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 Modern Optics

Mode expansion and photon operators in dispersive and absorbing dielectrics

Omar Di Stefano, Salvatore Savasta, R. Girlanda

Published Jan 1, 2001• 31 citations
Publisher

Abstract

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.

DOI
10.1080/09500340108235155

Related papers

Three-dimensional quantum-optical input–output relations for arbitrary planar dielectrics

Salvatore Savasta, Omar Di Stefano, R. Girlanda

We present a three-dimensional quantum theory of light scattering, absorption, and emission in arbitrary planar dielectric systems. The theory is based on a scheme for quantization of the electromagnetic field in dispersive and lossy arbitrary planar dielectrics that takes explicitly into account the finite extent of the medium. We present general quantum-optical input–output relations of the output TE and TM photon operators to the corresponding input photon operators and to the reservoir noise operators. These three-dimensional input–output relations are uniquely determined by knowledge of the classical light modes of the planar dielectric structure.

Journal of the Optical Society of America B•Feb 1, 2002•5 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

Three-dimensional quantization of the electromagnetic field in dispersive and absorbing inhomogeneous dielectrics

Ho Trung Dung, L. Knöll, Dirk‐Gunnar Welsch

A quantization scheme for the phenomenological Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive, and absorbing dielectric medium is developed. The classical Maxwell equations with spatially varying and Kramers-Kronig consistent permittivity are regarded as operator-valued field equations, introducing additional current- and charge-density operator fields in order to take into account the noise associated with the dissipation in the medium. It is shown that the equal-time commutation relations between the fundamental electromagnetic fields $\mathbf{E}^$ and $\mathbf{B}^$ and the potentials $\mathbf{A}^$ and $\stackrel{^}{\ensuremath{\varphi}}$ in the Coulomb gauge can be expressed in terms of the Green tensor of the classical problem. From the Green tensors for bulk material and an inhomogeneous medium consisting of two bulk dielectrics with a common planar interface it is explicitly proven that the well-known equal-time commutation relations of QED are preserved.

arXiv:quant-ph/9711039•Physical Review A•May 1, 1998•373 citations

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

Yin Xiao

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.

Journal of Huaihai Institute of Technology•Jan 1, 2002•0 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

Quantization of the electromagnetic field in dielectrics

B. Hüttner, Stephen Mark Barnett

We present a fully canonical quantization scheme for the electromagnetic field in dispersive and lossy linear dielectrics. This scheme is based on a microscopic model, in which the medium is represented by a collection of interacting matter fields. We calculate the exact eigenoperators for the coupled system and express the electromagnetic field operators in terms of them. The dielectric constant of the medium is explicitly derived and is shown to satisfy the Kramers-Kronig relations. We apply these results to treat the propagation of light in dielectrics and obtain simple expressions for the electromagnetic field in the medium in terms of space-dependent creation and annihilation operators. These operators satisfy a set of equal-space commutation relations and obey spatial Langevin equations of evolution. This justifies the use of such operators in phenomenological models in quantum optics. We also obtain two interesting relationships between the group and the phase velocity in dielectrics.

Physical Review A•Oct 1, 1992•631 citations
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.
We present a three-dimensional quantum theory of light scattering, absorption, and emission in arbitrary planar dielectric systems. The theory is based on a scheme for quantization of the electromagnetic field in dispersive and lossy arbitrary planar dielectrics that takes explicitly into account the finite extent of the medium. We present general quantum-optical input–output relations of the output TE and TM photon operators to the corresponding input photon operators and to the reservoir noise operators. These three-dimensional input–output relations are uniquely determined by knowledge of the classical light modes of the planar dielectric structure.
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 phenomenological Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive, and absorbing dielectric medium is developed. The classical Maxwell equations with spatially varying and Kramers-Kronig consistent permittivity are regarded as operator-valued field equations, introducing additional current- and charge-density operator fields in order to take into account the noise associated with the dissipation in the medium. It is shown that the equal-time commutation relations between the fundamental electromagnetic fields $\mathbf{E}^$ and $\mathbf{B}^$ and the potentials $\mathbf{A}^$ and $\stackrel{^}{\ensuremath{\varphi}}$ in the Coulomb gauge can be expressed in terms of the Green tensor of the classical problem. From the Green tensors for bulk material and an inhomogeneous medium consisting of two bulk dielectrics with a common planar interface it is explicitly proven that the well-known equal-time commutation relations of QED are preserved.
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.
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.
We present a fully canonical quantization scheme for the electromagnetic field in dispersive and lossy linear dielectrics. This scheme is based on a microscopic model, in which the medium is represented by a collection of interacting matter fields. We calculate the exact eigenoperators for the coupled system and express the electromagnetic field operators in terms of them. The dielectric constant of the medium is explicitly derived and is shown to satisfy the Kramers-Kronig relations. We apply these results to treat the propagation of light in dielectrics and obtain simple expressions for the electromagnetic field in the medium in terms of space-dependent creation and annihilation operators. These operators satisfy a set of equal-space commutation relations and obey spatial Langevin equations of evolution. This justifies the use of such operators in phenomenological models in quantum optics. We also obtain two interesting relationships between the group and the phase velocity in dielectrics.