Flat-top solitons and anomalous interactions in media with even-order dispersions and competing nonlinearities

Abstract

Flat-top (FT) solitons are optical pulses that arise from the balance of dispersion and self-phase modulation in media with the competing cubic-quintic nonlinearity. Previously, FT solitons were studied only in the case of the second-order dispersion ($m=2$). Following the recent observation of pure-quartic solitons (corresponding to $m=4$), we here construct families of FT solitons in the setting with pure-high-even-order dispersion (PHEOD), including $m=4,6,8$, and $10$, and address interactions between them. The PHEOD solitons are completely stable, and, unlike the conventional solitons, they feature oscillatory tails. Interactions between the PHEOD solitons are anomalous, featuring repulsion and attraction between in- and out-of-phase solitons, respectively. These results expand the variety of optical solitons maintained by diverse dispersive nonlinear media.

Figures (4)

• Figure 1: Families of numerically found PHEOD solitons of the FT type. (a) The propagation constant vs. the soliton's energy (shown on the logarithmic scale) for GVD$\ $orders $m=4,6,8,10$, compared to the $\beta (E)$ curve for conventional FT solitons, for $m=2$. (b) Profiles of the PHEOD and conventional FT solitons with a fixed energy, $E=30$. (c) The same as in (b), but on the logarithmic scale, to display oscillatory tails of the PHEOD FT solitons.
• Figure 2: The variation of profiles of the PHEOD solitons, produced by the numerical solution of Eq. (\ref{['system_psi1']}) with $m=4$, $6$, $8$, and $10$, for the soliton's energy taking values $0.1\leq E\leq 50$ with interval $\Delta E=0.1$.
• Figure 3: Linear-stability spectra and the perturbed evolution of the solitons for the GVD order $m=10$. The linear-stability spectra are plotted in the left panels with different energies: (a) $E=5$, (b) $E=30$, and (c) $E=50$, while the right panels (d-f) show the correponding stable evolution with initial random perturbations at a $5\%$ amplitude level.
• Figure 4: Interactions of the pure-decic flat-top solitons with different initial relative phase. Intensity input (solid lines), output (dashed lines) profiles and evolutions of the interacting solitons for the following cases: (a) and (d) interactions of ${\Psi_1(\mathit{E}=20)}$ and ${\Psi_2(\mathit{E} =4)}$ with the initial relative phase $\Delta\phi=0$, (b) and (e) interactions of ${\Psi_1(\mathit{E}=20)}$ and ${\Psi_2(\mathit{E}=20)}$ with the initial relative phase $\Delta\phi=0$, (c) and (f) interactions of ${\Psi_1(\mathit{E}=20)}$ and ${\Psi_2(\mathit{E}=20)}$ with the initial relative phase $\Delta\phi=\pi$.