The widely used split-step Fourier method has difficulties when solving partial differential equations with saturable gain. Here, we describe a modified split-step Fourier method, and we compare it to several different algorithms for solving the Haus mode-locking equation and related equations that are used to model mode-locked lasers and other optical oscillators and amplifiers with saturable gain. These equations all include the product of a scalar nonlinearity and a stiff nonlinear operator. We find that a modified split-step method is the easiest to program with the same level of reliability and accuracy as the other methods that we investigated.
© 2013 Optical Society of America
Lasers and Laser Optics
Original Manuscript: July 11, 2013
Revised Manuscript: October 1, 2013
Manuscript Accepted: October 1, 2013
Published: October 31, 2013
Shaokang Wang, Andrew Docherty, Brian S. Marks, and Curtis R. Menyuk, "Comparison of numerical methods for modeling laser mode locking with saturable gain," J. Opt. Soc. Am. B 30, 3064-3074 (2013)