Mathematical Description
The classical sinusoidal plane wave solution of the electromagnetic wave equation for the electric and magnetic fields is
where k is the wavenumber,
is the angular frequency of the wave, is an orthogonal matrix whose columns span the transverse x-y plane and is the speed of light.
Here
is the amplitude of the field and
is the Jones vector in the x-y plane.
If is rotated by radians with respect to and the x amplitude equals the y amplitude the wave is circularly polarized. The Jones vector is
where the plus sign indicates left circular polarization and the minus sign indicates right circular polarization. In the case of circular polarization, the electric field vector of constant magnitude rotates in the x-y plane.
If basis vectors are defined such that
and
then the polarization state can be written in the "R-L basis" as
where
and
Read more about this topic: Circular Polarization
Famous quotes containing the words mathematical and/or description:
“What is history? Its beginning is that of the centuries of systematic work devoted to the solution of the enigma of death, so that death itself may eventually be overcome. That is why people write symphonies, and why they discover mathematical infinity and electromagnetic waves.”
—Boris Pasternak (1890–1960)
“The great object in life is Sensation—to feel that we exist, even though in pain; it is this “craving void” which drives us to gaming, to battle, to travel, to intemperate but keenly felt pursuits of every description whose principal attraction is the agitation inseparable from their accomplishment.”
—George Gordon Noel Byron (1788–1824)