In the previous post we introduced a notion of light polarization that we can actually measure in the optical wavelength regime. What we actually measure are linear combinations of the quantities below:
When taking polarimetric measurements, we actually measure what we call the Stokes parameters, represented by
where
The Stokes parameters were originally defined this way because we can manufacture (and have been able to manufacture for awhile) optical elements which can allow us to measure these quantities:
- the irradiance.
- the relative amount of horizontal polarization (
) over the degree of vertical polarization ( ). - the relative amount of
polarization over the degree of polarization. - the relative amount of right circular polarization over left circular polarization.
However, only in modern classical electromagnetics have we formally defined them in proper statistical terms of the electric field. Since the Stokes parameters represent measurements, they are always real valued, i.e.,
Aside : conventions
There are some pitfalls to the Stokes parameters, it is quite obvious that the quantities defined above are dependent on 1) the handedness of the coordinate system, 2) the phase convention, and 3) the position of the observer.
Fortunately, nearly everyone in the physics, remote sensing, radar, and optics community use a right handed coordinate system. The problems arise from differing conventions among the communities about the last two convention choices, phase convention and the position of the observer. We urge the reader to be careful using wikipedia for Jones and Stokes polarization parameter definitions as different subsections incorrectly mix up these conventions! We must choose a single convention and adhere to it, otherwise our computations will result in nonsense. We have introduced changes to the wikipedia articles to correct this, but overzealous editors (who are not professionals in optics) continue to revert the corrections and we have chosen to no longer waste our time arguing with them.
Given the two different conventions we may use, there are four possible definitions for the Stokes parameters, and we will derive them here. First we will go over what exactly phase convention and the position of the observer are.
Light is always assume to propagate in the
Phase convention
Phase convention is a result of a duplicity of solutions which work when solving Maxwell’s differential equations. When solving the wave equation for linear media, superpositions of both
Remember that
Because physically we usually only have one propagation direction, we must choose a phase convention and stick to it. In these articles, we will always use the decreasing phase convention. The texts of Hecht, Jackson, Goodman, Born and Wolf use the decreasing phase convention. The texts of Gaskill, Collett, Jenkins and White use the increasing phase convention.
Position of the observer
We will now go over the position of the observer. This affects our definition of direction in a clockwise or counterclockwise sense. There are two possible definitions for the observer, looking into the beam or looking down the beam.
Looking into the beam assumes that the observer is looking toward the origin of the
Looking down the beam assumes that the observer is looking away from the origin of the
This definition determines what we call right (clockwise) or left (counterclockwise) circular, because it depends on which position you are observing in.
Now that the problem parameters are defined, we will continue this discussion in the next post and finish deriving the Stokes parameters depending on which conventions are used.
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