Polarization of light

Remarks

The pair $(E_x, E_y)$ is the Jones vector of the wave; multiplying it by a nonzero complex number changes only the amplitude and the time origin, not the polarization state. In the circular case, the sign of $\sin\delta$ gives the sense of rotation; the names left and right for the two senses follow different conventions in different fields. Light that is not monochromatic can be unpolarized or partially polarized, and is then described by Stokes parameters.

Example: $(E_x, E_y) = (1, i)$ gives, at $z = 0$, $\mathbf E = (\cos \omega t, \sin \omega t)$. Its tip moves on the unit circle, and indeed $\abs{E_x} = \abs{E_y}$ and $\delta = \pi/2$, so the light is circularly polarized.

Non-example: $(E_x, E_y) = (1, 2i)$ gives $\mathbf E = (\cos\omega t, 2\sin\omega t)$, an ellipse with unequal axes. It has $\delta = \pi/2$ but $\abs{E_x} \ne \abs{E_y}$, so it is not circular; it is elliptical.