Abstract

To derive the basic equations for weakly nonparaxial spatial solitons, we start with the Maxwell’s equations for media with striction Kerr nonlinearity (electric displacement D = (ε₀+ ε₂|E|²)E, other types of nonlinearity are treated similarly). For a stationary spatial soliton, field dependence on the longitudinal coordinate zis exp(iΓz), and the approximate equation for the transverse electric field E_⊥= E_x,E_ytakes the form: Here ${\Delta }_{\perp }={\nabla }_{\perp }^2$ is the transversal Laplacian, ωis the optical frequency, cis the light speed, and correction to the traditional parabolic equation is In the lowest order of the perturbation theory (Q_⊥= 0) there is a degenerate family of solitons with the same power (critical power of self-focusing). We choose the Townes’s cylindrically symmetric mode of self-trapping [1] with a linear field polarization: e_x0= E_x0(ρ), E_y0=0 (ρ,φare polar coordinates).

© 2000 IEEE