ar X iv : n lin / 0 40 50 43 v 1 [ nl in . P S ] 1 7 M ay 2 00 4 Nonlocal incoherent solitons

Incoherent solitons are partially coherent optical beams propagating without changing their shape in materials with a slow nonlinear response [1, 2]. Such nonlinear materials respond to the time averaged light intensity, which means that even though the phase of the partially coherent light beam fluctuates randomly, it still leads to a smooth light-induced refractive index change and subsequent trapping of the beam [3, 4, 5, 6, 7, 8, 9]. Incoherent solitons have been experimentally observed almost solely in photorefractive media, which exhibit a strong and sufficiently slow saturable Kerr-like nonlinearity [1, 2]. In inertial bulk Kerr media (2+1)-dimensional partially coherent beams are still unstable and will either diffract or self-focus unboundedly, depending on whether the power is above a certain critical value [10, 11, 12]. Incoherence counteracts self-focusing and leads to an increase of the critical power, but it cannot remove the collapse instability [10, 11]. Consequently all experimental observations of incoherent solitons have been in saturable materials, such as photorefractive materials [1] and liquid crystals [13]. Recently Peccanti et al. reported the first observation of incoherent solitons and their interaction in nematic liquid crystals [13]. Liquid crystals have a strong non-instantaneous saturable Kerr-like nonlinearity associated with light induced molecular reorientation [14, 15, 16, 17]. Their nonlinear response time ranges from tens to hundreds of milliseconds [14], which is sufficiently slow to allow for the formation of incoherent solitons. Apart from being inertial the nonlinear response of liquid crystals is also inherently spatially nonlocal, because the molecular reorientation induced by a light beam in a particular place will affect the orientation of