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Link to original content: http://farside.ph.utexas.edu/teaching/plasma/lectures/node70.html
Wave Polarization
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Wave Polarization

A pure right-handed circularly polarized wave propagating along the $z$-axis takes the form

$\displaystyle E_x$ $\displaystyle =A\,\cos(k\,z-\omega \,t),$ (5.56)
$\displaystyle E_y$ $\displaystyle = -A\,\sin (k\,z-\omega \,t).$ (5.57)

In terms of complex amplitudes, this becomes

$\displaystyle \frac{{\rm i}\,E_x}{E_y} = 1.$ (5.58)

Similarly, a left-handed circularly polarized wave is characterized by

$\displaystyle \frac{{\rm i}\,E_x}{E_y} = -1.$ (5.59)

The polarization of the transverse electric field is obtained from the middle line of Equation (5.42):

$\displaystyle \frac{{\rm i}\,E_x}{E_y} = \frac{n^2 -S}{D} = \frac{2\,n^2 - (R+L)}{R-L}.$ (5.60)

For the case of parallel propagation, with $n^2 = R$, the previous formula yields ${\rm i}\,E_x/E_y = 1$. Similarly, for the case of parallel propagation, with $n^2 = L$, we obtain ${\rm i}\,E_x/E_y = -1$. Thus, it is clear that the roots $n^2 = R$ and $n^2 = L$ in Equations (5.51)–(5.53) correspond to right- and left-handed circularly polarized waves, respectively.