, elliptical polarization
is the polarization
of electromagnetic radiation
such that the tip of the electric field vector
describes an ellipse
in any fixed plane intersecting, and normal
to, the direction of propagation. An elliptically polarized wave may be resolved into two linearly polarized waves
in phase quadrature
, with their polarization planes at right angles to each other. Since the electric field can rotate clockwise or counterclockwise as it propagates, elliptically polarized waves exhibit chirality
Other forms of polarization, such as circular and linear polarization, can be considered to be special cases of elliptical polarization.
Mathematical description of elliptical polarization
The classical sinusoidal
plane wave solution of the electromagnetic wave equation
for the electric
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.
is the amplitude of the field and
is the Jones vector in the x-y plane. Here is an angle that determines the tilt of the ellipse and determines the aspect ratio of the ellipse. If and are equal the wave is linearly polarized. If they differ by they are circularly polarized.