A Solid-State Three-Stage Nd:YVO₄ Laser Amplifier System Based on AOM Pulse Picker-Integrated Modulator

Abstract

In recent years, ultrafast bursts with high power have been applied in many significant fields. However, the peak power of the pulse train generated by fiber lasers is limited by fiber characteristics from nonlinear effects, which can only be at the level of milliwatt. In this research, the pulse frequency is reduced by an AOM pulse picker-integrated modulator. With M2 and pulse width guaranteed, the frequency of the reduced pulse train is amplified by a solid-state three-stage Nd:YVO₄ amplifier system. Finally, the peak power of the pulse train is increased. The final output pulse repetition rate of the experiment is 1 MHz with a pulse width of 8.09 picoseconds and a peak power of up to 3.7 MW.

1. Introduction

Picosecond green lasers with high pulse energy and high average power have important applications in many fields [1,2,3,4]. Compared with picosecond lasers with only one pulse (single pulse) per cycle at a certain repetition frequency, pulse train lasers composed of multiple picosecond pulses spaced in the nanosecond order have great application advantages. For short pulses with low pulse energies, multi-pass high gain amplification is often required first. Due to the obvious advantages in research and industry in recent years [5,6,7,8], a large number of picosecond lasers with high power and high repetition rate have been studied [9,10,11], especially lasers with good beam quality and narrow pulse width.

A master oscillator power amplifier (MOPA) is a common method for achieving high-power lasers with good beam quality. The low-power seed laser is amplified by cascaded amplifiers to increase the output power [12,13,14]. Fiber seed lasers and amplifiers have inherent advantages in MOPA systems [15,16]. Simplicity, reliability, low cooling requirements, and near-diffraction limited beam quality make it widely used. Fiber seeders have limited pulse peak power due to the characteristics of optical fibers. Nonlinear effects in the fiber (such as self-phase modulation and stimulated Raman scattering) and the low optical damage threshold caused by the small core diameter of the fiber contribute to most of the limitations.

Additionally, the limited pulse peak power of fiber seeders in MOPA systems necessitates the use of multiple stages of amplification to achieve the desired high-power output. Each amplifier stage further boosts the signal while maintaining the beam quality inherited from the initial fiber seed laser. Recent advances in thermal aberration compensation, such as the integration of a 4f system with a 0° reflector in Nd:YAG amplifiers, have demonstrated 73.7 mJ pulse energy with near-Gaussian beam quality (M² < 1.37) under 60.7 W pumping, effectively mitigating spherical aberration-induced beam degradation [17]. This cascading approach allows for the construction of laser systems capable of delivering kilowatt-level average powers with excellent beam characteristics.

To address the limitation of pulse peak power in fiber seeders, advanced techniques such as chirped pulse amplification (CPA) [18] are often incorporated into MOPA designs. This method effectively distributes the energy over a longer time frame, thereby reducing the peak power requirements of each amplifier stage and mitigating potential damage to the optical fibers [19,20]. Furthermore, dual-frequency MOPA architectures leveraging nonplanar ring oscillator (NPRO) seeds and ytterbium-doped fiber amplifiers (YDFAs) have achieved 5 W output at 1064 nm with ultra-low phase noise (−116.6 dBc/Hz at 10 kHz), enabling high-precision applications in photonic microwave generation and optical carrier light detection and ranging (LiDAR) [21].

While the limited pulse peak power of fiber seeders presents a constraint in MOPA systems, the inherent advantages of fiber-based technology, combined with innovative amplification techniques and advancements in fiber design, have made it possible to overcome this limitation. These developments have paved the way for the creation of high-power lasers with excellent beam quality, making MOPA systems an indispensable tool in various fields such as materials processing, medical applications, and scientific research. In view of the performance advantages and potential application values, in this research, we use a fiber solid system composed of an optical fiber seeder, pulse selector, and solid-state amplifier to achieve high peak power output of the pulse train. This solid-state system overcomes nonlinear effects such as stimulated Raman scattering and self-phase modulation inside the fiber [22,23], making it very favorable for use in practice.

2. Basic Theory of the Nd:YVO₄ Laser Amplifier System

The basic theory of the Nd:YVO₄ laser amplifier system involves ultrashort pulse propagation in fiber seed lasers, pulse picking using an acousto-optic modulator (AOM) and gain dynamics in Nd:YVO₄ amplifiers to achieve high peak powers.

2.1. Pulse Propagation and Nonlinear Effects in the Fiber Seed Laser

Ultrashort pulses generated in a mode-locked fiber laser propagate under the combined influence of dispersion and nonlinearity. Their evolution can be described by the nonlinear Schrödinger equation (NLSE)

$$\begin{array}{c}\mathrm{i}{\displaystyle \frac{\partial \mathrm{A}\left(\mathrm{z},\mathrm{t}\right)}{\partial \mathrm{z}}}-{\displaystyle \frac{{\mathsf{\beta }}_2}{2}}{\displaystyle \frac{{\partial }^2\mathrm{A}\left(\mathrm{z},\mathrm{t}\right)}{\partial {\mathrm{t}}^2}}+\mathsf{\gamma }{\left|\mathrm{A}\left(\mathrm{z},\mathrm{t}\right)\right|}^2\mathrm{A}\left(\mathrm{z},\mathrm{t}\right)=0\end{array}$$

(1)

where $\mathrm{A}\left(\mathrm{z},\mathrm{t}\right)$ is the slowly varying pulse envelope, and ${\mathsf{\beta }}_2$ is the group velocity dispersion (GVD) parameter given by

$${\mathsf{\beta }}_2={\displaystyle \frac{{\partial }^{2}k}{\partial {\omega }^2}}$$

(2)

where $\omega$ is the angular frequency and $k$ is the wave number.

$\mathsf{\gamma }$ is the nonlinear coefficient given by

$$\begin{array}{c}\mathsf{\gamma }={\displaystyle \frac{2\mathsf{\pi }{n}_2}{\mathsf{\lambda }{A}_{\mathrm{eff}}}}\end{array}$$

(3)

where $n_2$ is the nonlinear refractive index, $\mathsf{\lambda }$ is the operating wavelength, and $A_{\mathrm{eff}}$ is the fiber’s effective mode area.

A key nonlinear effect influencing pulse evolution is self-phase modulation (SPM), which introduces an intensity-dependent phase shift

$$\begin{array}{c}{\mathsf{\varphi }}_{\mathrm{NL}}\left(t\right)=\gamma L_{\mathrm{eff}}I\left(t\right)\end{array}$$

(4)

where $L_{\mathrm{eff}}$ is the effective fiber length and $I\left(t\right)$ is the instantaneous intensity. This results in spectral broadening, which is crucial for pulse shaping and compression.

2.2. Pulse Picking Using an Acousto-Optic Modulator

To reduce the seed laser’s repetition rate, an AOM is used as a pulse picker. The AOM operates based on Bragg diffraction, governed by the Bragg condition

$$\begin{array}{c}\mathsf{\lambda }={\displaystyle \frac{2n\mathsf{\Lambda }}{\sin \mathsf{\theta }}}\end{array}$$

(5)

where $n$ is the refractive index of the AOM medium, $\mathsf{\Lambda }$ is the acoustic wavelength, and $\theta$ is the Bragg angle. The diffraction efficiency $\eta$, which determines how much light is deflected into the desired diffraction order, is given by

$$\begin{array}{c}\eta ={\sin }^2\left({\displaystyle \frac{\mathsf{\pi }\mathsf{\Delta }nL}{\mathsf{\lambda }}}\right)\end{array}$$

(6)

where $\mathsf{\Delta }n$ is the refractive index modulation induced by the acoustic wave and $L$ is the interaction length. By adjusting the acoustic drive parameters, the AOM effectively selects pulses to achieve a lower repetition rate.

2.3. Gain Dynamics in Nd:YVO₄ Amplifiers

After pulse picking, the lower-repetition-rate pulse train is amplified using a solid-state three-stage Nd:YVO₄ amplifier system. The gain mechanism in Nd:YVO₄ amplifiers follows the population inversion model, where the small-signal gain coefficient $g_0$ is

$$\begin{array}{c}{g}_0={\mathsf{\sigma }}_e{N}_2-{\mathsf{\sigma }}_a{N}_1\end{array}$$

(7)

where $N_2$ and $N_1$ are the populations of the excited and ground states, and ${\mathsf{\sigma }}_e$ and ${\mathsf{\sigma }}_a$ are the emission and absorption cross sections, respectively.

The amplified signal power follows the exponential gain equation

$$\begin{array}{c}{P}_{\mathrm{out}}=P_{\mathrm{in}}\exp \left(g_{0}L\right)\end{array}$$

(8)

where $P_{\mathrm{in}}$ and $P_{\mathrm{out}}$ are the input and output power, and $L$ is the amplifier length.

At high input power, gain saturation occurs due to the depletion of excited-state ions, limiting further amplification. A multi-stage design is thus necessary to achieve high peak powers while maintaining beam quality.

3. Experimental Setup

The experimental setup of the MOPA laser system with a pulse picker and solid-state three-stage Nd:YVO₄ amplifiers is shown in Figure 1. A mode-locked fiber laser is used as the seed source. The average power of the seed laser is 80 mW with a frequency of 40 MHz. The pulse duration was independent of the repetition rate and was measured with an autocorrelator to be 8.09 picoseconds (ps), assuming a sech2 pulse shape (Figure 2). An AOM, as a pulse picker, is used to select the number of pulses varying from 1 to 10. The central wavelength of the seed laser is 1064.44 nm.

The picosecond seed laser passes through an acousto-optic modulator with the pulse picker driver. The computer uplink controls the driver to select output pulses in the frequency region of 100 kHz to 20 MHz. The output laser is reflected by the flat mirror M1 and M2 (HR 1064 nm), and then goes through an integrated isolator (ISO), which prevents the unwanted feedback to the seed laser. The laser transmits through the half-wave plates used to adjust its polarization angle. M3 reflects the laser into an optical isolator consisting of a polarization beam splitter (PBS), a Faraday rotator (FR), and a half-wave plate (λ/2), which serves to protect the optical components from being damaged by the amplifier laser pulse. The beam is then focused using a convex lens L1 with a focal length of 50 mm.

The first-stage amplifier used with 0.3 at. % doped Nd:YVO₄ as the gain media with the dimension of 3 × 3 × 16 mm³. To handle the generated heat load, the composite Nd:YVO₄ crystal is wrapped by 0.1 mm indium foil and is mounted in a water-cooled copper heat sink with a cooling water temperature of 25 °C. The laser diode (LD) pump source provides light with a central wavelength of 808 nm. The pump laser is collimated and focused by passing through two planoconvex lenses (L2 and L3, with focal lengths of 50 mm and 80 mm) set to achieve mode matching of the pump laser to that of the laser beam under amplification, thus maximizing the amplification efficiency. The dichroic mirror (DM1) shows high reflectivity (HR) at 1064 nm and high transmittance (HT) at 808 nm.

After passing through the dichroic mirror, the laser goes through the Nd:YVO₄ crystal and is reflected twice by the RSAM (Resonant SAM, which uses a semiconductor saturable absorber mirror structure with a GaAs substrate and an InGaAs quantum well absorption layer). RSAM filters out the optical noise immediately after the reflected pulse and allows the nonlinear optical behavior through the optical pulse to remain unaffected. The reflected laser beam then goes through Nd:YVO₄ crystal a second time. The laser is reflected by M4 and then returns to L1, λ/2, FR, and PBS. After being reflected by the mirror M5, the laser goes through the optical isolator (ISO2) of the second-stage amplifier and then enters the second double-pass amplification stage after being reflected by convex lens M6. The structure and pumping parameters of the second Nd:YVO₄ amplifier are the same as that of the first stage. The pre-amplified laser passes through the Nd:YVO₄ crystal twice to maximize the amplification efficiency before reflecting by convex lens M7 to the optical isolator of the third amplifier stage. Then, the laser enters the third stage double-pass Nd:YVO₄ amplifier. The structure of the third stage Nd:YVO₄ amplifier is the same as that of the second stage. Similarly, the laser goes through the Nd:YVO₄ crystal twice. Then, the amplified laser is reflected by convex lens M10 and M11 and finally output.

4. Validation Result and Discussion

The purpose of this experiment is to minimize the amplified spontaneous emission (ASE) of the output optical signal after passing through the three-stage amplifier to be as small as possible, the output power as large as possible, the spot as round as possible, and the M² as close to 1 as possible. The ASE will have a negative impact on the whole laser system, including affecting the stability of the amplification power and affecting the amplification effect of the light source.

The AOM, serving as a pulse picker, is used to reduce the frequency of the seed laser and select the number of output pulses. Setting the crossover factor to 40 results in the pulse frequency becoming 1 MHz. The pulse waveform is shown in Figure 3 when the number of pulses varies from 1 to 10. The time and intensity axis are in relative scale.

In three-stage amplifiers, output power increases with the number of pulses increasing, which is shown in Figure 4. The power of signal light increases with the number of pulses increasing, leading to the output power raising in the case of the same pumping gain. It can be observed that the output power decreases unexpectedly when the number of pulses is 10 in the third-stage amplifier. This is caused by gain saturation. In the third-stage amplifier, the gain medium experiences energy injection exceeding the gain recovery time at high pulse numbers (e.g., 10 pulses), leading to the depletion of the inverted population. The first two stages show less saturation due to lower pump powers.

The pump laser diodes generate the pump light. As is shown in Figure 5, pump power rises with the pump current increasing in three-stage amplifiers.

In the first-stage amplifier, the variation curve of output power and ASE with pump power is shown in Figure 6. When pump power increases, the pump beam will be reduced, which becomes a better match to the unchanged signal beam. When the pump power increases, the pump light facula will be reduced, while the signal one remains unchanged, resulting in a better match between the pump light and the signal light facula, where the amplified signal facula is better. As for ASE, the larger the number of pulses, the smaller the critical value of pump power where ASE occurs. Because of the negative effects on lasers from ASE, we usually control the value of pump power to prevent ASE from appearing.

In the second-stage amplifier, when the second-stage pump power is set to 71.4 W and the first-stage pump power is changed, the variation curve of output power and ASE are shown in Figure 7. The output power increases with increasing pump power. The trend is similar for different numbers of pulses. The overall output power increases at a slower rate. This is because the gain and loss of Nd:YVO₄ crystal reach dynamic equilibrium, resulting in amplification efficiency saturation. If the output power is increased through increasing the pump power of the first-stage amplifier, the efficiency will be poor. The critical pump power value of ASE is 13.4 W when the number of pulses is 1, 2, 4, and 13.05 W when the number of pulses is 8, 10. To avoid the negative effects of ASE surge, the first-stage pump power is set to a fixed value not exceeding the critical value in the post-stage amplifier.

Figure 8 shows the variation curves of ASE in the second- and third-stage amplifiers. In the third-stage amplifier, the pump power is changed while the first two-stage pump power is unchanged. The resulting ASE is always 0. In summary, ASE is mainly affected by the pump power of the first stage. Therefore, the ASE effect can be effectively avoided only by controlling the first-stage pump power.

In the second and third-stage amplifiers, the variation curves of output power are shown in Figure 9. Unlike the change pattern in the first stage, the growth rate of the output power does not decrease and the gain does not reach saturation. Therefore, in the amplifier, the amplification effect is achieved mainly by the pump power provided by the second- and third-stage pump driver, not the first stage.

As is shown in Figure 10, in the third-stage amplifier, the output power increases consistently without saturation. This indicates that the setting of the first stage pump current value controls the ASE at this time, leaving a lot of room for amplification gain.

5. Conclusions

In this research, a fiber solid laser amplified system with the pulse picker is presented. Using the solid-state amplifier configuration, the average output power achieved 30 mW in 8.09 ps pulse duration at a frequency of 1 MHz and a peak power of the single pulse attached to 3.7 MW approximately. The beam quality is well preserved with an M2 factor of 1.3. This shows that this solid-state MOPA system can generate beams with low frequency, high peak power, and great beam quality, which has great potential for industrial applications such as laser ablation.