Linear Polarization - Mathematical Description of Linear Polarization

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

.

Read more about this topic:  Linear 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)

    “Everything to which we concede existence is a posit from the standpoint of a description of the theory-building process, and simultaneously real from the standpoint of the theory that is being built. Nor let us look down on the standpoint of the theory as make-believe; for we can never do better than occupy the standpoint of some theory or other, the best we can muster at the time.”
    —Willard Van Orman Quine (b. 1908)