We report the first observation of self-trapping of a spatially incoherent optical beam in a nonlinear medium. Self-trapping occurs in both transverse dimensions, when diffraction is exactly balanced by photorefractive self-focusing. [S0031-9007(96)00610-2]

letters to nature 880 NATURE | VOL 387 | 26 JUNE 1997 absolute magnitude of M B Ϸ Ϫ 22:6 mag, or a lower limit for L B Ϸ 7 L ‫ء‬ , where L ‫ء‬ is a characteristic galaxy luminosity 33 . Thus, OT J065349+79163 is still significantly outshining any host galaxy for the most probable host luminosity range. The properties of the Mg absorption lead us to expect that once the OT has faded, the galaxy could be identified optically.Taken together, the source's compact optical appearance, a featureless continuum, X-ray emission and high redshift suggest a possible classification (independent of a burst event) as a BL Lac object 23 . One of the known characteristics of BL Lac objects is their variability from radio to g-ray wavelengths. We now evaluate the a posteriori probability that we might be seeing a BL Lac object by random coincidence with the g-ray error box. The surface density of BL Lac objects with Rosat X-ray flux f X գ 10 Ϫ 12 erg cm Ϫ 2 s Ϫ 1 is not very well known, but there are indications that this distribution is quite flat at low flux densities. A simple extrapolation for the expected number of BL Lacs with f X Ͼ 6 ϫ 10 Ϫ 13 erg cm Ϫ 2 s Ϫ 1 is 24 0.03 per square degree. Thus the probability of finding a BL Lac object within the 3-arcmin-radius localization region is ϳ2 ϫ 10 Ϫ 4 . The amplitude of the variability detected in the counterpart 13 over a few days is also larger than has been observed in studies of BL Lac object variability 25,26 . Although we cannot completely exclude the possibility that OT J065349+79163 is a chance coincidence of a BL Lac object with the GRB error circle, the probability of finding a random BL Lac object which also exhibits variability that is temporally correlated with a g-ray burst is quite small. Thus we conclude that the OT is probably associated with GRB970508, regardless of classification, though the strongest constraints naturally come from higher-energy emission.The high redshift of OT J065349+79163, its featureless spectrum and slowly decaying optical flux are consistent with the so-called fireball models for cosmological bursts 27-29 , which are efficient at emitting g-rays and produce power-law spectral energy distributions. The fluence 30 of GRB970508 in the energy range 20-1,000 keV was 3 ϫ 10 Ϫ 6 erg cm Ϫ 2 , and at the minimum redshift implied for OT J065349+79163, this burst would have a total g-ray energy of 7 ϫ 10 51 erg (assuming isotropic emission). This falls in the general range of typical g-ray burst energies from various cosmological models 31,32 .The remarkable progress in detecting X-ray and optical counterparts to GRBs has been made possible only by rapid localization of the burst by BeppoSAX and prompt dissemination of the coordinates by the BeppoSAX team. Further progress in understanding GRBs requires many more optical counterparts to be identified. It is clear from experience of the first two optical counterparts that, in order to obtain the critical data, the counterparts must be discovered and followed up spectroscopically within a few da...

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We present a modal theory of self-trapping spatially incoherent light beams in any general nonlinear media. We find that a self-trapped incoherent beam induces a multimode waveguide which guides the beam itself by multiply populating the guided modes. The self-trapping process alters the statistics of the incoherent beam, rendering it localized. We find the conditions for self-trapping ("existence region" in parameter space) and the correlation function of the incoherent self-trapped beam.[S0031-9007(97)04860-6] PACS numbers: 42.65.Jx, 42.65.Tg

We present the first experimental observation of multihump multimode solitons in nature. In a broader perspective, this is the first observation of a multihumped multimode self-trapped wave packet propagating in a dispersive nonlinear medium. Double-and triple-humped spatial profiles are found by incoherent population of two modes of the beams' self-induced waveguide (self-induced potential well).