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The Kerr effect results from the impressed electric field causes the assymetric molecules of the liquid to align with the field. This causes the liquid to become anisotropic and birefringent. The change in index is given by:
no-ne = K * E2 * lambda
A Kerr Cell is a cell containing the liquid (typically Nitrobenzene) between two flat parallel plates spaced several millimeters. A fairly high voltage (typically 10-20 kV) is placed on the plates..
If the field is such that the cell retards the extraordinary ray by a half wavelength, the polarization rotation will be 90 degrees. If a pair of polarizers is put around the cell, oriented at 45degrees, the assembly acts as a shutter. The voltage required to do this is called the "halfwavelength voltage".
At the half wave voltage, the following is true.
(no-ne)*d = lambda / 2
Note that the wavelength cancels out when rearranging and substituting to give:
Ehalfwave = sqrt( 1/ (2 * d * K))
d = 1 / (2 * K * E^2)
Sample Kerr Constants
For Nitrobenzene (K=2.4E-10 cm/V2 ) and 30 kV/cm (breakdown of air), d = 2.3 cm
(no-ne) = pE
where E is the applied field, and p is a proportionality constant:
A similar calculation to that for Kerr cells can be made to determine the half wave voltage for the cell.
Rotation = VBl
Verdet Constant (if l in millimeters, B in Tesla)
A peculiarity of Faraday rotation is that it rotates the same direction (e.g. Clockwise or Counterclockwise) no matter which direction the light is travelling. This can be used to make a one way light valve with two polarizers set at 45 degrees to each other.
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