Carrier-Mediated Nonlinear Dynamics and Device-Dependent Self-Pulsing in Silicon Photonic Waveguides and Microring Resonators

Silicon photonic waveguides support strong nonlinear interactions, but the same confinement that increases Kerr effects also strengthens two-photon absorption, free-carrier absorption, free-carrier dispersion, and optical heating. These processes act on different time scales and cannot be reduced to a universal material-only self-pulsing threshold. We develop a hierarchical model that separates straight-waveguide propagation from resonator feedback and then connects them through explicitly defined device parameters. The straight-waveguide calculation uses distributed linear loss, two-photon absorption, free-carrier absorption, and the Soref–Bennett carrier-dispersion relations with explicit unit conversion. A 500×220 nm silicon-on-insulator strip with Aeff = 0.065 µm2 is used as a reference geometry. Geometry-dependent loss is treated through measured propagation, sidewall-roughness, and bend-loss benchmarks. Carrier and thermal response times are kept as distinct low-pass processes. A single-bus microring then supplies the required phase-to-intensity conversion. For the published reduced thermal–free-carrier microring model at normalized detuning δ = −3, the calculated Hopf point is pH = 4.3194 with eigenvalues λ1,2 = ±i 7.1609 in thermal-time units. The same model reproduces an unstable fixed point at the published self-pulsing operating condition p = 18.676. A two-parameter stability map separates saddle-node bistability from finite-frequency Hopf onset. The manuscript closes with a proposed experimental sequence for measuring propagation loss, carrier lifetime, thermo-optic shift, resonator parameters, and self-pulsing spectra. The resulting framework treats self-pulsation as a device-dependent dynamical instability rather than a property inferred from the two-photon-absorption coefficient alone.