An Investigation of
`Spectrum' Polarizing Plates
Himadri (Soni) Kakran
Mentor: Dr. John Noé
Laser Teaching Center
Department of Physics & Astronomy
Stony Brook University
I decided to do a full-semester project in the Laser Teaching Center after I
saw and learned about all sorts of fascinating optical demonstrations and
devices at the beginning of the semester. I wanted my project to have something
to do with my field of study, Computer Engineering. Every computer engineer
should understand the functioning of liquid-crystal display (LCD) screens, so I
thought something related to this would make a good project.
Polarized light plays an essential role in the working of LCD screens, so I
decided to learn more about polarized light. (I knew about linearly polarized
light from high school physics, but I had never heard of elliptically polarized
A few weeks into the semester, we noticed that a new item was available
from Surplus Shed: `Spectrum Plates'
(item number L3692) that had been removed from some obsolete display device.
They were said to "work exactly like polarizing sheets but instead of just
getting darker the plates change to different colors." We decided to purchase
these unknown plates and try to figure out how they worked.
Polarized light describes the orientation of the electric field vector in light
waves. The general form of polarized light is elliptical where the tip of the
electric field vector describes an ellipse in the plane of projection. This
happens when the two components of electric field vector are out of phase and
are of different amplitudes. Furthermore, there are two special cases of
elliptically polarized light; linearly polarized and circularly
polarized. When the two components of electric field vector are in phase
the resultant light is linearly polarized whereas when the two components are
ninety degrees out of phase the resultant light is circularly polarized.
In order to form elliptically polarized light it is required that random light
(unpolarized light) be first passed through a linear polarizer and then through
a retarder. A retarder is a birefringent material having a different refractive
index along each of two perpendicular axes. Due to this difference in
refractive index the retarder (waveplate) creates a phase difference between
the components of the electric field vector along each axis. The retardance of
a wave plate can be expressed as:
here Δn is the difference in the two refractive indices, L is the
thickness of the waveplate and λ is the wavelength of the incident
light. As observed in the formula, the retardance(Γ) of a waveplate is
inversely proportional to wavelength(λ), provided Δn doesn't
change with wavelength.
Observations of the spectrum plates
Spectrum plates viewed through a linear polarizer sheet. The sheet
is rotated about 90 degrees
between the two images. Note also that the two
plates produce complimentary colors.
The first thing we noticed was that the plates produced a different
effect depending on which side was facing the unpolarized light
source. We labelled the two sides A and B and did the
following tests to try to figure out why it mattered which side faced
the light source.
First we placed side A down, facing the randomly polarized
light source, and observed the transmitted light through a linear
polarizer sheet (an analyzer). As we rotated the analyzer we observed
beautiful colors that changed as the analyzer sheet was rotated. The
resulting light was hypothesized to be elliptically polarized. As
discussed earlier, in order to obtain elliptically polarized light, it
is necessary to pass unpolarized light first though a linear polarizer
and then a retarder. Therefore, side A was assumed to be a
linear polarizer and side B was assumed to be a retarder.
Next, we turned the plate over, so that side B was down, facing
the light source. As we rotated the analyzer sheet we observed either
complete transmittion or zero transmission. We know that a retarder
has no effect on unpolarized light, so we concluded that the resulting
light was linearly polarized and therefore side A was a linear
polarizer and side B was a retarder, verifying our earlier
Thus the spectrum plates are a sandwich of a linear polarizer
[A] and a retarder [B].
So why then do colors appear? White light is a mixture of all visible
wavelengths, so the colors are all there from the beginning. But
different wavelengths have a different retardance, according to the
formula above, and therefore the ellipticity of the transmitted light
depends on wavelength. When analyzed with the final linear polarizer
the elliptically polarized light is passed to different degrees. In
other words some colors are suppressed or even totally blocked while
others are fully transmitted.
Determining retardance (theory)
The next step was to determine the relationship between the retardance
of the plate and wavelength of incident light. One can see from the
formula that the retardance of a waveplate is inversely proportional
to the wavelength of the incident light. Thus if a plot of retardance
vs. 1/wavelength was to be made, the graph should be a straight line
passing through the origin. Of course, this will be true only if
Δn is relatively independent of wavelength.
To construct a plot of retardance vs. 1/wavelength it was necessary to
measure the intensity of the resultant elliptically polarized light
for different wavelengths. This would help in determining the
retardance of the waveplate for each wavelength. Using the Jones
matrix analysis a formula was derived for the intensity of the
resulting light in terms of the retardance of the plate. The final
formula expressed the intensity of any arbitrarily polarized light
passed through a linear polarizer. The intensity of the resulting
light was found to be:
Here's the Jones matrix calculation I did to get this result.
Determining retardance (experiment)
As stated earlier the main goal was to determine the retardance of the
waveplate for certain wavelengths provided in the Laser Lab. Four different
lasers were used for the experiment.
In the setup, firstly the given laser was mounted on a stand. In front of which
the 'spectrum' plate was placed in an upright position with its linear
polarizer side facing the laser and the retardar side facing the opposite
direction. Next we placed a rotating analyzer followed by the photo-detector.
The photodetector was connected to a multimeter and the intensity of the
resulting light from the spectrum plates was recorded in milli-amperes.
The above rotating dial consisted of a mounted linear polarizer.
We measured the intensity of light as a function of the rotating analyzer angle
in increments of five degrees. An intensity verses angle plot was then created
using the measured values. A theory curve was also plotted on the same graph
using the earlier derived formula for the intensity of an arbitrary polarized
light. Using Excel and the square-sum formula, the different
parameters(amplitude, offset, retardance) were manipulated so as to best fit
the theory curve to the observed values. Thus, the value of retardance for the
given wavelength was determined. The above procedure was repeated for each
individual laser. It is to be noted that the retardance determined for each
wavelength was always between 0 and 180 degrees, as explained further below.
A sample set of data table and graph for the red laser.
Data Analysis and Result
As these experiments only determined the effective retardance(say x) of the
plates between 0 and 180 degrees, the next step was to determine the total
retardance of the 'spectrum' plates. Given the fact that this effective
retardance corresponds to many possible values of the total retardance
according to the relationship =m*(360)+-x where (m=1,2......), other values
greater than 180 degrees were calculated. We plotted these possible values of
total retardance as a function of 1/wavelength. Thus, by fitting a line from
the origin through the ambiguous measured retardance values, we determined the
total retardance of the 'spectrum' plates with respect to any wavelength.
Retardance vs. 1/wavelength graph of Plate 2
The calculated slope of the line was 3.547 * 10^(-6)
A good reference for Jones matrix calculus is:
Eugene Hecht, Optics, Third Edition, (Addison-Wesley)
COPYRIGHT 2009 ALL RIGHTS RESERVED HIMADRI KAKRAN