VOLUME 86, NUMBER 11 PHYSICAL REVIEW LETTERS 12 MARCH 2001 Dynamic Soliton-Like Modes Ming-Feng Shih* and Fang-Wen Sheu Department of Physics, National Taiwan University, Taipei 106, Taiwan (Received 11 October 2000) Incoherent optical spatial solitons require noninstantaneous nonlinearity, i.e., the local intensity fluc- tuation of the solitons must be faster than the medium can respond. Observing partially incoherent bicomponent solitons, we find that there exists a threshold speed. When the fluctuation of the soliton intensity, resulting from the time-varying interference of its constituent modes, is below the threshold, the soliton beam and its induced waveguide oscillate violently. Just above the threshold, the soliton-induced waveguide is observed to be dragged by the soliton beam. DOI: 10.1103/PhysRevLett.86.2281 PACS numbers: 42.65.Tg, 42.65.Sf An optical spatial soliton [1] is an optical beam that does not diffract due to the exact compensation from the self-focusing effect originating from the beam’s nonlinear interaction with the medium. It can also be viewed [2] as an optical beam that generates an optical waveguide via the medium nonlinearity, and the beam itself is the guided mode of this induced waveguide. When the light beam is the fundamental mode of its induced waveguide, the soli- ton is of the bright type, and, when the light beam is the second mode at cutoff, the soliton is of the dark type. In either case, the solitons are solely coherent entities, mean- ing that the phase difference between any two separated points is entirely predictable. Spatially incoherent optical spatial solitons [3–8] have attracted much research interest. To observe the spatially incoherent solitons, the nonlinearity must be “noninstan- taneous.” In a loose definition, it means the nonlinear re- sponse of medium is slow enough that it cannot respond to the relatively rapid local intensity fluctuation of the op- tical beam. The medium can only “see” the light intensity averaged over a period of time. In one analysis [4] for par- tially incoherent solitons that adopts the linear waveguide approach, it decomposes the solitons into the modes of its induced waveguide, and the relative phases between dif- ferent modes are quickly randomly varying. The local in- tensity of the beam is therefore fluctuating fast due to the varying random interferences of the constitutive modes. This averages, in the order of the material response time, to a smooth intensity profile, which via the material non- linearity generates a spatially smooth and temporally con- stant waveguide that can accommodate all the constitutive modes of the soliton beam. Now the questions arise: How fast should the local intensity fluctuate to make the non- linearity of the medium look noninstantaneous in order to form incoherent solitons? What happens to the incoherent solitons if the intensity fluctuation is not fast enough? To target such problems for the first time, we start the study experimentally with the multicomponent solitons [4] in the photorefractive strontium barium niobate (SBN:60) crystal. The nonlinearity is of the saturable type that can support multicomponent solitons, and its noninstantaneous response speed is proportional to the optical intensity [9]. The multicomponent solitons, belonging to the least com- plex category of the spatially partially incoherent solitons, are composed of only the fundamental and the second modes. The intensity fluctuation of the bicomponent soli- ton beam is controlled by varying the relative phase be- tween the two constituent modes. We find that, when the varying speed of the relative phase as well as the intensity fluctuation is much above a certain threshold, the medium looks noninstantaneous, and the partially incoherent op- tical spatial solitons form. However, as the speed of the intensity fluctuation is gradually reduced to be just above the threshold, we observe that the soliton beam and its induced waveguide move in a spatially and temporally dy- namic motion, in which the waveguide lags to the soli- ton beam. When the intensity fluctuation speed is further reduced to be below the threshold, the soliton beam and its induced waveguide begin to oscillate violently in the medium. We name these soliton phenomena as “dynamic soliton-like modes.” Although we experiment on the bi- component solitons, we believe such threshold behaviors may exist for other partially incoherent optical solitons [3] and be related to the modulation instability of partially in- coherent light [10]. Intuitively, one may understand why there is a thresh- old: The noninstantaneous medium takes the time- average intensity to yield its nonlinear index change, which is constant if the intensity fluctuation due to the interference of the two modes is too fast for the medium to respond. When the varying speed of the relative phase between the two modes is gradually reduced, the speed of the intensity fluctuation is also reduced. As a result, the medium can gradually respond and yield a time-varying index perturbation as compared to the constant index change. The magnitude of the time-varying index pertur- bation also becomes larger as the speed of the intensity fluctuation becomes slower. At the beginning, when the intensity fluctuation is relatively fast and the index pertur- bation is very small, the soliton beam can fine-adjust and reshape itself due to the robustness of the stable soliton. As the intensity fluctuation becomes slower and the index perturbation becomes larger, at some point, the soliton beam can no longer adjust itself to its stationary soliton 0031-9007 01  86(11)  2281(4)$15.00 © 2001 The American Physical Society 2281