8th International Conference on Squeezed States and Uncertainty Relations, Puebla, Mexico, 9 - 13 June 2003, pp.34-41
Ray optics is needed in all optical measurement processes. In ray optics, the basic scientific language consists of two-by-two matrices. The Jones matrix in polarization is two-by-two, the S-matrix for multilayer optics is two-by-two, the lens and translation matrices in lens optics are two-by-two, the laser cavity matrices are also two-by-two. There are many other two-by-two matrices in optics. These small matrices are mathematically simple enough, but also form a representation of the six-parameter Lorentz group. Those parameters are needed for the generators of the Lie algebra, consisting of three rotation generators and three squeeze generators. On the other hand, only one squeeze and two rotation matrices are needed to start constructing the most general form of the two-by-two matrices needed in optics, as well as in the Lorentz group. The S-matrix in multilayer optics is used to illustrate this point. It is shown that multilayer optics can serve as an analogue computer for Wigner's little groups, group contractions, and group expansions. Conversely, the Lorentz group is the basic language for most, if not all, of the optical instruments used in laboratories.