Engineering Rogue Waves via Multimode Interactions in Integrated Waveguides
Gülsüm Yaren Durdu, Azka Maula Iskandar Muda, Uğur Teğin
TL;DR
The paper addresses how multimode interactions in integrated Si3N4 waveguides govern rogue-wave formation. It uses a multimode nonlinear Schrödinger equation framework with stochastic noise to seed modulation instability across four TE modes, extracting nonlinear couplings from mode overlaps. Findings show that excitation of the fundamental mode alone yields stable propagation with exponential-like statistics, whereas multimode excitations or higher-order mode excitation produce heavy-tailed statistics with rogue events exceeding $8σ$. Intermodal four-wave mixing and spatiotemporal beating provide efficient MI channels, accelerating energy localization and extreme peaks. The work introduces modal excitation as a practical control parameter for engineering extreme spatiotemporal events on photonic chips, with potential applications to on-chip supercontinuum generation and frequency combs.
Abstract
We explore rogue wave formation in multimode silicon nitride (Si$_3$N$_4$) waveguides with multimode nonlinear Schrödinger equation-based simulations. Pure fundamental-mode excitation produces smooth propagation without extreme events, whereas higher-order modes or multimode superpositions yield heavy-tailed statistics with bursts exceeding the $8σ$ threshold. These results reveal that rogue wave generation in integrated waveguides is controlled not only by material properties such as nonlinearity and dispersion but also by modal excitation and intermodal nonlinear interactions. Our results identify modal control as a new degree of freedom for engineering extreme spatiotemporal events on photonic chips, with implications for on-chip supercontinuum generation, frequency combs, and nonlinear wave management.