# Linear polarization

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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.

Historically, the orientation of a polarized electromagnetic wave has been defined in the optical regime by the orientation of the electric vector, and in the radio regime, by the orientation of the magnetic vector.

### 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 c 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 $\alpha_x^{ } , \alpha_y$ are equal,

This represents a wave polarized at an angle θ 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

### References

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