Quasistatic Oscillations in Subwavelength Particles: Can One Observe Energy Eigenstates?

Abstract

In increasing the capabilities of the optical and microwave techniques further into the subwavelength regime, quasistatic resonant structures have 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 measure only either the electric or 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, 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 is analyzed. It is shown that in the case of MS potential scalar wave function, one can observe quasistatic retardation effects and obtain a proper formulation of the energy eigenstate problem.Here the frequency ω is also introduced as a parameter. The mode expansion relies on the existence of an orthogonal and complete set of real electric-field eigenfunctions E n and eigenvalues ε n . For a composite consisting of the metal component

Magnetoelectric Near Fields

“…In Ref. [47] it was discussed that in a case of the surface plasmon resonances in subwavelength optical metallic structures no retardation processes characterized by the electric dipole-dipole interaction and described exclusively by electrostatic wave function ( . Such a behavior can be obtained in a ferrite particle in a form of a quasi-2D disk.…”

Electrodynamics of Magnetoelectric Media and Magnetoelectric Fields

“…In a quasi-2D ferrite disk, with the disk axis oriented along z, the Walker-equation solution for the MS-potential wave function is written in a cylindrical coordinate system as: [53,63,66] = C (z)̃(r, )…”

“…The MDMs in a ferrite disk are characterized by topologically distinct structures of the fields. Using electromagnetic boundary conditions, one obtains the following equation for a membrane wave function on a lateral surface of a ferrite disk of radius : [53,63,66,67] (̃) r= − − (̃) r= + = 0 (33)…”

“…Because of the spin-orbit interaction between the spin and orbital rotation angular momenta of magnetization, there exists another quadratic relationship between the electric and magnetic field components in a near-field structure, in addition to the Equation (39). It was shown [26,53,63,64,66] that outside a MDM ferrite sample there is also the region with…”

“…This equation shows that the modes in a ferrite disk are MS waves standing along the z axis and propagating along an azimuth coordinate in a certain (given by a direction of a normal bias magnetic field) azimuth direction. For the known solution of the wave function ( , ) r t   , the power flow density is viewed as a current density [66,67]:…”