The University of Hong Kong
Department of Physics
PHYS2426 Intermediate Experimental Physics Laboratory
Experiment No. 2426-12: The Faraday Effect
K.F. Ho/Dr. S.W. Fan/Prof. P.K. MacKeown/August 2000
Aim:
The objective of this experiment is to use an optical setup to observe the Faraday
Rotation Effect described by equation (1) in flint glass. The wavelength dependence
of the Verdet constant in equation (2) is observed as a result of wavelength dispersion
in a material medium.
Background:
In 1845 Michael Faraday discovered that the manner in which light propagates
through a material medium could be influenced by an externally applied magnetic
field. He found that when linearly polarized light passed through a piece of glass, the
plane of polarization was rotated in the presence of a strong magnetic field applied in
the direction of propagation of the light. The Faraday Effect was one of the earliest
indications of the interrelationship between electromagnetism and light Ref. [1].
The effect is used today in applications, and in fundamental physics research. In one
application, the Faraday Effect has been used to make optical modulators, Ref. [1].
Such devices can be employed as light switches.
A more current (1999) application of the Faraday Effect is to monitor the extremely
fast electron spin precession in semiconductor and semiconductor quantum well
materials, Ref [2,3].
Classical Theory of the Faraday Effect
Verdet Constant and Angle of Rotation
The angle  , through which the plane-of-vibration of the electric field rotates, is
given by the empirically determined expression
  VBd
(1)
where B is the applied magnetic field (in Tesla), d is the length of the medium
traversed (in cm), and V= V (  ) is a proportionality factor known as the Verdet
constant which depends on the wavelength of the light. The unit for V is usually
expressed as radian per Tesla meter (1Tesla=10000Gauss). A representative value for
V in the case of flint glass is 31700 min of arc/T m (0.0317 min of arc/Gauss cm)
from Ref. [1].
2426-12 The Faraday Effect
This experiment has three basic parts (completion of
each depends upon the scheduled time):
(1) Calibration of the magnetic field using a Gauss
meter.
(2) Investigation of the rotation of the plane of
polarization, at various settings of the magnetic field,
and for a fixed wavelength of light.
(3) Investigation of the rotation of the plane of
polarization, at a fixed magnetic field and for different
wavelength of light.
Relation to Circular Birefringence
Polarized light passing through the electronic structure of some material media may
undergo optical rotation - the phenomenon of circular birefringence. A beam of
linearly polarized light can be thought of as a superposition of left and right circularly
polarized components with equal amplitudes. For a material that is birefringent, the
indices of refraction are different for the left and right circularly polarized
components of light passing through the material. Each polarization component
traverses the sample with a different refractive index and thus with a different speed.
On leaving the sample, left and right circular components are out of phase. The
superposition of the two circular polarizations again results in linearly polarized light
but with its plane of polarization rotated from its original direction before entering the
sample.
Passage of Light Through a Dispersive Medium in a Magnetic Field
In a non-birefringent material, how can an applied magnetic field cause the left and
right circularly polarized light to have different indices of refraction? It arises from
the interaction of the electrons in the medium with the radiation. However, these
electrons are not free, they are bound in the atomic orbits, and when there is a
magnetic field applied these orbits precess about the field direction - Larmor
precession. As a result from the point of view of the electrons, the two circularly
rotating components of the radiation appear to have different frequencies
(wavelengths), and if the refractive index depends on the wavelength, n  n(  ) , the
propagation velocity of the two components will differ. As shown in the appendix
this gives rise to a net rotation of the electric vector given by (1), where the constant V
is given by
 e  dn 
V ( )  

 2m c d 
(2)
where  is the wavelength of the linearly polarized. This is the expression for the
Verdet constant, in units of min arc/(Tesla cm), and it has the value of
 dn 
V  10083   .
 d 
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2426-12 The Faraday Effect
Experiment:
Apparatus
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Transformer Power Supply for lamp (Leybold model 52125)
5 Amps Current Supply for Magnets
Digital multimeter for measurement of magnet current
A Gauss meter with Hall probe
Two coils 250 turns for magnets
Pasco OS 8020 fiber optic light guide and meter display
Halogen Lamp Housing w/100W lamp (Leybold model 45064)
Picture Slider and holder for color filters
Linear polarizer with coarse rotation
Linear polarizer with fine rotation (1deg resolution)
Focusing lens with 50mm focal length
Two linear rails
Five Adjustable optical mounts
Rectangular flint glass sample
Four Color filters
Setup
(see Fig.3)
Procedure:
Halogen Lamp and Current Supply
Before starting the experiment, check that the necessary items are situated with the
experimental setup.
(1) Check to see if the halogen lamp is working properly. With the Leybold
(model 52125) lamp current supply TURNED OFF, connect two wires from
the Leybold supply to the rear connectors of the black halogen lamp unit,
which should have already been placed on the optical rail.
(2) On the model 52125 use the left and right most output connectors, since this
would give the required output current of 10Amps to the lamp unit. After the
electrical connection is made, turn the lamp supply on. If the lamp and/or
current supply are working, the lamp should turn on immediately and be very
bright. The lamp may need to be stabilized initially for 10 minutes so leave it
on for the duration of the experiment.
(Caution: Try not to touch the lamp housing, it can get very HOT very soon.
Also never disconnect the current supply wires while the lamp is on. This may
cause electrical sparks at the connectors.)
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2426-12 The Faraday Effect
Magnetic Field Calibration
In this part of the experiment, the magnetic field between the two shaped magnet pole
pieces is calibrated as a function of the magnet supply current.
(1) First, carefully remove the piece of flint glass placed between the magnet
pole faces. Place the piece of flint glass gently into the (black) 35mm film
container.
(2) Identify the gauss meter and its accompanied Hall probe. The meter may be a
Lakeshore or a UniLab model 612003 gauss meter with a LCD display. Use a
clamp stand and clamp to fasten the Hall probe. On the UniLab meter, use the
2000mT range (10Gauss/1mTesla). If the 200mT range is used the displayed
result should be divided by 10. On either unit, with the probe fastened, move
the clamp stand so that the tip of the Hall probe is situated in the space
between the coned pole pieces.
(3) Connect two wires to the two 250 turns coils to a magnet current supply.
Make sure that the current supply is turned off before the connections are
made. The two coils are situated immediately below the coned magnet pole
pieces. The connections between these two coils should be in series. Place a
multimeter in series with the coils to monitor the current that is supplied by
the magnet current supply.
(4) Turn on the gauss meter and set the meter reading to zero. Then turn on the
magnet current supply and slowly increase the current to the magnets.
Increment the current in steps of approximately 0.5Amps up to a maximum of
8Amps. For each value of the current, record the reading from the gauss
meter.
(5) Make a plot of the measured magnetic field(in Gauss unit) versus the current.
This should be a straight line with nearly zero intercept. After the last current
value has been measured, slowly, decrease the supply current to the magnets
so that the current reduces back to zero.
Focusing Light onto the Fiber Optic Cable
The Pasco OS-8020 Photometer
A Pasco model OS-8020 photometer is used to detect the polarized light. his
photometer can measure light level down to a sensitivity of 0.1lux (the level of
illuminance on a night with a full moon). The light intensity level, from the polarized
beam in a darkened room, is in the range of 0.1-3 lux, and depends on the wavelength
of the light.
Alignment of Polarizers
(1) Turn on the halogen lamp by switching on the lamp power supply (Model
52125).
(2) A picture slider is placed after the condenser lens on the lamp housing (see
figure 2). The picture slider has two positions and can accommodate up to
two color filters. Place just one color filter into placed in the holder. Move
the picture slider into a position so that only white light comes out from the
lamp.
(3) The beam of white light should pass through the holes of the coned magnet
pole pieces. Two linear polarizers should be in place on the optical rail and in
the path of the light beam. One is situated between the lamp and the magnet
(refer to figure 3 for details). This polarizer is used to form linearly polarized
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2426-12 The Faraday Effect
light from the lamp. The second polarizer, called an analyzer, is placed
between the magnet and a focusing lens (focal length of 50mm).
(4) Rotate the analyzer polarizer so that maximum brightness can be observed
when a piece of paper (or a white screen) is placed just after the analyzer.
Remove the piece of paper. At this point, the transmission axes of the two
polarizers should be nearly parallel.
Focus of Light Beam
(1) An optical fiber should be mounted, on a stand, as the rightmost component
on the optical rail, and the opening in the fiber is placed directly along the
beam path. Next, slowly move the f=50mm, focusing lens, along the optical
rail so that the halogen lamplight is focused directly onto the entrance of the
optical fiber. This may cause the focused light beam to exceed the entrance
diameter of the fiber cable. This is acceptable since we need to get as much
light into the fiber as possible. Similarly, the brightness of the focused spot
can be simultaneously monitored on the Pasco meter display.
(2) To obtain a focused spot, no further adjustment of the lamp would be needed.
However, due to repeated usage of the experimental setup, the position of the
lamp, along the rail, may change from time to time. If a sharp image of the
lamp cannot be made, by simply moving the f=50mm lens along the optical
rail, then a focused image may also be obtained by slowly moving the
adjustment rod connected to the lamp (see figure 1). To do this, first loosen
the arresting screw that holds the adjustment rod. Make sure to lock the
arresting screw when a sharp image is formed at the entrance position of
optical fiber.
Color Filter and Zeroing of the Light Meter
(1) Place a color filter into one of the empty slots of the slide holder. Place the
piece of flint glass back into position between the coned magnet pole pieces.
The white light from the lamp should still be able to reach the entrance of the
fiber optics cable.
(2) Move the picture slider so that the color filter blocks the white light and only
light from the color filter is observed. In a darkened room, one can observe
the dim colored light at the entrance of the fiber optics cable.
(Important: The analog meter connected to the optics cable needs to be
properly adjusted in order to obtain reliable results.)
(3) Place a piece of paper in front of the optics cable, to block the colored light
beam. Now, adjust the zero offset, so that the meter reading is nearly zero.
Next, adjust the sensitivity on the meter so that the needle deflects to nearly
full scale. For this, the gain on the meter may also need to be adjusted.
Remove the piece of paper from the beam path. The meter reading should
now be roughly stable and fluctuations of one or two small divisions may be
observable.
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2426-12 The Faraday Effect
Figure 1. Pasco OS-8020 photometer. Fiber optics cable not shown.
Arresting Screw
Picture Slider
Lamp Adjustment Rod
Connecting wires to
AC 12V/10A supply
Figure 2. Leybold model 450 64 Halogen Lamp Housing w/picture slider
Figure 3. The optical fiber from the Pasco OS-8020 photometer (not shown) is
placed to the left of the 50mm focal length lens. The optical fiber is mounted so
that the focused light beam covers the entrance to the fiber.
(Keep in mind that scattered light from flash lights or the swing arm desk lamp
used in nearby experiments may affect the above zero offset adjustment.)
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2426-12 The Faraday Effect
Measurement of the Angle of Rotation
The rotation angles are to be measured for two settings: one is without magnetic field
and the other with the magnetic field applied to the flint glass sample. The simplest
way to do this would be, with no applied field, to set the polarizer and analyzer axes
parallel, i.e. to give maximum intensity, and when the field is applied to find the
rotation of the analyzer necessary to restore this maximum.
However, because of the Malus' law, I  I 0 cos 2  , where  is the angle between the
plane of polarization of the incident light and the axis of the analyzer, the intensity is
least sensitive to the angle at the maximum ( dI / d  0 , also true at the minimum).
The rotation necessary to restore the signal when    / 4 is a more sensitive
measure of the angle of rotation, and it is this method which is described below.
Rotation angle as a function of the applied magnetic field.
With no applied magnetic field.
(1) Slowly rotate the analyzer so as to get a maximum reading, I 0 (largest meter
deflection), on the light meter. You may need to try locating the maximum
by rotating the axis of the polarizer several times. Record the angle value,
where this maximum occurs.
(2) Rotate the analyzer to angles on either side of the maximum I 0 , such that the
measured intensities are 50% of I 0 . Record the angle values and designate
these as  L , R for the angles on the left and right sides of I 0 respectively.
(3) Repeat steps (1) and (2) five times and find the average values  L ,  R
together with their errors. The error in the average is obtained from the
standard deviation of the five measurements.
Use different kinds of color filter, and start magnet supply current for 5 Amps.
The color filters are labeled with serial numbers on them, the wavelength for
maximum transmission of the filters are listed below.
(Important: When changing the color filters, handle the filters by the square edges,
and try avoid touching the glass portion of the filters.)
Color Filters
Wavelength (nm)
Serial no.
Violet
440
46813
Blue w/violet
450
46811
Blue-green
520
46809
Yellow
570
46805
(1) Repeat steps (1) to (3) as in section With no applied magnetic field above, to
find the average values  L' ,  R' .
(2) During the measurement, record any changes in the supply current and include
these changes as part of the error for the magnetic field measurement.
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2426-12 The Faraday Effect
(3) The Faraday rotation angle,  , is obtained from the difference in the average
angle values,    '   , for the two cases with and without applied magnetic
field.
(4) Plot the average rotation angle  for  L' ,  R' versus magnetic field.
(5) Repeat the above procedures for magnetic current 6,7 and 8 Amps.
Investigation of the wavelength dispersion of flint glass
(1) Using a fixed value of the magnetic field set the magnet supply current so that
the current meter reads 5amps.
(2) Repeat steps (1) to (3) as in section Use different kinds of color filter above,
to obtain values of  L' ,  R' and  for the other color filters.
(3) Plot a graph of  versus the color filter wavelength.
References:
(1) E. Hecht, Optics 3rd. Edition (Addison Wesley, 1998), p.362.
(2) Lu J. Sham, "Closer to Coherence Control", Science vol. 277, 1258 (1997).
(3) J.M. Kikkawa et al, "Room-Temperature Spin Memory in Two-Dimensional
Electron Gases", Science vol. 277, 1284 (1997).
(4) F. L. Pedrotti and P. Bandettini, "Faraday rotation in the undergraduate
advanced laboratory", Am. J. Phys. 58 (6) 542 (1990).
(5) F.J. Loeffler, "A Faraday rotation experiment for the undergraduate physics
laboratory", Am. J. Phys. 51 (7) 661 (1983).
(6) D.A. Van Baak, "Resonant Faraday rotation as a probe of atomic dispersion",
Am. J. Phys. 64 (6) 724 (1996).
(7) RCA Photomultiplier Handbook.
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