Amplitude of eliptically polarised light In elliptically polarized light, can one define something called amplitude of Electric field? If yes, how do we determine it?
 A: Well, you use the amplitude $|\mathbf E|$ of the electric field to find the total amount of energy carried by the electromagnetic wave; the root-mean-square magnitude of the Poynting vector for an EM plane wave is
$$
\left< S \right> = \frac{\epsilon_0 c}2 |\mathbf E|^2
.
$$
You seem to be after a way to specify the degree of elliptical polarization, which is a little bit different.
Elliptical polarization requires light to have two different plane polarization states with a specific relative phase between them. To find the long axis of your polarization ellipse, you would put a plane polarizer between your light source and your light detector.  You'll see the maximum transmission $I_\text{max}$ when the polarizer is parallel to the long axis of the ellipse, and the minimum transmission $I_\text{min}$ when the polarizer is parallel to the short axis of the ellipse.  The linear polarization of the beam is therefore 
$$
P_\text{linear} = \frac{I_\text{max}-I_\text{min}}{I_\text{max}+I_\text{min}}
$$
and the partial amplitudes $I_\text{max,min}$ are related the parameters $a,b$ of the polarization ellipse.
Notice that circularly polarized light has zero linear polarization, since its polarization ellipse has $a=b$, but is different from unpolarized light because the phase between the two components is coherent. To distinguish between circular-polarized light and unpolarized light, you repeat the test above with circular rather than linear polarizers. (However a circular-polarizing filter is usually a quarter-wave plate or film in front of a linear polarizer.) Elliptically polarized light will exhibit both nonzero linear and nonzero circular polarization.
