Mathematical Description of Linear Polarization
The classical sinusoidal plane wave solution of the electromagnetic wave equation for the electric and magnetic fields is (cgs units)
for the magnetic field, where k is the wavenumber,
is the angular frequency of the wave, and is the speed of light.
Here
is the amplitude of the field and
is the Jones vector in the x-y plane.
The wave is linearly polarized when the phase angles are equal,
- .
This represents a wave polarized at an angle with respect to the x axis. In that case the Jones vector can be written
- .
The state vectors for linear polarization in x or y are special cases of this state vector.
If unit vectors are defined such that
and
then the polarization state can written in the "x-y basis" as
- .
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