Dark spatial optical solitons in planar gradient waveguides in the Z-cut of the 3m symmetry crystals

The propagation of light beams is studied in a planar photorefractive waveguide fabricated by high-temperature diffusion of metal ions in the Z-cut substrate of the 3m symmetry crystal. The wave equations are obtained for single-mode light beams with TE and TM polarisations in planar diffusion waveguides, which take into account the two-dimensional distribution of the optical field. Expressions are found for a nonlinear change in the refractive index when the photovoltaic mechanism makes a dominant contribution to the photorefractive effect. The propagation of single-mode light beams is analysed numerically for a Ti:Fe:LiNbO₃ waveguide fabricated by the successive diffusion of titanium and iron into lithium niobate. It is shown that single-mode light beams with a smooth amplitude envelope can propagate without significant changes in the region of a dip in the intensity modelling a dark soliton. The relations between the amplitude and width of a dark spatial soliton are obtained for the TM modes of a photorefractive planar waveguide.