Linear polarization - Citizendia

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. Classical electromagnetism (or classical electrodynamics) is a theory of Electromagnetism that was developed over the course of the 19th century most prominently Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges See polarization for more information. Polarization ( ''Brit'' polarisation) is a property of Waves that describes the orientation of their oscillations

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. Radio is the transmission of signals by Modulation of electromagnetic waves with frequencies below those of visible Light.

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)

$\mathbf{E} ( \mathbf{r} , t ) = \mid \mathbf{E} \mid \mathrm{Re} \left \{ |\psi\rangle \exp \left [ i \left ( kz-\omega t \right ) \right ] \right \}$

$\mathbf{B} ( \mathbf{r} , t ) = \hat { \mathbf{z} } \times \mathbf{E} ( \mathbf{r} , t )$

for the magnetic field, where k is the wavenumber,

$\omega_{ }^{ } = c k$

is the angular frequency of the wave, and $c$ is the speed of light. The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of Electromagnetic waves through a medium In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges Wavenumber in most physical sciences is a Wave property inversely related to Wavelength, having SI units of reciprocal meters Do not confuse with Angular velocity In Physics (specifically Mechanics and Electrical engineering) angular frequency

Here

$\mid \mathbf{E} \mid$

is the amplitude of the field and

$|\psi\rangle \ \stackrel{\mathrm{def}}{=}\ \begin{pmatrix} \psi_x \\ \psi_y \end{pmatrix} = \begin{pmatrix} \cos\theta \exp \left ( i \alpha_x \right ) \\ \sin\theta \exp \left ( i \alpha_y \right ) \end{pmatrix}$

is the Jones vector in the x-y plane. Amplitude is the magnitude of change in the oscillating variable with each Oscillation, within an oscillating system In Optics one can describe Polarization using the Jones calculus, invented by R

The wave is linearly polarized when the phase angles $\alpha_x^{ } , \alpha_y$ are equal,

$\alpha_x = \alpha_y \ \stackrel{\mathrm{def}}{=}\ \alpha$ .

This represents a wave polarized at an angle $θ$ with respect to the x axis. In that case the Jones vector can be written

$|\psi\rangle = \begin{pmatrix} \cos\theta \\ \sin\theta \end{pmatrix} \exp \left ( i \alpha \right )$ .

The state vectors for linear polarization in x or y are special cases of this state vector.

If unit vectors are defined such that

$|x\rangle \ \stackrel{\mathrm{def}}{=}\ \begin{pmatrix} 1 \\ 0 \end{pmatrix}$

and

$|y\rangle \ \stackrel{\mathrm{def}}{=}\ \begin{pmatrix} 0 \\ 1 \end{pmatrix}$

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.

This article contains material from the Federal Standard 1037C, which, as a work of the United States Government, is in the public domain. Sinusoidal plane-wave solutions are particular solutions to the Electromagnetic wave equation. In Electrodynamics, circular polarization (also circular polarisation) of Electromagnetic radiation is a Polarization such that the tip of the In Electrodynamics, elliptical polarization is the Polarization of Electromagnetic radiation such that the tip of the Electric field vector Federal Standard 1037C, entitled Telecommunications Glossary of Telecommunication Terms is a United States Federal Standard issued by the General Services Administration A work of the United States government, as defined by United States copyright law, is "a work prepared by an officer or employee of the U The public domain is a range of abstract materials &ndash commonly referred to as Intellectual property &ndash which are not owned or controlled by anyone

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Mathematical description of linear polarization

References

See also