Stable high-order solitons in spiral potentials

Abstract

We present a comprehensive study of optical solitons supported by spiral potentials in media with the cubic-quintic (CQ) nonlinearity. A variety of families of stationary states, including fundamental and high-order (excited) in-phase, out-of-phase, and hybrid-phase ones, are found. The linear stability analysis, corroborated by direct simulations, demonstrates that all upper-branch nonlinear states in potentials with different azimuthal indices are \emph{completely stable}, which rarely occurs in soliton physics. Our findings suggest spiral potentials as an effective means for multistable optical trapping, with potential applications in all-optical data processing.

Figures (7)

• Figure 1: (a-c) The spiral potential defined by Eq. (\ref{['Eq2']}). (d-f) Spectra of discrete eigenvalues $b$ of the linearized version of Eq. (\ref{['Eq3']}). Values $n$ are sequential numbers of the eigenvalues for $N=1$ in (a, d), $2$ in (b, e), and $3$ in (c, f). The other parameters of the spiral potential (\ref{['Eq2']}) are $r_{0}=6,T=2\pi$, and $V_{0}=50$.
• Figure 2: Profiles of fundamental (a, b), third-order (c, d), and fifth-order (e, f) spiral solitons, with $b=3.0$ in (a, c, e) and $1.9$ in (b, d, f). All panels pertain to $N=1$ in Eq. (\ref{['Eq2']}). Here and in other figures, the plotted domain is $(x,y)\in \lbrack 20,+20]$.
• Figure 3: (a) Power $U$ vs. propagation constant $b$ for the fundamental (red), third-order (blue), and fifth-order (black) solitons. (b) The angular coordinates $\theta _{1}$ (blue) and $\theta _{2}$ (red) of the inner and outer endpoints of the “ skeleton” vs. $b$, for the upper-branch fundamental solitons (the formal jump of $\theta _{2}$ from $0^{\mathrm{o}}$ to $360^{\mathrm{o}}$ implies that the dependence is actually continuous). The bottom panels: the instability growth rate vs. $b$ for the third-order (c) and fifth-order (d) solitons belonging to the lower branch. Red dots correspond to the propagation examples presented in Fig. \ref{['fig7']}.
• Figure 4: Examples of solitons in the spiral potential (\ref{['Eq2']}) with $N=2$. (a) and (b): The in- and out-of-phase fundamental states, respectively. (c) and (d): The in- and out-of-phase second-order states, respectively. All panels pertain to $b=2.2$.
• Figure 5: (a) Power $U$ vs. $b$ for the in-phase and out-of-phase fundamental (blue) and second-order (red) two-arm ($N=2$) solitons. (b) Coordinates of the inner (blue) and outer (red) endpoints of the two arms (stars and circles, respectively) of fundamental in-phase solitons vs. $b$. (c) The peak value $|\psi |$$_{\mathrm{max}}$ of the fundamental (blue) and second-order (red) solitons vs. $b$. (d) The instability growth rate $\lambda _{\mathrm{re}}$ vs. $b$ for the lower-branch fundamental in-phase solitons.