Abstract

Three-dimensional (1+2D) spatial solitons have been well known since the early 1960's [1,2] as the unstable equilibrium state between self-focusing and diffraction. Theory have shown that below a certain critical power, the soliton beam diffracts away into radiation, while above this threshold, suffers catastrophic self-focusing [3,4]. However, although experiment corroborates this result, it should be noted that the 1+2D soliton instability is predicted from an incomplete mathematical model, namely, the nonlinear Schrödinger (NLS) equation that is based on the paraxial approximation. The 1+2D NLS equation makes the physically unreasonable prediction that the soliton beam will collapse to a singularity within a finite distance [3,4]. The arrest of catastrophic collapse observed experimentally has been explained by appealing to either saturation [5,6] or nonlocality [7-9] of the nonlinearity. However, the problem of singularity simply breaks up by recognizing that the paraxial model is not fit to describe a strongly collapsing beam and that the effects of nonparaxiality [10-12] and polarization coupling [13] should be incorporated into the model.

© 1998 Optical Society of America