Spatiotemporal solitary modes in a twisted cylinder waveguide pipe with the self-focusing Kerr nonlinearity
arXiv:1712.03543 · doi:10.1016/j.cnsns.2018.07.040
Abstract
We study the spatiotemporal solitary modes that propagate in a hollow twisted cylinder waveguide pipe with a self-focusing Kerr nonlinearity. Three generic solitary modes, one belonging to the zero-harmonic (0H) and the other two belonging to the first-harmonic (1H), are found in the first rotational Brillouin zone. The 0H solitary modes can be termed as a quasi-1D (one-dimensional) temporal soliton. Their characteristics depend only on the energy flow. The 1H solitary mode can be termed a quasi-2D (two-dimensional) bullet, whose width is much narrower than the angular domain of the waveguide. In contrast to the 0H mode, the characteristics of the 1H solitary mode depend on both their energy flow and the rotating speed of the waveguide. We demonstrate numerically that the 1H solitary modes are stable when their energy flow is smaller than the threshold norm of the \emph{Townes soliton}. The boundaries of the bistable area for these two types of solitary modes are predicted by the analyses via two-mode approximation. This prediction is in accordance with the numerical findings. We also demonstrate analytically that the 1H solitary mode of this system can be applied to emulate the nonlinear dynamics of solitary modes with 1D Rashba spin-orbit (SO) coupling by optics. Two degenerated states of the 1H solitary mode, semi-dipole and mixed mode, are found from this setting via the mechanism of SO coupling. Collisions between the pair of these two types of solitary modes are also discussed in the paper. The pair of the 0H solitary mode features only the elastic collision, whereas the pair of 1H solitary modes can feature both elastic and inelastic collision when the total energy flow of the two modes are smaller or close to the threshold norm of the \emph{Townes soliton}.
arXiv comment6 figures, 52 references
References in corpus (33)
- Degenerate Quantum Gases with Spin-Orbit Coupling
- Quantum Phases of Vortices in Rotating Bose-Einstein Condensates
- Condensation of `composite bosons' in a rotating BEC
- The creation of two-dimensional composite solitons in spin-orbit-coupled self-attractive Bose-Einstein condensates in free space
- Stability of two-dimensional spatial solitons in nonlocal nonlinear media
- Two-dimensional solitons and quantum droplets supported by competing self- and cross-interactions in spin-orbit-coupled condensates
- Vortex solitons in two-dimensional spin-orbit coupled Bose-Einstein condensates: effects of the Rashba-Dresselhaus coupling and the Zeeman splitting
- Structural phase transitions of vortex matter in an optical lattice
- Three-dimensional spatiotemporal optical solitons in nonlocal nonlinear media
- Pinning of vortices in a Bose-Einstein condensate by an optical lattice
- Two-dimensional solitons in dipolar Bose-Einstein condensates with spin-orbit coupling
- Two-dimensional dipolar gap solitons in free space with spin-orbit coupling
- Bose-Einstein Condensates in Rotating Lattices
- Collapse of spin-orbit coupled Bose-Einstein condensates
- Hidden vortices in a Bose-Einstein condensate in a rotating double-well potential
- Two- and one-dimensional gap solitons in spin-orbit-coupled systems with Zeeman splitting
- Topological Winding and Unwinding in Metastable Bose-Einstein Condensates
- Stabilization of spatiotemporal solitons in Kerr media by dispersive coupling
- Creating solitons by means of spin-orbit coupling
- Anisotropic semi-vortices in dipolar spinor condensates controlled by Zeeman splitting
- Dynamical vortex phases in a Bose-Einstein condensate driven by a rotating optical lattice
- Nonlinear modes and symmetry breaking in rotating double-well potentials
- One-dimensional description of a Bose-Einstein condensate in a rotating closed-loop waveguide
- Self-trapping under the two-dimensional spin-orbit-coupling and spatially growing repulsive nonlinearity
- One- and two-dimensional solitons in PT-symmetric systems emulating the spin-orbit coupling
- Formation and structure of vortex lattices in a rotating double-well Bose-Einstein condensate
- Discrete solitons and scattering of lattice waves in guiding arrays with a nonlinear -symmetric defect
- Bloch Structures in a Rotating Bose-Einstein Condensate
- Rashba-type Spin-orbit Coupling in Bilayer Bose-Einstein Condensates
- Dark solitons in dual-core waveguides with dispersive coupling
- Switch between the types of the symmetry breaking bifurcation in optically induced photorefractive rotational double-well potential
- Buffering and Trapping Ultrashort Optical Pulses in Concatenated Bragg Gratings
- Femtosecond soliton diode on heterojunction Bragg-grating structure
Cited by in corpus (3)
- Two-dimensional composite solitons in Bose-Einstein condensates with spatially confined spin-orbit coupling
- Symmetry breaking of a matter-wave soliton in a double-well potential formed by spatially confined spin-orbit coupling
- Nonlinear modes in spatially confined spin-orbit-coupled Bose-Einstein condensates with repulsive nonlinearity