Two- And three-dimensional light bullets in a Kerr medium with dispersion management

In this paper we treat two and three dimensional light bullets by somewhat different methods. In both cases stability is achieved for some parameters. In the first case we propose a scheme for stabilizing spatiotemporal solitons (STS) in media with cubic self-focusing nonlinearity and "dispersion management", i.e., a layered structure inducing periodically alternating normal and anomalous group-velocity dispersion. We develop a variational approximation for the STS, and verify results by direct simulations. A stability region for the 2D (two-dimensional) STS is identified. A new stable object, in the form of a periodically oscillating bound state of two subpulses, is also found. We go on to also demonstrate a possibility to stabilize fully three-dimensional spatiotemporal solitons ("light bullets") in the same self-focusing Kerr media by means of a combination of dispersion management in the longitudinal direction and periodic modulation of the refractive index in one of the transverse directions. Assuming the usual model based on the paraxial nonlinear Schrödinger equation for the local amplitude of the electromagnetic field, the analysis relies upon the variational approximation. A predicted stability area is identified in the model's parameter space.