We derive a non-paraxial ve ct or equation clarifying every modification terms.We have,for the first time to ou r knowledge,obtained the analytical law for non-paraxial propagation for arbitr ary input beams using variational approach.The obtained results are in good agre ement with numerical simulations.Furthermore,we have investigated the roles of n on-paraxial and vectorial effects in self-focusing of very narrow beams by a m odulation theory.It is shown that both effects can arrest catastrophic collapse of the beam,leading to a periodic focusing-defocusing oscillation.For the aspec t of co...
