Kerr effect

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:

n_o-n_e = K * E² * lambda

where:
lambda is the wavelength of the light
E is the electric field strength
K is the Kerr constant

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.

(n_o-n_e)*d = lambda / 2

where
d is length of cell
other variables as above.

Note that the wavelength cancels out when rearranging and substituting to give:

E_halfwave = sqrt( 1/ (2 * d * K))
for calculating the halfwave E field

d = 1 / (2 * K * E^2)
for calculating required length of cell

Sample Kerr Constants

Nitrobenzene	2.4E-10 cm/V2
Glasses	3E-14 to 2E-23 cm/V2
Water	4.4E-12 cm/V2

For Nitrobenzene (K=2.4E-10 cm/V² ) and 30 kV/cm (breakdown of air), d = 2.3 cm

Pockels

(n_o-n_e) = 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.

KDP (Potassium Dihydrogen Phosphate)	3.6E-11 meter/Volt
Deuterated KDP (KD*P)	8.0E-11 meter/Volt
Lithium Niobate (LiNbO3)	3.7E-10 meter/Volt

Faraday

Rotation = VBl

where
Rotation in radians
V is Verdet Constant
B is the magnetic field strength
l is the length

Verdet Constant (if l in millimeters, B in Tesla)

fused quartz	0.004
dense flint glass	0.11
Benzene	0.0087

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.