Simple, exact analytical solutions of Maxwell's equations are given for the TE-type self-guided modes of a medium that has a power-law dependence on intensity I(q) for the continuum values of q. An analytical criterion shows that such spatial solitons are stable for q < 2 only. Our derivation is novel in that solitons are borrowed from the known modes of the sech(2) profile (linear) waveguide, rather than by solving the nonlinear wave equation. The results reveal the change in soliton propagation as the nonlinear medium itself changes.
We demonstrate, in both two and three dimensions, how a self-guided beam in a non-Kerr medium is split into two beams on weak illumination. We also provide an elegant physical explanation that predicts the universal character of the observed phenomenon. Possible applications of our findings to guiding light with light are also discussed.
The physics of nonlinear couplers is dictated by its normal modes, modes that are found from linear (axially uniform) couplers. Elementary power-flow arguments establish whether the mode is stable or unstable. These facts provide the bifurcation diagram that fully characterizes nonlinear coupling.
Poynting's vector theorem describes power flow on twin-core couplers with arbitrary axial perturbations, both linear and nonlinear. This bypasses the coupled amplitude formulation and unifies nonlinear two-mode interactions in general.
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