Narrow light beams with linear polarization in a Kerr medium

Within the curl-curl type vector equation describing a monochromatic light wave in a focusing Kerr medium, the transverse structure of extremely narrow, linearly polarized self-focused optical beams is found numerically with a high accuracy. For such two-dimensional spatial solitons with their width as just about one wavelength, all the three components of electric field are essential. Since the solitons are ``saddle points'' of some functional, the numerical method used here is a relaxation procedure, with the functional being minimized on stable modes, and maximized on almost all unstable modes. The only remaining unstable mode of common amplitude is stabilized by fixing the energy flux across the beam cross-section.