Estimate of the limiting value of the diameter of a self-focusing channel in a medium with cubic nonlinearity

An estimate of the limiting value of the diameter of a self-focusing channel in a medium with cubic nonlinearity is obtained by solving the exact Maxwell equations for a uniform circular waveguide. It is shown that such a waveguide can, in principle, be realized. However, if the power carried by the wave exceeds the critical value by 1%, the diameter of the waveguide is ~2λ and the field in the waveguide reaches ~10⁶ cgs esu. The energy dissipation processes which arise in this situation imply that a medium cannot retain cubic nonlinearity.