Quasistatic oscillations in subwavelength particles: Can one observe energy eigenstates?

In increasing the capabilities of the optical and microwave techniques further into the subwavelength regime, quasistatic resonant structures has attracted considerable interest. Electromagnetic responses of electrostatic (ES) plasmon resonances in optics and magnetostatic (MS) magnon resonances in microwaves give rise to a strong enhancement of local fields near the surfaces of subwavelength particles. In the near-field regions of subwavelength particles one can only measure the electric or the magnetic field with accuracy. Such uncertainty in definition of the electric or magnetic field components raises the question of energy eigenstates of quasistatic oscillations. The energy eigenstate problem can be properly formulated when potential functions, used in the quasistatic-resonance problems, are introduced as scalar wave functions. In this case, one should observe quasistatic-wave retardation effects still staying in frames of the quasistatic description of oscillations in a subwavelength particle. In this paper, we analyze the problem of energy quantization of ES resonances in subwavelength optical metallic structures with plasmon oscillations and MS resonances in subwavelength microwave ferrite particles with magnon oscillations. We show that in a case of MS-potential scalar wave function one can observe quasistatic retardation effects and obtain a proper formulation of the energy eigenstate problem.