Elliptical polarization: Difference between revisions

Revision as of 22:35, 27 May 2016

Revision as of 05:07, 8 July 2016

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The orientation of the ellipse is given by the angle <math>\phi </math> the semi-major axis makes with the x-axis. This angle can be calculated from

:<math> \tan2\phi=\tan2\theta\cos\beta</math>.

If <math>\beta= 0</math>, the wave is [[linear polarization|linearly polarized]]. The ellipse collapses to a straight line <math>(A=|\mathbf{E}|, B=0</math>) oriented at an angle <math>\phi=\theta</math>. This is the case of superposition of two simple harmonic motions (in phase), one in the x direction with an amplitude <math>|\mathbf{E}| \cos\theta</math>, and the other in the y direction with an amplitude <math>|\mathbf{E}| \sin\theta </math>. When <math>\beta</math> increases from zero, i.e., assumes positive values, the line evolves into an ellipse that is being traced out in the counterclockwise direction (looking intoin the direction of the propagating wave); this then corresponds to Left''left-Handedhanded Ellipticalelliptical Polarizationpolarization''; the semi-major axis is now oriented at an angle <math>\phi\neq\theta </math>. Similarly, if <math>\beta</math> becomes negative from zero, the line evolves into an ellipse that is being traced out in the clockwise direction; this corresponds to Right''right-Handedhanded Ellipticalelliptical Polarizationpolarization''.

If <math>\beta=\pm\pi/2</math> and <math>\theta=\pi/4</math>, <math> A=B=|\mathbf{E}|/\sqrt{2}</math>, i.e.,the wave is [[circular polarization|circularly polarized]]. When <math>\beta=\pi/2</math>, the wave is left-circularly polarized, and when <math>\beta=-\pi/2</math>, the wave is right-circularly polarized.