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⊥= Ex,Eytakes the form: Here 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: ex0= Ex0(ρ), Ey0=0 (ρ,φare polar coordinates).
© 2000 IEEE
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