Ultranarrow optical beams in quadratically nonlinear media

The vector Maxwell equations for the first-and second-harmonic planar beams are solved with allowance made for the nonlinear diffraction that weakens quadratic nonlinearity. The structure of the transverse and longitudinal components of the electromagnetic field of a parametric soliton is calculated for different values of the wave vector and phase mismatch. Exact analytic expressions are obtained for the self-similar profiles of extremally narrow solitons, and it is shown that the width has a fundamental limit of the order of a wavelength in a linear medium.