The possibility of self-trapping of optical beams due to an intensity-dependent refractive index was recognized in the early days of nonlinear optics. However, it was soon realized that in a three-dimensional medium, in which light diffracts in two transverse dimensions, self-trapping is not stable and leads to catastrophic collapse and filamentation. Stable self-trapping was then found to be feasible in two-dimensional media, in which the optical beam diffracts only in one transverse direction. Subsequently, the connection between self-trapping and soliton theory, and a complete analogy between spatial and temporal solitons were established. Whereas the formation of temporal solitons requires a balance between dispersion and nonlinear phase modulation, spatial solitons owe their existence to the balancing of diffraction with wavefront curvature induced by the nonlinear refractive index profile of the propagation medium.

To observe a spatial soliton one must limit diffraction to one transverse direction, which can be achieved in a planar optical waveguide. The first experiments of this type were conducted using a multimode liquid waveguide (CS2 confined between a pair of glass slides). Formation of spatial optical solitons in single-mode planar glass waveguides was reported shortly afterwards.

Kerr nonlinearity

The simplest nonlinearity capable of producing self-trapping (leading to soliton formation in a planar waveguide) is a Kerr nonlinearity, obtained when the refractive index of the medium has an intensity-dependent term of the formwhere I = |E|2 is the electric field intensity of the optical beam.