We consider the self-focusing in uniaxial gyrotropic media at axially symmetric geometry, i.e., when the wave beam and the gyration vector g are parallel to the principal axis. Dissipation is neglected and the nonlinearity is of the Kerr type. It is shown that when g is directed along the wave normal, i.e., g.n > 0, there is a detrapping of the nonlinearly self-trapped wave beam. The detrapping increases with the narrowing of the beam and this results in the final defocusing of the wave. If g is antiparallel to the wave normal, (g.n) < 0, there is no detrapping and finally a homogeneous wave beam is formed. The results obtained are beyond the theory based on the nonlinear Schrodinger equation.
Karpman, V. I., & Shagalov, A. G. (1992). Self-focusing in uniaxial gyrotropic media. Qualitative and numerical investigation. Physical Review A, 46(1), 518-524. https://doi.org/10.1103/PhysRevA.46.518