Elliptical polarization: Difference between revisions

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In [[electrodynamics]], '''elliptical polarization''' is the [[polarization]] of [[electromagnetic radiation]] such that the tip of the [[electric field]] [[Vector (spatial)|vector]] describes an [[ellipse]] in any fixed plane intersecting, and [[Surface normal|normal]] to, the direction of propagation. An [[elliptically polarized wave]] may be resolved into two [[linear polarization|linearly polarized wave]]s in [[Quadrature_phase|phase quadrature]] with their polarization planes at right angles to each other.

AllOther forms of polarization can be considered elliptical, includingsuch as [[circular polarization|circular]] and [[linear polarization]], can be considered to be special cases of elliptical polarization.

<p>

==Example <p>==

ByIf applyingan electromagnetic wave is created by multiple dipole antennas driven bywith 90° degree [[phase shiftsshift]]s relative to one another, Electricthe electric field vector will rotate, inwith athe direction (clockwise or counterclockwise direction) depending on the sign of the phase shift.

<p>

Example <p>

The angle between the electric field vector and the '''x''' axis is given by

phase{E}=tan-1{Ey/Ex} <p>

:<math>\Phi(\mathbf{E})=\tan^{-1}{E_y\over E_x},</math>

|E| = (Ex^2 +Ey^2)^0.5<p>

where <math>E_x</math> and <math>E_y</math> are perpendicular [[vector component|components]] of the electric field vector. If the x and y components have a 90° phase shift between them, these components are given by

Ey=(Eyo)*sin(wt)<p>

:<math>E_y=E_{yo} \sin(wt+\phi),\ \mathrm{and}\,</math>

Ex=(Exo)*sin(wt+pi/2)<p>

:<math>E_x=E_{xo} \sin(wt+\phi+{\pi \over 2}),</math>

|E| = E<p>

where <math>\phi\,</math> is an arbitrary phase, and <math>E_xo</math> and <math>E_yo</math> are the [[amplitude]]s of the x and y components of the field. It can then be shown that

phase{E} = wt<p>

:<math>\Phi(\mathbf{E}) = \omega t,</math>

which indicates that the electric field vector will rotaterotates with an [[angular velocity]] w,<math>\omega</math>. inSince thisthe particularphase shift on <math>E_x</math> is casepositive, the rotation is counterclockwise. If Eyo<math>E_{yo} = ExoE_{xo}</math>, thisthe ispolarization calledis circular polarization. If they are different, it is called elliptical polarization .

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[[Category:Polarization]]

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