Peilong Yang | Searcharxiv

arXiv2026

Geometric Parametric Instability in Nonlinear Multipass Cells

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 Schr\"odinger 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.

physics.optics↗

arXiv2026

Photon-conserving Raman soliton attractors in focusing and defocusing Kerr media

The sign of the Kerr nonlinear coefficient has long been regarded as irrelevant to the direction of the Raman-induced soliton self-frequency shift. Yet the standard generalized nonlinear Schr\"odinger equation (GNLSE) predicts a frequency shift that depends on the sign of the nonlinearity, which leads to an unphysical blue shift in the defocusing case. We resolve this inconsistency by deriving the time-domain form of the photon-conserving GNLSE (pcGNLSE) from its established frequency-domain counterpart. The derivation reveals that photon-number conservation imposes two sign modifications relative to the standard GNLSE: the Raman-shift coefficient acquires the absolute value of the Kerr nonlinear coefficient in place of its signed counterpart, and the self-steepening-Raman dissipation term likewise carries an absolute-value prefactor rather than a signed one. These two modifications jointly guarantee a universal spectral redshift and monotonically decreasing pulse energy during propagation, irrespective of the signs of the Kerr nonlinear coefficient and its frequency derivative. Applying the method of moments to the time-domain pcGNLSE with appropriate chirped ans\"atze, we derive closed-form evolution equations for five pulse parameters and establish explicit attractor conditions under which bright or dark Raman solitons propagate with constant peak power. Direct numerical integration of the pcGNLSE confirms all analytical predictions and demonstrates that the standard GNLSE fails qualitatively, predicting unphysical energy growth and spectral blueshift in the negative-nonlinearity regime. The results provide a rigorous analytical framework for Raman soliton dynamics in materials with negative third-order susceptibility, with direct implications for soliton-based devices in emerging semiconductor waveguide and microresonator platforms.

physics.optics↗