1. Introduction

Pulsed lasers in nanosecond region with high pulse energy and high repetition rate are the sources of choice for many applications such as laser detection, laser ignition and micromachining. Q-switching is an effective and widely used method to generate laser pulses with high pulse energy and with pulse width of nanoseconds to tens of nanoseconds. However, such high repetition rate, high energy, short pulsed lasers are relatively difficult to obtain although they could be amplified by master oscillator power amplification (MOPA), it’s mainly attributed to the following two reasons. First, the pulse width of common Q-switched laser is variable depending on many factors like the operating repetition rate, gain of the active medium and the transmission of the output coupler [1–3]. Thus, the pulse width is not a constant, rather it can increase with the rise of repetition rate. Second, the pulse energy of high frequency pulsed laser will be limited by the average power, the heat dissipation and the heat capacity of the active medium.

Cavity dumping, also known as the pulse transmission mode (PTM), is a technique for short and stable pulse generation. Cavity dumping technique is an approach to solve the problem that pulse width increases with the increase of pulse repetition rate. The pulse width of cavity-dumped laser is determined by optical path length (OPL) of the cavity and switching speed of the Q-switch system [3,4]. And if the switching time is fast enough, the pulse width can be just the round-trip time of light in the resonator [5]. By using cavity-dump technique, the laser pulse width would not vary with the factors like operating repetition rate, gain of the active medium or the output coupler. And once the resonator and the Q-switch system (Pockels cell and its electric driver) are determined, the pulse width of the laser would be constant, thus the short pulses with high repetition rate can be obtained through the cavity dumping technique. In addition, the cavity-dumped Q-switched lasers also have advantage of lower laser threshold since there is no output coupling during the growth of the giant pulse within the resonator [5]. In 2016, Lachlan Harris et al. presented a cavity-dumped Er:YAG laser with pulse width of 4.5 ns and peak power of 2 MW [5]. In the same year, Ping He et al. presented a cavity-dumped Nd:GdVO₄ laser with pulse width of 5.5ns and peak power of 18.5 kW at repetition rate of 50 kHz [3].

Burst-mode laser technique is an alternative approach to overcome the challenges associated with conventional high-average-power continuously pulsed DPSS lasers. Burst-mode laser can produce laser pulse with high energy and high repetition rate within the burst duration and then pump shuts down for cooling until the next cycle, thus enabling high pulse peak power with low average system power [6,7]. In 2013, Mikhail N. Slipchenko et al. presented a diode-pumped quasi-continuous burst-mode laser and achieved 1064.3 nm output energy of 120 mJ per pulse at 10 Hz in 30 ms burst duration by utilizing two single-pass and one double-pass diode-pumped amplifiers [6].

Combining burst-mode technique and cavity-dumped Q-switch technique, it is relatively easy and convenient to obtain lasers with high pulse energy and short pulse width at high repetition rates. And for the aim of meeting the requirement of laser diagnostics for fluid dynamic measurements, high-speed planar imaging and so on, amplification of this laser was investigated to produce output of higher energy while maintaining the short pulse width and high repetition rate. In this paper, a cavity-dumped burst-mode laser and its amplification have been investigated, burst energy of 1.89 J, peak power of 2.87 MW and pulse width of 3.3 ns were obtained at repetition rate of 100 kHz in 10 Hz pulse trains. This is the first time that MOPA laser combining with the cavity-dumping and burst-mode techniques be demonstrated to our best knowledge.

2. Experimental setup and theoretical analysis

Figure 1 shows schematic diagram of the experimental laser, including the master oscillator, amplifier stage one and amplifier stage two. M1-M4 are plane mirrors with high reflectivity at 1064 nm. A LD side-pumped Nd:YAG rod with length of 75 mm, cross section diameter of Φ3 mm and a Nd³⁺ doping concentration of 1.1 at.% works as gain medium in the master oscillator. In each amplifier stage, an LD side-pumped Nd:YAG rod with length of 75 mm, cross section diameter of Φ5 mm and a Nd³⁺ doping concentration of 0.6 at.% serves as the gain medium. This laser is 2ms long-pulse pumped and thus works in burst mode. The cavity length of the master oscillator is 280 mm and the cavity of each amplifier stage is 220 mm.

 

Fig. 1 Schematic diagram of the experimental setup.

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As output light of the cavity-dumped master oscillator is linear polarized, we use a polarized beam splitter cube (PBS cube, 12.7mm) combining with a zero-order quarter wave plate (QWP) and a reflector (M3 or M4) to build a dual-pass structure for each amplifier stage. With the dual-pass structure, laser can pass through gain medium and be amplified twice in each amplifier, and thus the energy extraction efficiency can be improved. Besides, the double-pass structure is more efficient for scaling the output power of the pulsed oscillator [8–10]. And multi-pass multi-rod structure can usually avoid the gain loss problem caused by internal scattering due to defects or whispering modes in single-rod single-pass system [11].

The Pockels cell is made of KD*P crystals and drove by electric pulses with voltage set at the quarter-wave voltage of approximate 3350 V and pulse duration set at 25 ns. In previous works, KD*P crystal mostly be used at repetition rate lower than 5 kHz. In most cases, the impact of piezoelectric effect becomes severe when repetition rate exceeds 5-10 kHz, post sub-pulses occur and pulse also widened at high frequency operations. However, the impact of piezoelectric effect can be avoided by shortening the pulse width of modulation voltage to tens of nanoseconds. By applying the very short 25 ns modulation voltage pulse, the impact of piezoelectric effect of the KD*P crystal can be avoided. The cavity-dumping cycle has the following three steps. Firstly, no voltage is applied to the Pockels cell, the P-polarized light from the PBS passes through the QWP twice in the round-trip and turns to the S-polarized light, then being reflected out of the master oscillator. Secondly, the quarter-wave voltage is applied to the Pockels cell, the Pockels cell works as a QWP and the light can pass through the PBS back and forth, and the oscillation starts between M1 and M2. Thirdly, the voltage is removed, the light in the cavity can be reflected out by the PBS during a round-trip and a new cycle starts. The repetition rate of the Pockels cell is adjustable up to 100 kHz. The profiles of the voltage pulse waveforms of the Pockels cell driver was measured at repetition rate of 100 kHz, as shown in Fig. 2 and it can be measured that the rising time and falling time of the voltage pulses are both approximate 10 ns.

 

Fig. 2 Waveform profiles of the output electrical pulses of the Pockels cell driver measured at repetition rate of 100 kHz. (a) – pulse train; (b) – single pulse.

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The refractive indices of the Nd:YAG rod, PBS cube (made of silica) and QWP (made of silica) are 1.82, 1.45 and 1.45 respectively and the refractive indices of the Pockels cell which made of KD*P (about 30mm in length) are 1.46 for n_e and 1.49 for n_o. The optical path length of the master oscillator is about 362 mm according to the size and refractive index of each component. Thus the round-trip time, which is the theoretical pulse width regardless of the switching time, is about 2.42 ns.

The variations of laser field energy in the cavity and population inversion energy in the active medium show the dynamic process of cavity dumping. According to R. B. Chesler and D. Maydan’s work published in 1971 [12], we have the following equations describing the cavity dumping cycle theoretically.

Where $N$ is the number of atoms at excited upper state multiplied by the laser transition energy $E$, and $F$ is the number of coherent laser photons in cavity multiplied by $E$. $N_0$ and $F_0$ are optimum values for CW operation by maximizing output power, given by

The parameter $\zeta$ is the spontaneous decay rate of the upper laser state, which equals to the reciprocal of the duration of fluorescence. $\epsilon \equiv c\Delta /2L$, where c is the speed of light, $\Delta$ is the round-trip loss and $L$ is the optical path length of cavity. $\text{Φ}\equiv R\beta /\zeta \epsilon$ which is the ratio of pumping rate to threshold pumping rate and $R$ is the number of atoms pumped up per second multiplied by $E$. $\beta =c\sigma /ALE$, which describes the stimulated emission and $\sigma$ is the laser transition cross section.

_$f$, $n$ and $s$ are variables defined to investigate the cavity dumping cycle and the variable $t$ is the time, given by Eqs. (5)-(7). We set one cavity dumping cycle extends from $s=0$ to $s=\tau$. $\gamma \equiv ({\text{Φ}}^{1/2}-1)\tau$.

The equations above can describe the cavity dumping cycle effectively when the laser repetition rate is much higher than $\zeta$, but tend to be inaccurate or even invalid if the laser repetition rate is approaching or below $\zeta$ [12]. In the case that repetition rate is higher than the spontaneous decay rate $\zeta$, the optical conversion efficiency varies little with repetition rate and the laser works efficiently. However, operating at repetition rate below the spontaneous decay rate $\zeta$ leads to increasingly inefficient as repetition rate decreases. For Nd:YAG laser with a fluorescence lifetime of 230 μs, the spontaneous decay rate is $\zeta \approx 4348\text{Hz}$. And for efficient operation, the minimum repetition rate of the experimental master oscillator would not be set below 4348 Hz. The optical path length $L$ of this laser is 362 mm according to the calculations above. For repetition rate of 100 kHz, the time of one cavity dumping cycle is $\tau /\epsilon =1\times {10}^{-5}\text{s}$. Figure 3 shows the theoretical calculation results of the time evolution of the field energy $F$ and the inversion energy $N$ normalized against their time average values $F_0$ and $N_0$ in four different groups of parameters ($\text{Φ}=2$, $\Delta =0.1$; $\text{Φ}=2$, $\Delta =0.01$; $\text{Φ}=4$, $\Delta =0.1$; $\text{Φ}=4$, $\Delta =0.01$). It illustrates that the increment in pumping rate and round-trip loss results in a more instantaneous process of laser generation and higher normalized field energy.

 

Fig. 3 Theoretical calculation results of normalized field energy $F/F_0$ and normalized inversion energy $N/N_0$ versus time. Black for $\text{Φ}=2$ and $\Delta =0.1$, resulting in $\epsilon \approx 4.14\times {10}^7{\text{s}}^{-1}$, $\gamma \approx 171.5$ and $\tau \approx 414$. Blue for $\text{Φ}=2$ and $\Delta =0.01$, resulting in $\epsilon \approx 4.14\times {10}^6{\text{s}}^{-1}$, $\gamma \approx 17.15$ and $\tau \approx 41.4$. Red for $\text{Φ}=4$ and $\Delta =0.1$, resulting in $\epsilon \approx 4.14\times {10}^7{\text{s}}^{-1}$, $\gamma \approx 414$ and $\tau \approx 414$. Green for $\text{Φ}=4$ and $\Delta =0.01$, resulting in $\epsilon \approx 4.14\times {10}^6{\text{s}}^{-1}$, $\tau \approx 41.4$ and $\tau \approx 41.4$.

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3. Results and discussions

We studied the laser performances of master oscillator at the repetition rate from 5 kHz to 100 kHz when the pump energy was measured to 1.8 J at the pump duration of 2 ms. As shown in Fig. 4, the single pulse energy and peak power reach 22 mJ and 6.1 MW respectively at repetition rate of 5 kHz, 0.84 mJ and 0.26 MW respectively at repetition rate of 100 kHz. The output lasers show pulse widths of 3.5 ± 0.3 ns, average output power of 1.9 ± 0.3 W and burst energy of 0.19 ± 0.03 J at repetition rates ranging from 5 kHz to 100 kHz. The approximate 10 ns of falling time of the Pockels cell driving voltage is the main factor contributing to the switching time, and the measured pulse width is about 1 ns larger than the theoretical minimum value due to the switching time. The average output power, burst energy and pulse width shows no significant variation when repetition rate varies from 5 kHz to 100 kHz, which in agreement with the theoretical prediction in above section. As the optical conversion efficiency varies little with repetition rate in the case that the repetition rate is higher than the spontaneous decay rate $\zeta$ of 4348 Hz, the average output power keeps nearly constant as the pumping power is constant. According to the pumping energy of 1.8 J per burst and the nearly constant intensity of the output burst energy, the optical-optical conversion efficiency of the master oscillator is approximately 11%. The single pulse energy and peak power shows inverse relationship with the increase of repetition rates as shown in Fig. 4.

 

Fig. 4 Master oscillator: average power, burst energy, single pulse energy, peak power and pulse width versus repetition rate.

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The output laser waveform profiles of single pulses and pulse trains of the master oscillator operated at repetition rates of 10 kHz, 50 kHz and 100 kHz are shown in Figs. 5(a)-5(c). It can be seen that the pulse width keeps short stably by using cavity-dumped electro-optic Q-switch technique even if repetition rate increases to 100kHz, and no deterioration of performance (like post sub-pulses) caused by the piezoelectric effect. Therefore, effective amplification can be implemented to achieve both high pulse energy and short pulse width at high repetition rates.

 

Fig. 5 Single pulses and pulse trains waveform profiles of output lasers of the master oscillator and amplifiers.

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The burst energy of 0.16 J obtained from master oscillator at the repetition rate of 100 kHz was injected to the two dual-pass laser amplifiers. Figures 5(d)-5(e) shows waveform profiles of single pulses and pulse trains of the single stage amplification and dual stage amplification. We use the coefficient of variation (CV, the ratio of the standard deviation to the mean) to describe the dispersion of the energy values of single pulses in pulse train. The CV of output pulse intensity decreases as the repetition rate increases. The results can be seen from Figs. 5(a)-5(c) that the intensity of single pulses in pulse train tends to be more consistent as repetition rate increases. Amplification process also has the effect which diminishing the CV, the results shown in Figs. 5(c)-5(e). This is because that single pulses with higher power cause higher degree of gain saturation and as a result the higher power pulses are less amplified than the lower power pulses.

As shown in Fig. 6(b), through the dual-stage dual-pass amplification, the average power, burst energy, peak power and single pulse energy reach 18.9 W, 1.89 J, 2.87 MW and 9.47 mJ, respectively, when the pump energy of each amplifier stage was measured to 4.3 J for pump duration of 2 ms. For single-stage dual-pass amplification, the average power, burst energy, peak power and single pulse energy is 9.1 W, 0.91 J, 1.42 MW and 4.55 mJ when pump energy is 4.3 J per 2 ms duration. Pulse width of the amplified laser is 3.1 ± 0.3 ns. Energy extraction efficiency was measured to 30% for amplifier stage 2 and 20% for amplifier stage 1, as shown in Figs. 6(a) and 6(b). The energy extraction efficiency shows approximately logarithmic relationship with amplifier pump energy.

 

Fig. 6 Average power, burst energy, peak power, single pulse energy, pulse width and energy extraction efficiency versus amplifier pump energy and amplifier pump average power. (a) – results of amplifier stage 1; (b) – results of amplifier stage 2 while pump pulse energy of stage 1 set at 4.3 J.

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The maximum power amplification factor (the ratio of output power to input power) is approximately 5.4 (7.3 dB) for the amplifier stage 1 and approximately 2.1 (3.2 dB) for the amplifier stage 2. For the amplifier stage 2, as the input laser energy is much higher than that of amplifier stage 1, the power amplification factor is reduced due to gain saturation. But also because of gain saturation, the energy extraction efficiency for amplifier stage 2 is higher than that for amplifier stage 1.

As shown in Fig. 7, burst energy keeps approximately linear relationship with pumping duration varying from 500 μs to 2 ms. Besides, pulse width, peak power and energy extraction efficiency show no significant variation with the increase of pump duration from 500 μs to 2 ms.

 

Fig. 7 Burst energy, peak power, pulse width and energy extraction efficiency versus burst duration. (a) – results of single stage amplification; (b) – results of dual stage amplification.

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Figure 8 shows the laser intensity distribution and beam quality factors measured at Q-switch repetition rate of 100 kHz with the burst energy of 1.89 J. The laser intensity shows a Gaussian distribution, as shown in Fig. 8(b). The beam quality factors M² were measured to 5.7 and 4.5 in the two orthogonal directions by a traveling 90/10 knife-edge method, the results are shown in Figs. 8(a) and 8(c).

 

Fig. 8 The output beam profiles and beam quality factors measured at 100 kHz with 1.89 J burst energy.

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4. Conclusion

In this work, a cavity-dumped electro-optic Q-switched burst-mode laser and its dual-stage dual-pass amplification have been investigated. The dynamic process of cavity dumping has been theoretically simulated and the laser performance has been experimentally demonstrated. This scheme of laser has been proven to be efficient, relatively easy and convenient to obtain lasers with high pulse energy and short pulse width at high repetition rates. In amplification operation, the average output power, burst energy, peak power, single pulse energy reach 18.9 W, 1.89 J, 2.87 MW, 9.47 mJ, respectively, at Q-switch repetition rate of 100 kHz and pump duration of 2 ms. The pulse width is almost constant to be 3.1 ± 0.3 ns. The maximum energy extraction efficiency reaches 30% for amplifier stage 2 and 20% for amplifier stage 1. This laser with high pulse energy, short pulse width at high repetition rates has great potential in laser diagnostics for fluid dynamic measurements, high-speed planar imaging and so on.