A pair of light beams that have orthogonal polarizations and equal intensity can be generated through reflection and refraction of a monochromatic light at a dielectric surface. Sytematic procedures to design beam splitters which can produce such output light beams are described in this thesis. Two designs that are of particular interest are prismatic substrates coated by a single layer and a double layer of thin films. Specific examples of each beam splitter in the visible and infrared are included. The performance of each beam splitter as a function of incidence angle, film thickness, and wavelength is also discussed.

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.