We report for the first time on simultaneously longitudinal and transverse self-mode locking in a diode-pumped Nd:YVO 4 laser to achieve a pulse train traveling along the zigzag multi-pass trajectories in the degenerate cavity. At a pump power of 2.5 W, the average output powers in the mode-locked operation are 490 mW and 520 mW for the M-mode and Z-mode, respectively. The pulse widths are measured to be approximately 22.2 and 21.1 ps for the M-mode and Z-mode, respectively.

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The criterion for achieving the self-mode-locking (SML) in an optically pumped semiconductor laser (OPSL) with a linear cavity is systematically explored. Experimental results reveal that the occurrence of SML can be assisted by the existence of high-order transverse modes. Numerical analysis is performed to confirm that the critical pump power for obtaining the SML operation agrees very well with the pump threshold for exciting TEM 1,0 mode. The present finding offers an important insight into laser physics and a useful indication for obtaining the SML operation in OPSLs.

We quantitatively investigate the influence of high-order transverse modes on the self-mode locking (SML) in an optically pumped semiconductor laser (OPSL) with a nearly hemispherical cavity. A physical aperture is inserted into the cavity to manipulate the excitation of high-order transverse modes. Experimental measurements reveal that the laser is operated in a well-behaved SML state with the existence of the TEM(0,0) mode and the first high-order transverse mode. While more high-order transverse modes are excited, it is found that the pulse train is modulated by more beating frequencies of transverse modes. The temporal behavior becomes the random dynamics when too many high-order transverse modes are excited. We observe that the temporal trace exhibits an intermittent mode-locked state in the absence of high-order transverse modes.

We develop a practical method to achieve harmonically self-mode-locked operation in a Nd:YVO 4 1.34-µm laser for the generation of high-repetition-rate pulse trains. We exploit a gain medium with partial-reflection coating at the lasing wavelength to introduce effective mode selection. We numerically demonstrate that the coated gain medium can effectively modify the mode spacing of the laser cavity to be the harmonics of the free spectral range of the gain medium when the optical cavity length is adjusted to be commensurate with the optical length of the gain medium. We further employ a coated Nd:YVO 4 crystal to realize harmonically mode-locked operation with a highest repetition rate of up to 32.1 GHz. At a pump power of 11.5 W, the average output power of 2.3 W is generated with a pulse duration as short as 5.7 ps. The locking range for the cavity length is also experimentally explored.