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

American Journal of Physics

Optical Faraday rotation

P. R. Berman

Published Feb 12, 2010• 23 citations
Publisher

Abstract

Three calculations of optical Faraday rotation are presented in which a linearly polarized field is incident on a medium of harmonic oscillators in the presence of a longitudinal magnetic field. The rotation of the plane of polarization of the field is evaluated using classical oscillators and the Lorentz force equation, quantum oscillators and the Heisenberg equations of motion, and quantum oscillators and a Schrödinger equation approach. It is shown that a simple argument, based on the assumption that a circularly polarized field drives either Δm=1 or Δm=−1 transitions on absorption (m is the magnetic quantum number), leads to an incorrect result for the Verdet constant.

DOI
10.1119/1.3266970

Related papers

Resonant magneto-optical rotation: new twists in an old plot

Dmitry Budker

Nonlinear in laser power, near-resonant light-atom interaction leads to a number of spectacular modifications of a well-known effect -polarization plane rotation in a magnetic field applied along the direction of light propagation.In particular, the rotation can be enhanced by up to nine orders of magnitude compared to the linear case.Faraday effect [ 1 ] is the rotation of the plane of linear light polarization by a medium in a magnetic field applied in the direction of light propagation.In 1898, Macaluso and Corbino eJ, studying absorption spectra of the alkali atoms in the presence of magnetic fields, discovered that the Faraday effect in the vicinity of resonance absorption lines also had a distinct resonant character.The essence of the Macaluso-Corbino effect can be illustrated by considering a simple case of a F= 1 ~ F'=O transition (Fig. 1 ).Linearly polarized light incident on the sample can be resolved into two counter-rotating circular components ( cr~.In the absence of a magnetic field, the M=±l sublevels are degenerate and the optical resonance

•Dec 1, 1997•0 citations

Effect of a nonlinear refractive index on Faraday rotation

Yi Yu, Richard K. Osborn

A theory for the nonlinear (with respect to the electric field) Faraday effect has been developed and applied to a simple model. Within the framework of this model, our analysis shows that the ratio of the nonlinear Verdet constant to the linear Verdet constant is proportional to the intensity of the incident light and depends on the frequency of light, the excitation energy of the model molecule, and the temperature of the medium. This ratio is small under ordinary conditions. However, under certain circumstances it may become large enough for experimental observation.

Physical Review A•Jun 1, 1977•8 citations

Magnetic optical activity in intense laser fields. I. Self-rotation and Verdet constant

Suzanne Giraud-Cotton, V.Paul Kaftandjian, Lewis S. Klein

The Faraday rotation and circular dichroism of dilute gases in longitudinal magnetic fields and subject to strong radiation fields are studied. The use of irreducible tensorial sets as bare-atom states which are then dressed by the laser field allows a simple incorporation of the various multipole relaxation rates into the theory. The treatment considers magnetic fields which produce Zeeman shifts much smaller than inverse collision times but which may be greater or smaller than the multipole relaxation rates. Doppler broadening is also considered. Explicit expressions are given for dipole transitions in a two-level system with arbitrary angular momentum for strong and weak magnetic fields.

Physical Review A•Oct 1, 1985•39 citations

Non-Faraday rotation of photon-echo polarization in ytterbium vapor

Н. Н. Рубцова, В. Н. Ищенко, Хворостов Евгений Борисович +3 more

Non-Faraday rotation of photon-echo polarization was investigated at the $J=1\ensuremath{\leftrightarrow}J=0$ transition in a wide range of longitudinal magnetic field strength. The echo was generated at the intercombination transition $(6s6p)^{3}P_{1}\ensuremath{\rightarrow}(6{s}^{2})^{1}S_{0}$ of $^{174}\mathrm{Yb}$ by two resonant laser pulses of linear (parallel or mutually orthogonal) polarization. A detailed analysis of the echo polarization performed by an angled echo technique has shown quite different behavior in the weak and strong magnetic field limits. The photon echo has polarization close to linear at a magnetic field strength $\mathcal{B}\ensuremath{\leqslant}5\phantom{\rule{0.3em}{0ex}}\mathrm{G}$; its polarization plane rotates around the magnetic field vector clockwise or counterclockwise depending on the magnetic field orientation relative to the wave vector. The photon-echo polarization components and echo power oscillate as functions of $\mathcal{B}$. As the magnetic field increases, the oscillations become smaller and almost disappear at a magnetic field $\mathcal{B}\ensuremath{\approx}40\phantom{\rule{0.3em}{0ex}}\mathrm{G}$; the photon echo does not disappear at this magnetic field, but its polarization vector no longer has a preferred orientation. Numerical calculations of the photon echo generated at a spectral wide line agree with the experimental behavior of the photon-echo polarization for an arbitrary magnetic field.

Physical Review A•Aug 10, 2004•34 citations

Interaction Of Light With Atoms In External Fields

Dmitry Budker, Derek F Kimball, David P. DeMille

Abstract When linearly polarized light propagates through a medium immersed in a magnetic field, the plane of light polarization at the output is rotated (Fig. 4.1); this effect was observed by Michael Faraday almost one hundred and fifty years ago (Faraday 1855). In 1898, the Italian physicists D. Macaluso and O. M. Corbino discovered that Faraday rotation was resonantly enhanced near atomic absorption lines (Macaluso and Corbino 1898).

•Jul 24, 2008•0 citations

Magnetic field rotation of a strong resonance radiation polarization plane in the media with Doppler-broadened transitions of 01 and 10 types

Sergey V. Fomichev

For atomic media with resonant Doppler-broadened transitions of J=0 to J'=1 or J=1 to J'=0 type and taking into account the relaxation due to depolarizing collisions a theory of nonlinear magneto-optic polarization phenomena is developed. The theory is valid in the case of both arbitrary resonance linearly-polarized radiation intensity and arbitrary external magnetic field spatial orientation. The Faraday and Voigt geometries are analysed in detail, and in the case of the Faraday geometry the effect is considered of a noncompensated magnetic field transverse component on the shape of a dependence relating the radiation polarization plane rotation angle to a magnetic field longitudinal component. In the case of the Voigt geometry an essential effect is found of the angle between the radiation initial polarization and transverse magnetic field vectors on the character of the dependence relating the radiation polarization plane rotation angle to the transverse magnetic field magnitude.

Journal of Physics B Atomic Molecular and Optical Physics•Nov 28, 1991•6 citations
Three calculations of optical Faraday rotation are presented in which a linearly polarized field is incident on a medium of harmonic oscillators in the presence of a longitudinal magnetic field. The rotation of the plane of polarization of the field is evaluated using classical oscillators and the Lorentz force equation, quantum oscillators and the Heisenberg equations of motion, and quantum oscillators and a Schrödinger equation approach. It is shown that a simple argument, based on the assumption that a circularly polarized field drives either Δm=1 or Δm=−1 transitions on absorption (m is the magnetic quantum number), leads to an incorrect result for the Verdet constant.
Nonlinear in laser power, near-resonant light-atom interaction leads to a number of spectacular modifications of a well-known effect -polarization plane rotation in a magnetic field applied along the direction of light propagation.In particular, the rotation can be enhanced by up to nine orders of magnitude compared to the linear case.Faraday effect [ 1 ] is the rotation of the plane of linear light polarization by a medium in a magnetic field applied in the direction of light propagation.In 1898, Macaluso and Corbino eJ, studying absorption spectra of the alkali atoms in the presence of magnetic fields, discovered that the Faraday effect in the vicinity of resonance absorption lines also had a distinct resonant character.The essence of the Macaluso-Corbino effect can be illustrated by considering a simple case of a F= 1 ~ F'=O transition (Fig. 1 ).Linearly polarized light incident on the sample can be resolved into two counter-rotating circular components ( cr~.In the absence of a magnetic field, the M=±l sublevels are degenerate and the optical resonance
A theory for the nonlinear (with respect to the electric field) Faraday effect has been developed and applied to a simple model. Within the framework of this model, our analysis shows that the ratio of the nonlinear Verdet constant to the linear Verdet constant is proportional to the intensity of the incident light and depends on the frequency of light, the excitation energy of the model molecule, and the temperature of the medium. This ratio is small under ordinary conditions. However, under certain circumstances it may become large enough for experimental observation.
The Faraday rotation and circular dichroism of dilute gases in longitudinal magnetic fields and subject to strong radiation fields are studied. The use of irreducible tensorial sets as bare-atom states which are then dressed by the laser field allows a simple incorporation of the various multipole relaxation rates into the theory. The treatment considers magnetic fields which produce Zeeman shifts much smaller than inverse collision times but which may be greater or smaller than the multipole relaxation rates. Doppler broadening is also considered. Explicit expressions are given for dipole transitions in a two-level system with arbitrary angular momentum for strong and weak magnetic fields.
Non-Faraday rotation of photon-echo polarization was investigated at the $J=1\ensuremath{\leftrightarrow}J=0$ transition in a wide range of longitudinal magnetic field strength. The echo was generated at the intercombination transition $(6s6p)^{3}P_{1}\ensuremath{\rightarrow}(6{s}^{2})^{1}S_{0}$ of 174Yb^{174}\mathrm{Yb}174Yb by two resonant laser pulses of linear (parallel or mutually orthogonal) polarization. A detailed analysis of the echo polarization performed by an angled echo technique has shown quite different behavior in the weak and strong magnetic field limits. The photon echo has polarization close to linear at a magnetic field strength $\mathcal{B}\ensuremath{\leqslant}5\phantom{\rule{0.3em}{0ex}}\mathrm{G}$; its polarization plane rotates around the magnetic field vector clockwise or counterclockwise depending on the magnetic field orientation relative to the wave vector. The photon-echo polarization components and echo power oscillate as functions of B\mathcal{B}B. As the magnetic field increases, the oscillations become smaller and almost disappear at a magnetic field $\mathcal{B}\ensuremath{\approx}40\phantom{\rule{0.3em}{0ex}}\mathrm{G}$; the photon echo does not disappear at this magnetic field, but its polarization vector no longer has a preferred orientation. Numerical calculations of the photon echo generated at a spectral wide line agree with the experimental behavior of the photon-echo polarization for an arbitrary magnetic field.
For atomic media with resonant Doppler-broadened transitions of J=0 to J'=1 or J=1 to J'=0 type and taking into account the relaxation due to depolarizing collisions a theory of nonlinear magneto-optic polarization phenomena is developed. The theory is valid in the case of both arbitrary resonance linearly-polarized radiation intensity and arbitrary external magnetic field spatial orientation. The Faraday and Voigt geometries are analysed in detail, and in the case of the Faraday geometry the effect is considered of a noncompensated magnetic field transverse component on the shape of a dependence relating the radiation polarization plane rotation angle to a magnetic field longitudinal component. In the case of the Voigt geometry an essential effect is found of the angle between the radiation initial polarization and transverse magnetic field vectors on the character of the dependence relating the radiation polarization plane rotation angle to the transverse magnetic field magnitude.