Compact 50 W All-Solid-State Picosecond Laser System at 1 kHz

: Compact, stable, high-power and high repetition rate picosecond laser systems are excellent sources for optical parametric chirped pulse ampliﬁcation systems and laser satellite ranging systems. Compared with the traditional complex high-power ampliﬁer, this article reports a compact high-power picosecond laser system at a repetition rate of 1 kHz based on Nd:YAG bulk crystal. The thermal lens e ﬀ ect limits the regenerative ampliﬁer to directly output higher energy. For this reason, multi-stage traveling-wave ampliﬁers are usually used to gradually increase the laser pulse energy. So as to achieve a compact structure, a regenerative ampliﬁer that can output higher power at 1 kHz is designed in the laser system. The regenerative ampliﬁer can output the power of 6.5 W at the pump power of 41.5 W; the beam quality of M 2 factor was about 1.3. A more ﬂexible thermal depolarization compensation structure is applied in the side-pumped ampliﬁer, which can e ﬀ ectively compensate for thermal lens e ﬀ ect and thermal depolarization at di ﬀ erent pump powers. Finally, the laser pulse can achieve an output power higher than 50 W at 1 kHz after passing through an end-pumped traveling-wave ampliﬁer and a side-pumped traveling wave ampliﬁer.


Introduction
The development of short-pulse laser technology in recent years has tremendous impetus in the developing of industrial micro-machining, scientific research and medical equipment [1]. High repetition rate and high-power picosecond laser is an excellent light source for material cold working, pumping high repetition rate optical parametric chirped pulse amplification (OPCPA) system, laser satellite ranging, UV light generation, terahertz generation, and imaging [2][3][4]. Passive Q-switching technology can be used to directly output picosecond pulses, however the pulse duration is usually more than 500 ps. Shorter pulse width can usually be obtained by mode-locking techniques. The oscillator of Nd:YVO 4 usually can get a pulse width of 10~100 ps at the wavelength of 1064 nm. Due to the large gain factor of the regenerative amplifier, it is very suitable for amplifying low-energy seed pulses. The structure of the regenerative amplifier is an optical resonator, so it has good beam directivity and beam quality. Based on the characteristics of the regenerative amplifier, the regenerative amplifier is very suitable as a pre-amplifier. Usually seed pulses can be amplified to several millijoules by regenerative amplifier. The traveling-wave amplifier can be used as a post-amplifier. Traveling-wave amplifiers have two pumping methods: side pumping and end pumping. The beam quality and polarization characteristics of the end-pumped amplifier is better however, and the output power is relatively low due to the limitation of the end-pumped power.

Picosecond Oscillator
The seed pulses were generated by a Nd:YVO4 oscillator pumped with a 2 W, 808 nm continuous wave (CW) laser diode. The laser crystal was an a-cut, 0.5 at. % Nd-doped YVO4 crystal with a size of 3 × 3 × 5 mm 3 . The mirror of M1 was plane-concave mirror with 200 mm radius of curvature. M2 and M3 had 75 mm radius of curvature. The mirror of OC was an output coupler mirror with transmission rate of 10%. Semiconductor saturable absorption mirror (SESAM) can help the oscillator run in a mode-locking state and provided ~300 mW average power at 80 MHz repetition rate. The oscillator used an etalon with the length of 0.5 mm to directly get ~52 ps laser pulses at 1064 nm, as shown in Figure 2.

Regenerative Amplifier
The seed pulses were input to a Nd:YAG regenerative amplifier. The crystal in the cavity was a 0.3 at % Nd-doped YAG crystal with a size of 3 × 3 × 40 mm 3 , which was wrapped with indium foil and mounted tightly on a thermoelectric cooler (TEC) copper heat sink. The crystal surface was

Picosecond Oscillator
The seed pulses were generated by a Nd:YVO 4 oscillator pumped with a 2 W, 808 nm continuous wave (CW) laser diode. The laser crystal was an a-cut, 0.5 at. % Nd-doped YVO 4 crystal with a size of 3 × 3 × 5 mm 3 . The mirror of M1 was plane-concave mirror with 200 mm radius of curvature. M2 and M3 had 75 mm radius of curvature. The mirror of OC was an output coupler mirror with transmission rate of 10%. Semiconductor saturable absorption mirror (SESAM) can help the oscillator run in a mode-locking state and provided~300 mW average power at 80 MHz repetition rate. The oscillator used an etalon with the length of 0.5 mm to directly get~52 ps laser pulses at 1064 nm, as shown in Figure 2.

Picosecond Oscillator
The seed pulses were generated by a Nd:YVO4 oscillator pumped with a 2 W, 808 nm continuous wave (CW) laser diode. The laser crystal was an a-cut, 0.5 at. % Nd-doped YVO4 crystal with a size of 3 × 3 × 5 mm 3 . The mirror of M1 was plane-concave mirror with 200 mm radius of curvature. M2 and M3 had 75 mm radius of curvature. The mirror of OC was an output coupler mirror with transmission rate of 10%. Semiconductor saturable absorption mirror (SESAM) can help the oscillator run in a mode-locking state and provided ~300 mW average power at 80 MHz repetition rate. The oscillator used an etalon with the length of 0.5 mm to directly get ~52 ps laser pulses at 1064 nm, as shown in Figure 2.

Regenerative Amplifier
The seed pulses were input to a Nd:YAG regenerative amplifier. The crystal in the cavity was a 0.3 at % Nd-doped YAG crystal with a size of 3 × 3 × 40 mm 3 , which was wrapped with indium foil and mounted tightly on a thermoelectric cooler (TEC) copper heat sink. The crystal surface was

Regenerative Amplifier
The seed pulses were input to a Nd:YAG regenerative amplifier. The crystal in the cavity was a 0.3 at % Nd-doped YAG crystal with a size of 3 × 3 × 40 mm 3 , which was wrapped with indium foil and mounted tightly on a thermoelectric cooler (TEC) copper heat sink. The crystal surface was coated with 1064 nm and 808 nm antireflection films. The M7 to M12 were high reflectors. M7 curved mirrors had 780 mm radius of curvature, while M8 had −1400 mm radius of curvature, and the other mirrors were plane mirrors. Due to thermal effects, the crystal acted as a thermal lens in the cavity. It was found that as the focal length of the crystal thermal lens becomes shorter, the beam waist radius at the crystal also becomes larger in this cavity. Therefore, under different pump powers, the cooling power of the TEC for the crystal should also change accordingly. The pump laser was a 300 W fiber-coupled quasi-CW (QCW) laser diode with a 600 µm core diameter centered at 808 nm (DILAS, Mainz, Germany), which was controlled by a trigger signal with gate width of 180 µs at 1 kHz. By optimizing the focal length of the thermal lens crystal, the regenerative cavity can achieve maximum output power of 6.5 W at pump power of 41.5 W. Figure 3 shows the beam quality (M 2 factor) of the output pulses measured by a commercial M 2 factor instrument (M2-200S-FW, Ophir-Spiricon Inc., North Logan, UT, USA). The M 2 value in x and y direction were 1.327 and 1.445 respectively with the output power of 6.5 W.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 9 coated with 1064 nm and 808 nm antireflection films. The M7 to M12 were high reflectors. M7 curved mirrors had 780 mm radius of curvature, while M8 had −1400 mm radius of curvature, and the other mirrors were plane mirrors. Due to thermal effects, the crystal acted as a thermal lens in the cavity. It was found that as the focal length of the crystal thermal lens becomes shorter, the beam waist radius at the crystal also becomes larger in this cavity. Therefore, under different pump powers, the cooling power of the TEC for the crystal should also change accordingly. The pump laser was a 300 W fibercoupled quasi-CW (QCW) laser diode with a 600 μm core diameter centered at 808 nm (DILAS, Mainz, Germany), which was controlled by a trigger signal with gate width of 180 μs at 1 kHz. By optimizing the focal length of the thermal lens crystal, the regenerative cavity can achieve maximum output power of 6.5 W at pump power of 41.5 W. Figure 3 shows the beam quality (M 2 factor) of the output pulses measured by a commercial M 2 factor instrument (M2-200S-FW, Ophir-Spiricon Inc., North Logan, UT, USA). The M 2 value in x and y direction were 1.327 and 1.445 respectively with the output power of 6.5 W.

End-Pumped Amplifier
According to the regenerative amplifier presented above, we had obtained high-quality beam quality laser pulses. Higher pulse power required more traveling-wave amplifiers. In comparison with end-pumped traveling-wave amplifier, side-pumped traveling-wave can achieve higher singlepass gain. However, due to that the population inversion is more evenly distributed in end-pumped medium, end-pumped traveling-wave amplifier can obtain higher beam quality. The picosecond laser system used a hybrid power amplifier consisting of an end-pumped single-pass amplifier and a side-pumped double-pass amplifier. A 3 × 3 × 40 mm 3 , 0.3 at % Nd-doped YAG crystal, which was wrapped with indium foil and mounted tightly on a TEC copper heat sink at 20 °C, was used as a gain medium in the end-pumped single-pass amplifier. A 300 W fiber-coupled quasi-CW laser diode with a 600 μm core diameter centered at 808 nm (DILAS, Germany) was used as a pump source for end-pumped amplifier. The QCW laser diode produced 200 μs pulses at the repetition of 1 kHz and focused on the Nd:YAG crystal via a lens system. When the laser pulses output by regenerative amplifier traversed the medium with an inverted population, the pulse power was amplified higher. In order to improve the amplification efficiency, the diameter of seed pulses should match with pump pulses in Nd:YAG crystal. L3 was a plane-convex lens used to adjust the beam size of the laser pulses. The measured power curve and beam image are shown in Figure 4. The picosecond pulses were amplified to 10.8 W after the end-pumped single-pass amplifier, corresponding to an optical efficiency of 17.7%.

End-Pumped Amplifier
According to the regenerative amplifier presented above, we had obtained high-quality beam quality laser pulses. Higher pulse power required more traveling-wave amplifiers. In comparison with end-pumped traveling-wave amplifier, side-pumped traveling-wave can achieve higher single-pass gain. However, due to that the population inversion is more evenly distributed in end-pumped medium, end-pumped traveling-wave amplifier can obtain higher beam quality. The picosecond laser system used a hybrid power amplifier consisting of an end-pumped single-pass amplifier and a side-pumped double-pass amplifier. A 3 × 3 × 40 mm 3 , 0.3 at % Nd-doped YAG crystal, which was wrapped with indium foil and mounted tightly on a TEC copper heat sink at 20 • C, was used as a gain medium in the end-pumped single-pass amplifier. A 300 W fiber-coupled quasi-CW laser diode with a 600 µm core diameter centered at 808 nm (DILAS, Germany) was used as a pump source for end-pumped amplifier. The QCW laser diode produced 200 µs pulses at the repetition of 1 kHz and focused on the Nd:YAG crystal via a lens system. When the laser pulses output by regenerative amplifier traversed the medium with an inverted population, the pulse power was amplified higher.
In order to improve the amplification efficiency, the diameter of seed pulses should match with pump pulses in Nd:YAG crystal. L3 was a plane-convex lens used to adjust the beam size of the laser pulses. The measured power curve and beam image are shown in Figure 4. The picosecond pulses were amplified to 10.8 W after the end-pumped single-pass amplifier, corresponding to an optical efficiency of 17.7%.

Side-Pumped Amplifier
Since the power of the side-pumped module is extremely high, the thermal effect of the gain medium is relatively obvious. The non-uniform temperature distribution could cause thermally induced birefringence inside the crystal. For a Nd:YAG rod in which the z axis is in the [1 1 1] direction, the principle of axes of thermally induced birefringence are radial and tangential within the rod cross-section. Therefore, when the linear polarized beam traverses the gain medium, the tangential and radial components could experience different phase retardation, resulting in significant depolarization [15]. The compensation of birefringence is a significant issue for the Nd:YAG rod side-pumped amplifier [16][17][18][19].
The Nd:YAG crystal is an isotropic medium. The refractive index ellipsoid is a regular sphere without thermally induced birefringence. The refractive index ellipsoid is where the In the Equation ( where the elastomeric coefficient ijkl π is a fourth-order tensor and the kl σ is deformation tensor.
The beam propagates along the z-axis direction, so there is no polarization component in the zdirection. Equation (2) can become

Side-Pumped Amplifier
Since the power of the side-pumped module is extremely high, the thermal effect of the gain medium is relatively obvious. The non-uniform temperature distribution could cause thermally induced birefringence inside the crystal. For a Nd:YAG rod in which the z axis is in the [1 1 1] direction, the principle of axes of thermally induced birefringence are radial and tangential within the rod cross-section. Therefore, when the linear polarized beam traverses the gain medium, the tangential and radial components could experience different phase retardation, resulting in significant depolarization [15]. The compensation of birefringence is a significant issue for the Nd:YAG rod side-pumped amplifier [16][17][18][19].
The Nd:YAG crystal is an isotropic medium. The refractive index ellipsoid is a regular sphere without thermally induced birefringence. The refractive index ellipsoid is where the B i = 1/n 2 i = 1/n 2 o , i = 1, 2, 3 are principal refractive indexes. The refractive index ellipsoid with thermally induced birefringence is In the Equation (3), ∆B ij implies the change of index with thermally induced birefringence, and B 011 = B 022 = B 033 = 1/n 2 o , B 012 = B 013 = B 023 = 0. According to previous studies, where the elastomeric coefficient π ijkl is a fourth-order tensor and the σ kl is deformation tensor. In order to simplify the calculation, the form converted into a matrix is ∆B m = π mn σ n , m, n = 1, 2, 3, 4, 5, 6.
Appl. Sci. 2020, 10, 6891 6 of 9 The beam propagates along the z-axis direction, so there is no polarization component in the z-direction. Equation (2) can become The new principle refractive indexes can be given by the following formula: The angle α between the axis with thermal birefringence and the original axis can be given by the formula: The difference of phase retardation between tangential and radial components is By swapping the phases of the tangential and radial components of polarization and traversing the thermally-induced birefringent crystal again, an equal phase retardation can be achieved at each point within the crystal cross section. When the beam passes through the depolarized crystal for the second time, if the beam distribution at each point in the z direction is the same as the first, the depolarization can be perfectly compensated. Figure 5 shows the simulation patterns of thermal depolarization and perfect compensation for the side-pumped amplifier.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 9 ( ) The new principle refractive indexes can be given by the following formula: The angle α between the axis with thermal birefringence and the original axis can be given by the formula: The difference of phase retardation between tangential and radial components is By swapping the phases of the tangential and radial components of polarization and traversing the thermally-induced birefringent crystal again, an equal phase retardation can be achieved at each point within the crystal cross section. When the beam passes through the depolarized crystal for the second time, if the beam distribution at each point in the z direction is the same as the first, the depolarization can be perfectly compensated. Figure 5 shows the simulation patterns of thermal depolarization and perfect compensation for the side-pumped amplifier. The gain medium is equivalent to a thick lens in the side-pumped amplifier, and the collimated beam will become a convergent beam after passing through the crystal. A convergent beam can usually be collimated by a concave lens, however, the convergence angle is different at different pump powers in the side-pumped amplifier. To solve this problem, the side-pumped amplifier can apply the structure shown in Figure 6. The matrix after the beam passes through the gain crystal can be defined as r θ       , r and θ are the waist radius and divergent angle respectively. The ABCD matrix of the beams passing through the optics in the Figure 6 can be expressed as: The gain medium is equivalent to a thick lens in the side-pumped amplifier, and the collimated beam will become a convergent beam after passing through the crystal. A convergent beam can usually be collimated by a concave lens, however, the convergence angle is different at different pump powers in the side-pumped amplifier. To solve this problem, the side-pumped amplifier can apply the structure shown in Figure 6. The matrix after the beam passes through the gain crystal can be defined as r θ , Appl. Sci. 2020, 10, 6891 7 of 9 r and θ are the waist radius and divergent angle respectively. The ABCD matrix of the beams passing through the optics in the Figure 6 can be expressed as: l r L f θ θ = + − . (11) l is a dependent variable, affected by variables θ and r . Therefore, the l can vary with different pump powers of the side-pumped amplifier. The matrix where the beam returns to the crystal surface again can be expressed as: FR was a 45° Faraday Rotator, and a roundtrip in a 45° FR was equivalent to a single pass in a 90° rotator. With this structure, the tangential and radial components of polarization can exchange phase retardation, and the divergent angle changed from θ to -θ , while the diameter of the beam was invariant. This is an ideal structure for birefringence compensation in a single-rod amplifier. Finally, the 10.8 W picosecond pulses from amplifiers presented above were input to the sidepumped double-pass amplifier. The side-pumped module consisted of a φ6 × 160 mm 3 , 0.5 at % Nddoped YAG crystal side-pumped by QCW laser diode. The maximum output power (at 110 A) of the side-pumped module was 1008 W with the pulse duration of 180 μs at the repetition of 1 kHz. In this experiment, by using the depolarization compensation technique described above, the side-pumped module working at a current of 70 A and output power of 50 W can be obtained. Figure 7 shows the power curve and beam image of the laser system. The length of l can be obtained according to Figure 6: l is a dependent variable, affected by variables θ and r. Therefore, the l can vary with different pump powers of the side-pumped amplifier. The matrix where the beam returns to the crystal surface again can be expressed as: FR was a 45 • Faraday Rotator, and a roundtrip in a 45 • FR was equivalent to a single pass in a 90 • rotator. With this structure, the tangential and radial components of polarization can exchange phase retardation, and the divergent angle changed from θ to −θ, while the diameter of the beam was invariant. This is an ideal structure for birefringence compensation in a single-rod amplifier.
Finally, the 10.8 W picosecond pulses from amplifiers presented above were input to the side-pumped double-pass amplifier. The side-pumped module consisted of a ϕ6 × 160 mm 3 , 0.5 at % Nd-doped YAG crystal side-pumped by QCW laser diode. The maximum output power (at 110 A) of the side-pumped module was 1008 W with the pulse duration of 180 µs at the repetition of 1 kHz. In this experiment, by using the depolarization compensation technique described above, the side-pumped module working at a current of 70 A and output power of 50 W can be obtained. Figure 7 shows the power curve and beam image of the laser system.

Discussion and Conclusions
In summary, this paper proposes a compact, high-power and high repetition picosecond laser system. Seed pulses were obtained via a Nd:YVO 4 oscillator with etalon in cavity. The seed pulses were input into a homemade regenerative amplifier, which can overcome the limitation of the beam waist radius due to the thermal lens effect under high power pumping. Maximum output power of the regenerative amplifier was 6.5 W at 1 kHz, and the beam quality of M 2 factor was about 1.3. The homemade regenerative amplifier worked in the state that output power was 5 W, as a pre-amplifier for a subsequent amplifier. The pulses were amplified to 10.8 W via an end-pumped single-pass amplifier. In order to compensate for the thermal depolarization of the side-pumped amplifier, we made a theoretical analysis of the depolarization compensation and applied a more flexible depolarization compensation structure. After the picosecond laser pulses traversed the side-pumped amplifier, the pulses' power was amplified to more than 50 W at 1 kHz. This is a simple and compact structure in which the output power can achieve more than 50 W at 1 kHz. The compact high-power picosecond laser will be a perfect source for high power OPCPA systems in the future.