We investigated design issues for the power scaling of a picosecond Nd:YVO4 master-oscillator power amplifier system with a photorefractive phase-conjugate mirror by using standard beam propagation analysis. We also demonstrated a 25 W diffraction-limited pico-second output. A corresponding extraction efficiency of 31 % was achieved.
©2006 Optical Society of America
A side-pumped bounce amplifier, in which a very high inversion population density is produced in a shallow absorption depth near the pump face, has been successfully demonstrated to generate high power as well as highly efficient outputs in the CW or nanosecond regime [1–4]. The use of a neodymium-doped yittrium vanadate (Nd:YVO4) [5–7], which has a large stimulated emission cross-section as well as a broad emission-band compared with the conventional Nd:YAG, is a promising solution for high average-power pico-second lasers.
Recently, high-quality master-oscillator power amplifiers (MOPA) utilizing a phase-conjugate mirror (PCM) based on a photorefractive rhodium-doped barium titanate (Rh:BaTiO3)  have been reported to generate >10 W diffraction-limited pico-second output by our group . The PCM is capable of producing high power and high beam-quality output from the Nd:YVO4 amplifier, while showing relatively poor thermal properties. The system is promising for applications in nonlinear optics, spectroscopy and industrial applications, such as laser machining and laser display.
In this paper, we analyze the amplified mode of phase-conjugate master oscillator power amplifier systems, using the standard approach based on the complex q beam parameter and ray transfer (ABCD) matrices. We also address the design issues for power scaling of the system to compensate for strong thermal lensing within the Nd:YVO4 amplifier. An output power of up to 25 W in a near-diffraction-limited beam from 81 W was demonstrated. Also, a corresponding extraction efficiency of 31 % was obtained. These are the highest values, to the best of our knowledge, obtained using a pico-second phase conjugate MOPA system.
2. Beam propagation analysis
Note that different propagating characteristics for the horizontal and vertical planes must be considered in the bounce amplifier, whose thermal lens shows a strong astigmatism. Also, the matrix elements must be complex, as in the amplifier when the optical system has an ellipsoidal gain aperture (Gaussian aperture) with a quadratic varying amplitude gain. The Gaussian aperture of 1/e 2 intensity radius αi (i=H,V) is given by 
A schematic diagram for numerical modeling is presented in Fig. 1. In our previous publication, configuration 1 was used. The collimated master laser beam with a diameter of 1 mm was focused by a vertical cylindrical lens VCL (f = 100 mm) onto the amplifier. The amplified master laser was relayed to the amplifier again by 4f imaging optics formed by a prism mirror and a spherical lens L1 (f = 100 mm). After passing through the amplifier twice, the amplified beam was relayed onto a phase conjugate-mirror by a vertical cylindrical lens, VCL, and two spherical lenses L2 (f = 150 mm) and L3 (f = 100 mm). To improve the output power of the system, a 150-mm focal length horizontal cylindrical lens, HCL, was introduced. The purpose of this lens was to correct the horizontal thermal lens at a high pump level. After passing through the HCL, the amplified beam was collimated and relayed to the PCM with imaging optics (magnification factor of ~ 0.67) formed by spherical lenses L2 and L3. And then, the αH and αV were 1mm and 0.2mm, respectively.
The simulated beam size onto the PCM at various thermal lens powers is shown in Fig. 2. Without the HCL (configuration 1), the horizontal spot becomes larger than the PCM aperture (~ϕ 5 mm), around the horizontal thermal lens power of ~8 m-1. And the vertical spot is also diverged as the increase of thermal lens power, because the relay optics including spherical lenses L2 and L3 does not produce an image of the vertically collimated beam onto the PCM. In configuration 2, the horizontal thermal lens is well corrected and the spot is sufficiently smaller than the PCM aperture, even for a horizontal thermal lens power of 20 m-1. Also, the vertical spot size was 1–2 mm in the vertical thermal lens region of 10–100 m-1. We can expect that configuration 2 will improve the output power of the system at a higher pump level.
The numerically simulated horizontal thermal lensing slope to the pump power in the amplifier by using the conventional thermal diffusion equation was estimated to be 0.13 m- 1/W. We then assumed that the quantum defect of the pump-to-lasing photon energy mainly contributed to a fractional heat load in the amplifier and the pump beam size onto the amplifier was 0.2 mm × 18 mm.
From this estimation, we can expect that configuration 2 will allow to produce an efficient output from the system, even for a pump level of ~150 W.
3.1 Phase-conjugate master-oscillator power-amplifier system
Figure 3 shows the experimental setup of the phase-conjugate amplifier system. The amplifier used was a transversely diode-pumped 1 at % a-cut Nd:YVO4 crystal with dimensions of 20 mm × 5 mm × 2 mm. The end surfaces of the crystal were AR-coated for 1 μm and wedged at 5° relative to the normal of the pump face to prevent self-lasing within the crystal. The crystal mount temperature was maintained at ~10 °C by a water re-circulating chiller. The pump diode was a 50 W CW 809 nm single-bar diode array, and its output was focused to be a line with dimensions of 0.2 mm × 18 mm on the crystal. The polarization of the output was parallel to the c-axis of the crystal.
A commercial CW mode-locked Nd:YVO4 laser used for a master laser had a pulse duration of 7 ps and a pulse repetition frequency of 100 MHz. The spatial form of the output showed TEM00 profile, and the corresponding M 2 factor was <1.2. To prevent optical feedback to the master laser, an optical isolator was formed by a polarizing beam splitter (PBS), a Faraday rotator (FR) and a half wave plate (HWP1). The master laser beam was focused by a cylindrical lens (VCL, f = 100 mm) to be a line, thereby yielding a good spatial overlap between the master laser and the ellipsoidal gain volume. The external incident angle of the master laser beam with respect to the pump surface was 12°. The amplified master laser was retro-reflected and relayed to the amplifier by 4f imaging optics formed by a prism mirror and a spherical lens L1 (f = 100 mm). And then, the external incident angle of the amplified master laser beam with respect to the pump surface was 18°. After passing through the amplifier twice, the amplified beam was collimated by two cylindrical lenses VCL (f = 100 mm) and HCL (f = 150 mm), and it was relayed onto a phase-conjugate mirror based on a BaTiO3 crystal by the optical systems mentioned above. The polarization of the amplified beam was rotated using a HWP2 to lie in an extra-ordinary plane of a Rh:BaTiO3 crystal.
The BaTiO3 crystal with 1000 ppm Rh ion doping was 0°-cut to the normal of the c-axis, and its dimensions were 8 mm × 7 mm × 8 mm. The crystal faces were AR coated for 1 μm. The crystal mount temperature was maintained at ~ 20 °C. A self-pumped, phase-conjugate mirror was formed by the BaTiO3 crystal and an external loop cavity with 4f imaging optics. The angle of the external loop cavity was 15°. With this system, the phase conjugation built up within a couple of minutes, and then, its reflectivity was measured typically to be ~50 %. The phase conjugation of the amplified master beam returned automatically to the amplifier again. After passing through the amplifier, the output was ejected off by the PBS.
Because the loop cavity length (~60 cm) was much longer than the coherence length of the master laser (~3 mm), the formation of reflection and 2k gratings was prevented. Thus, frequency-narrowing effects due to the severe Bragg’s selectivity of reflection and 2k gratings were negligible.
3.2 Experimental results
The experimental output power as a function of the input master laser power at a pump power of 45 W is shown in Fig. 4. Configuration 2 was used. Saturation of the output power was seen at an input power of <10 mW, because of the extremely high gain of the amplifier. The solid curve in Fig. 4 shows plots numerically simulated by using the partitioned amplifier and continuous-wave gain saturation formula model mentioned in our previous publication . There is a good agreement between the simulated curve and the experimental data.
The experimental output power as a function of the pump power is shown in Fig. 5. The output power was almost proportional to the pump power, and the maximum output power reached up to 17.6 W at a pump power of 50 W. This value is 1.5-times higher than that mentioned in our previous report. The corresponding extraction efficiency was ~35 %.
When configuration 1 was used, saturation of the output power was observed around a pump power of 45 W. Above a pump power of 50 W, the output power started to decrease. These effects were induced because the strong horizontal thermal lens did not allow recollection of the amplified beam into the PCM.
The spatial form of the output exhibited a near-Gaussian profile [Fig. 6(a)]. Also, its beam-propagation factor, M 2, was <1.5. On the contrary, the beam propagation factor, , of the incident amplified beam onto the phase conjugate mirror was 4.4. These results show that the system allowed us to compensate for thermal distortions inside the amplifier.
Experimental intensity autocorrelation traces are shown in Fig. 6(b). The phase-conjugate MOPA output had a pulse-duration (FWHM) of 8 ps for a Gaussian-shaped pulse, while the signal pulse exhibited a pulse-duration (FWHM) of 7 ps. There was no significant pulse broadening. A beam propagation analysis shows that the present system recollects the amplified beam into the PCM at a pump power region below ~150 W. We replaced the single pump diode by a three-bar diode array stack bar with optics for fast-axis collimation. Then, a maximum output power of 25 W was achieved at a pump power of 81 W, as shown in Fig. 7. The corresponding extraction efficiency was ~31 %. Further power scaling was limited by the performance of the diode power supply as well as the amplifier warming up by increased thermal load due to insufficient energy extraction.
We investigated the design issues for the power scaling of a master oscillator power amplifier system utilizing a photorefractive phase conjugate mirror to compensate for strong thermal lensing within the Nd:YVO4 amplifier by using the standard beam propagation analysis based on the complex q beam parameter and ray transfer (ABCD) matrices. We also demonstrated a 25 W high-quality output from the system. Also, a corresponding extraction efficiency of 31 % was obtained. Power handling of a Rh:BaTiO3 crystal without damage was reported previously to be around 1 kW/cm2 at 1.06 μm . This value is much higher than the incident beam intensity onto the Rh:BaTiO3 crystal (<150 W/cm2) in this system. A further improvement of the output power can be expected without damage of the Rh:BaTiO3 crystal by the refinements of the diode power supply as well as the heat removal of the amplifier.
The authors acknowledge support from a scientific research grant-in-aid (16032202, 18360031) from the Ministry of Education, Science and Culture of Japan and the Japan Society for the Promotion of Science.
References and links
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