Proceedings Article | 18 April 2006
KEYWORDS: Matrices, Polarization, Optical components, Coherence (optics), Tissue optics, Tissues, Biomedical optics, Quantum optics, Birefringence, Magnetism
Group theory is a mathematical method, largely used in applications like quantum mechanics and radar theory, which allows establishing a direct relation between the elements of different groups and that can be easily extended to optics. The groups of the special unitary matrices, SU(n), possess a great importance in the field of optics, as they can be related to the light polarization, planar propagation properties and optical devices properties. By means of the Pauli,
Gell-Mann and Dirac matrices, respectively for n=2, n=3 and n=4, a corresponding coherence matrix can be defined. In the case of n=2, this coherence matrix describes the behavior of optical radiation at any case, polarized, depolarized or partially polarized light. For n=3, it can be used for the analysis of non-planar waves. Finally, for n=4, the coherence matrix allows the analysis of the polarization properties of the optical devices, from linear and deterministic media to highly scattering or depolarizing media. In this work, the theoretical background of the group theory and its application to optics is described, and some examples of its application are presented, for instance, the description of optical devices by the Quaternions and the application of 4x4 coherence matrix for the characterization of biological tissues by means of the entropy-factor.
