Stokes’ polarization theorem proven to be flawed

June 1, 2008
In 1852, George Gabriel Stokes appeared to have proven the theorem that any light beam is equivalent to the sum of two independent light beams, one of which is completely polarized and the other completely unpolarized.

In 1852, George Gabriel Stokes appeared to have proven the theorem that any light beam is equivalent to the sum of two independent light beams, one of which is completely polarized and the other completely unpolarized. Now, more than 150 years later, professor Emil Wolf of the University of Rochester (Rochester, NY), co-author with Nobel-laureate Max Born of the well-known book Principles of Optics, has shown that Stokes’ proof of this theorem is flawed and Wolf presents a condition for the theorem to be valid.

Beginning with defining four parameters that describe the polarization state of electromagnetic beams, Stokes “proved” his theorem by expressing each of the four parameters as the sum of two terms; one representing fully polarized contributions, the other completely unpolarized contributions. But because each of the parameters is a function of position and, therefore, represents local behavior of a beam, it cannot provide information about the global behavior throughout a region of space. Understanding of the global behavior of light became possible only through the recent formulation (2003) by Wolf of the so-called unified theory of coherence and polarization. By applying this theory to Stokes’ problem, Wolf shows that Stokes’ “decomposition” is valid only for some, but not for all beams. Contact Emil Wolf at [email protected].

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