INTERACTION OF SOLITONS WITH A STRONG INHOMOGENEITY IN A NONLINEAR-OPTICAL FIBER

We consider the interaction of fundamental and higher-order solitons with a strong localized inhomogeneity of the dispersion or nonlinear coefficient in a nonlinear optical fiber. The inhomogeneities are modeled by delta functions in the corresponding nonlinear Schrodinger equations, but they are not treated as small perturbations. Actually, they could also represent long pieces of, respectively, (i) linear or (ii) zero-dispersion fiber inserted into the bulk fiber, which is of wider interest for applications than the inhomogeneities proper. We obtain analytically a pulse transformed by the inhomogeneity and then calculate its soliton content by means of numerical solution of the corresponding Zakharov-Shabat equations. It is found that an inhomogeneity in the nonlinearity can split the incoming fundamental soliton (1-soliton) into a symmetric pair of separating small-amplitude solitons, although. the larger part of the initial energy will be lost in this case in the generation of dispersive waves (continuous radiation). In contrast to this, an inhomogeneity in the dispersion only attenuates the output soliton but never splits it. We obtain a more interesting result upon considering the interaction of a-solitons with the nonlinearity inhomogeneity: a moderately strong inhomogeneity can split the 2-soliton into it symmetric pair of separating fundamental solitons, generating only a fairly small amount of dispersive waves. (Here, an n soliton is a solitary pulse with an amplitude n times that of a soliton but with the same width.) This result may be important for applications, as it is well known that the soliton lasers generate pulses in the form of a-solitons. We thus predict that an inserted piece of the zero-dispersion fiber can effectively transform 2-solitons into equal and separating fundamental solitons of good quality. For comparison, we also consider the same problem for the 1.5- and 2.5-solitons; in the latter case, a third soliton may be generated. The results obtained can be applied as well to nonlinear waveguides of other physical origin, e.g., guides for internal waves in the ocean.