Stabilization and Destabilization of Multimode Solitons in Nonlinear Degenerate Multi-Pass Cavities

Optical solitons in multimode nonlinear optical systems offer a unique platform for exploring the interplay of nonlinearity, dispersion, and spatial mode coupling, offering insights into complex nonlinear wave phenomena. Multi-pass cavities (MPCs) incorporating nonlinear Kerr media serve as prototypical systems, enabling high-efficiency supercontinuum generation and pulse compression. However, stabilizing femtosecond laser pulses in solid-medium-based MPCs (solid MPCs) under strong Kerr nonlinearity remains a significant challenge due to multimode coupling, which disrupts beam stability. In this work, we address this challenge by investigating the stability of laser pulses in MPCs using Floquet and perturbation model. We identify novel mode-coupling-suppression (MCS) medium lengths, where destructive interference among multimode wave components suppresses coupling and facilitates soliton stabilization. Under MCS conditions, our simulations demonstrate stable beam propagation in solid MPCs with nonlinear phases up to 1.5{\pi} per pass, achieving >13-fold pulse compression with excellent spatio-spectral homogeneity. Our findings offer valuable guidance for designing advanced MPCs with tailored Kerr media.