Subwavelength spatial solitons in optical media with non-Kerr nonlinearities

We consider very narrow time-independent spatially localized solutions (spatial solitons), whose width may be comparable to or smaller than the carrier wavelength, in two- and three-dimensional waveguides with the cubic-quintic or saturable nonlinearity. Equations describing the shape of the solitons are derived directly from the Maxwell equations, taking into account terms which are neglected in the usual paraxial (nonlinear Schrödinger) approximation, which is valid for solitons whose width is much larger than the wavelength. We consider both transverse electric and transverse magnetic solitons, and show that, in all cases, there is a finite minimum value of the soliton's width, which is attained at a certain value of the propagation constant (an internal parameter of the family of soliton solutions), and the width diverges at some larger value of the propagation constant, which is an existence border for the soliton family. The full similarity of the results obtained for both the cubic-quintic and saturable nonlinearities suggests that the same general conclusions apply to narrow bright solitons in any model featuring nonlinearity saturation in some form.