Hierarchy of coupled mode and envelope models for bi-directional microresonators with Kerr nonlinearity
Dmitry V. Skryabin
Abstract
We consider the interaction of counter-propagating waves in a bi-directionally pumped ring microresonator with Kerr nonlinearity. We introduce a hierarchy of the mode expansions and envelope functions evolving on different time scales set by the cavity linewidth and nonlinearity, dispersion, and repetition rate, and provide a detailed derivation of the corresponding hierarchy of the coupled mode and of the Lugiato-Lefever-like equations. An effect of the washout of the repetition rate frequencies from the equations governing the dynamics of the counter-propagating waves is elaborated in details.
Topics & Concepts
HierarchyPhysicsEnvelope (radar)Laser linewidthNonlinear systemMode (computer interface)Set (abstract data type)OpticsSuperposition principleKerr effectRepetition (rhetorical device)Kerr nonlinearityCoupled mode theoryQuantum mechanicsDispersion (optics)Statistical physicsResonatorCore (optical fiber)Measure (data warehouse)Mode couplingNonlinear opticsDynamics (music)MathematicsQuantum electrodynamicsRing (chemistry)Advanced Fiber Laser TechnologiesPhotonic and Optical DevicesMechanical and Optical Resonators