International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 27, Pages 1403-1422

Optical leptons

Lubomir M. Kovachev

Institute of Electronics, Bulgarian Academy of Sciences, Sofia 1784, Bulgaria

Received 2 January 2003

Copyright © 2004 Lubomir M. Kovachev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We obtain optical vortices with classical orbital momentum =1 and spin j=±1/2 as exact solutions of a system of nonlinear Maxwell equations (NMEs). Two kinds of Kerr-type media, namely, those with and without linear dispersion of the electric and the magnet susceptibility, are investigated. The electric and magnetic fields are represented as sums of circular and linear components. This allows us to reduce the NME to a set of nonlinear Dirac equations (NDEs). The vortex solutions in the case of media with dispersion admit finite energy, while the solutions in case of media without dispersion admit infinite energy. The amplitude equations are obtained from equations of nonstationary optical and magnetic response (dispersion). This includes also the optical pulses with time duration of order of and less than the time of relaxation of the media (femtosecond pulses). The possible generalization of NME to a higher number of optical components and a higher number of and j is discussed.