Mathematical Analysis
In 1941 R. Clark Jones developed a method to represent polarization of light using vectors. Named after its inventor, these vector are called Jones Vectors. A Jones Vector has the form
,
where Ex and Ex are the amplitudes of the x and y components of the electric field, j is the imaginary number and represents the phases of the x and y components. Then in this applet, the polarized light may be represent by the Jones Vector
where x is the magnitude of the x-component as display on the applet in the range of 0 to 10.
In many applications, we are not interested in the exact amplitudes. In these cases we would simplify the mathematics by normalizing the Jones Vector, i.e. the magnitude of the vector, |J| is 1. The following is a table to summarizes a few special cases of polarization and their normalized Jones Vectors,
| Linearly polarized light in the x direction |
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| Linearly polarized light in the y direction |
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Right hand circularly polarized light
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| Left hand circularly polarized light |
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