8 research outputs found
On the Lugiato-Lefever Model for Frequency Combs in a Dual-Pumped Ring Resonator with an Appendix on Band Structures for Periodic Fractional Schrödinger Operators
Global continua of solutions to the Lugiato–Lefever model for frequency combs obtained by two-mode pumping
We consider Kerr frequency combs in a dual-pumped microresonator as time-periodic and spatially -periodic traveling wave solutions of a variant of the Lugiato-Lefever equation, which is a damped, detuned and driven nonlinear Schrödinger equation given by . The main new feature of the problem is the specific form of the source term which describes the simultaneous pumping of two different modes with mode indices and . We prove existence and uniqueness theorems for these traveling waves based on a-priori bounds and fixed point theorems. Moreover, by using the implicit function theorem and bifurcation theory, we show how non-degenerate solutions from the 1-mode case, i.e. , can be continued into the range . Our analytical findings apply both for anomalous and normal dispersion, and they are illustrated by numerical simulations
Bandwidth and conversion-efficiency analysis of Kerr soliton combs in dual-pumped resonators with anomalous dispersion
Kerr frequency combs generated in high-Q microresonators offer an immense potential in many applications, and predicting and quantifying their behavior, performance and stability is key to systematic device design. Based on an extension of the Lugiato-Lefever equation we investigate in this paper the perspectives of changing the pump scheme from the well-understood monochromatic pump to a dual-tone configuration simultaneously pumping two modes. For the case of anomalous dispersion we give a detailed study of the optimal choices of detuning offsets and division of total pump power between the two modes in order to optimize single-soliton comb states with respect to performance metrics like power conversion efficiency and bandwidth. Our approach allows also to quantify the performance metrics of the optimal single-soliton comb states and determine their trends over a wide range of technically relevant parameters