The 1342 nm A-O Q-switched oscillator experiment is carried out. With various PRFs, Fig. 4 displays the average output power as a function of absorbed pump power. The output power increases linearly with the increase of absorbed pumping power under 7.13 W. The output power at high PRF is significantly more than that of low PRF at a high pump level. It drops down quickly after peaking at a high pump power of 7.13 W at high repetition frequencies of 40–100 kHz. The maximum output power value could be maintained in the 7.13–7.98 W pump power at low PRFs of 20 kHz. These are mostly explained by the intense heat effects on the laser crystal and Q-switch, which result in the cavity being unstable and a sharp drop in output power. The highest output power is 2.0 W with a repetition frequency of 100 kHz and an absorbed pump power of 6.28 W, achieving an optical conversion efficiency of 31.8% and a slope efficiency of 33.7%. The pulse widths are 5.1 ns, 6.0 ns, 7.4 ns, 9.8 ns, 15.9 ns with the repetition frequencies of 20 kHz, 40 kHz, 60 kHz, 80 kHz, and 100 kHz, respectively, with the absorbed pump power of 6.28 W, as shown in Table 1 (*t**exp*).

Table 1

The theoretical values and experimental results of the pulse width with different PRFs

PRF (kHz) | 20 | 40 | 60 | 80 | 100 |

*n**0* (cm-3) | 6.8×1018 | 3.8×1018 | 2.6×1018 | 2.0×1018 | 1.6×1018 |

*n**f* (cm-3) | 7.4×1015 | 8.5×1016 | 1.9×1017 | 2.7×1017 | 3.2×1017 |

*t**cal* (ns) | 2.2 | 3.3 | 5.0 | 8.0 | 14.8 |

*t**exp* (ns) | 5.1 | 6.0 | 7.4 | 9.8 | 15.9 |

The pulse width can be expressed as follows [7]

$${t_{cal}}=\frac{{2L/c}}{{1 - \ln ({r_1}) - \xi }}\frac{{{n_0} - {n_f}}}{{{n_0} - {n_{th}}[1+\ln ({n_0}/{n_f})]}}$$

1

where *c* is the speed of light, *L* is the cavity length,\({n_0}=K\tau {P_p}(1 - {e^{ - 1/f\tau }})\), *f* is the PRF, *P**p* is the pump power, and *τ* is the fluorescent lifespan. The formula *K* = *ηn*th*/τP*th, where *P*th is the threshold pump power, *η* is the absorption efficiency, and *n*th is the threshold inversion density, is obtained using the equation[16]: \({n_{th}}=\frac{1}{\sigma }[\frac{1}{l}\ln {(\xi \sqrt {{r_1}{r_2}} )^{ - 1}}+\beta ]\), where σ is the stimulated emission cross-section, which can be calculated using Ref. [17], *l* is the laser crystal’s length, *ξ* is the single pass transmission, *r**1* and *r**2* are the the M1’s and M2’s reflectances, and *β* is the laser crystal’s loss coefficient. The relation:\({n_f}={n_0}{e^{ - {n_0}l\sigma /\gamma }}\) can be used to calculate *n**f*, where\(\gamma =1 - \xi \sqrt {{r_1}{r_2}} {e^{ - \beta l}}\) is a cavity loss factor. The parameters used in the theoretical calculations in Table 2 can be used to determine the output single pulse width at various repetition rates. The results are given in Table 1(*n**0*, *n**f*, *t**cal*).

Table 2

Parameters used in theoretical pulse width calculations

*τ* | 110 *µ*s |

*c* | 3.0*×*1010 cm/s |

*η* | 0.92 |

*P**th* | 0.36 W |

*σ* | 1.59*×*10*−* 19 cm2 |

*l* | 0.8 cm |

*ξ* | 0.98 |

*r**1* | 1 |

*r**2* | 0.82 |

*β* | 0.02 cm− 1 |

*L* | 4 cm |

*P**p* | 6.83 W |

Experimental results are generally consistent with theoretical calculations, which show that the cavity design for A-O Q-switching is sensible and optimal. The calculation's presumption that inversion and photon density would remain constant across the laser crystal’s transverse section could be the cause of the difference. It restricts the precision with which pulse width and pulse formative time are calculated[16, 18].

The oscillator laser then goes into the two power amplifiers with an average power of 2.0 W, a PRF of 100 kHz, a pulse width of 15.9 ns, and a beam quality factor of Mx2=1.05 and My2=1.08. Figure 5 depicts the relationship between the two-stage Nd:YVO4 amplifiers’ output power and the total absorb LD pump power. With the absorbed pump power in each stage of 88.9 W, the output power of 12.55 W and 20.40 W are achieved from the first and second amplifiers with the optical extraction efficiency of 11.87% and 8.83%, respectively. Because of the diffraction loss, depolarized loss, and absorption loss caused by the Nd:YVO4 rod and mirrors, the slope of the output power of the second-stage amplifier has dropped when compared to the first-stage amplifier. The total optical gain of the two-stage power amplifiers is 10.2.

The mathematical description of the beam quality factor M2 for the wavefront aberrations and beam intensity distributions separately [19, 20],

\({M^2}=\sqrt {{{\left( {M_{{diff}}^{2}} \right)}^2}+{{\left( {M_{{ab}}^{2}} \right)}^2}}\)

where \(M_{{ab}}^{2}\)is the phase term and\(M_{{diff}}^{2}\)is the amplitude term. Spherical aberration is the dominant factor affecting the beam quality (\(M_{{ab}}^{2}\)). The laser beam is close to Gaussian intensity distribution at the locations of 700 mm and 1620 mm, i.e., the\(M_{{diff}}^{2}\)term is close to 1. The variation of the spherical aberration coefficient becomes the main part in changing the beam quality. Thus, as mentioned above, the beam quality deteriorates after 700 mm (Crystal 1) and improves after 1620 mm (Crystal 2). Due to Crystal 1’s positive spherical aberration, the oscillator’s beam quality degrades after goes through the first amplifier, and the measurement of the beam quality factor is Mx2=1.91 and My2=1.85. Beam quality deterioration is mainly caused by spherical aberration. The beam with negative spherical aberration is compensated by Crystal 2 with positive spherical aberration after passing through the second amplifier, considerably reducing the spherical aberration and enhancing the beam quality. As shown in Fig. 6, the final beam quality factor is decreased with Mx2=1.45 and My2=1.34.

As shown in Fig. 7(a), the laser pulse width is measured to be about 14.8 ns. After the two-stage amplifiers, the final pulse of the output laser is very smooth. Compared to the oscillator, the pulse width is slightly narrower, but the gain narrowing effect[21] is minimal. The main reason is that the pulse width of the laser does not reach the femtosecond order. Figure 7(b) shows the output laser multipulse distribution. The repetition rate is 100 kHz. Each pulse has the same shape and is relatively stable.