Wave Polarization
A pure right-handed circularly polarized wave propagating along the
$z$-axis takes the form
$\displaystyle E_x$
$\displaystyle =A,円\cos(k,円z-\omega ,円t),$
(5.56)
$\displaystyle E_y$
$\displaystyle = -A,円\sin (k,円z-\omega ,円t).$
(5.57)
In terms of complex amplitudes, this becomes
$\displaystyle \frac{{\rm i},円E_x}{E_y} = 1.$
(5.58)
Similarly, a left-handed circularly polarized wave is characterized by
$\displaystyle \frac{{\rm i},円E_x}{E_y} = -1.$
(5.59)
The polarization of the transverse electric field is obtained from the
middle line of Equation (5.42):
$\displaystyle \frac{{\rm i},円E_x}{E_y} = \frac{n^2 -S}{D} = \frac{2,円n^2 - (R+L)}{R-L}.$
(5.60)
For the case of parallel propagation, with
$n^2 = R$, the previous formula
yields
${\rm i},円E_x/E_y = 1$. Similarly, for the case of parallel propagation,
with
$n^2 = L$, we obtain
${\rm i},円E_x/E_y = -1$. 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.