High-repetition-rate laser pulse sources have extensive applications in fields such as high-speed optical communications, optical clocks, wireless communications, high-capacity optical networks, quantum communications, and laser ranging. Researchers have proposed various methods to achieve high-repetition-rate laser pulses, including self-mode-locked lasers, passive mode-locked solid-state lasers, quantum-well Bragg-Perot lasers, harmonic mode-locked erbium-doped fiber lasers, and quantum-well Bragg-Perot mode-locked lasers. Owing to their compact structure and low cavity loss, self-mode-locked lasers are promising for obtaining high-repetition-rate laser pulse signals. However, achieving high-repetition-rate self-mode-locked laser pulses theoretically requires an extremely short laser cavity that makes it challenging for solid-state lasers to achieve a high-power output. This study presents a high-repetition-rate harmonic mode-locked laser based on an Nd∶YVO₄ crystal that successfully achieves a harmonic mode-locked pulse output corresponding to the free spectral range of the gain medium by precisely adjusting the optical length of the resonant cavity.

First, a realistic model for laser longitudinal mode selection simulation is established based on standard tool effects. Through simulation experiments, it is discovered that when the ratio of the optical length of the gain medium to that of the resonant cavity is a simple fraction q/p (where q and p are positive integers), the longitudinal mode spacing of the laser is modified to p times the original longitudinal mode spacing, which is also equal to q times the free spectral range of the gain medium. Subsequently, a simulation model for harmonic mode-locked lasers is established based on the damping harmonic oscillator model. Simulation experiments show that good harmonic mode-locked pulses can be obtained only when the ratio of the optical length of the gain medium to that of the resonant cavity is close to the simple fraction q/p. To validate these theoretical results, four sets of harmonic mode-locked Nd∶YVO₄ lasers with different gain-medium lengths are designed and experimentally studied. The harmonic mode-locked pulse outputs of these four laser sets are investigated along with the relationship between the lockable range of the optical length of the resonant cavity and that of the gain medium.

In the experiments, the optical length of the gain medium is fixed at 11.0, 22.0, 35.2, and 44.0 mm for the four laser sets. A comprehensive scan of the optical length of the resonant cavity is performed to study the effect of the ratio of the optical lengths of the gain medium to that of the resonant cavity on the laser pulse output. The experimental results show that when the ratio of the optical length of the gain medium to the optical length of the resonant cavity is close to 1/3, 2/5, and 3/7, the longitudinal mode spacing of the four laser sets is modified to one, two, and three times the free spectral range of the gain medium, respectively, and the laser output is harmonic mode-locked pulses corresponding to 1, 2, and 3 times the free spectral range of the gain medium. When the optical length of the gain medium is fixed, a lockable range exists for the optical length of the resonant cavity. When the optical length of the resonant cavity exceeds this lockable range, the laser output often exhibits the characteristics of multi-pulse-mode locking. Furthermore, the lockable range of the optical length of the resonant cavity is positively correlated with the optical length of the gain medium. To assess the stability of the laser output, an Nd∶YVO₄ harmonic-mode-locked laser with a physical gain medium length of 20 mm is selected for long-term observation. The experimental results show that when laser outputs are the first, second, and third harmonics corresponding to the free spectral range of the gain medium, the spectral drifts within half an hour are 0.011, 0.018, and 0.010 nm, respectively, and the amplitude fluctuation of the laser pulse within 100 ns is 3.26%, 4.85%, and 3.61%, respectively.

This study successfully achieves harmonic mode-locked pulse outputs in four sets of Nd∶YVO₄ lasers with different gain medium lengths. Theoretical analysis and experimental research reveal that when the ratio of the optical length of the gain medium to the optical length of the resonant cavity is very close to a simple fraction q/p, the longitudinal mode spacing of the resonant cavity is modified to q times the free spectral range of the gain medium, and the laser output consists of harmonic mode-locked pulses corresponding to q times the free spectral range of the gain medium. At optical lengths of 11.0 mm and 25.8 mm for the gain medium and resonant cavity, respectively, a third harmonic mode-locked pulse with a repetition frequency of 40.92 GHz and a pulse duration of 24.4 ps is achieved. At a pump power of 6.57 W, the average output power is 790.7 mW. Furthermore, the optical length of the resonant cavity has a lockable range that is positively correlated with the optical length of the gain medium. These findings provide important references for the design and optimization of harmonic mode-locked lasers to ensure stable mode-locked pulse output. Future research will explore experiments using laser crystals with different doping concentrations but the same geometric length to verify the repeatability and generality of these conclusions and to further optimize the performance of harmonic mode-locked lasers.