Transverse excess noise factor and transverse mode locking in a gain-guided laser

We use the Collins integral together with a rate equation to calculate the transverse mode profiles near g1g2 = 1/4 in a tightly focused end-pumped Nd:YVO4 laser. The transverse mode locking is confirmed from the mode decomposition into the degenerate empty-cavity eigenmodes and from the observation of beam profile variation along the propagation distance. We obtain that the calculated transverse excess noise factor without considering the thermal effect is consistent with the previous research and it depends on the pump size. We further study the influence of the thermal lens effect on the K factor and discuss how to suppress the laser instabilities that occur near the degeneracy.