Study of the interaction of the optical radiation with media by means of the group theory: description and applications

D. Pereda-Cubián; J. L. Arce-Diego; F. Fanjul-Vélez; L. V. Wang

doi:10.1117/12.675868

18 April 2006 Study of the interaction of the optical radiation with media by means of the group theory: description and applications

D. Pereda-Cubián, J. L. Arce-Diego, F. Fanjul-Vélez, L. V. Wang

Author Affiliations +

Proceedings Volume 6180, Photonics, Devices, and Systems III; 61802E (2006) https://doi.org/10.1117/12.675868
Event: Photonics, Devices, and Systems III, 2005, Prague, Czech Republic

Abstract

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.

Citation Download Citation

D. Pereda-Cubián, J. L. Arce-Diego, F. Fanjul-Vélez, and L. V. Wang "Study of the interaction of the optical radiation with media by means of the group theory: description and applications", Proc. SPIE 6180, Photonics, Devices, and Systems III, 61802E (18 April 2006); https://doi.org/10.1117/12.675868

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available