Self-focusing and spatial modes in free space and nonlinear waveguides

Abstract

A unified criterion of self-focusing, applicable to both freely propagating beams and waveguide modes, is proposed, with the self-focusing threshold defined as the critical peak power needed to induce a refractive-index step capable of trapping one more spatial mode. For freely propagating beams and high-order waveguide modes, this definition is shown to recover the canonical expression for the critical power of self-focusing routinely used in nonlinear optics. In the limiting case of low-order guided modes, the proposed definition is found to be fully consistent with the earlier criteria of self-focusing in a waveguide.