Circular polarization: Difference between revisions

Revision as of 06:13, 21 November 2006

Revision as of 18:22, 23 November 2006

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is the [[amplitude]] of the field and

:<math> |\psi\rangle \equiv \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} </math>

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

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If unit vectors are defined such that

:<math> |R\rangle \equiv \stackrel{\mathrm{def}}{=}\ \begin{pmatrix} 1 \\ i \end{pmatrix} </math>

and

:<math> |L\rangle \equiv \stackrel{\mathrm{def}}{=}\ \begin{pmatrix} 1 \\ -i \end{pmatrix} </math>

then the polarization state can written in the "R-L basis" as

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where

:<math> \psi_R \equiv \stackrel{\mathrm{def}}{=}\ \left ( {\cos\theta -i\sin\theta \over \sqrt{2} } \right ) \exp \left ( i \alpha_x \right ) </math>

and

:<math> \psi_L \equiv \stackrel{\mathrm{def}}{=}\ \left ( {\cos\theta +i\sin\theta \over \sqrt{2} } \right ) \exp \left ( i \alpha_x \right ) </math>.

==References==