Self-guided waves and exact solutions of the nonlinear Helmholtz equation

The paraxial wave theory is known to lead to inaccurate predictions in self -focusing of optical beams. The nonlinear Helmholtz equation describes more accurately wave propagation in dispersive, spatially local, Kerr-type medi a. We derive rigorous bright and dark solutions to the nonlinear Helmholtz equation in a full three-dimensional form. These expressions are new and un ique. The solutions are obtained with a multidimensional extension of the ( paraxial) nonlinear Schrodinger equation. We also establish energy conserva tion laws for both nonlinear wave equations in terms of spatial currents. O ur results give insight, for example, into the diffraction and breakup of t ightly confined nonlinear fields. (C) 2000 Optical Society of America [S074 0-3224(00)00704-9]. OCIS codes: 190.3270, 190.5530, 240.4350.