- E. Ding and J. N. Kutz, “Operating regimes, split-step modeling, and the Haus Master Mode-Locking Model,” Journal of the Optical Society of America B 26 2290-2300 (2009).
- E. Ding and J. N. Kutz, “Stability Analysis of the Mode-Locking Dynamics in a Laser Cavity with a Passive Polarizer,” Journal of the Optical Society of America B 26 1400-1411 (2009).
It has been approximately two decades since it was first established experimentally that stable and robust mode-locking (generation of femtosecond optical pulses) could be achieved using a passive polarizer as effective intensity discrimination mechanism. Development of such femtosecond lasers has found uses in multi-user biology facilities, medical clinics, manufacturing environments, and even in mobile facilities and aircraft. Despite the wide-spread commercial and academic use, the underlying theory quantifying the mode-locking stability and dynamics remains incomplete. This research mainly focuses on modeling as well as stability analysis of ring cavity lasers mode-locked by wave-plates and polarizer.
Low Dimensional Models
In this project a low-dimensional model is constructed via a variational reduction that characterizes the mode-locking dynamics in a laser cavity with a passive polarizer, which allows for an explicit analytical prediction of the mode-locked state and its corresponding stability. The stability analysis requires a center manifold reduction, which reveals that the solution decays to the mode-locked pulse on a timescale dependent on the gain bandwidth and the net cavity gain. Quantitative and qualitative agreement is achieved between the full PDE model and the low-dimensional model, thus providing for an excellent design tool for characterizing and optimizing mode-locking performance.
All-Normal-Dispersion Laser Mode-Locking
In this project we develop a split-step averaging method to characterize the mode-locking dynamics of the All-Normal-Dispersion (ANDi) laser mode-locked with a combination of wave-plates and a passive polarizer. The model explicitly accounts for the fiber birefringence and arbitrary alignment of wave-plates/polarizer angles. The general averaging scheme results in the cubic-quintic Ginzburg-Landau equation (CQGLE) at the leading order and the Seift-Hohenberg equation (SHE) at next order. A prediction of operating regimes of the ANDi laser is obtained, which allows for a direct comparison between theory and experiment.