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A diode-pumped joule class in a 10 Hz output Nd:YLF ring amplifier has been developed. A phase conjugate plate was developed as a wavefront corrector for the residual wavefront distortion of an Nd:YLF rod. We have demonstrated a 0.46 J output of 10 ns pulse duration at 10 Hz repetition rate with 1.5 nJ of input energy. The effective gain of the ring amplifier system was 84.8 dB. To our knowledge, this is the highest magnification with joule-level output energy in a single-stage amplifier system that has ever been built. As a preamplifier system, this system contributed a demonstration of 21.3 J in a 10 Hz output diode-pumped Nd:glass zigzag slab laser system with a stimulated Brillouin scattering-phase conjugation mirror. We describe a robust and effective method of wavefront correction for high-energy laser systems.
©2010 Optical Society of America
1. Introduction
A high-energy pulse diode-pumped solid-state laser (DPSSL) with high beam quality is required for various applications. Above all, a laser source as a preamplifier for high-energy large laser amplifier systems [1–7] is suitable for such DPSSLs to make a contribution to the stability and reliability of a large system. In some national projects, 1 joule-class 10 Hz DPSSLs have been developed as the front end of a 100 joule-class system [4–7]. The concept of 1 joule-class output energy with higher magnification using a single-stage amplifier system is more attractive than a multistage amplifier chain system [7–10] because of the total system compactness and simplicity.
The output pulse energy from a single longitudinal mode-pulsed fiber oscillator or laser diode and a broad bandwidth mode-locked oscillator are extremely low. A regenerative amplifier is one candidate for a preamplifier for a large DPSSL system. The output pulse energy, however, has been limited to the 100 mJ level, mainly because of optical damage to the components. When the nano-joule-level seed energy from a single-mode fiber laser is amplified to the 1 joule level by one single-stage amplifier, a useful compact laser amplifier is realized as a preamplifier for the 100 J class DPSSL.
We present a diode-pumped 1053 nm Nd:YLF amplifier with high pulse energy and high beam quality. This system is designed in a ring laser scheme, and it has two DPSSL amplifiers, each with a 1-cm-diameter laser crystalline rod. The rod with a 1 cm aperture has residual wavefront distortion resulting from the process of crystal growth.
A wavefront corrector for this application needs to have high spatial resolution of the sub-millimeter order and high damage threshold of 10 J/cm2. A deformable mirror (DM) is ordinarily available for wavefront correction; however, it is relatively expensive.
We propose a phase conjugate plate (PCP) as a useful new wavefront corrector. The wavefront corrector provides higher spatial resolution of three-dimensional surface figures and higher laser damage threshold of solid-state optical transparent materials than the DMs. This optical element provides the same function as a DM, which compensates for the distorted wavefront by transmitting a PCP. The PCP is made of fused silica, and its surface is figured three-dimensionally by the technique of magnetorheological finishing (MRF). The MRF technique utilized a small polishing spot formed on a rotating wheel carrying a ribbon of magnetorheological (MR) fluid that contains a polishing abrasive. As the ribbon of MR fluid passes between the poles of a powerful electromagnet, the MR fluid viscosity increases on the ribbon, where it produces a three-dimensional surface figure [11].
The MRF can figure a PCP surface with the inverse shape of a specific wavefront pattern. The surface of the PCP we used was processed at a nanometer resolution for depth and at the sub-millimeter level for width. This paper reports the evaluation of fidelity between the design and the fabrication of the PCP and the demonstration of a diode-pumped 1053 nm Nd:YLF ring amplifier system with PCPs. The laser system demonstrates 0.46 J at 10 Hz with a magnification of 84.8 dB. To our knowledge, this is the highest magnification with joule-level output energy in a single-stage amplifier system that has ever been built. Actually, this system performed as a preamplifier for the diode-pumped Nd:glass zigzag slab laser “HALNA” that resulted in 21.3 J output energy at 10 Hz [12].
2. Wavefront correction of Nd:YLF rod
Nd:YLF is suitable as the laser material of joule-class energy lasers because of its longer fluorescence lifetime compared with other Nd-doped laser materials, and its aperture can be grown to the centimeter class. A master oscillator power amplifier (MOPA) system of 1.8 J at 5 Hz with single longitudinal-mode output flash lamp pumped Nd:YLF was developed by Zuegel et al. at the Laboratory for Laser Energetics at Rochester University for a prototype of a front-end system for OMEGA-EP [13]. They corrected the transmitted wavefront distortion of Nd:YLF rods (25.4 mm diameter, 110 mm length) from 0.60 to 0.11 lambda (at 1053 nm) by figuring the rod ends using MRF. However, direct processing of the rod end using MRF to increase the spatial resolution has been difficult. Spatial resolution of wavefront correction, in the case of processing on to laser gain material, is limited by the transmitting beam aperture in the laser gain material. A PCP achieves higher spatial resolution to expand the beam aperture and figuring area of the PCP without any changes in the laser amplification parameter. Additionally, a PCP corrects not only the residual wavefront in the optical element but also the high-order thermally induced wavefront aberrations in high-average power lasers [14].
Transmitted wavefront distortion in a Nd:YLF rod with a length of 120 mm and diameter of 10 mm (Northrop Grumman Corp.) measured by a Shack–Hartmann wavefront sensor (Imagin Optics Inc.) is shown in Fig. 1(a) . The wavefront was distorted to 0.43 μm peak-to-valley (PV) and to 0.1 μm root mean square (RMS) in an aperture of 80%. First, we designed a PCP for this Nd:YLF rod and simulated a phase mismatch between the wavefront and the designed PCP. A conjugated phase pattern of a residually distorted wavefront [shown in Fig. 1(a)] was calculated using a Zernike polynomial of degree three for configuring the PCP. The designed PCP surface figure is shown in Fig. 1(b). The corrected wavefront pattern calculated by the summation of the data of Figs. 1(a) and 1(b) is shown in Fig. 1(c). The corrected wavefront was expected to improve to 0.17 μm PV and 0.03 μm RMS in an aperture of 80%. The wavefront distortion decreased by 60% PV and 70% RMS. After these results were obtained, we fabricated a PCP figuring the pattern design by using a Zernike polynomial of degree three.
Fig. 1 Estimation of wavefront correction by PCP. (a) Wavefront of transmitted light from Nd:YLF rod; (b) conjugating phase calculated by Zernike polynomial of degree three; (c) corrected wavefront simulated numerically.
The experimental results of wavefront correction for the Nd:YLF rod with the PCP are shown in Fig. 2 . Figure 2(a) is a transmitted wavefront of the Nd:YLF rod, Fig. 2(b) is a transmitted wavefront of the PCP, and Fig. 2(c) is a transmitted wavefront of both the rod and the PCP. The residual wavefront of the Nd:YLF rod shown in Fig. 1(a) and Fig. 2(a) has been reproducibly measured similar to astigmatism. Figure 2(b) shows a close conjugate wavefront aberration of Fig. 2(a). The machining accuracy of the fabricated PCP using MRF was evaluated to have 0.06 μm of tolerance RMS as the difference from the figure designed by the Zernike polynomial [15]. In these results, the dominant astigmatism–aberration of the Nd:YLF rod decreased in Fig. 2(c). The total aberration in the Nd:YLF rod of 0.365 μm PV and 0.072 μm RMS were improved to 0.212 μm PV and 0.045 μm RMS at an 80% aperture.
Fig. 2 Experimental results of wavefront correction of Nd:YLF rod combined with PCP. (a) Transmitted wavefront distortion of Nd:YLF rod; (b) transmitted wavefront of PCP; (c) corrected wavefront.
The diminution rates for each aberration were evaluated to compare the Zernike coefficients in Fig. 2. The Zernike coefficients up to degree three for the Nd:YLF rod, the PCP, and the corrected wavefront are graphed in Fig. 3 . In the figure the blue bars show the results for the Nd:YLF rod, the green bars show the results for the PCP, and the red bars show the results for the corrected wavefront. The Nd:YLF rod has an aberration of positive astigmatism at 0 deg and 45 deg with Zernike coefficients of 0.162 and 0.158. In contrast, the PCP has a large aberration of negative astigmatism with Zernike coefficients of −0.125 and −0.058. As a result, the Zernike coefficients of the corrected wavefront improved to 0.041 and 0.060. Consequently, the Zernike coefficient of astigmatism and coma decreased from the aberration of a non-corrected Nd:YLF rod to less than half. The remaining focus aberration can be simply adjusted using a lens pair in the laser system.
Fig. 3 Comparison of Zernike coefficients between wavefront aberrations of Nd:YLF rod, PCP, and corrected wavefront.
3. Laser system with phase conjugate plates
We developed a high-amplification, high-energy-output, diode-pumped Nd:YLF ring amplifier with the wavefront correction by use of the PCP technique. A schematic diagram of the system is shown in Fig. 4 . The system consists of a front end, two Nd:YLF rod amplifier heads (HEAD1, 2), two PCPs (PCP1, 2), two vacuum spatial filters with a telescope (VSF1, 2), a Pockels cell (PC2), two polarization beam splitters (PBS1, 2), and a half wave plate (HWP). In this ring system, the direction of propagation is consistently counterclockwise. The laser pulse is amplified during round trips in the system. The diameter of the Nd:YLF rods are 9 mm for the HEAD1 and 10 mm for the HEAD2. Each rod is side-pumped by 15-bar stacked, jet-type water-cooled laser diode (LD) modules from 6 directions with a total peak intensity of 9 kW (Hamamatsu Photonics K. K.) [16,17]. The expected initial small-signal gains of HEAD1 and HEAD2 are 4 and 3.3, respectively. A PCP is placed after each head. The VSFs are used for apodizing, image-relaying, and prevention of parasitic oscillation. The diameter of the pinhole is 20 F/λ in each VSF.
Fig. 4 Schematic diagram of diode-pumped Nd:YLF ring amplifier system layout. SLM-FL, single longitudinal mode fiber laser; FI, Faraday isolator; EP, beam expander; PC, Pockels cell; SA, serrated aperture; PBS, polarization beam splitter; HWP, half wave plate; HEAD, LD pumped laser head; VSF, vacuum spatial filter; PCP, phase conjugate plate.
A front end consists of a single longitudinal-mode cw fiber laser (SLM-FL), a Faraday isolator (FI), a beam expander (EP), and a Pockels cell (PC1). SLM-FL output power is 1 W with a line width of 10 kHz at 1053 nm wavelength. The cw laser beam is shaped into a pulse with 10 ns pulse duration at 10 Hz repetition rate by PC1. The seed pulse is apodized by a serrated aperture (SA) and injected into the ring system at PBS1, which has a high optical damage threshold of 15 J/cm2 and the typical extinction ratio of 1:1000. The injected seed pulses around the ring optical loop in the system, while the PC2 acts as a half wave plate. The optical gain including losses for a round trip is typical 10. In this architecture, in which the laser beam propagates in one direction in the system, a laser gain in system can be optimized by controlling the number of round trips in one round. Finally, the amplified laser pulse is ejected from the PBS2.
Temporal overlapping of the high-energy laser pulses causes not only optical damage but also reduction of output energy. A temporal increase of photon fluence by overlapping in active laser media induces a reduction of effective gain. In our ring system, the optical path length is designed to 6.5 m in order to prevent overlapping in 10 ns pulse duration at any optical component. In the case of a layout designed to arrange a component inline, the optical path length for a round trip would be more than 13 m. The system footprint including the front-end system is put at 1.2 m x 2.4 m.
4. Results and discussions
First, in order to make a comparison with and without PCP, the output beam quality of the near-field pattern (NFP) and the far-field pattern (FFP) is evaluated. The NFP and FFP at the PCPs not installed in the setup are shown in Figs. 5(a) and 5(b). In this experiment, a multi-longitudinal-mode (MLM) pulse oscillator is used as a front end. The input pulse is TEM00 mode, 10 ns pulse duration, and flat-top pattern. The laser pulse makes a round trip five times in the system. The NFP has a near flat-top pattern with a filling factor 0.5, defined as the ratio of the average intensity in the beam area to the peak intensity. On the other hand, the FFP consists of multi-spots with Mx2 3.8 and MY2 3.6. The FFP cannot focus into the pinhole at a circulation number of more than 5. In the case of the system without the PCPs, laser amplification is limited to approximately 105 (50 dB) times.
Fig. 5 Output pattern characteristic. (a),(b) NFP and FFP without PCP. (c),(d) NFP and FFP with PCP.
The NFP and FFP with the PCP installed in the setup are shown in Figs. 5(c) and 5(d), respectively. The SLM-FL described in Section 3 is used as the input pulse. The round-trip number is nine. The NFP is nearly a flat top without a hotspot with a filling factor of 0.4. The FFP is focused in a single spot with side lobes. M2 is evaluated at Mx2 2.6 and MY2 2.7. The M2 is improved from 3.8 to 2.7 by the PCP. The FFP still maintains focus ability in spite of 9 round trips. Therefore a practical effect of the wavefront compensation technique using a PCP has been demonstrated. Figure 6 shows encircled energy ratios in various areas of the FFPs with and without the PCP system. The horizontal axis is a times-of-diffraction limit (TDL) and the vertical axis is the ratio of energy encircled in the area. Then the encircled energy ratio at the diffraction limit increases from 13.5% to 35.3% [14].
Characteristics of output energy are shown in Fig. 7 . The horizontal axis is the pump energy of the LD and the vertical axis is the output energy of the ring system. The line and plots show the computational and experimental results. The experimental results are in good agreement with the calculation based on the rate equation. The 0.46 J of output energy at 10 Hz repetition rate is achieved with the round-trip number of 9 by compensation of the wavefront using the PCP. The conversion efficiency from LD output energy to the amplified laser output energy is 6.2%. When the laser is amplified in the round trip over the 9th circulation, parasitic oscillation is observed. In our calculation, the laser gain at the 9th circulation is estimated to reduce the initial gain from 10 to 4.6. This result indicates that the energy extraction from the Nd:YLF rods is saturated. The input energy is estimated to be 1.5 nJ by the PIN photodiode. As a result, a 3.1 x 108 (84.8 dB) magnification is obtained. To our knowledge, this is the highest gain achieved in a single amplifier system. As a front end and a preamplifier system, this system contributes a demonstration of 21.3 J, 10 Hz output by a Nd:glass zigzag slab DPSSL system with SBS-PCM.
Fig. 7 Characteristics of output energy. The circles show the experimental results, and the lines show the calculation results.
In addition, we have experimented with an increased seed pulse in order to confirm further power scaling in the performance of energy extraction. To reduce the system losses, the circulation number is decreased to 5 and the PCPs are removed from the system. An MLM front end is used with an input energy of 0.14 mJ. Output energy of 0.96 J is obtained with an optical-to-optical conversion efficiency of 12.9%. This result indicates the potential for joule-class output energy. For 1 J output with higher magnification, the prevention of parasitic oscillation is required. Reducing the transverse mode of the ring system with a pinhole is an effective method to suppress amplified spontaneous emission (ASE). In this laser system, the laser beam quality requires a diffraction limit to propagate in a low transverse mode system. A PCP is realized to correct a wavefront with over a third-order Zernike polynomial by increasing the resolution of three-dimensional polishing on the PCP to expand a figuring area.
5. Conclusion
We have developed high-energy output with a high-gain LD-pumped Nd:YLF rod ring amplifier as a preamplifier of a 20 J x 10 Hz output LD-pumped Nd:glass laser with an SBS-PCM. A PCP was developed as a wavefront corrector for residual wavefront distortion of the Nd:YLF rod. A wavefront distortion of 0.365 μm P-V and 0.072 μm RMS was improved to 0.212 μm and 0.045 μm at an 80% aperture by the PCP. We have achieved 0.46 J output energy at 10 Hz repetition rate with an amplification of 3.1 x 108 (84.8dB) by compensation of the wavefront using the PCP. The beam quality is estimated at M2 = 2.7. As a front end and a preamplifier system, this system contributes a demonstration of 21.3 J at 10 Hz output in the laser system.
In the case of a laser amplifier that operates in a steady-state in the same condition, a wavefront correction by a PCP is useful as a method because it is low cost and robust. A PCP is suitable for the presented ring laser system because this system is designed on the assumption that the laser amplifier operates in a steady-state in one pumping condition.
Acknowledgments
The authors thank Dr. Y. Sasama and Dr. T. Takahashi (Okamoto Optics Works, Inc., Japan) for their technical support with the fabrication of the PCP.
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