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POLARIZATION
The purpose of this laboratory exercise is to study the polarization properties of an electromagnetic plane
wave. The following polarization components are used in this work, a sheet or prism polarizer, a half-wave
plate and a quarter wave plate. A helium-neon laser operating at the red 633 nm wavelength is used as the
light source.
Polarized electromagnetic wave
The solution of Maxwell's equations for an electromagnetic plane wave shows that the electric and
magnetic vectors lie in planes normal to the direction of propagation (see Lecture notes and Exercises). The
components of the electric vector (Ex and Ey) oscillating in two perpendicular directions add up and the
resulting vector describes, in general, an ellipse. Such a plane wave is said to be elliptically polarized.
Depending on the difference in the phase  and the amplitudes of the components (equal or not), the
polarization state of the resulting vector can be degenerated into a linear or circular polarization (Fig. 1).
Figure 1. Possible polarization states of a plane wave.
The polarization state of the electromagnetic wave can be studied by using polarizing components in which
the effect of crystal birefringence is used. Widely used polarization prisms are made of two pieces of calcite
glued together by using Canada balsam (Glan-Thompson prism) or with an air gap in between (Glan-Taylor
prism). These prisms can be used for the production of linearly polarized light.
Figure 2. Glan-Thompson (a) and Glan-Taylor (b) polarizers. Transmitted light is almost 100% linearly polarized.
Another type of polarizers, called sheet polarizers, are usually made of thin films consisting of long polymer
molecules all oriented in certain direction. The molecules have been made conductive by doping the
polymer with iodine. When the E field oscillates along the same axis as the molecules are oriented, the
energy of the field gets absorbed and transformed into heat. When the E field is perpendicular to the so
called molecular “wire-grid”, the light will be transmitted (Fig. 2)
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th
Figure 3. A wire grid polarizer transmits the field that is perpendicular to the wires (Figure from Optics, 4 ed., E.Hecht).
Malus’s law
The maximum transmittance of the incident light Io occurs when the electric vector oscillates in the plane
parallel to the polarization plane of the polarizer. The intensity of the transmitted beam I decreases when
the polarizer is further rotated. This decrease is described by Malus's law
I  I 0 cos 2  ,
where  is the angle between the electric vector of incident light and the polarization plane of the polarizer.
Retarders (Wave plates)
The polarization orientation or the state of the light beam can be changed by using retardation plates
(wave-plates). A common retardation plate is cut from a birefringent crystal in such a way that the optic
axis is parallel to the surface planes of the wave plate. Depending on the crystal type (positive uniaxial or
negative uniaxial), the optic axis is either fast or slow axis. This means that light polarized in the orientation
of the optic axis travels either faster or slower compared to its orthogonal component. The cause for the
difference in speed is due to double refractive index inherent to the crystal (hence the name birefringence).
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Figure 4. Principle of the half-wave plate. The e-wave (grey periods) propagates faster than the o-wave. Emerging constituent
components have relative phase difference of  = 180 deg. Linearly polarized light has remained linearly polarized but oscillates in
th
neighbouring quadrants (Figure from Optics 4 ed., Hecht).
Commonly used retardation components are /2- and /4-wave plates (Fig 4 and 5) usually made of quartz
or mica. The name wave plate refers to fact that orthogonally polarized components of light experience a
phase difference of /2 or  when exiting the plate (see Fig 1 and 5). This is achieved by cutting the crystal
to very exact thickness so that the phase shift is precisely half or quarter of the wavelength. Because of
material dispersion, wave plates function properly only at the wavelength they were designed to.
Figure 5. Half-wave plate (/2) and quarter-wave plate (/4).
For more detailed information about the wave plates look sections 8.4.2 and 8.7.1 in Optics 4th ed, Hecht.
EXPERIMENT
The aim of the laboratory exercise is to study the polarization properties of the monochromatic
electromagnetic wave by using several polarization components. The work comprises of two stages. In the
first stage, the performance of the polarizers is studied and Malus's law is to be confirmed. The obtained
experience in conjunction with the theoretical background from the lecture notes is thereafter used to
identify the types of the retardation plates.
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List of equipment
- A HeNe laser at 633-nm wavelength and power supply,
- Two polarizers mounted in the rotation stages,
- Two undefined retardation plates mounted in the rotation stages,
- A silicon photodiode and a digital multimeter,
- Opto-mechanical components.
The laser should be handled with extreme care.
Be aware of NOT directing the laser beam into anybody’s eye!
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Measurements
1. Malus’s law
The measurement set-up for the confirmation of Malus's law is shown in Fig. 6. In the measurements two
polarizers are used. One polarizer is used to linearly polarize the laser beam. By rotating the other polarizer
(analyzer) the linearly polarized light is attenuated. The detector and the digital multimeter are used to
observe the changes in the intensity when the laser beam is attenuated.
a) Make sure that the laser is directed towards the detector and that possible reflections will not
reach people in the laboratory room. Switch the laser on. Be careful when touching the laser, try
not to move it, since the laser beam acts as an optical axis for all components used in the
experiment,
Figure 6. Measurement set-up for the study of the polarization effects and components.
b) Adjust the mode of the multimeter to DCI and set the integration time to 2 seconds (NPLC 100). Set
the range at first to 100 mA. Observe the reading and reduce the range if necessary. Use smallest
range possible but avoid overload.
c) Mount only one polarizer into the laser beam first. Do not touch the glass surfaces of the
polarizers! The left one depicted in Figure 6. The polarizer is properly aligned when the backreflection from the polarizer is almost co-axial with the incident beam and seen on the iris
diaphragm placed between the laser and the polarizer. Avoid targeting the back-reflected beam
directly back to the laser.
d) By, simultaneously, rotating the polarizer and looking at the reading of the multimeter find out the
position of the polarizer at which the reading value is the highest. Remember that the stability of
the intensity in the laser beam is ±1 %. This position corresponds to the maximum transmittance of
the linearly polarized light. Record the position of the polarizer. Keep the polarizer in its position for
the whole experiment.
Hint: It is easier to find the minimum position and then rotate the polarizer to the maximum
position. What is the amount of rotation?
e) Mount the analyzer into the beam. The analyzer is properly aligned when the back-reflection from
the analyzer is seen on the housing of the polarizer. Repeat step d for the analyzer. The position of
the analyzer will be used as a reference for a 0-degree rotation angle for further measurements,
f)
Block the beam by placing a piece of dark object as close as possible to the laser. Record the
reading (3 samples) of the multimeter to get the background signal of the detector,
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g) Open the laser beam. Take three consequent readings of the photocurrent generated. Record the
reading values for 0-degree rotation angle in the Measurement Table. By rotating the analyzer by a
step of 30 record the reading of the multimeter. Repeat the measurements three times at each
rotation angle,
h) Restore the position of the analyzer corresponding to the maximum transmittance of the light in
the measurement system,
i)
In the calculations, the measured background of the detector has to be taken into account, i.e
substitute from the photocurrent readings. Calculate also the theoretical relative intensity passing
through the rotated analyzer and list the values into Measurement Table. The last column in the
Measurement Table indicates the agreement between the measured and the predicted values of
the relative intensity passing through the rotated analyzer:
I
I

    ,ave 2 0,ave  1 100% ,
 cos 

where I0 is the photocurrent at maximum transmittance position and I is the photocurrent at
rotated positions.
2. Retardation plates
The measurement set-up for identification of the retardation plates is similar to that of shown in Fig. 6. In
this part, two types of retardation plates, /2- and /4- wave plates, is to be identified. Do not touch the
surfaces of the wave plates!
a) Mount the retardation plate marked as #1 into holder. Rotate the plate in such a way that the angle
between the polarization plane of the laser beam and the fast axis of the retardation plate is 45".
Direction of the fast axis of the plate is marked on the plate housing.
b) By, simultaneously, rotating the analyzer and looking at the reading of the multimeter, determine
the type of the plate based on the principle of the retardation plates. Record the type in the
Measurement Table subsection 2a,
c) Remove item #1 and restore the position of the analyzer corresponding to the maximum
transmittance of the light in the measurement system,
d) Repeat steps 2a-2d for the retardation plate #2
e) Mount the /2-wave plate into the holder. Set the angle between the polarization plane of the
laser beam and the optical axis of the retarder to 0. Record the reading of the multimeter in the
Measurement Table subsection 2b. Rotate the plate by steps of 10 and the analyzer by steps 20.
In each rotation angle record the photocurrent value. In the calculations, substitute the background
signal measured in the 1st stage
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Measurement table
Date and time:
Names and student numbers:
1. Malus’s law
Maximum transmittance:
Component:
Background signal of the detector:
Position [ ]
Dark current ID [mA]
Polarizer
Analyzer
Confirmation of the Malus’s law:
Rotation
angle,
-0 []
Reading,
I [mA]
Photocurrent,
Average
photocurrent,
I’ [mA]
(I-ID)
I’,ave [mA]
Relative intensity
Measured
Calculated
Difference, Δ
[%]
I' ,ave I' 0 ,ave cos 2   0 
0
30
60
90
120
150
180
Conclusions:
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2. Wave plates
Wave plate type:
#1 is _____ -wave plate
#2 is _____ -wave plate
Half-wave plate:
Rotation angle of
the wave plate,
Rotation angle of
the analyzer,
 []
a []
0
0
10
20
20
40
30
60
Reading,
Photocurrent,
Relative intensity,
I [mA]
I’ [mA]
I , I , 0
(I-ID)
Conclusions:
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