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 Physics B Atomic Molecular and Optical Physics

The absorption of arbitrarily polarized light by atoms and molecules

Matthew Fewell

Published Jul 14, 1993• 8 citations
Publisher

Abstract

The theory of the incoherent absorption of light by quantum systems is examined to determine how the transition probabilities of the substates of an initial energy level vary as the polarization of the exciting radiation is altered. The aim is to identify polarizations for which the spread of transition rates among the substates of an energy level is a minimum. To achieve this, a new set of quantization axes is proposed for the case of elliptical polarization. The definition of these new axes is based on a consideration of Poincare's sphere. As the polarization is varied, the axes move smoothly between the sets of axes conventionally used for linear and circular polarization. Using these axes, expressions are derived for the transition probability for the absorption of a photon of specified polarization by a specified substate of the initial level. This expression applies to any multipolarity of transition and covers the case of partial polarization.

DOI
10.1088/0953-4075/26/13/017

Related papers

Quantum Electrodynamic Theory of Light Radiation

Guang S. He

Abstract The quantum electrodynamic theory, based on the quantization of the electromagnetic field, introduces the concept of photon and the related photon creation operator, photon annihilation operator, and photon number operator. It is used to describe stimulated Raman scattering, stimulated Kerr scattering, and various multiphoton excitation processes. Within this theoretical regime the light (as a photon field) and molecules are treated as a combined quantum mechanical system. The light emission or absorption is always accompanied by the quantum transition of the whole system from its initial eigenstate to the final eigenstate. The molecular emission or absorption probability rate is determined by the corresponding transition matrix elements of the interaction Hamiltonian operator.

•Feb 25, 2022•0 citations

Radiative Transitions between Discrete Quantum States

Greg J. Tallents

Radiation can change the energy state of matter via three optical processes: spontaneous emission, absorption and stimulated emission. In spontaneous emission, an excited atomic or molecular state decays to a lower energy state with the emission of a photon of energy equal to the difference in the quantum state energies. Photon absorption is the reverse process, with a photon causing excitation from a lower to an excited quantum state. Stimulated emission was first proposed by Einstein in a paper published in 1917. He attempted to balance spontaneous emission and photon absorption, but could not get the correct balance without the postulated process of stimulated emission (see Section 4.2). With stimulated emission, an excited quantum state is stimulated to decay to a lower quantum state by an impinging photon. The existing photon survives with another identical photon being created (so that energy is conserved). The rates at which radiative transitions occur can be calculated using quantum mechanics. The time-dependent Schrodinger equation is used with the system wavefunction comprising time-varying linear combinations of the two wavefunctions for the lower and upper quantum states. In semi-classical treatments, an atom is treated quantum mechanically with the radiation field treated classically. There is a perturbation in energy associated with, say, the electric field of the radiation interacting with the electric dipole of the atom, though other interactions can be significant if the electric dipole interaction energy is small. In absorption, for example, a differential equation representing the change in ‘weighting’ of the wavefunction from the lower to upper state is obtained. A ‘time constant’ for the speed of change represents the rate of the radiative process. We examine the quantum mechanical nature of radiation absorption in Section 10.1 before discussing (Section 10.3) another important parameter arising with radiative transitions between discrete bound quantum states: the lineshape function. Quantum Theory of the Atom–Radiation Interaction An expression for the Einstein B-coefficient for photo-absorption is derived using quantum mechanics in this section. Einstein determined the detailed balance relationship between the rates of spontaneous emission, photo-absorption and stimulated emission when light interacts with an atom by considering an atomic system of two energy levels which are in equilibrium with a black-body radiation field. We use a semi-classical treatment where the atom is treated quantum mechanically and the radiation field is treated as a classical oscillating electric field.

Cambridge University Press eBooks•Feb 20, 2018•0 citations

The scattering of partially polarized light by oriented atoms

M. Ya. Agre

A compact expression is derived for the cross section of scattering of arbitrarily polarized light by oriented atomic systems, in which the dependence on the geometric parameters and on the Stokes parameters preassigning the state of partial polarization of incident radiation is explicitly separated. It is found that the cross section of any photoprocess accompanied by photon absorption (stimulated emission) contains the sum of the products of the circular and linear dichroisms of the process by the respective Stokes parameters. The effect of the atomic orientation and of the dissipation of light energy on the polarization singularities and angular distribution of scattered light is investigated. In particular, it is demonstrated that, in the case of an open dissipation channel, the angular distribution remains dependent on the atomic orientation even in the case of zero degree of circular polarization of scattered radiation.

Journal of Experimental and Theoretical Physics•Sep 1, 2001•0 citations

Scattering of partially polarized light by aligned atoms

M. Ya. Agre

A compact expression for the cross section of scattering of an arbitrarily polarized light by aligned atomic systems is obtained, in which the dependence on the geometric parameters and the Stokes parameters specifying the state of partial polarization of the incident radiation is represented in explicit form. The effect of atomic alignment and the processes of dissipation of the light energy on the polarization specific features and the angular distribution of the scattered light is investigated. In particular, it is shown that, if a dissipative channel is accessible, the angular distribution and the degree of linear polarization of scattered light depend on the degree of circular polarization of the incident radiation η 2 . Dissipative processes also induce the circular polarization of the light scattered by aligned atoms when η 2 =0.

Optics and Spectroscopy•Apr 1, 2002•2 citations

Angular Distribution in the Two-Quantum Atomic Photoeffect

Edmond Arnous, Serge Klarsfeld, S T Wane

Total and differential two-photon ionization cross sections are derived in the framework of perturbation theory, assuming a simple one-electron atomic model. It is shown that for an unpolarized target the angular distribution of the ejected electrons has the general form $\mathrm{a}+b{cos}^{2}\ensuremath{\theta}+c{cos}^{4}\ensuremath{\theta}$, whatever the quantum numbers $n$, $l$, of the initial energy level, and the state of polarization (linear or circular) of the incident radiation. The total transition rates for circularly and for linearly polarized light are quite different from each other. For an arbitrary $\mathrm{nl}$ state, the theoretically allowed maximum value of their ratio is $\frac{3}{2}$. Further analytical and numerical results are presented for hydrogen. The Appendix contains several useful summation formulas for spherical harmonics.

Physical Review A•May 1, 1973•53 citations

Kinetics of atoms in the field produced by elliptically polarized waves

Прудников Олег Николаевич, А. В. Тайченачев, Anatolii M Tumaikin +1 more

The kinetics of atoms with degenerate energy levels in the field produced by elliptically polarized waves is considered in the semiclassical approximation. Analytic expressions for the force acting on an atom and for the diffusion coefficient in the momentum space are derived for the optical transition J g =1/2→J e = 1/2 in the slow atom approximation. These expressions are valid for an arbitrary one-dimensional configuration of the light field and for an arbitrary intensity. The peculiarities of the atomic kinetics are investigated in detail; these peculiarities are associated with ellipticity of light waves and are absent in particular configurations formed by circularly or linearly polarized waves, which were considered earlier.

Journal of Experimental and Theoretical Physics•Mar 1, 2004•20 citations
The theory of the incoherent absorption of light by quantum systems is examined to determine how the transition probabilities of the substates of an initial energy level vary as the polarization of the exciting radiation is altered. The aim is to identify polarizations for which the spread of transition rates among the substates of an energy level is a minimum. To achieve this, a new set of quantization axes is proposed for the case of elliptical polarization. The definition of these new axes is based on a consideration of Poincare's sphere. As the polarization is varied, the axes move smoothly between the sets of axes conventionally used for linear and circular polarization. Using these axes, expressions are derived for the transition probability for the absorption of a photon of specified polarization by a specified substate of the initial level. This expression applies to any multipolarity of transition and covers the case of partial polarization.
Abstract The quantum electrodynamic theory, based on the quantization of the electromagnetic field, introduces the concept of photon and the related photon creation operator, photon annihilation operator, and photon number operator. It is used to describe stimulated Raman scattering, stimulated Kerr scattering, and various multiphoton excitation processes. Within this theoretical regime the light (as a photon field) and molecules are treated as a combined quantum mechanical system. The light emission or absorption is always accompanied by the quantum transition of the whole system from its initial eigenstate to the final eigenstate. The molecular emission or absorption probability rate is determined by the corresponding transition matrix elements of the interaction Hamiltonian operator.
Radiation can change the energy state of matter via three optical processes: spontaneous emission, absorption and stimulated emission. In spontaneous emission, an excited atomic or molecular state decays to a lower energy state with the emission of a photon of energy equal to the difference in the quantum state energies. Photon absorption is the reverse process, with a photon causing excitation from a lower to an excited quantum state. Stimulated emission was first proposed by Einstein in a paper published in 1917. He attempted to balance spontaneous emission and photon absorption, but could not get the correct balance without the postulated process of stimulated emission (see Section 4.2). With stimulated emission, an excited quantum state is stimulated to decay to a lower quantum state by an impinging photon. The existing photon survives with another identical photon being created (so that energy is conserved). The rates at which radiative transitions occur can be calculated using quantum mechanics. The time-dependent Schrodinger equation is used with the system wavefunction comprising time-varying linear combinations of the two wavefunctions for the lower and upper quantum states. In semi-classical treatments, an atom is treated quantum mechanically with the radiation field treated classically. There is a perturbation in energy associated with, say, the electric field of the radiation interacting with the electric dipole of the atom, though other interactions can be significant if the electric dipole interaction energy is small. In absorption, for example, a differential equation representing the change in ‘weighting’ of the wavefunction from the lower to upper state is obtained. A ‘time constant’ for the speed of change represents the rate of the radiative process. We examine the quantum mechanical nature of radiation absorption in Section 10.1 before discussing (Section 10.3) another important parameter arising with radiative transitions between discrete bound quantum states: the lineshape function. Quantum Theory of the Atom–Radiation Interaction An expression for the Einstein B-coefficient for photo-absorption is derived using quantum mechanics in this section. Einstein determined the detailed balance relationship between the rates of spontaneous emission, photo-absorption and stimulated emission when light interacts with an atom by considering an atomic system of two energy levels which are in equilibrium with a black-body radiation field. We use a semi-classical treatment where the atom is treated quantum mechanically and the radiation field is treated as a classical oscillating electric field.
A compact expression is derived for the cross section of scattering of arbitrarily polarized light by oriented atomic systems, in which the dependence on the geometric parameters and on the Stokes parameters preassigning the state of partial polarization of incident radiation is explicitly separated. It is found that the cross section of any photoprocess accompanied by photon absorption (stimulated emission) contains the sum of the products of the circular and linear dichroisms of the process by the respective Stokes parameters. The effect of the atomic orientation and of the dissipation of light energy on the polarization singularities and angular distribution of scattered light is investigated. In particular, it is demonstrated that, in the case of an open dissipation channel, the angular distribution remains dependent on the atomic orientation even in the case of zero degree of circular polarization of scattered radiation.
A compact expression for the cross section of scattering of an arbitrarily polarized light by aligned atomic systems is obtained, in which the dependence on the geometric parameters and the Stokes parameters specifying the state of partial polarization of the incident radiation is represented in explicit form. The effect of atomic alignment and the processes of dissipation of the light energy on the polarization specific features and the angular distribution of the scattered light is investigated. In particular, it is shown that, if a dissipative channel is accessible, the angular distribution and the degree of linear polarization of scattered light depend on the degree of circular polarization of the incident radiation η 2 . Dissipative processes also induce the circular polarization of the light scattered by aligned atoms when η 2 =0.
Total and differential two-photon ionization cross sections are derived in the framework of perturbation theory, assuming a simple one-electron atomic model. It is shown that for an unpolarized target the angular distribution of the ejected electrons has the general form $\mathrm{a}+b{cos}^{2}\ensuremath{\theta}+c{cos}^{4}\ensuremath{\theta}$, whatever the quantum numbers nnn, lll, of the initial energy level, and the state of polarization (linear or circular) of the incident radiation. The total transition rates for circularly and for linearly polarized light are quite different from each other. For an arbitrary nl\mathrm{nl}nl state, the theoretically allowed maximum value of their ratio is 32\frac{3}{2}23​. Further analytical and numerical results are presented for hydrogen. The Appendix contains several useful summation formulas for spherical harmonics.
The kinetics of atoms with degenerate energy levels in the field produced by elliptically polarized waves is considered in the semiclassical approximation. Analytic expressions for the force acting on an atom and for the diffusion coefficient in the momentum space are derived for the optical transition J g =1/2→J e = 1/2 in the slow atom approximation. These expressions are valid for an arbitrary one-dimensional configuration of the light field and for an arbitrary intensity. The peculiarities of the atomic kinetics are investigated in detail; these peculiarities are associated with ellipticity of light waves and are absent in particular configurations formed by circularly or linearly polarized waves, which were considered earlier.