Stabilization of three-dimensional light bullets by a transverse lattice in a Kerr medium with dispersion management

Abstract

We demonstrate a possibility to stabilize three-dimensional spatiotemporal solitons ("light bullets") in self-focusing Kerr media by means of a combination of dispersion management in the longitudinal direction (with the group-velocity dispersion alternating between positive and negative values) and periodic modulation of the refractive index in one transverse direction, out of the two. The analysis is based on the variational approximation (results of direct three-dimensional simulations will be reported in a follow-up work). A predicted stability area is identified in the model's parameter space. It features a minimum of the necessary strength of the transverse modulation of the refractive index, and finite minimum and maximum values of the soliton's energy. The former feature is also explained analytically.

Multidimensional semi-gap solitons in a periodic potential

“…Crossing the lower border of the existence domain (1) leads to disintegration of the localized state into linear Bloch waves (radiation) [19]. In the case of the attractive cubic nonlinearity (which corresponds to BEC where atomic collisions are characterized by a negative scattering length, while this is the case of the normal, self-focusing Kerr effect), 2D and 3D solitons can be stabilized not only by the potential lattice whose dimension is equal to that of the ambient space, but also by low-dimensional periodic potentials, whose dimension is smaller by one, i.e., 2D and 3D solitons can be stabilized by a quasi-1D [5,6] or quasi-2D [5,6,7] OL, respectively [in the former case, the qualitative estimate (1) for the width of the stability region at small ε is correct too]; however, 3D solitons cannot be stabilized by a quasi-1D lattice potential [5,6] [this is possible if the 1D potential is applied in combination with the Feshbach-resonance management, i.e., periodic reversal of the sign of the nonlinearity coefficient [20], or in combination with dispersion management, i.e., periodically alternating sign of the local GVD coefficient [21]]. Solitons can exist in such settings because the attractive nonlinearity provides for stable self-localization of the wave function in the free direction (one in which the low-dimensional potential does not act), essentially the same way as in the 1D NLS equation, and, simultaneously, the lattice stabilizes the soliton in the other directions (in the 3D model with the quasi-1D OL potential, the selflocalization in the transverse 2D subspace, where the potential does not act, is possible too, but the resulting soliton is unstable, the same way as the above-mentioned Townes soliton).…”

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

“…There are many theoretical − numerical and analytical − studies on light bullets using the 3D nonlinear Schrödinger (NLS) equation [1] with a modified nonlinearity [6,7], nonlinear dissipation [16], and/or dispersion [17]. Dispersion and nonlinearity management can stabilize light bullets in a medium with cubic nonlinearity [18]. Solitons have also been studied in the coupled NLS equation [19].…”

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

“…Nonlinear dissipation in the complex cubic-quintic Ginzburg-Landau equation also stabilizes the bullets [18]. Dispersion management can stabilize light bullets in a medium with cubic nonlinearity [19]. There has been variational study of light bullets in a cubic-quintic medium [20] where a condition of stability was obtained.…”