AI 中文总结
该研究从理论和数值上证明非线性多通腔（MPCs）中存在几何参量不稳定性（GPI），推导了其弗洛奎特准相位匹配条件，预测了可调边带，可为宽带多色光产生提供机制，也可能影响非线性脉冲压缩的光束质量。
AI 中文摘要
几何参量不稳定性（GPI）是由纵向周期性多模演化引发的离散光谱边带的共振增长，此前主要在渐变折射率光纤中开展研究。本文从理论和数值两方面证明，GPI可在充入气体的非线性多通腔（MPCs）中发生。通过将模匹配的MPC映射至等效波导，我们推导了由信号-闲频对相对于泵浦对的单次通过古伊相位失衡所决定的弗洛奎特准相位匹配条件。该理论预测了小信号增益和带宽；考虑泵浦耗尽的耦合模模型（CMM）进一步将最大转换分数与剩余相位失配关联，CMM预测了与不同径向指数和弗洛奎特阶相关的多个几何可调边带对。对于5巴的氩气，当考虑ps=1、h=0分支时，改变腔几何结构可将边带失谐从约96太赫兹移至46太赫兹。我们采用截断多模广义非线性薛定谔方程（MMGNLSE）模型，结合对应每个光谱模式含一个光子的半经典随机种子开展数值模拟，MMGNLSE模拟重现了预测的边带频率，并揭示了保留径向通道间的泵浦耗尽与竞争。因此，MPCs中的GPI可能会限制非线性脉冲压缩中的空间光束质量，同时为宽带多色光产生提供一种可调谐机制。
英文摘要
Geometric parametric instability (GPI) is the resonant growth of discrete spectral sidebands enabled by longitudinally periodic multimode evolution and has been studied primarily in graded-index fibers. Here we show theoretically and numerically that GPI can occur in gas-filled nonlinear multipass cells (MPCs). By mapping a mode-matched MPC onto an equivalent waveguide, we derive a Floquet quasi-phase-matching condition governed by the single-pass Gouy-phase imbalance of the signal--idler pair relative to the pump pair. The theory predicts the small-signal gain and bandwidth. A pump-depleted coupled-mode model (CMM) further relates the maximum converted fraction to the residual phase mismatch. The CMM predicts multiple geometrically tunable sideband pairs associated with different radial indices and Floquet orders. For argon at $5$~bar, varying the cavity geometry shifts the sideband detuning from approximately $96$ to $46$~THz when the $p_{\mathrm{s}}=1$, $h=0$ branch is considered. A truncated multimode generalized nonlinear Schrödinger equation (MMGNLSE) model is used for numerical simulations with a semiclassical stochastic seed corresponding to one photon per spectral mode. The MMGNLSE simulations reproduce the predicted sideband frequencies and reveal pump depletion and competition among the retained radial channels. GPI in MPCs may therefore limit spatial beam quality in nonlinear pulse compression while providing a tunable mechanism for broadband multicolor generation.
Comments13 pages, 9 figures
