Elastic collision and molecule formation of spatiotemporal light bullets in a cubic-quintic nonlinear medium

Abstract

We consider the statics and dynamics of a stable, mobile three-dimensional (3D) spatiotemporal light bullet in a cubic-quintic nonlinear medium with a focusing cubic nonlinearity above a critical value and any defocusing quintic nonlinearity. The 3D light bullet can propagate with a constant velocity in any direction. Stability of the light bullet under a small perturbation is established numerically. We consider frontal collision between two light bullets with different relative velocities. At large velocities the collision is elastic with the bullets emerge after collision with practically no distortion. At small velocities two bullets coalesce to form a bullet molecule. At a small range of intermediate velocities the localized bullets could form a single entity which expands indefinitely leading to a destruction of the bullets after collision. The present study is based on an analytic Lagrange variational approximation and a full numerical solution of the 3D nonlinear Schrödinger equation.

Dynamics of vortex-antivortex pairs and rarefaction pulses in liquid light

“…Moreover, it would be worth considering the three dimensional cubic-quintic case, which supports top-flat stable spatiotemporal solitons [59,60] and vortices [59,61]. Their collsional dynamics has been analyzed in [62,63] but the dynamics of dark traveling waves has not been described yet. Using the cubic defocusing Schrödinger equation, interesting dynamical analysis of the interplay of rarefaction pulses, vortex rings and vortex lines in 1+3 dimensions have been presented in the context of Bose-Einstein condensates [64][65][66] and superfluids [67].…”

Symmetry breaking, Josephson oscillation and self-trapping in a self-bound three-dimensional quantum ball

“…Motivated by the above consideration, in this paper we study SSB, Josephson oscillation [17][18][19][20] and self trapping in a 3D self-bound attractive matter-wave quantum ball [26][27][28] placed in a parity-symmetric (a) 1D double-well potential or (b) a 1D Gaussian potential along the z axis. These 1D potentials are necessary for SSB; however, these potentials act in 1D and thus have no effect on the localization of the 3D quantum ball.…”

“…The mathematical structure of the non-linear mean-field GP equation is the same as that of the NLS equation used to study pulse propagation in non-linear optics, although the physical meaning of the different terms is distinct in two cases. Hence, in a cubic-quintic non-linear medium [30][31][32] one can have a stable mobile 3D spatiotemporal light bullet 28,29 and a SSB can occur in that context also.…”

“…These 1D potentials are necessary for SSB; however, these potentials act in 1D and thus have no effect on the localization of the 3D quantum ball. The 3D quantum ball is stabilized in the presence of a repulsive three-body interaction and an adequate two-body attraction above a critical value [26][27][28] . It has been demonstrated that a tiny three-body repulsion stops the collapse and can stabilize a 3D quantum ball for zero 26 and non-zero angular momenta 29 .…”

Observation of Photon Droplets and Their Dynamics

“…The definition of a photon droplet does not require stationarity, however, if a droplet is initiated in the ground state, then its stationary behavior will coincide with the solitons described above. Liquid light states have also been proposed, arising from the balance between higher order, cubic-quintic nonlinearities [20][21][22] that are distinct from the photon droplets. In the photon droplet framework, a beam of light propagating in a nonlocal nonlin-ear medium is treated as a many-body system where the photon-photon interaction is mediated by the nonlinearity ∆n.…”