effect

Faraday effect

The Faraday effect is the rotation of the plane of polarization of light in a material under a magnetic field.
19 related articles · 4 formulas · 2 who worked here

Description

In 1845, Michael Faraday sought a connection between light and magnetism and discovered that heavy glass placed in a strong magnetic field changes the polarization of transmitted light. This became the first proof of the unity of electromagnetism. Essentially, the magnetic field makes the medium anisotropic for light — as if light were forced to go up a spiral staircase where one turn is steeper than the other.

History

Discovered by Michael Faraday in 1845 after years of trying to detect the influence of magnetism on light. Experimenting with samples of heavy flint glass (lead glass) placed between the poles of a powerful electromagnet, he noticed the rotation of the plane of polarization. This phenomenon, along with the discovery of electromagnetic induction, formed the basis of the concept of the unified nature of electricity, magnetism, and light, later developed by James Clerk Maxwell.

How it works

Used in optical isolators (valves) to prevent back-reflections in laser systems, circulators, and modulators. In astrophysics, measurement of Faraday rotation from pulsars and radio sources is used to map magnetic fields in the interstellar and intergalactic medium. Limits of applicability: limited by medium transparency and saturation in strong fields; applicable from radio to ultraviolet radiation.

In practice

Allows building optical isolators in lasers and measuring magnetic fields in the interstellar medium.

Fun fact

Faraday had been trying to find the effect for several years unsuccessfully until he took super-transparent lead glass from a chandelier. It turned out that ordinary glass gave too weak a rotation.

Concept graph →

Formulas

$$\Delta\theta = \mathrm{RM} \cdot \lambda^2$$
Rotation of polarization angle proportional to wavelength squared.
What is in the formula
ΔθvariableRotation angle of polarization plane — polarization rotation angle radian
λvariableWavelength of light — wavelength metre
RMconstantRotation measure, proportional to integrated electron density times magnetic field along the line of sight — rotation measure = varies (e.g., 0.812 rad m^-2 for typical radian per metre squared
δθ={rm}*λ^2 · 2604.27480
$$\text{RM} = \frac{e^3}{2\pi m_e^2 c^4} \int n_e B_\parallel \, dl$$
Rotation measure is proportional to the integral of electron density times parallel magnetic field along the line of sight.
What is in the formula
n_evariableelectron number density — electron number density per cubic metre
B_parallelvariablemagnetic field component along line of sight — magnetic flux density tesla
dlvariableinfinitesimal path element along line of sight metre
econstantelementary charge — elementary charge = 1.602176634e-19 coulomb
m_econstantelectron rest mass — electron mass = 9.1093837015e-31 kilogram
cconstantspeed of light in vacuum — speed of light = 299792458 metre per second
∫operatorsummation over the line of sight — integral operator
{rm}=0.81\intn_eb_\paralleldl · 2606.22354
$$p_m = p_0 \, \exp(-2 \sigma_{\rm RM}^2 \lambda^4)$$
Polarization degree decays exponentially with wavelength due to Faraday rotation dispersion.
What is in the formula
p_mvariableobserved polarization degree — polarization degree
p_0variableintrinsic polarization degree (without Faraday effects) — polarization degree
σ_RMvariabledispersion of rotation measure along the line of sight — rotation measure dispersion radian per square metre
λvariablewavelength of radiation — wavelength metre
expoperatorexponential function — exponential
p_m(f)=p*\exp(-2σ_{\rmrm}^2λ^4) · 2607.00505
p_m=p\exp(-2σ_{rm}^2λ^4) · 2607.00505v1
$$\mathrm{RM} = \frac{e^3}{2\pi m_e^2 c^4} \int_0^L n_e(s) B_\parallel(s) \, ds$$
Rotation measure quantifies Faraday rotation in plasma.
What is in the formula
RMvariableRotation measure — rotation measure radian per metre squared
n_evariableElectron number density — number density per metre cubed
B_parallelvariableMagnetic field component along line of sight — magnetic field tesla
svariablePath length along line of sight — length metre
LvariableTotal path length through plasma — length metre
econstantCharge of a single electron — elementary charge = 1.602176634e-19 coulomb
m_econstantRest mass of an electron — electron mass = 9.1093837015e-31 kilogram
cconstantSpeed of light in vacuum — speed of light = 299792458 metre per second
∫operatorIntegration along the line of sight — integral operator
{rm}=0.812\int_0^ln_e(s)b_\parallel(s)ds\quad{[radm^{-2}]} · 2607.02665v1
rm=\frac{e^3}{2πm_e^2c^4}\int_0^dn_eb_{\parallel}dl · 2607.05289v1

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