Linearly polarized narrow light beams in a Kerr medium

The transverse structure of linearly polarized extremely narrow self-focused optical beams has been determined numerically with a high accuracy using the curl–curl vector equation describing a monochromatic light wave in a focusing Kerr medium. All three electric field components are significant for such two-dimensional spatial solitons with the width of only about one wavelength. Since solitons are the “saddle points” of a certain functional, the numerical method used here is a relaxation procedure, where the functional is minimized over stable modes and is maximized over almost all unstable modes. The only remaining unstable mode of the general amplitude is stabilized by fixing the energy flux through the beam cross section.