Theory of mode-locked lasers containing a reverse saturable absorber

An analytic solution is presented for mode-locking a laser using a saturable absorber and reverse saturable absorber with long relaxation times compared to the temporal pulse widths. A reverse saturable absorber is a material with an excited-state absorption cross section larger than the ground-state absorption cross section, where increasing the incident light intensity increases the absorption. The reverse saturable absorber plays an important role in mode-locking laser materials where individual pulses cannot saturate the gain. A numerical example of mode-locking a CW alexandrite laser with a reverse saturable absorber and a saturable absorber is presented.