Collision-induced shape transformations of partially coherent solitons

Partially coherent solitons are objects which have recently attracted a great deal of attention @1–10#. Focusing of the spatially partially coherent beams has been suggested as early as in 1967 @11# and studied subsequently in @12,13#. On the other hand, temporally incoherent solitons have been considered in the original works of Hasegawa @14–16#, both for plasma waves and for nonlinear pulses in multimode fibers. However, the creation of incoherent solitons in optical fibers requires unrealistically high pulse energies. In contrast, photorefractive materials allow experimental studies at very low optical powers as they generally exhibit strong nonlinear self-action effects @17–21#. In fact, the first experiments with the partially coherent soliton have been conducted with photorefractive nonlinearity @1,2,6#. The interaction of partially coherent solitons ~PCS! is an interesting area of research and it has only been addressed in the recent works @8,22#. In the present paper, we experimentally demonstrate new collisional properties of PCS. Namely, we have discovered that the PCS may have variable shape @23# and that the collision of the PCS leads to a transformation of the soliton profile. In order to explain these phenomena we will first briefly discuss the main features of partially coherent solitons considering the solvable model of a Kerrlike medium. However, the nonlinear susceptibility of a general nonlinear medium, such as a photorefractive crystal, is usually well approximated by a saturable nonlinearity. Therefore, we will comment on PCS in a saturable nonlinearity discussing experimental results. It has been shown that incoherent solitons can be represented as N self-trapped mutually incoherent wave packets which represent modes of the self-induced waveguide @5,6#. From this point of view, incoherent solitons are analogous to higher-order vector solitons which can also be considered as multimoded self-induced waveguides @24#. One of the physical reasons which makes various modes phase independent ~incoherent! is a slow response of the nonlinear medium. Usually in photorefractive media the response time is much slower than the random fluctuation of the phases of the par-