Operative Approach to Quantum Electrodynamics in Dispersive Dielectric
Objects Based on a Polarization Modal Expansion
- URL: http://arxiv.org/abs/2108.03668v5
- Date: Tue, 2 Aug 2022 14:30:08 GMT
- Title: Operative Approach to Quantum Electrodynamics in Dispersive Dielectric
Objects Based on a Polarization Modal Expansion
- Authors: Carlo Forestiere and Giovanni Miano
- Abstract summary: We apply a Hopfield type scheme to account for the dispersion and dissipation of the matter.
We keep the polarization and the electromagnetic field distinct to enable the treatment of the polarization and electromagnetic fluctuations on equal footing.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this paper we deal with the macroscopic electromagnetic response of a
finite size dispersive dielectric object, in unbounded space, in the framework
of quantum electrodynamics using the Heisenberg picture. We apply a Hopfield
type scheme to account for the dispersion and dissipation of the matter. We
provide a general expression of the polarization density field operator as
functions of the initial conditions of the matter field operators and of the
electromagnetic field operators. It is a linear functional whose kernel is a
linear expression of the impulse response of the dielectric object that we
obtain within the framework of classical electrodynamics. The electric field
operator is expressed as a function of the polarization density field operator
by means of the dyadic Green's function for the free space. The statistical
functions of these operators are classical functionals of the statistics of the
initial conditions of the matter field operators and of the electromagnetic
field operators, whose kernels are linear or multilinear expressions of the
impulse response of the dielectric object. We keep the polarization and the
electromagnetic field distinct to enable the treatment of the polarization and
electromagnetic fluctuations on equal footing. We expand the polarization
density field operator in terms of the static longitudinal and transverse modes
of the object to diagonalize the Coulomb and Ampere interaction energy terms of
the Hamiltonian in the Coulomb gauge. We expand the radiation fields in terms
of the transverse plane wave modes of free space. Few static longitudinal and
transverse modes are needed to calculate each element of the impulse response
matrix for dielectric objects with sizes of the order up to
$\min\limits_{\omega}\{c_0/[\omega \sqrt{|{\chi}(\omega)|}]\}$ where
${\chi}(\omega)$ is the susceptibility of the dielectric.
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