy breathing” is presented for spherical Ag and Au nanoparticles with radii of 10 и 33 nm, respectively. Calculations were conducted for these nanoparticles embedded into the cell cytoplasm near the frequencies of their surface plasmon resonances.