▎ 摘　　要

A strict mathematical framework combining perturbation theory and temporal coupled-mode theory is developed to model graphene-induced saturable absorption in graphene-enhanced nanophotonic resonators. To allow for loss saturation in graphene, a power-dependent model of its surface conductivity is carefully introduced, based on the underlying physics. The framework is then cautiously unfolded to capture the two-dimensional nature of graphene and its interaction with the electromagnetic mode, additionally allowing one to incorporate any bulk or sheet material that is subject to saturable loss, together with other nonlinear effects. Both exact and approximative approaches are introduced, revealing the capabilities of the proposed framework to address the effect of saturable absorption. A graphene-enhanced silicon slab ring resonator is examined using the developed framework, uncovering its excellent accuracy and its capability to downgrade the computational complexity of a full-wave nonlinear simulation to a phenomenological but physically definitive differential equation. The potential of the resonant structure to act as an optically addressed switching element is being demonstrated, exposing high extinction ratio and low power requirements. Finally, it is illustrated how the framework is capable of capturing the rich dynamics of a resonant system that may additionally exhibit Kerr-and/ or free-carrier-induced optical bistability and self-pulsation.