In physics, the Faraday effect or
Faraday rotation is a magneto-optical
phenomenon—that is, an interaction
between light and a magnetic field in a
medium. The Faraday effect causes a
rotation of the plane of polarization
which is linearly proportional to the
component of the magnetic field in the
direction of propagation. Formally, it
is a special case of
gyroelectromagnetism obtained when the
dielectric permittivity tensor is
diagonal.
Discovered by Michael Faraday in 1845,
the Faraday effect was the first
experimental evidence that light and
electromagnetism are related. The
theoretical basis of electromagnetic
radiation was completed by James Clerk
Maxwell in the 1860s and 1870s. This
effect occurs in most optically
transparent dielectric materials under
the influence of magnetic fields.
The Faraday effect is caused by left and
right circularly polarized waves
propagating at slightly different
speeds, a property known as circular
birefringence. Since a linear
polarization can be decomposed into the
superposition of two equal-amplitude
circularly polarized components of
opposite handedness and different phase,
the effect of a relative phase shift,
induced by the Faraday effect, is to
rotate the orientation of a wave's
linear polarization.
The Faraday effect has a few
applications in measuring instruments.
For instance, the Faraday effect has
been used to measure optical rotatory
power and for remote sensing of magnetic
fields. The Faraday effect is used in
spintronics research to study the
polarization of electron spins in
semiconductors. Faraday rotators can be
used for amplitude modulation of light,
and are the basis of optical isolators
and optical circulators; such components
are required in optical
telecommunications and other laser
applications.
History
By 1845, it was known through the work
of Fresnel, Malus, and others that
different materials are able to modify
the direction of polarization of light
when appropriately oriented, making
polarized light a very powerful tool to
investigate the properties of
transparent materials. Faraday firmly
believed that light was an
electromagnetic phenomenon, and as such
should be affected by electromagnetic
forces. He spent considerable effort
looking for evidence of electric forces
affecting the polarization of light,,
starting with decomposing electrolytes.
However, his experimental methods were
not sensitive enough, and the effect was
only measured thirty years later by John
Kerr.
Faraday then attempted to look for the
effects of magnetic forces on light
passing through various substances.
After several unsuccessful trials, he
happened to test a piece of "heavy"
glass, containing traces of lead, that
he had made during his earlier work on
glass manufacturing. Faraday observed
that when a beam of polarized light
passed through the glass in the
direction of an applied magnetic force,
the polarization of light rotated by an
angle that was proportional to the
strength of the force. He was later able
to reproduce the effect in several other
solids, liquids, and gases by procuring
stronger electromagnets.
The discovery is well documented in
Faraday's daily notebook, which has
since been published. On 13 Sept. 1845,
in paragraph #7504, under the rubric
Heavy Glass, he wrote:
He summarized the results of his
experiments on 30 Sept. 1845, in
paragraph #7718, famously writing:
Physical Interpretation of the Faraday
effect
The linear polarized light that is seen
to rotate in the Faraday effect can be
seen as consisting of the superposition
of a right- and a left- circularly
polarized beam. We can look at the
effects of each component separately,
and see what effect this has on the
result.
In circularly polarized light the
direction of the electric field rotates
at the frequency of the light, either
clockwise or counterclockwise. In a
material, this electric field causes a
force on the charged particles
comprising the material. The affected
motion will be circular, and circularly
moving charges will create their own
field in addition to the external
magnetic field. There will thus be two
different cases, the created field will
be parallel to the external field for
one polarization, and in the opposing
direction for the other polarization
direction - thus the net B field is
enhanced in one direction and diminished
in the opposite direction. This changes
the dynamics of the interaction for each
beam and one of the beams will be slowed
down more than the other, causing a
phase difference between the left- and
right-polarized beam. When the two beams
are added after this phase shift, the
result is again a linearly polarized
beam, but with a rotation in the
polarization direction.
The direction of polarization rotation
depends on the properties of the
material through which the light is
shone. A full treatment would have to
take into account the effect of the
external and radiation-induced fields on
the wavefunction of the electrons, and
then calculate the effect of this change
on the refractive index of the material
for each polarization, to see whether
the right- or left circular polarization
is slowed down more.
Mathematical formulation
Formally, the magnetic permeability is
treated as a non-diagonal tensor as
expressed by the equation:
The relation between the angle of
rotation of the polarization and the
magnetic field in a transparent material
is:
where
β is the angle of rotation
B is the magnetic flux density in the
direction of propagation
d is the length of the path where the
light and magnetic field interact
is the Verdet constant for the material.
This empirical proportionality constant
varies with wavelength and temperature
and is tabulated for various materials.
A positive Verdet constant corresponds
to L-rotation when the direction of
propagation is parallel to the magnetic
field and to R-rotation when the
direction of propagation is
anti-parallel. Thus, if a ray of light
is passed through a material and
reflected back through it, the rotation
doubles.
Some materials, such as terbium gallium
garnet have extremely high Verdet
constants. By placing a rod of this
material in a strong magnetic field,
Faraday rotation angles of over 0.78 rad
can be achieved. This allows the
construction of Faraday rotators, which
are the principal component of Faraday
isolators, devices which transmit light
in only one direction. The Faraday
effect can, however, be observed and
measured in a Terbium-doped glass with
Verdet constant as low as.
Similar isolators are constructed for
microwave systems by using ferrite rods
in a waveguide with a surrounding
magnetic field.
A thorough mathematical description can
be found here
Faraday rotation in the interstellar
medium
The effect is imposed on light over the
course of its propagation from its
origin to the Earth, through the
interstellar medium. Here, the effect is
caused by free electrons and can be
characterized as a difference in the
refractive index seen by the two
circularly polarized propagation modes.
Hence, in contrast to the Faraday effect
in solids or liquids, interstellar
Faraday rotation has a simple dependence
on the wavelength of light, namely:
where the overall strength of the effect
is characterized by RM, the rotation
measure. This in turn depends on the
axial component of the interstellar
magnetic field B||, and the number
density of electrons ne, both of which
vary along the propagation path. In
Gaussian cgs units the rotation measure
is given by:
or in SI units:
where
ne(s) is the density of electrons at
each point s along the path
B||(s) is the component of the
interstellar magnetic field in the
direction of propagation at each point s
along the path
e is the charge of an electron;
c is the speed of light in a vacuum;
m is the mass of an electron;
' is the vacuum permittivity;
The integral is taken over the entire
path from the source to the observer.
Faraday rotation is an important tool in
astronomy for the measurement of
magnetic fields, which can be estimated
from rotation measures given a knowledge
of the electron number density. In the
case of radio pulsars, the dispersion
caused by these electrons results in a
time delay between pulses received at
different wavelengths, which can be
measured in terms of the electron column
density, or dispersion measure. A
measurement of both the dispersion
measure and the rotation measure
therefore yields the weighted mean of
the magnetic field along the line of
sight. The same information can be
obtained from objects other than
pulsars, if the dispersion measure can
be estimated based on reasonable guesses
about the propagation path length and
typical electron densities. In
particular, Faraday rotation
measurements of polarized radio signals
from extragalactic radio sources
occulted by the solar corona can be used
to estimate both the electron density
distribution and the direction and
strength of the magnetic field in the
coronal plasma.
Faraday rotation in the ionosphere
Radio waves passing through the Earth's
ionosphere are likewise subject to the
Faraday effect. The ionosphere consists
of a plasma containing free electrons
which contribute to Faraday rotation
according to the above equation, whereas
the positive ions are relatively massive
and have little influence. In
conjunction with the earth's magnetic
field, rotation of the polarization of
radio waves thus occurs. Since the
density of electrons in the ionosphere
varies greatly on a daily basis, as well
as over the sunspot cycle, the magnitude
of the effect varies. However the effect
is always proportional to the square of
the wavelength, so even at the UHF
television frequency of 500 MHz, there
can be more than a complete rotation of
the axis of polarization. A consequence
is that although most radio transmitting
antennas are either vertically or
horizontally polarized, the polarization
of a medium or short wave signal after
reflection by the ionosphere is rather
unpredictable. However the Faraday
effect due to free electrons diminishes
rapidly at higher frequencies so that at
microwave frequencies, used by satellite
communications, the transmitted
polarization is maintained between the
satellite and the ground.
Faraday rotation of semiconductors
Due to spin-orbit coupling, undoped GaAs
single crystal exhibits much larger
Faraday rotation than glass. Considering
the atomic arrangement is different
along the and plane, one might think the
Faraday rotation is polarization
dependent. However, experimental work
revealed an immeasurable anisotropy in
the wavelength range from 880–1,600 nm.
Based on the large Faraday rotation, one
might be able to use GaAs to calibrate
the B field of the terahertz
electromagnetic wave which requires very
fast response time. Around the band gap,
the Faraday effect shows resonance
behavior.
More generally, semiconductors return
both electro-gyration and a Faraday
response in the high frequency domain.
The combination of the two is described
by gyroelectromagnetic media, for which
gyroelectricity and gyromagnetism may
occur at the same time.
Faraday rotation of organic materials
In organic materials, Faraday rotation
is typically small, with a Verdet
constant in the visible wavelength
region on the order of a few hundred
degrees per Tesla per meter, decreasing
proportional to  in this region. While
the Verdet constant of organic materials
does increase around electronic
transitions in the molecule, the
associated light absorption makes most
organic materials bad candidates for
applications. There are however also
isolated reports of large Faraday
rotation in organic liquid crystals
without associated absorption.
Faraday rotation in plasmonic/magnetic
materials
In 2009  γ-Fe2O3-Au core-shell
nanostructures were synthesized to
integrate magnetic and plasmonic
properties into one composite. Faraday
rotation with and without the plasmonic
materials was tested and rotation
enhancement under 530 nm light
irradiation was observed. Researchers
claim that the magnitude of the
magneto-optical enhancement is governed
primarily by the spectral overlap of the
magneto-optical transition and the
plasmon resonance.
The reported composite
magnetic/plasmonic nanostructure can be
visualized to be a magnetic particle
embedded in a resonant optical cavity.
Because of the large density of photon
states in the cavity, the interaction
between the electromagnetic field of the
light and the electronic transitions of
the magnetic material is enhanced,
resulting in a larger difference between
the velocities of the right- and
left-hand circularized polarization,
therefore enhancing Faraday rotation.
See also
Magneto-optic Kerr effect
Electro-optic Kerr effect
Faraday rotator
Scientific phenomena named after people
Inverse Faraday effect
Optical rotation
QMR effect
Voigt effect
Polarization spectroscopy
Magnetic circular dichroism
Faraday Cage
References
External links
Faraday Rotation
Electro-optical measurements
