Field quantization in inhomogeneous absorptive dielectrics

Abstract

The quantization of the electromagnetic field in a three-dimensional inhomogeneous dielectric medium with losses is carried out in the framework of a damped-polariton model with an arbitrary spatial dependence of its parameters. The equations of motion for the canonical variables are solved explicitly by means of Laplace transformations for both positive and negative time. The dielectric susceptibility and the quantum noise-current density are identified in terms of the dynamical variables and parameters of the model. The operators that diagonalize the Hamiltonian are found as linear combinations of the canonical variables, with coefficients depending on the electric susceptibility and the dielectric Green function. The complete time dependence of the electromagnetic field and of the dielectric polarization is determined. Our results provide a microscopic justification of the phenomenological quantization scheme for the electromagnetic field in inhomogeneous dielectrics.

Electromagnetic field quantization in a linear polarizable and magnetizable medium

“…Suttorp and Wubs in the framework of the damped polarization model, have quantized the electromagnetic field in an absorptive medium with spatial dependence of its parameters [7]. They have solved the equations of motion of the dielectric polarization and the electromagnetic field by means of the Laplace transformation for both positive and negative times.…”

“…The heat bath interacts with the medium in a suitable way. In this model, the magnetic property of the medium is not included [5,7].…”

Electromagnetic field quantization in a magnetodielectric medium with external charges

“…In this point of view the polarizability of the medium is a result of the properties of the heat bath and accordingly, the polarizability should be defined in terms of the dynamical variables of the medium. In this method, contrary to the damped polarization model, polarizability and absorptivity of the medium are not independent of each other [12,13]. Furthermore, if the medium is magnetizable, as well as polarizable, the medium can be modelled with two independent collection of harmonic oscillators, so that one of these collections describes the electric properties and the other describes the magnetic properties of the medium.…”

“…This should be done in such a away that the interaction between light and matter will generate both dispersion and damping of the light field. In an attempt to overcome these problems, by taking the polarization of the medium as a dissipative quantum system and based on the Hopfield model of a dielectric [10,11], a canonical quantization of the electromagnetic field inside a dispersive and absorptive dielectric can be presented, where the polarization of the dielectric is modelled by a collection of interacting matter fields [12,13]. The absorptive character of the medium is modelled through the interaction of the matter fields with a reservoir consisting of a continuum of the Klein-Gordon fields.…”

Equivalence between the Hamiltonian and Langevin noise descriptions of plasmon polaritons in a dispersive and lossy inhomogeneous medium

“…It is central to observe that the DLN approach is a direct development of the historical works by Rytov and others [53][54][55][56] which, based on some considerations about the standard fluctuation dissipation theorem for electric currents [57], was used for justifying Casimir and thermal forces (for recent developments of such phenomenological 'fluctuational electrodynamics' techniques in the context of nanotechnology see [58][59][60][61][62][63]). Few years ago, it was proposed that the equivalence between the Hamiltonian and DLN approaches should finally be rigorous [64][65][66][67][68][69][70]. However, we recently showed [71][72][73] that a full Hamiltonian description, generalizing the Huttner-Barnett results [14][15][16][17][18][19][20] and valid for any inhomogeneous dielectric systems, must not only include the material oscillator degrees of freedom, i.e., like in the DLN method, but also add the previously omitted quantized photonic degrees of freedom associated with fluctuating optical waves coming from infinity and scattered by the inhomogeneities of the medium [72].…”