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The problem of the stability of solitons in second-harmonic-generating mediawith normal group-velocity dispersion (GVD) in the second-harmonic (SH) field,which is generic to available chi^(2) materials, is revisited. Using aniterative numerical scheme to construct stationary soliton solutions, anddirect simulations to test their stability, we identify a fullsoliton-stability range in the space of the system's parameters, including thecoefficient of the group-velocity-mismatch (GVM). The soliton stability islimited by an abrupt onset of growth of tails in the SH component, the relevantstability region being defined as that in which the energy loss to the tailgeneration is negligible under experimentally relevant conditions. Wedemonstrate that the stability domain can be readily expanded with the help oftwo "management" techniques (spatially periodic compensation of destabilizingeffects) - the dispersion management (DM) and GVM management. In comparisonwith their counterparts in optical fibers, DM solitons in the chi^(2) mediumfeature very weak intrinsic oscillations.

optics communications

Stability of temporal solitons in uniform and "managed" quadratic  nonlinear media with opposite group-velocity dispersions at fundamental and  second harmonics