The group theory allows one to study different branches of physics using the same set of commutation
relations. It is shown that a formulation of the polarization optics that depends on
the representations of the Lorentz group is possible. The set of four Stokes parameters, which
is a standard tool of polarization optics, can be used to form a four-vector that is physically
unrelated but mathematically equivalent to the space-time four-vector of the special relativity.
By using the Stokes parameters, it is also possible to generate four-by-four matrix representations
of the ordinary optical filters that are traditionally represented with the two-by-two Jones
matrices. These four-by-four matrices are treated as the entities of the Lorentz group. They
are like the Lorentz transformations applicable to the four-dimensional polarization space.
Besides, optical decoherence process can be formulated within the framework of the SO(3,2)
de Sitter group. The connection between the classical and quantum mechanical descriptions
of the polarization of light allows the extension of the Stokes parameters to the quantum domain.
In this respect, the properties of the polarization of the two-photon system can also be
studied within the framework of the Lorentz group.
| Identifer | oai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/12614773/index.pdf |
| Date | 01 September 2012 |
| Creators | Oktay, Onur |
| Contributors | Baskal Baykal, Sibel |
| Publisher | METU |
| Source Sets | Middle East Technical Univ. |
| Language | English |
| Detected Language | English |
| Type | M.S. Thesis |
| Format | text/pdf |
| Rights | To liberate the content for METU campus |
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