Resonance frequency and radiative Q-factor of plasmonic and dieletric modes of small objects

The electromagnetic scattering resonances and modes of a nonmagnetic object much smaller than the incident wavelength in vacuum can be either described by the electroquasistatic approximation of the Maxwell's equations if its permittivity is negative or by the magnetoquasistatic approximation if its permittivity is positive and sufficiently high. Nevertheless, these two approximations fail to correctly account for the frequency shift and the radiative broadening of the resonances when the size of the object becomes comparable to the wavelength of operation. In this paper, the radiation corrections to the electroquasistatic and magnetoquasistatic resonances and modes of arbitrarily shaped objects are derived, which only depend on the quasistatic current modes. Then, closed-form expressions of the frequency shift and the radiative Q-factor of both plasmonic and dielectric modes of small objects are introduced, where the dependencies on the material and the size of the object are factorized. In particular, it is shown that the radiative Q-factor explicitly depends on the multipolar components of the quasistatic mode and its corrections.