Quantization of Macroscopic Electrodynamics in Absorptive Dielectrics of Finite Size in Unbounded Space
Year: 2021
Type: preprint
Abstract: An operative approach to the quantization of macroscopic electrodynamics for absorptive dielectrics of finite size in unbounded space is presented. It is based on the combination of a Hopfield-type model for the polarization of the dielectric, and an expansion of the polarization density field in terms of the static longitudinal and transverse modes of the dielectric object, which only depend on its shape and size. To account for the dissipation of the matter, the polarization is described through a continuum of oscillating harmonic fields that are linearly coupled the electromagnetic field. The Coulomb gauge is applied, the Coulomb electric field is expressed in terms of the polarization field, and the radiation field is expanded in terms of transverse plane waves in free space. The Heisenberg equations for the coordinate operators of the polarization density field are obtained in a closed form. The initial state of the radiation and matter comes into play through the driving operators. Even if the equations for the longitudinal and transverse coordinate operators of the polarization are coupled due to the interaction of the polarization with the radiation, few longitudinal and transverse modes are needed for dielectrics with size of the same order of the characteristic wavelength $\lambda_c=\min\limits_{\omega}\{c_0/[\omega \sqrt{|{\chi}(\omega)|}]\}$ where ${\chi}(\omega)$ is the macroscopic susceptibility of the dielectric in the frequency domain. Eventually, the polarization density field operator and the electric field operator are expressed in terms of the driving field operators by the same relations of the classical electrodynamics.
Source: arXiv (Cornell University)
Authors: Carlo Forestiere, Giovanni Miano
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3205817699