524
E. Kamenetskii
and magnetic fields underlies the conservation of energy and momentum for electromagnetic fields [1]. Recently, it was shown that this dual symmetry determines
the conservation of optical (electromagnetic) chirality [2, 3]. Based on an analysis of
the interaction of chiral light and chiral specimens, new mechanisms of enantiomer
discrimination and separation in optics have been proposed [2–8]. Since chiroptical
effects are usually hampered by weak chiral light-matter interaction, it is argued
that to enhance the chiral effects it is necessary that the near field remains chiral
in the process. Different plasmonic and dielectric nanostructures have recently been
proposed as a viable route for near-field enhancement of chiral light-matter interactions [9–11]. In a more general sense, one can say that this is an attempt to enhance
the near-field intensity while preserving the ME properties. However, the following
fundamental questions arise: Can one really observe effects of the near-field magnetoelectricity in dynamic regimes. What are the symmetry properties of such dynamic
ME fields?
The question on relationships between magnetoelectricity and electromagnetism
is a subject of a strong interest and numerous discussions in microwave and optical
wave physics and material sciences. The problem of the near-field magnetoelectricity
in electromagnetism is a topical problem. Evanescent fields are oscillating fields
whose energy is spatially concentrated in the vicinity of the oscillating currents. In
classical electrodynamics we know only two types of local (subwavelength) electric
currents: linear and circular. These types of currents determine elementary electric
and magnetic dipole oscillations in matter. The electric polarization is parity odd
and time-reversal even. At the same time, the magnetization is parity even and timereversal odd [1]. These symmetry relation cast doubt on the idea of a local (subwavelength) coupling of two, electric and magnetic, small dipoles. When the violation of
the invariances under space reflection parity and time inversion are necessary conditions for the emergence of the ME effect, the same symmetry properties should be
observed for the near fields—the ME near fields.
The uniqueness of the proposed ME near fields can be shown by analyzing vacuum
near fields originated from a scatterer made of a ME structure. In this connection, it is
worth noting that in a case of usual (non-ME) material structures one can distinguish
two kinds of the EM near fields: (a) near fields originated from EM wave resonances
and (b) near fields originated from dipole-carrying resonances. The former fields,
abbreviated as EM NFs, are obtained based on the full-Maxwell-equation solutions
with use of Mie theory [12]. The latter fields, abbreviated as DC NFs, are observed
when the electric or magnetic dipole-carrying oscillations (such, for example, as
surface plasmons [13–15] and magnons [16–18]) take place. Notably, in accordance
with Mie theory one can observe EM NFs with magnetic responses originated from
small nonmagnetic dielectric resonators, both in microwaves [19] and optics [20–22].
In a case of DC NFs, strong coupling of EM waves with electric or magnetic dipolecarrying excitations, called polaritons, occur [16, 23]. Importantly, the spatial scale
of the DC NFs is much smaller than the spatial scale of the EM NFs in the same
E. Kamenetskii
and magnetic fields underlies the conservation of energy and momentum for electromagnetic fields [1]. Recently, it was shown that this dual symmetry determines
the conservation of optical (electromagnetic) chirality [2, 3]. Based on an analysis of
the interaction of chiral light and chiral specimens, new mechanisms of enantiomer
discrimination and separation in optics have been proposed [2–8]. Since chiroptical
effects are usually hampered by weak chiral light-matter interaction, it is argued
that to enhance the chiral effects it is necessary that the near field remains chiral
in the process. Different plasmonic and dielectric nanostructures have recently been
proposed as a viable route for near-field enhancement of chiral light-matter interactions [9–11]. In a more general sense, one can say that this is an attempt to enhance
the near-field intensity while preserving the ME properties. However, the following
fundamental questions arise: Can one really observe effects of the near-field magnetoelectricity in dynamic regimes. What are the symmetry properties of such dynamic
ME fields?
The question on relationships between magnetoelectricity and electromagnetism
is a subject of a strong interest and numerous discussions in microwave and optical
wave physics and material sciences. The problem of the near-field magnetoelectricity
in electromagnetism is a topical problem. Evanescent fields are oscillating fields
whose energy is spatially concentrated in the vicinity of the oscillating currents. In
classical electrodynamics we know only two types of local (subwavelength) electric
currents: linear and circular. These types of currents determine elementary electric
and magnetic dipole oscillations in matter. The electric polarization is parity odd
and time-reversal even. At the same time, the magnetization is parity even and timereversal odd [1]. These symmetry relation cast doubt on the idea of a local (subwavelength) coupling of two, electric and magnetic, small dipoles. When the violation of
the invariances under space reflection parity and time inversion are necessary conditions for the emergence of the ME effect, the same symmetry properties should be
observed for the near fields—the ME near fields.
The uniqueness of the proposed ME near fields can be shown by analyzing vacuum
near fields originated from a scatterer made of a ME structure. In this connection, it is
worth noting that in a case of usual (non-ME) material structures one can distinguish
two kinds of the EM near fields: (a) near fields originated from EM wave resonances
and (b) near fields originated from dipole-carrying resonances. The former fields,
abbreviated as EM NFs, are obtained based on the full-Maxwell-equation solutions
with use of Mie theory [12]. The latter fields, abbreviated as DC NFs, are observed
when the electric or magnetic dipole-carrying oscillations (such, for example, as
surface plasmons [13–15] and magnons [16–18]) take place. Notably, in accordance
with Mie theory one can observe EM NFs with magnetic responses originated from
small nonmagnetic dielectric resonators, both in microwaves [19] and optics [20–22].
In a case of DC NFs, strong coupling of EM waves with electric or magnetic dipolecarrying excitations, called polaritons, occur [16, 23]. Importantly, the spatial scale
of the DC NFs is much smaller than the spatial scale of the EM NFs in the same