Simulation Methods for Rare Events in Nonlinear Lightwave Systems

摘要

The objectives of this project were to develop new hybrid analytical/computational methods that are capable of simulating the rare events that are the determining factors of the performance of lightwave systems and devices. These methods use the following: (1) analytical techniques, such as perturbation and asymptotic methods, to guide numerical simulations using importance sampling; and (2) adaptive numerical methods, such as the multicanonical Monte Carlo and cross-entropy methods, to perform the simulation of rare events when guiding analytical models are not available. The above methods can be used to evaluate the performance of specific optical systems and devices, including ultra-high-precision optical clocks based upon mode-locked fiber lasers, and optical clocks and other devices based upon hybrid opto- electronic oscillators. In each case, the goal is to use the methods to develop models that can accurately predict the performance of these devices, as well as determine the failure modes that are the limiting factors in their performance. The author has developed methods based upon soliton perturbation theory and importance sampling to simulate rare events in lightwave systems, including mode-locked laser systems. A key step to using the methods based upon soliton perturbation theory is to use an approximate version of the system dynamics to determine the locations in the large-dimensional state space that most contribute to the desired rare events (e.g., errors). In this method, calculus of variations applied to the approximate system allows the most significant rare events to be located, and then fully detailed importance-sampled Monte- Carlo simulations in the vicinity of these locations properly determines the probabilities of these rare events and corrects for any errors made by the approximations in determining the system dynamics.