I have a question regarding this topic. According Stokes Parameters theory, unpolarized light could be described as a superposition of two independent beams of equal intensity and orthogonal polarization. For instance, using Stokes vectors:


$I_0\begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} = \frac{I_0}{2}\begin{pmatrix} 1 \\ 1 \\ 0 \\ 0 \end{pmatrix} + \frac{I_0}{2}\begin{pmatrix} 1 \\ -1 \\ 0 \\ 0 \end{pmatrix} $


$I_0\begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} = \frac{I_0}{2}\begin{pmatrix} 1 \\ 0 \\ 0 \\ 1 \end{pmatrix} + \frac{I_0}{2}\begin{pmatrix} 1 \\ 0 \\ 0 \\ -1 \end{pmatrix} $

My question is: can I generate unpolarized light in a lab by combining two different light beams which fulfill the previous requirements?

  • $\begingroup$ Are you missing a factor of 1/2? $\endgroup$
    – G. Paily
    Nov 26, 2014 at 0:56

1 Answer 1


Adding two stokes vectors does not give you the stokes vector for the combination of the two beams. For example, adding a beam of horizontal and vertical polarization would make a beam of 45deg (linear) polarization. In order to add two beams you would have to come up with a Muller matrix $M_\vec{a}$ for adding $\vec{x}$ to $\vec{a}$.

Unpolarized light has a an equal chance to be in each direction so it cannot be the sum of a (finite) number of distinct polarizations. In practice unpolarized light in the lab can be made, for example, with a birefriengent wedge (Cornu de-polarizer). This light would have polarization that changes along the axis of the wedge (spatially). Rotating waveplates can also make random polarization as a function of time. What 'counts' as unpolarized in an experiment depends on the application.

  • $\begingroup$ Good! is good to know what actually happens in the lab. However, I am still wondering if the addition of those two Stokes vectors have any physical implication. $\endgroup$ Nov 26, 2014 at 2:55
  • 1
    $\begingroup$ I cannot think of any meaning to associate with the sum of two stokes vectors. Since it is not summing the electric fields, there is no superposition principle. The stokes vector space is useful to describe all types of polarization, but general transformations are matrices not operations on the vector. $\endgroup$
    – DBC
    Nov 26, 2014 at 18:16

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