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 the Optical Society of America B

One-photon electrodynamics in optical fiber with fluorophore systems I One-photon correspondence principle for electromagnetic field propagation in matter

Rod W. C. Vance, Francois J. Ladouceur

Published Mar 15, 2007• 3 citations
Publisher

Abstract

A system of coupled quantum harmonic oscillators (QHOs) whose Hamiltonian conserves photon number begets a one-photon correspondence principle (OPCoP), which allows solutions to the classical linear Maxwell equations for propagation in matter to be reinterpreted as a precise description of a one-photon state. We state, prove, and explore the OPCoP, whereby the vast extant body of linear, sourceless optical waveguide theory [Optical Waveguide Theory (Chapman & Hall, 1983)] can be applied to the exact analysis of one-photon propagation in optical fibers.

DOI
10.1364/josab.24.000928

Related papers

One-photon electrodynamics in optical fiber with fluorophore systems II One-polariton propagation in matter and fibers from the one-photon correspondence principle

Rod W. C. Vance, Francois J. Ladouceur

A system of coupled quantum harmonic oscillators whose Hamiltonian conserves photon number begets a one-photon correspondence principle (OPCoP), which allows solutions to the classical linear Maxwell equations for propagation in matter to be reinterpreted as precise descriptions of one-photon states. With the help of the OPCoP, we derive the linear classical Maxwell equations from the Schrödinger equation for one-polariton state evolution. The role of the matter's initial quantum state in setting the macroscopic medium parameters is made explicit. It is shown that most of the kinds of linear Maxwell equations possible follow from this model, thus showing that the vast extant body of linear, sourceless optical waveguide theory [Optical Waveguide Theory (Chapman and Hall, 1983)] can be applied to the exact analysis of one-photon propagation in optical fibers.

Journal of the Optical Society of America B•Mar 15, 2007•3 citations

One-photon electrodynamics in optical fiber-fluorophore systems: III One-polariton propagation in fluorophore-driven fibers

Rod W. C. Vance, Francois J. Ladouceur

A simple model of the electromagnetic field coupled to matter as a system of coupled quantum harmonic oscillators (QHOs) with a photon number conserving Hamiltonian is specialized to a translationally invariant optical fiber and then equipped with a QHO model for a one-photon fluorophore source. In the narrowband fluorescence limit, this fluorophore model becomes the same as the classical model for a current loop antenna.

Journal of the Optical Society of America B•May 17, 2007•2 citations

One-Photon Electrodynamics in Fibre-Fluorophore Systems

Rod W. C. Vance, Francois J. Ladouceur

We show how Maxwell's equations describe one-photon propagation in optical fibre - fluorophore systems. In particular, macroscopic electromagnetic field measurements on a system at ordinary power levels precisely define the system's one-photon states.

International Conference on Optical Internet•Jun 1, 2007•0 citations

Electrodynamics I: Macroscopic Interaction of Light and Matter

Michael E. Thomas

Thus far, we have developed the properties of the electromagnetic field at optical frequencies, based on Maxwell’s equations. These equations further give a classical macroscopic perspective on the coupling of the propagation media to the field, as presented in Chapter 2. The macroscopic properties of a medium are based on averaged microscopic properties. The microscopic energy structure of matter was presented in Chapter 3, covering gases, solids, and liquids by employing mostly quantum models. We now proceed to the next level of development, the dynamic description of the interaction between the optical field and the propagation medium as a function of the field frequency and propagation media variables (e.g., energy structure, temperature, and pressure). In this chapter, the classical electromagnetic field is coupled to discrete frequency oscillators via Newton’s equation of motion. This approach leads to the popular classical oscillator model, often presented in introductory books on lasers. The classical oscillator model is an incomplete theory and can be only a semiempirical model. In the next chapter, a more detailed and comprehensive approach, which also includes statistical and quantum mechanics, is used leading to robust semiclassical and quantum oscillator models. This chapter and the next are the basis for the applied models presented in Part II of this book. Classical electrodynamics is based on Maxwell’s equations, as given in Chapter 2, and the Lorentz force relation, as given below: . . . F = q[E + (v × B)]. (4.1) . . . These equations cover the classical description of the interaction of light and matter. The first term in Eq. 4.1 represents coupling of the electric field to the medium. As discussed in Chapter 2 (Section 2.2), the leading mechanism for this is the electric dipole moment. To see that this is the coupling mechanism in the first term, consider the potential function driving this force, F = −∇V(r) = −∇(−qr · E). The above expression contains the dipole moment, as defined in Chapter 2. The second term in Eq. 4.1 represents coupling of the magnetic field to the medium.

Oxford University Press eBooks•Sep 28, 2006•1 citation

Introduction

Malin Premaratne, Govind Prasad Agrawal

In this introductory chapter we focus on the interaction of optical fields with matter because it forms the basis of signal amplification in all optical amplifiers. According to our present understanding, optical fields are made of photons with properties precisely described by the laws of quantum field theory [1]. One consequence of this wave–particle duality is that optical fields can be described, in certain cases, as electromagnetic waves using Maxwell's equations and, in other cases, as a stream of massless particles (photons) such that each photon contains an energy h ν, where h is the Planck constant and ν, is the frequency of the optical field. In the case of monochromatic light, it is easy to relate the number of photons contained in an electromagnetic field to its associated energy density. However, this becomes difficult for optical fields that have broad spectral features, unless full statistical features of the signal are known [2]. Fortunately, in most cases that we deal with, such a detailed knowledge of photon statistics is not necessary or even required [3, 4]. Both the linear and the nonlinear optical studies carried out during the last century have shown us convincingly that a theoretical understanding of experimental observations can be gained just by using wave features of the optical fields if they are intense enough to contain more than a few photons [5]. It is this semiclassical approach that we adopt in this book. In cases where such a description is not adequate, one could supplement the wave picture with a quantum description.

Cambridge University Press eBooks•Feb 3, 2011•0 citations

Quantum propagation in fibers and waveguides

P. D. Drummond, Mark S. Hillery

Optical fibers are the backbone of the world's communication systems. They also represent the simplest example of a photonic device, where photons in waveguides replace electrons in wires. More sophisticated devices than this can be made, in which all the optical components – including multiple waveguided modes – are integrated on a chip. It is important to understand the quantum noise properties of these systems. While in some respects these systems can be treated as one-dimensional, there are additional features. Dispersion is due not just to material properties, but also to the waveguide geometry. The nonlinearity comes from a combination of material and geometric properties as well. There is, of course, a quantum aspect to these photonic devices, in which quantum noise occurs due to random effects caused by nonlinearity and gain. Optical devices based on waveguides are, of course, not just simple fibers. One can have multiple waveguides with various types of linear coupling. The intrinsic nonlinearity of the dielectric leads to four-wave mixing, which can be an important source of correlated photons, both for fundamental tests of quantum mechanics, and for applications in quantum information. It is often essential to include effects due to anisotropies of various types, as well as material dispersion. In dielectrics, another effect that should be included is the coupling of vibrational modes of the (solid) dielectric to the propagating field, which gives rise to Raman and Brillouin scattering effects. This allows us to obtain a more detailed and correct theory of quantum noise than the simplified case treated in Chapter 3.

Cambridge University Press eBooks•Mar 27, 2014•0 citations
A system of coupled quantum harmonic oscillators (QHOs) whose Hamiltonian conserves photon number begets a one-photon correspondence principle (OPCoP), which allows solutions to the classical linear Maxwell equations for propagation in matter to be reinterpreted as a precise description of a one-photon state. We state, prove, and explore the OPCoP, whereby the vast extant body of linear, sourceless optical waveguide theory [Optical Waveguide Theory (Chapman & Hall, 1983)] can be applied to the exact analysis of one-photon propagation in optical fibers.
A system of coupled quantum harmonic oscillators whose Hamiltonian conserves photon number begets a one-photon correspondence principle (OPCoP), which allows solutions to the classical linear Maxwell equations for propagation in matter to be reinterpreted as precise descriptions of one-photon states. With the help of the OPCoP, we derive the linear classical Maxwell equations from the Schrödinger equation for one-polariton state evolution. The role of the matter's initial quantum state in setting the macroscopic medium parameters is made explicit. It is shown that most of the kinds of linear Maxwell equations possible follow from this model, thus showing that the vast extant body of linear, sourceless optical waveguide theory [Optical Waveguide Theory (Chapman and Hall, 1983)] can be applied to the exact analysis of one-photon propagation in optical fibers.
Thus far, we have developed the properties of the electromagnetic field at optical frequencies, based on Maxwell’s equations. These equations further give a classical macroscopic perspective on the coupling of the propagation media to the field, as presented in Chapter 2. The macroscopic properties of a medium are based on averaged microscopic properties. The microscopic energy structure of matter was presented in Chapter 3, covering gases, solids, and liquids by employing mostly quantum models. We now proceed to the next level of development, the dynamic description of the interaction between the optical field and the propagation medium as a function of the field frequency and propagation media variables (e.g., energy structure, temperature, and pressure). In this chapter, the classical electromagnetic field is coupled to discrete frequency oscillators via Newton’s equation of motion. This approach leads to the popular classical oscillator model, often presented in introductory books on lasers. The classical oscillator model is an incomplete theory and can be only a semiempirical model. In the next chapter, a more detailed and comprehensive approach, which also includes statistical and quantum mechanics, is used leading to robust semiclassical and quantum oscillator models. This chapter and the next are the basis for the applied models presented in Part II of this book. Classical electrodynamics is based on Maxwell’s equations, as given in Chapter 2, and the Lorentz force relation, as given below: . . . F = q[E + (v × B)]. (4.1) . . . These equations cover the classical description of the interaction of light and matter. The first term in Eq. 4.1 represents coupling of the electric field to the medium. As discussed in Chapter 2 (Section 2.2), the leading mechanism for this is the electric dipole moment. To see that this is the coupling mechanism in the first term, consider the potential function driving this force, F = −∇V(r) = −∇(−qr · E). The above expression contains the dipole moment, as defined in Chapter 2. The second term in Eq. 4.1 represents coupling of the magnetic field to the medium.
In this introductory chapter we focus on the interaction of optical fields with matter because it forms the basis of signal amplification in all optical amplifiers. According to our present understanding, optical fields are made of photons with properties precisely described by the laws of quantum field theory [1]. One consequence of this wave–particle duality is that optical fields can be described, in certain cases, as electromagnetic waves using Maxwell's equations and, in other cases, as a stream of massless particles (photons) such that each photon contains an energy h ν, where h is the Planck constant and ν, is the frequency of the optical field. In the case of monochromatic light, it is easy to relate the number of photons contained in an electromagnetic field to its associated energy density. However, this becomes difficult for optical fields that have broad spectral features, unless full statistical features of the signal are known [2]. Fortunately, in most cases that we deal with, such a detailed knowledge of photon statistics is not necessary or even required [3, 4]. Both the linear and the nonlinear optical studies carried out during the last century have shown us convincingly that a theoretical understanding of experimental observations can be gained just by using wave features of the optical fields if they are intense enough to contain more than a few photons [5]. It is this semiclassical approach that we adopt in this book. In cases where such a description is not adequate, one could supplement the wave picture with a quantum description.
Optical fibers are the backbone of the world's communication systems. They also represent the simplest example of a photonic device, where photons in waveguides replace electrons in wires. More sophisticated devices than this can be made, in which all the optical components – including multiple waveguided modes – are integrated on a chip. It is important to understand the quantum noise properties of these systems. While in some respects these systems can be treated as one-dimensional, there are additional features. Dispersion is due not just to material properties, but also to the waveguide geometry. The nonlinearity comes from a combination of material and geometric properties as well. There is, of course, a quantum aspect to these photonic devices, in which quantum noise occurs due to random effects caused by nonlinearity and gain. Optical devices based on waveguides are, of course, not just simple fibers. One can have multiple waveguides with various types of linear coupling. The intrinsic nonlinearity of the dielectric leads to four-wave mixing, which can be an important source of correlated photons, both for fundamental tests of quantum mechanics, and for applications in quantum information. It is often essential to include effects due to anisotropies of various types, as well as material dispersion. In dielectrics, another effect that should be included is the coupling of vibrational modes of the (solid) dielectric to the propagating field, which gives rise to Raman and Brillouin scattering effects. This allows us to obtain a more detailed and correct theory of quantum noise than the simplified case treated in Chapter 3.