Linear polarization: Difference between revisions

Revision as of 23:20, 22 November 2006

Revision as of 18:27, 24 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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The wave is linearly polarized when the phase angles <math> \alpha_x^{ } , \alpha_y </math> are equal,

:<math> \alpha_x = \alpha_y \equiv \stackrel{\mathrm{def}}{=}\ \alpha </math>.

This represents a wave polarized at an angle <math> \theta </math> with respect to the x axis. In that case the Jones vector can be written

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If unit vectors are defined such that

:<math> |x\rangle \equiv \stackrel{\mathrm{def}}{=}\ \begin{pmatrix} 1 \\ 0 \end{pmatrix} </math>

and

:<math> |y\rangle \equiv \stackrel{\mathrm{def}}{=}\ \begin{pmatrix} 0 \\ 1 \end{pmatrix} </math>

then the polarization state can written in the "x-y basis" as