Circular polarization: Difference between revisions

Revision as of 19:51, 14 November 2006

Revision as of 06:13, 21 November 2006

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Circular (and elliptical) polarization is possible because the propagating electric (and magnetic) fields can have two orthogonal components with independent amplitudes and phases (and the same frequency).

A circularly polarized wave may be resolved into two [[linear polarization|linearly polarized]] waves, of equal amplitude, in [[Quadrature_phaseQuadrature phase|phase quadrature]] (90 degrees apart) and with their planes of polarization at right angles to each other.

Circular polarization may be referred to as ''right'' or ''left'', depending on the direction in which the electric field vector rotates. Unfortunately, two opposing, historical conventions exist. In [[physics]] and [[astronomy]], polarization is defined as seen from the ''receiver'', such as a [[telescope]] or [[radio telescope]]. By this definition, if you could stop time and look at the electric field along the beam, it would trace a helix which is the same shape as the same-handed screw. For example, right circular polarization produces a right threaded (or forward threaded) [[screw]]. In the U.S., [[Federal Standard 1037C]] also defines the handedness of circular polarization in this manner. In [[electrical engineering]], however, it is more common to define polarization as seen from the ''source'', such as from a transmitting antenna. To avoid confusion, it is good practice to specify "as seen from the receiver" (or transmitter) when polarization matters.

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==Mathematical description of circular polarization==

The [[Classical physics | classical]] [[sinusoidal]] plane wave solution of the [[electromagnetic wave equation]] for the [[Electric field | electric]] and [[Magnetic field | magnetic]] fields is (cgs units)

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

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is the [[Jones vector]] in the x-y plane.

If <math> \alpha_y </math> is rotated by <math> \pi / 2 </math> radians with respect to <math> \alpha_x </math> and the x amplitude equals the y amplitude the wave is [[Circular polarization | circularly polarized]]. The Jones vector is

:<math> |\psi\rangle = {1\over \sqrt{2}} \begin{pmatrix} 1 \\ \pm i \end{pmatrix} \exp \left ( i \alpha_x \right ) </math>

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==References==

*{{cite book |author=Jackson, John D.|title=Classical Electrodynamics (3rd ed.)|publisher=Wiley|year=1998|id=ISBN 047130932X0-471-30932-X}}

==See also==

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*[[Elliptical polarization]]

*[[photon polarization]]

[[Category:Polarization]]