# Linear polarization

In electrodynamics, **linear polarization** or **plane polarization** of electromagnetic radiation is a confinement of the electric field vector or magnetic field vector to a given plane along the direction of propagation. See polarization for more information.

The orientation of a linearly polarized electromagnetic wave is defined by the direction of the electric field vector.^{[1]} For example, if the electric field vector is vertical (alternately up and down as the wave travels) the radiation is said to be vertically polarized.

## 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 be written in the "x-y basis" as

- .

## See also

- Sinusoidal plane-wave solutions of the electromagnetic wave equation
- Polarization
- Photon polarization

## References

- Jackson, John D. (1998).
*Classical Electrodynamics (3rd ed.)*. Wiley. ISBN 0-471-30932-X.

- ↑ Shapira, Joseph; Shmuel Y. Miller (2007).
*CDMA radio with repeaters*. Springer. p. 73. ISBN 0-387-26329-2.

## External links

- Animation of Linear Polarization (on YouTube)
- Comparison of Linear Polarization with Circular and Elliptical Polarizations (YouTube Animation)

This article incorporates public domain material from the General Services Administration document "Federal Standard 1037C".ja:直線偏光