The polarization states along with the mathematical conditions and corresponding figures ( polarization ellipses) are as follows. These are called degenerate polarization states: (1) linearly horizontal/vertical polarized light (LHP/LVP), (2) linear ±45° polarized light (L+45P/L–45P), and (3) right/left circularly polarized light (RCP/LCP). In general, the optical field is elliptically polarized, but there are several combinations of amplitude and phase that are especially important. Because of the amplitudes E 0 x and E 0 y and the phase δ are constant, the polarization ellipse remains fixed as the polarized beam propagates. The figure also shows the rotated ξ-η coordinate system. A plot of the nonstandard polarization ellipse is shown below. Nevertheless, the field components E x( z, t) and E y( z, t) continue to be time-space dependent. In the equation, the time-space propagator has been explicitly eliminated. Because the equation refers to polarized light, the equation is called the polarization ellipse. The above equation describes an ellipse in its nonstandard form. However, eliminating the time-space propagator ω t - kz between the two equations leads to the equation of an ellipse, namely, By themselves, these equations are not particularly revealing. According to Fresnel's theory, E x( z, t) and E y( z, t) describe sinusoidal oscillations in the x-z and y-z planes, respectively (see the figure on p.
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