Elliptical light bullets

Stable three-dimensional spinning optical solitons supported by competing quadratic and cubic nonlinearities

“…The scaled equations describing the reversible generation of the second harmonic (SH) from a single fundamental-frequency (FF) component u, in the presence of the self-defocusing cubic nonlinearity, dispersion and diffraction in the (3+1)-dimensional geometry, are well known [12,13,23,30,31]:…”

“…[23] as follows: (1) assume different GVD coefficients at the two harmonics, σ being their ratio [12], but neglects the Poynting-vector walkoff between the harmonics, and assumes that the temporal group-velocity mismatch between them [14,41,42] has been compensated. On the other hand, in the case σ = 1 the model possesses an additional spatiotemporal spherical symmetry [12,13]. Below, we will display results for the case σ = 1, assuming that the groupvelocity mismatch may be neglected in this case too.…”

“…They result from the simultaneous balance of diffraction and group-velocity dispersion (GVD) by self-focusing. Although they cannot be stable in the uniform self-focusing Kerr (χ (3) ) medium [8], stability can be achieved in saturable [3,6,10], quadratically nonlinear (χ (2) ) [2,12,13,14], and graded-index Kerr media [15]. STS can also be found in off-resonance two-level systems [17], in self-induced-transparency media [18], as well as in engineered tandem structures incorporating quadratically nonlinear slices [19].…”

Vortical light bullets in second-harmonic-generating media supported by a trapping potential

“…Due to this circumstance, the χ (2) solitons were originally created, in the spatial domain, as stable (2+1)-dimensional beams [8]. The possibility of the creation of fully localized 3D spatiotemporal solitons is suggested too by the absence of the collapse [9][10][11][12]. This has not been achieved yet in experiments, the best result being a spatiotemporal soliton which is self-trapped in the longitudinal and one transverse directions, while the confinement along the other transverse coordinate was provided by the waveguiding structure [13,14].…”

Formation and stability of multidimensional structures in optics and atomic condensate: recent theoretical studies

“…The solitons in media with the cubic self-focusing nonlinearity, obeying the nonlinear Schroedinger (NLS) equation, are unstable in two and three dimensions, because of the occurrence of beam collapse 11,12 However, several possibilities to arrest the intrinsic wave collapse were considered, such as the use of quadratically nonlinear optical media that support solitons for all physical dimensions [13][14][15][16][17][18] . The (2+1)-dimensional light bullet formation was achieved in quadratically nonlinear crystals by generating the necessary anomalous GVD via achromatic phase matching 19 .…”