Method of designing astigmatic compensation cavity for mode-locked laser based on propagation circle

The cavities of ultrashort pulsed lasers are mostly based on folded resonators with multi-mirrors. Astigmatism is an important issue to affect the performance of the mode-locked laser. An effective method of astigmatic ally compensating a continuous-wave passively mode-locked laser is presented in this paper. This method, in which the resonator propagation circle graphic theory is used, is easy and intuitive to seek the optimal location of the semiconductor saturable absorber mirror (SESAM), where the astigmatism can be compensated. Theoretical results show that the tangential and the sagittal spot size at the SESAM are equal and that the astigmatism can be compensated, when an SESAM is located at the tangential and the sagittal propagation circle intersection. The mode-locked resonator is insensitive to external perturbation including the vibration and the change of the thermal lens focal length, which leads to the instability of the mode locking operation. The antijamming ability of the resonator is outstanding. The experimental results indicate that the mode-locked laser works in a stabilized continuous-wave mode locking state and operates extremely steadily, when the SESAM is located at the tangential and the sagittal propagation circle intersection. The experimental results of the mode locking lasers show good agreement with the theoretical studies.