Analysis of passive additive-pulse mode locking with eigenmode theory

The equation of motion for the coupled cavities of additive-pulse mode locking is solved by the eigenvalue method. The pulse evolution and self-starting condition for passive operation is analyzed. It is shown that the laser configuration is equivalent to an intracavity interferometer, and a phase modulation across the pulse is the essential element for mode locking. With the method developed, transient pulse evolution of an initial seed pulse can be calculated and thereby optimized. It is found that the pulse shortening rate is linear with respect to the number of round trips. The duration for the initial pulse to shorten to a steady state is proportional to its initial width and inversely proportional to the nonlinear coefficient.>