Fast compression of pure-quartic solitons in nonlinear optical fibers via shortcuts to adiabaticity

TL;DR

This work tackles fast compression of pure-quartic solitons in nonlinear fibers with negative quartic dispersion by developing a variational description and a shortcuts-to-adiabaticity (STA) protocol. The approach first builds an adiabatic reference using an effective-potential picture for the PQS width under slowly varying nonlinearity $f(z)=\exp\left(2\int_0^z g(z')\,dz'\right)$, then prescribes a nonadiabatic width trajectory via inverse engineering and reconstructs the required gain/loss profile $g(z)$ to realize fast, high-fidelity compression to a target width. Numerically, STA compresses the PQS over a distance almost an order of magnitude shorter than the adiabatic benchmark, while maintaining high fidelity; residual breathing and pedestal formation are observed near the end, attributed to internal PQS modes and limitations of the Gaussian variational model. The results offer a practical route to engineered ultrafast PQS shaping and highlight avenues for enhancing robustness and extending the method to joint dispersion/nonlinearity management and higher-order effects. The core insight is that STA, via carefully designed $g(z)$ and $f(z)$, can harness the nonlinear PQD–Kerr interplay to achieve rapid, controlled soliton compression with potential impact on high-peak-power pulse processing in PQD-based systems.

Abstract

Pure-quartic solitons (PQSs) supported by negative fourth-order dispersion have recently attracted considerable interest. In this work, we study both adiabatic and nonadiabatic compression of PQSs in nonlinear optical fibers with pure quartic dispersion in the presence of distributed gain and loss. Within a variational framework, we show that, for weak constant gain, the adiabatic compression dynamics can be mapped onto the motion of an effective particle in a slowly deformed potential, providing an intuitive physical picture. To overcome the long propagation distance required by conventional adiabatic condition, we exploit shortcuts to adiabaticity (STA) based on inverse engineering and derive analytical gain-loss profiles, with appropriate boundary conditions that realize a prescribed fast compression over a shorter propagation distance. Numerical simulations confirm the theoretical predictions and indicate a minimum propagation distance below which noticeable waveform distortion emerges. Compared with standard adiabatic references, the STA design significantly reduces the required compression distance while maintaining high-fidelity PQS evolution.

Figures (5)

• Figure 1: Effective potential $V(a)$ as a function of the PQS width $a$ at different propagation distances $z$ for constant gain $g(z)\equiv 0.02$ in the anomalous-PQD regime ($\beta_4=-1$). The curves correspond to $z=0$ (dotted), $z=30$ (dashed), $z=60$ (dash-dotted), and $z=90$ (solid). As $z$ increases, the minimum of $V(a)$ shifts to smaller $a$, indicating adiabatic compression driven by the gradual increase of the effective nonlinearity $f(z)=\exp(2gz)$.
• Figure 2: Adiabatic evolution of the quasi-stationary width $a_c(z)$ versus propagation distance $z$. The dash-dotted curve shows the variational prediction from Eq. \ref{['eq:ac']}, whereas the solid curve shows the numerical simulation of Eq. \ref{['eq:NLSE_nd']}. The inset compares the initial Gaussian ansatz (dashed blue) with the numerically obtained PQS profile (solid purple). Parameters are consistent with Fig. \ref{['fig:Vaz']}.
• Figure 3: (a) STA-designed gain/loss profiles $g(z)$ for two compression distances, $z_f=9$ (solid red) and $z_f=6$ (dash-dotted blue), under the same boundary conditions $a(0)=1$ and $a(z_f)=0.3$. (b) Evolution of the width $a$ of the pulse versus propagation distance $z$ at $z_f=9$ . The solid red and dash-dotted blue curves represent direct numerical calculation and the STA-designed trajectory, respectively.
• Figure 4: Spatiotemporal evolution of Gaussian soliton under the adiabatic (a) and STA (b) protocols, respectively. Parameters are consistent with Figs. \ref{['fig:ac_num']} and \ref{['fig:sta_two_panels']}. Panels (c) and (d) show the intensity profiles and normalized spectra at the instants when the width $a(z)$ is maximal (solid red) and minimal (dashed blue).
• Figure 5: Fidelity $F$ as a function of propagation distance $z_f$ for STA protocols. Parameters are the same as those in Fig. \ref{['fig:sta_two_panels']}.