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NULL TRANSMISSION ELLIPSOMETRY
In general, the ellipsometric parameters D
and Y
describe the orientation and ellipticity of polarized light.   Physically
for free-standing film, Y
represents the effect of the film on the orientation of polarized light
and D
is related to the biaxiality of the film.   The basic idea of ellipsometry
is to measure the optical parameters, D
and Y
of the film.
Here the figure on the right shows real system picture.   Cartoons
below show system schematic figures.
As shown in
Figure (a), before the laser beam enters the oven, the linear polarized
light passes through a 1/4 wave plate and becomes circular polarized.
  Then the laser beam passes through the window, polarizer, compensator,
sample, a second polarizer (called analyzer) and window.   Finally
it reaches the detector.   The incident angle of the laser beam
is 45o.   The compensator is another 1/4 wave-plate with
its fast axis fixed at 45o to the axis.   Positive angles
are defined as clockwise rotations when looking along the light propagating
direction ( ).   The polarizer and analyzer are
installed in two rotation stages.  Their orientations are controlled
by a computer via a motion controller.   The resolution of the motion
controller is 0.001o.  
In Figure (b), and are the polarizations
parallel and perpendicular to the incident plane of the beam traveling
in the direction, respectively.   Based on these coordinates, the
ellipsometric parameters are defined as follows:   D
is the necessary phase lag between the p- and s-components of the incident
light for the transmitted light to be polarized at an angle Y+90o
relative to the axis.
These two ellipsometric parameters, D
and Y,
are found by rotating the polarizer and analyzer until a null signal
is registered at the detector.   With the configuration described
above, the D=
-2Pn + 90, Y=An,
where Pn and An are the angles of the polarizer
and analyzer relative to the axis.
Then
by studying D
and Y
, molecular packing in the free-standing film can be figured out.  
For example, for a two-layer film as shown left, D
is different for the two cases in which the orientation of electric
field is changed by 180o.   By observing the difference
of D
with different orientation of electric field, different molecular structure
can be notified.   Simulation will be performed to confirm the molecular
arrangement using 4x4 matrix methods.   The figure below presents
three distinct Y
versus D
curves corresponding to three different surface structures observed
at different temperatures in one special liquid crystal compound.
Three curves describe three distinct surface structures (1) nonplanar,
(2) anticlinic and (3) synclinic respectively.   Cartoon beside the figure
shows these three structures.   Symbols are the data and solid lines are
simulation results.
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