Transcript Study of the Faraday Effect In the Laboratory Conducted by

Study of the Faraday Effect In the Laboratory
Conducted by Andreas Gennis and Jason Robin
Presented by Andreas Gennis
The Basis of the Faraday Effect
What is the Faraday Effect?
University of Rochester
Fall 2007
Phy 243W
Advanced Experimental Techniques
Professor Regina Demina, Sergey Korjenevski,
David Starling
My setup
The Faraday effect can be best described with
the aid of the dielectric tensor.
An isotropic
material in the presence of a z-oriented
magnetic field, yields diagonal elements which
are equivalent and one non-zero off-diagonal
element coupling the x and y-components of the
electric field. The dielectric tensor would appear
as such:
ε
ε=
ε´
-ε´
0
0
ε
0
0
ε
In a material without optical absorption, ε is real
and ε´ is imaginary. The more general case of
an absorbing material gives complex values for
both ε and ε´. For dielectrics with diamagnetic
or paramagnetic properties, the off-diagonal
value is proportional to the applied magnetic
field H, while for ferromagnetic and
ferrimagnetic media the element is proportional
to the magnetization M. From the equality seen
below,
Polarized light propagating through a medium and in the same direction as
an externally applied magnetic field, will undergo a rotation.
How the Faraday Effect is used in Practice
The Faraday rotation of radio waves emitted from pulsars
is studied in astronomy to measure the galactic magnetic
field, which permeates the interstellar medium.
B = H + 4πM
we can lay the blame on the magnetic field B.
Polarized light propagating in a dielectric along
the direction of the B field receives different
refractive indices for its right and left-circularly
polarized components.
The California Institute of Technology has used polarized
light emitted from GPS transmitters to measure the total
ionospheric electron content. This data is used to edit
current models of the ionosphere.
A laser (located on the right) of wavelength 630-680 nm passes through a polarizer
(not pictured), through a dielectric located within a solenoid, and traverses one last
polarizer before entering a detector (located on the left).
Data Analysis
For a small range of wavelengths, the relation between the
angle of rotation of the polarization and the magnetic field
simplifies to:
θF = VBL
where the length of the dielectric (L, in cm) is given, the
magnetic field is controlled (B, in mT), and the angle of
rotation is measured (θF, in radians). By varying the magnetic
field, the Verdet constant (V) can be measured.
My Results
n± = (ε ± iε´)^½
Thus, linearly polarized light passing a length L
through the material, experiences a relative
phase shift between the two circular polarized
components.
∆φ = 2πL (n+ - n-) / λ
Of course, the change in the relative phase
between the right and left-circularly polarized
components of the light, is the same as a
rotation in the polarization of linearly polarized
light. This rotation is the Faraday angle:
θF = ½∆φ
In going through a perpendicularly magnetized dielectric
at normal incidence, the two components of a circularly
polarized wave experience different refractive indices.
Each emerge from the medium with a different phase and
amplitude. The amplitudes of the emergent beams are
labeled here by a+ and a–, and their phase difference by
∆φ. The superposition of the circular polarization states
produce elliptical polarization. The angle of rotation of the
major axis of the ellipse from the horizontal direction
(which is here the direction of the incident linear
polarization) is given by θF = ½∆φ, and the ellipticity η is
given by tan η = (a+ - a-)/(a+ + a-).
The data, with a resistance of 2.68 in the solenoid, gave a
Verdet constant of 1.45*10^-4 a factor of 2 larger than the
accepted value