Second-harmonic generation in a plane nonlinear optical antiwaveguide

We consider second-harmonic generation in a plane nonlinear antiwaveguide with an isotropic core and cladding and a reverse (relative to waveguide) distribution of the linear refractive index. The structure may support a light beam near the core in a certain interval of optical power. The cross section of the beam in such stability regions is very small, of the order of the light wavelength, whereas the optical density is very high, of the order of a self-focusing one. The second-harmonic generation in the structure is stimulated by the high density and applying a constant electric field. The waveguide for the second harmonic is produced by the powerful fundamental and depends on the form of its eigenmodes. We show that in parametric regions corresponding to the stability regions a continuum of second-harmonic eigenmodes at an invariable propagation constant exists and find necessary conditions for the phase matching.