Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Huaihai Institute of Technology

The Photic Field Quantization in Plane Divisional Uniform Absorbing and Dispersive Dielectrics

Yin Xiao

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

The photic field in the plane divisional uniform absorbing and dispersive dielectrics is quantized by the canonical quantum theory and the classical Green's function of the system. The concrete forms of the leftwards\|traveling and rightwards\|traveling polariton and photon operators in the dielectrics and the cavity are determined by use of the identical idea of the contrast with the homogeneous media and the vacuum case, and the quantized expressions of light field in every region are given. Results show that the polariton and the photon operators can be expressed by the forms of the media noise along the propagation with phase weight, and they are closely related to the media distribution, parameters and the light frequency.

Related papers

Mode expansion and photon operators in dispersive and absorbing dielectrics

Omar Di Stefano, Salvatore Savasta, R. Girlanda

We present a one-dimensional quantization scheme for the electromagnetic field in arbitrary planar absorbing and dispersive dielectrics, taking into account explicitly the finite extent of media. The complete form of the electric field operator includes a part that corresponds to the free fields incident from the vacuum towards the medium and a particular solution which can be expressed by using the classical Green-function integral representation of the electromagnetic field. By expressing the classical Green function in terms of the light modes of the dielectric structure, we obtain a natural generalization to absorbing media of the familiar method of mode expansion which strictly applies to non-absorbing media. As an application of our mode expansion, we obtain general quantum-optical input-output relations relating the output photon operators in vacuum to the input photon operators and to the reservoir noise operators. The input-output relations obtained are uniquely determined by the knowledge of the classical light modes of the planar system. We finally show that our quantization scheme for arbitrary planar dielectrics satisfies the prescribed equal-time commutation relations of QED.

Journal of Modern Optics•Jan 1, 2001•31 citations

Electromagnetic field quantization in absorbing dielectrics

Reza Matloob, R. Loudon, Stephen Mark Barnett +1 more

The electromagnetic field is quantized in dielectric media that show both loss and dispersion. The complex dielectric function of the medium is assumed to be a known function and the loss is modeled by Langevin forces in the forms of noise current operators. The noise current correlation function is related to the assumed dielectric function by the fluctuation-dissipation theorem. Field quantization is carried out for the infinite homogeneous dielectric, the semi-infinite dielectric, and the dielectric slab, where the fields in the second and third cases are restricted to propagation perpendicular to the dielectric surfaces. The forms of the vector potential operator are obtained in the different spatial regions for all three geometries, and in each case the required canonical commutation relation for the vector potential and its conjugate generalized momentum operator is verified. The spatial dependence of the vacuum field fluctuations is calculated for the two dielectric geometries that have surfaces.

Physical Review A•Dec 1, 1995•292 citations

Electromagnetic field quantization in absorbing dielectrics. II

Reza Matloob, R. Loudon

A quantization scheme for the electromagnetic field in absorbing dielectrics developed previously is extended to cover more complicated arrangements of dielectric media and to investigate various limiting cases of the general formalism. The limiting cases include media that have vanishing imaginary parts in their dielectric functions, because either the refractive index or the extinction coefficient vanishes. The further limit of a unit real dielectric function establishes the connection of the formalism with the well-known quantized field expressions in free space. Detailed calculations are presented for the quantization in the system of two different absorbing dielectrics in contact at a plane interface and for the cavity formed in the free space between two separated absorbing dielectrics. The forms of the field operators are determined for both systems, the canonical commutation relations are verified, and the spectra of the vacuum field fluctuations are calculated and illustrated. The calculations are restricted throughout to fields that propagate perpendicular to the dielectric interfaces. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Jun 1, 1996•112 citations

Electromagnetic field quantization and quantum optical input-output relation for grating

Tiecheng Wang

A quantization scheme is developed for the radiation and higher order electromagnetic fields in one dimensional periodic, dispersive and absorbing dielectric medium. For this structure, the Green function is solved based on the plane wave expansion method, thus the photon operators, commutation relations and quantum Langevin equations are given and studied based on the Green function approach, moreover, the input-output relations are also derived. It is proved that this quantum theory can be reduced back to that of the predecessors' study on the homogenous dielectric. Based on this method, we find that the transformation of the photon state through the lossy grating is non-unitary and that the notable non-unitary transformation can be obtained by tuning the imaginary part of the permittivity, we also discussed the excellent quantum optical properties for the grating which are similar to the classical optical phenomena. We believe our work is very beneficial for the control and regulation of the quantum light based on gratings.

Scientific Reports•Dec 27, 2019•2 citations

Green-function approach to the radiation-field quantization for homogeneous and inhomogeneous Kramers-Kronig dielectrics

Toralf Gruner, D.‐G. Welsch

A quantization scheme for the radiation field in dispersive and absorptive linear dielectrics is developed, which applies to both bulk material and multilayer dielectric structures. Starting from the phenomenological Maxwell equations, where the properties of the dielectric are described by a permittivity consistent with the Kramers-Kronig relations, an expansion of the field operators is performed that is based on the Green function of the classical Maxwell equations and preserves the equal-time canonical field commutation relations. In particular, in frequency intervals with approximately vanishing absorption the concept of quantization through mode expansion for dispersive dielectrics is recognized. The theory further reveals that weak absorption gives rise to space-dependent mode operators that spatially evolve according to quantum Langevin equations in the space domain. To illustrate the applicability of the theory to inhomogeneous structures, the quantization of the radiation field in a dispersive and absorptive one-interface dielectric is performed. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Mar 1, 1996•388 citations

Quantization of the radiation field in an anisotropic dielectric medium

Wei Li, Liu Shi-bing, Yang Wei

There are both loss and dispersion characteristics for most dielectric media. In quantum theory the loss in medium is generally described by Langevin force in the Langevin noise (LN) scheme by which the quantization of the radiation field in various homogeneous absorbing dielectrics can be successfully actualized. However, it is invalid for the anisotropic dispersion medium. This paper extends the LN theory to an anisotropic dispersion medium and presented the quantization of the radiation field as well as the transformation relation between the homogeneous and anisotropic dispersion media.

Chinese Physics B•Jun 1, 2009•4 citations
The photic field in the plane divisional uniform absorbing and dispersive dielectrics is quantized by the canonical quantum theory and the classical Green's function of the system. The concrete forms of the leftwards|traveling and rightwards|traveling polariton and photon operators in the dielectrics and the cavity are determined by use of the identical idea of the contrast with the homogeneous media and the vacuum case, and the quantized expressions of light field in every region are given. Results show that the polariton and the photon operators can be expressed by the forms of the media noise along the propagation with phase weight, and they are closely related to the media distribution, parameters and the light frequency.
We present a one-dimensional quantization scheme for the electromagnetic field in arbitrary planar absorbing and dispersive dielectrics, taking into account explicitly the finite extent of media. The complete form of the electric field operator includes a part that corresponds to the free fields incident from the vacuum towards the medium and a particular solution which can be expressed by using the classical Green-function integral representation of the electromagnetic field. By expressing the classical Green function in terms of the light modes of the dielectric structure, we obtain a natural generalization to absorbing media of the familiar method of mode expansion which strictly applies to non-absorbing media. As an application of our mode expansion, we obtain general quantum-optical input-output relations relating the output photon operators in vacuum to the input photon operators and to the reservoir noise operators. The input-output relations obtained are uniquely determined by the knowledge of the classical light modes of the planar system. We finally show that our quantization scheme for arbitrary planar dielectrics satisfies the prescribed equal-time commutation relations of QED.
The electromagnetic field is quantized in dielectric media that show both loss and dispersion. The complex dielectric function of the medium is assumed to be a known function and the loss is modeled by Langevin forces in the forms of noise current operators. The noise current correlation function is related to the assumed dielectric function by the fluctuation-dissipation theorem. Field quantization is carried out for the infinite homogeneous dielectric, the semi-infinite dielectric, and the dielectric slab, where the fields in the second and third cases are restricted to propagation perpendicular to the dielectric surfaces. The forms of the vector potential operator are obtained in the different spatial regions for all three geometries, and in each case the required canonical commutation relation for the vector potential and its conjugate generalized momentum operator is verified. The spatial dependence of the vacuum field fluctuations is calculated for the two dielectric geometries that have surfaces.
A quantization scheme for the electromagnetic field in absorbing dielectrics developed previously is extended to cover more complicated arrangements of dielectric media and to investigate various limiting cases of the general formalism. The limiting cases include media that have vanishing imaginary parts in their dielectric functions, because either the refractive index or the extinction coefficient vanishes. The further limit of a unit real dielectric function establishes the connection of the formalism with the well-known quantized field expressions in free space. Detailed calculations are presented for the quantization in the system of two different absorbing dielectrics in contact at a plane interface and for the cavity formed in the free space between two separated absorbing dielectrics. The forms of the field operators are determined for both systems, the canonical commutation relations are verified, and the spectra of the vacuum field fluctuations are calculated and illustrated. The calculations are restricted throughout to fields that propagate perpendicular to the dielectric interfaces. \textcopyright{} 1996 The American Physical Society.
A quantization scheme is developed for the radiation and higher order electromagnetic fields in one dimensional periodic, dispersive and absorbing dielectric medium. For this structure, the Green function is solved based on the plane wave expansion method, thus the photon operators, commutation relations and quantum Langevin equations are given and studied based on the Green function approach, moreover, the input-output relations are also derived. It is proved that this quantum theory can be reduced back to that of the predecessors' study on the homogenous dielectric. Based on this method, we find that the transformation of the photon state through the lossy grating is non-unitary and that the notable non-unitary transformation can be obtained by tuning the imaginary part of the permittivity, we also discussed the excellent quantum optical properties for the grating which are similar to the classical optical phenomena. We believe our work is very beneficial for the control and regulation of the quantum light based on gratings.
A quantization scheme for the radiation field in dispersive and absorptive linear dielectrics is developed, which applies to both bulk material and multilayer dielectric structures. Starting from the phenomenological Maxwell equations, where the properties of the dielectric are described by a permittivity consistent with the Kramers-Kronig relations, an expansion of the field operators is performed that is based on the Green function of the classical Maxwell equations and preserves the equal-time canonical field commutation relations. In particular, in frequency intervals with approximately vanishing absorption the concept of quantization through mode expansion for dispersive dielectrics is recognized. The theory further reveals that weak absorption gives rise to space-dependent mode operators that spatially evolve according to quantum Langevin equations in the space domain. To illustrate the applicability of the theory to inhomogeneous structures, the quantization of the radiation field in a dispersive and absorptive one-interface dielectric is performed. \textcopyright{} 1996 The American Physical Society.
There are both loss and dispersion characteristics for most dielectric media. In quantum theory the loss in medium is generally described by Langevin force in the Langevin noise (LN) scheme by which the quantization of the radiation field in various homogeneous absorbing dielectrics can be successfully actualized. However, it is invalid for the anisotropic dispersion medium. This paper extends the LN theory to an anisotropic dispersion medium and presented the quantization of the radiation field as well as the transformation relation between the homogeneous and anisotropic dispersion media.