Resonant behavior of dielectric objects (electrostatic resonances)

Resonant behavior of dielectric objects occurs at certain frequencies for which the object permittivity is negative and the free-space wavelength is large in comparison with the object dimensions. Unique physical features of these resonances are studied and a novel technique for the calculation of resonance values of permittivity, and hence resonance frequencies, is proposed. Scale invariance of resonance frequencies, unusually strong orthogonality properties of resonance modes, and a two-dimensional phenomenon of "twin" spectra are reported. The paper concludes with brief discussions of optical controllability of these resonances in semiconductor nanoparticles and a plausible, electrostatic resonance based, mechanism for nucleation and formation of ball lightning.