Symmetry-mediated nonlinear coupling and spatiotemporal pulse dynamics in multimode silicon nitride waveguides

Abstract

We present a systematic computational study of spatiotemporal nonlinear pulse propagation in multimode thin-film silicon nitride (SiN) waveguides. By solving the generalized multimode nonlinear Schrödinger equation for a 6 µm wide waveguide supporting six TE modes, we investigate how excitation symmetry and modal power distribution shape intermodal four-wave mixing, soliton fission, dispersive-wave generation, and mode-resolved energy transfer. The launched mode combination sets the symmetry content of the propagating field and thereby mediates which nonlinear coupling terms can participate through the parity selection rule of the fully vectorial coupling tensor. Even-mode excitation confines the accessible terms mainly to the even-mode subspace, whereas mixed even/odd excitation allows both parity families to contribute. Full-vectorial propagation simulations show that nonlinear overlap, phase mismatch, temporal walk-off, dispersion, and launched modal power determine the strength of these allowed contributions. Among the simulated cases, mixed-parity excitation produces the broadest finite spectral span, reaching a 5.81 µm bandwidth at the −30dB level when evaluated within the SiN material transparency window. These results clarify how modal symmetry can be used as a practical design principle for engineering broadband nonlinear dynamics in integrated multimode SiN waveguides.