Abstract

The self-phase locking of a stimulated Brillouin scattering-phase conjugate mirror (SBS-PCM) allows a simple and scalable coherent beam combination of existing lasers. We propose a simple optical system composed of a rotating wedge and a concave mirror to overcome the power limit of the SBS-PCM. Its phase locking ability and the usefulness on the beam-combination laser are demonstrated experimentally. A four-beam combination is demonstrated using this SBS-PCM scheme. The relative phases between the beams were measured to be less than λ/24.7.

© 2016 Optical Society of America

1. Introduction

A high-power laser with a pulse width of several ns, a repetition rate exceeding 10 Hz, and a power level of more than 1 kW has many applications in both scientific and industrial fields [1]. Laser peening, holographic machining, neutron/proton generation, inertial nuclear fusion, and high-power laser weapons require this type of high-power laser. When the size of the active medium is increased for the operation of a high-power laser, the thermal gradient in the medium induces severe problems such as wavefront distortion, thermally induced birefringence, and other nonlinear effects. To overcome these problems, many research groups are concentrating on multi-slab lasers [2], thin disk lasers [3], and the use of cryogenic laser materials [2,4]. Nevertheless, amplified spontaneous emission (ASE) fundamentally limits the size of the laser medium [5,6]. As a result, it is very difficult to build such a powerful laser using only one laser beam.

In order to overcome these limitations and achieve ultra-high-power lasers, a coherent beam combination technique is one of the most promising options. The coherent beam combination requires the sub-beams to have the same wavefront, with their relative phases locked to the same value [7]. A multi-pass amplifier employing a phase-conjugate mirror as an end mirror can compensate for amplifier-induced wavefront distortion, making it one of the simplest passive solutions to meet the wavefront requirements of the coherent beam combination.

The stimulated Brillouin scattering-phase conjugate mirror (SBS-PCM) is a typical phase-conjugate mirror for high-power lasers [8,9]. However, because the SBS process is instigated by thermal noise [10], the phase of the SBS conjugate beam is inherently random. As a result, beam-combination lasers using a SBS-PCM tend to have complicated optical layouts and tend to be very difficult to scale up [11]. In 2005, Kong et al. proposed a very simple self-phase-locked SBS-PCM (SPL-SBS-PCM) that locks the phase of the SBS beam using its own feedback beam [12–14]. This SPL-SBS-PCM has no optical overlapping between beams, and the number of combined beams can be easily increased.

The typical SBS medium of a high-power beam-combination laser is a fluorocarbon liquid, which has good optical properties and a high damage threshold [15]. Even though its absorption coefficient is small compared to other SBS materials, the reflectivity and fidelity of the SBS-PCM begin to degrade when the input laser power exceeds several hundred watts due to localized heating along the beam path. In 2001, Yoshida et al. showed that the input power limit of the SBS-PCM can be increased by continuously moving a focal spot inside the medium using a rotating wedge [16]. In this way, the heat load is distributed to a large volume and the reflectivity and fidelity can be improved significantly. Meanwhile, the SBS-PCM with the rotating wedge in Yoshida’s scheme is not self-phase-locking and cannot be utilized in a coherent beam-combination laser. Over the past decade, we have attempted to discover a means of employing both self-phase locking and a rotating wedge in the SBS-PCM system. Recently, we found a special but simple optical configuration which enables a coherent beam combination of kW-level high-power lasers.

In this paper, we propose a new simple optical system composed of a rotating wedge and a concave mirror in a SPL-SBS-PCM (RW-SSP) and demonstrate successfully a four-beam-combination laser using it. Due to its simple setup and straightforward scalability, an ultra-high-power laser, i.e., a dream laser, can be realized.

2. Rotating wedge self-phase locked SBS-PCM (RW-SSP)

The design principles are as follows: (1) The focal point should be moving and the path lengths to these focal points should be identical. (2) There should be a feedback beam, and the path lengths from the feedback mirror to the focal points should be constant. (3) The incident angle at the feedback mirror should be 0 degrees to maintain maximum phase locking ability.

Figure 1(a) shows the optical paths inside the RW-SSP which satisfy all three of the aforementioned conditions. In front of the SBS cell, the wedge rotates about the optical axis, and the rear window of the cell is a HR coated concave mirror. All the optics except the wedge are rotationally symmetric about the optical axis. Therefore, for any refracted angle, the optical path is rotationally symmetric around the optic axis. Figure 1(b) shows a photograph of the experimental apparatus of the RW-SSP. A servo motor (Panasonic MDME152G1G) is employed to rotate the wedge.

 

Fig. 1 Rotating wedge SPL-SBS-PCM; (a) a schematic diagram of the optical design principle, (b) a picture of the rotating wedge SPL-SBS-PCM. A wedge is driven by a servo motor.

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In reality, the optics cannot be aligned perfectly. And any slight deformation or misalignment induces a large path length fluctuation when the wedge is rotating. Considering the repetition rate of the laser (10 Hz, which is also the path length measurement rate) and the rotational speed of the wedge, we must limit the path length fluctuation less than several λ. However, the typical path length fluctuation after an initial alignment process was about 50-100 λ. To compensate this fluctuation, we displaced the SBS cell transversely to find a proper position having minimum fluctuation.

There can be many types of misalignment, and one can expect a large residual path length fluctuation after a displacement along the x and y axes. Fortunately, in the simulation, the residual error was less than 0.1 λ for all sources of misalignment with reasonable values. Figure 2 shows a typical simulation result of the path length fluctuation. The x and y axes are the position of the SBS cell, and the color indicates the peak to peak value of the path length when the wedge is rotating. Simulation conditions are as follows: the wedge is translated by 0.3 mm and 0.5 mm in the x and y directions, respectively; the rotation axis of the wedge is tilted by 0.015 deg. in the y direction; and the front glass of the cell is tilted by −0.03 deg. and 0.02 deg. in the x and y directions, respectively.

 

Fig. 2 Simulation result for the path length fluctuation (peak to peak); the wedge is translated by 0.3 mm and 0.5 mm in the x and y directions, respectively, when z-axis is the optic axis; the rotation axis of the wedge is tilted by 0.015 deg. in the y direction; and the front glass of the cell is tilted by −0.03 deg. and 0.02 deg. in the x and y directions, respectively.

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In our experiment, there was remaining path length fluctuation of 1 to 3 λ after the alignment depending on the rotating-wedge/SBS-cell combination. We surmised that this was due to the surface irregularity of the optics and the gap in the ball bearing of the rotating wedge mount.

3. Experimental setup and results

Figure 3 shows the experimental setup. The input beam is a single mode, Q-switched laser beam with a pulse width of 7.5 ns. The input beam passes through an isolator, and a half wave plate 1 (HWP1) and a polarizing beam splitter 1 (PBS1) reduce the energy of the beam. After passing through a periscope, HWP2 and PBS2 divide the beam into two sub-beams with the same energy. Each beam passes through a wedge and another pair of HWP and PBS to be divided further. Four sub-beams with an equal energy of 45 mJ are the beams that will be combined. We will call them beam 1 through beam 4. Except for beam 1, the three beams are reflected by 45 degree mirrors attached by piezoelectric transducers (PZTs). At the end of each beam line, SPL-SBS-PCM with a rotating wedge, explained in section 2, reflects the beam back to their incoming direction.

 

Fig. 3 Experimental setup of the four-beam combination experiment using the RW-SSP; ISO, optical isolator; HWP, half wave plate; PBS, polarizing beam splitter; W, wedge; PZT, 45 degree mirror attached piezoelectric transducer; RW, rotating wedge device; Cell, SBS cell; QWP, quarter wave plate; and EM, energymeter.

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Beam 1 and beam 2 are combined at PBS3 (beam 12). Wedge 1 reflects a part of the combined beam. This reflected beam enters the Hadamard-type phase detector. Using energy measurements, the relative phase between beam 1 and beam 2 can be calculated. The details of the detector were explained in a previous paper [13]. The measurements are done in real time and the applied voltage at PZT1 changes according to

ΔV1[V]=C[V/rad]*ΔΦ12[rad],
where ΔV1 is the differential change of the PZT1’s voltage, ΔΦ12 is the relative phase between beam 1 and beam 2, and C is the control constant. The length of the PZT1 varies with the applied voltage on it, and the path length of beam 2 also changes with the voltage. Since the typical movement range is in the order of several micrometers, the displacement of the beam perpendicular to the beam direction does not significantly alter the alignment of the SBS-PCM. Note that the movement of the PZT is done between the pulses, and not an intra-pulse process.

Figure 4(a) shows the rms values of ΔΦ12 with different Cs. Each measurement was done for 120 s (1200 shots). Due to inherent π ambiguity of the measurement process and the lower measurement limit of the energymeters, the range of the calculated relative phase is restricted to about −0.15 λ to 0.15 λ. Nevertheless, when the relative phase is controlled at near 0, the phase lies well within the measurement range and the rms phase error is stable across repeated measurements. When the wedge is not rotating (stationary cell, black line), the main reasons for the phase fluctuation are stochastic phase noise from the SBS process and path length fluctuation due to air turbulence. Both effects are small and the rms values of the relative phases are near λ/40 with an appropriate choice of C. However, when C is large, the rms phase error increases due to overcompensation. When the wedge is rotating at 0.5 rpm (rotating cell, red line), the relative phase swings with a peak to peak value of about 3 λ due to rotation. Figure 4(b) shows the phase measurement signal when C is 0.05. The phase is undercompensated and drifts well above and below 0. In Fig. 4(c), C is 0.2. The relative phase is stabilized to λ/27. In Fig. 4(d), C is 0.5. Although the signal is stabilized near 0, the phase is overcompensated and the fluctuation is larger than (b). We chose the value of C to be 0.2 for the remaining experiments.

 

Fig. 4 Experimental results of two beam combination; (a) the rms values of relative phase with different values of C; (b), (c), and (d), typical phase measurement signals during 120 s when C is 0.05, 0.2, and 0.5, respectively.

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We also did a phase measurement for the combination of beam 3 and beam 4 (beam 34). In this case, the applied voltage at PZT2 was varied. We adjusted the polarizations of the combined beams for two combined beams to proceed toward the output at PBS2. The relative phase between beam 12 and beam 34 was measured at the output. The voltages of PZT2 and PZT3 were adjusted according to that measurement to compensate for the phase difference.

Figure 5 shows the experimental results of the four-beam combination using the RW-SSP. The relative phases between the beams are presented during 10 minutes (6000 shots). The rms values of the relative phases are λ/26.7 (between beam 1 & 2), λ/28.8 (between beam 3 & 4), and λ/24.7 (between beam 12 & 34).

 

Fig. 5 Experimental results of a four-beam combination; (a) the relative phases between combining beams during 10 min shows an rms fluctuation of λ/26.7 (beam 1 & 2), λ/28.8 (beam 3 & 4), and λ/24.7 (beam 12 & 34), and (b) detailed results during the first minute.

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Figure 6 shows the PZT voltages during the experiment. A deformed sinusoidal pattern clearly shows the path length change due to the rotation of the wedges. In addition, air turbulence made the path length drift in the long term. Lack of a steep change indicated that the relative phase was well compensated for and no 2π phase jump occurred during the experiment.

 

Fig. 6 Applied voltages of 3 PZTs during the four-beam combination experiment.

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4. Conclusion

We developed a self-phase locked SBS-PCM system that can handle high average power laser over kW level. Using the RW-SSP, we demonstrated successfully its feasibility by coherently combining four beams at a low power level (10 Hz, 45 mJ). The relative phases between the beams were able to be controlled accurately for less than λ/24.7 during 10 minutes. When the average power of the laser increases, the rotating speed of the wedge should be optimized to relax the thermal load of the SBS-PCM. The RW-SSP has a simple setup and number of combining beams can be easily scaled. Note that the RW-SSP can be employed in the coherent beam combination laser system having MOPA scheme. Therefore, ultra-high-power lasers, so called a dream laser, can be realized.

We are currently developing a four-beam-combining high-power laser called the “Kumgang laser.” The repetition rate of the Kumgang is 10 kHz and the pulse energy incident on the SBS-PCM will be several tens of mJ. The RW-SSP will be applied to the Kumgang laser for high-power coherent beam combination.

Acknowledgments

This work was supported by the ‘Dual Use Technology Program’ at the Agency for Defense Development (ADD) of the Republic of Korea (UM12012RD1).

References and links

1. J. Hecht, Understanding Lasers: An Entry-Level Guide, 3rd Edition (John Wiley & Sons, Inc., 2008), Chap. 12.

2. M. Divoky, P. Sikocinski, J. Pilar, A. Lucianetti, M. Sawicka, O. Slezak, and T. Mocek, “Design of high-energy-class cryogenically cooled Yb3+:YAG multislab laser system with low wavefront distortion,” Opt. Eng. 52(6), 064201 (2013). [CrossRef]  

3. J.-P. Negel, A. Loescher, A. Voss, D. Bauer, D. Sutter, A. Killi, M. A. Ahmed, and T. Graf, “Ultrafast thin-disk multipass laser amplifier delivering 1.4 kW (4.7 mJ, 1030 nm) average power converted to 820 W at 515 nm and 234 W at 343 nm,” Opt. Express 23(16), 21064–21077 (2015). [CrossRef]   [PubMed]  

4. S. Banerjee, K. Ertel, P. D. Mason, P. J. Phillips, M. Siebold, M. Loeser, C. Hernandez-Gomez, and J. L. Collier, “High-efficiency 10 J diode pumped cryogenic gas cooled Yb:YAG multislab amplifier,” Opt. Lett. 37(12), 2175–2177 (2012). [CrossRef]   [PubMed]  

5. D. Lowenthal and J. M. Eggleston, “ASE effects in small aspect ratio laser oscillators and amplifiers with nonsaturable absorption,” IEEE J. Quantum Electron. 22(8), 1165–1173 (1986). [CrossRef]  

6. V. Chvykov, J. Nees, and K. Krushelnick, “Transverse amplified spontaneous emission: The limiting factor for output energy of ultra-high power lasers,” Opt. Commun. 312, 216–221 (2014). [CrossRef]  

7. T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11(3), 567–577 (2005). [CrossRef]  

8. H. Yoshida, M. Nakatsuka, T. Hatae, S. Kitamura, T. Sakuma, and T. Hamano, “Two-beam-combined 7.4 J, 50 Hz Q-switch pulsed YAG laser system based on SBS phase conjugation mirror for plasma diagnostics,” Jpn. J. Appl. Phys. 43(No. 8A), L1038–L1040 (2004). [CrossRef]  

9. L. Tong, Z. Zhao, L. Cui, C. Liu, J. Chen, Q. Gao, and C. Tang, “400-Hz pulsed single-longitudinal-mode Nd:YAG laser with more than 100-mJ pulse energy and good beam quality,” Laser Phys. 21(1), 52–56 (2011). [CrossRef]  

10. R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42(9), 5514–5521 (1990). [CrossRef]   [PubMed]  

11. R. H. Moyer, M. Valley, and M. C. Cimolino, “Beam combination through stimulated Brillouin scattering,” J. Opt. Soc. Am. B 5(12), 2473–2489 (1988). [CrossRef]  

12. H. J. Kong, S. K. Lee, D. W. Lee, and H. Guo, “Phase control of a stimulated Brillouin scattering phase conjugate mirror,” Appl. Phys. Lett. 86(5), 051111 (2005). [CrossRef]  

13. H. J. Kong, J. S. Shin, J. W. Yoon, and D. H. Beak, “Phase stabilization of the amplitude dividing four-beam combined laser system using stimulated Brillouin scattering phase conjugate mirrors,” Laser Part. Beams 27(01), 179–184 (2009). [CrossRef]  

14. J. S. Shin, S. Park, H. J. Kong, and J. W. Yoon, “Phase stabilization of a wave-front dividing four-beam combined amplifier with stimulated Brillouin scattering phase conjugate mirrors,” Appl. Phys. Lett. 96(13), 131116 (2010). [CrossRef]  

15. H. Park, C. Lim, H. Yoshida, and M. Nakatsuka, “Measurement of stimulated brillouin scattering characteristics in heavy fluorocarbon liquids and perfluoropolyether liquids,” Jpn. J. Appl. Phys. 45(6A), 5073–5075 (2006). [CrossRef]  

16. H. Yoshida, A. Ohkubo, H. Fujita, and M. Nakatsuka, “Thermally induced effects of stimulated Brillouin scattering via phase-conjugation mirror for repetitive laser pulse,” Rev. Laser Eng. 29(2), 109–114 (2001). [CrossRef]  

References

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  1. J. Hecht, Understanding Lasers: An Entry-Level Guide, 3rd Edition (John Wiley & Sons, Inc., 2008), Chap. 12.
  2. M. Divoky, P. Sikocinski, J. Pilar, A. Lucianetti, M. Sawicka, O. Slezak, and T. Mocek, “Design of high-energy-class cryogenically cooled Yb3+:YAG multislab laser system with low wavefront distortion,” Opt. Eng. 52(6), 064201 (2013).
    [Crossref]
  3. J.-P. Negel, A. Loescher, A. Voss, D. Bauer, D. Sutter, A. Killi, M. A. Ahmed, and T. Graf, “Ultrafast thin-disk multipass laser amplifier delivering 1.4 kW (4.7 mJ, 1030 nm) average power converted to 820 W at 515 nm and 234 W at 343 nm,” Opt. Express 23(16), 21064–21077 (2015).
    [Crossref] [PubMed]
  4. S. Banerjee, K. Ertel, P. D. Mason, P. J. Phillips, M. Siebold, M. Loeser, C. Hernandez-Gomez, and J. L. Collier, “High-efficiency 10 J diode pumped cryogenic gas cooled Yb:YAG multislab amplifier,” Opt. Lett. 37(12), 2175–2177 (2012).
    [Crossref] [PubMed]
  5. D. Lowenthal and J. M. Eggleston, “ASE effects in small aspect ratio laser oscillators and amplifiers with nonsaturable absorption,” IEEE J. Quantum Electron. 22(8), 1165–1173 (1986).
    [Crossref]
  6. V. Chvykov, J. Nees, and K. Krushelnick, “Transverse amplified spontaneous emission: The limiting factor for output energy of ultra-high power lasers,” Opt. Commun. 312, 216–221 (2014).
    [Crossref]
  7. T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11(3), 567–577 (2005).
    [Crossref]
  8. H. Yoshida, M. Nakatsuka, T. Hatae, S. Kitamura, T. Sakuma, and T. Hamano, “Two-beam-combined 7.4 J, 50 Hz Q-switch pulsed YAG laser system based on SBS phase conjugation mirror for plasma diagnostics,” Jpn. J. Appl. Phys. 43(No. 8A), L1038–L1040 (2004).
    [Crossref]
  9. L. Tong, Z. Zhao, L. Cui, C. Liu, J. Chen, Q. Gao, and C. Tang, “400-Hz pulsed single-longitudinal-mode Nd:YAG laser with more than 100-mJ pulse energy and good beam quality,” Laser Phys. 21(1), 52–56 (2011).
    [Crossref]
  10. R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42(9), 5514–5521 (1990).
    [Crossref] [PubMed]
  11. R. H. Moyer, M. Valley, and M. C. Cimolino, “Beam combination through stimulated Brillouin scattering,” J. Opt. Soc. Am. B 5(12), 2473–2489 (1988).
    [Crossref]
  12. H. J. Kong, S. K. Lee, D. W. Lee, and H. Guo, “Phase control of a stimulated Brillouin scattering phase conjugate mirror,” Appl. Phys. Lett. 86(5), 051111 (2005).
    [Crossref]
  13. H. J. Kong, J. S. Shin, J. W. Yoon, and D. H. Beak, “Phase stabilization of the amplitude dividing four-beam combined laser system using stimulated Brillouin scattering phase conjugate mirrors,” Laser Part. Beams 27(01), 179–184 (2009).
    [Crossref]
  14. J. S. Shin, S. Park, H. J. Kong, and J. W. Yoon, “Phase stabilization of a wave-front dividing four-beam combined amplifier with stimulated Brillouin scattering phase conjugate mirrors,” Appl. Phys. Lett. 96(13), 131116 (2010).
    [Crossref]
  15. H. Park, C. Lim, H. Yoshida, and M. Nakatsuka, “Measurement of stimulated brillouin scattering characteristics in heavy fluorocarbon liquids and perfluoropolyether liquids,” Jpn. J. Appl. Phys. 45(6A), 5073–5075 (2006).
    [Crossref]
  16. H. Yoshida, A. Ohkubo, H. Fujita, and M. Nakatsuka, “Thermally induced effects of stimulated Brillouin scattering via phase-conjugation mirror for repetitive laser pulse,” Rev. Laser Eng. 29(2), 109–114 (2001).
    [Crossref]

2015 (1)

2014 (1)

V. Chvykov, J. Nees, and K. Krushelnick, “Transverse amplified spontaneous emission: The limiting factor for output energy of ultra-high power lasers,” Opt. Commun. 312, 216–221 (2014).
[Crossref]

2013 (1)

M. Divoky, P. Sikocinski, J. Pilar, A. Lucianetti, M. Sawicka, O. Slezak, and T. Mocek, “Design of high-energy-class cryogenically cooled Yb3+:YAG multislab laser system with low wavefront distortion,” Opt. Eng. 52(6), 064201 (2013).
[Crossref]

2012 (1)

2011 (1)

L. Tong, Z. Zhao, L. Cui, C. Liu, J. Chen, Q. Gao, and C. Tang, “400-Hz pulsed single-longitudinal-mode Nd:YAG laser with more than 100-mJ pulse energy and good beam quality,” Laser Phys. 21(1), 52–56 (2011).
[Crossref]

2010 (1)

J. S. Shin, S. Park, H. J. Kong, and J. W. Yoon, “Phase stabilization of a wave-front dividing four-beam combined amplifier with stimulated Brillouin scattering phase conjugate mirrors,” Appl. Phys. Lett. 96(13), 131116 (2010).
[Crossref]

2009 (1)

H. J. Kong, J. S. Shin, J. W. Yoon, and D. H. Beak, “Phase stabilization of the amplitude dividing four-beam combined laser system using stimulated Brillouin scattering phase conjugate mirrors,” Laser Part. Beams 27(01), 179–184 (2009).
[Crossref]

2006 (1)

H. Park, C. Lim, H. Yoshida, and M. Nakatsuka, “Measurement of stimulated brillouin scattering characteristics in heavy fluorocarbon liquids and perfluoropolyether liquids,” Jpn. J. Appl. Phys. 45(6A), 5073–5075 (2006).
[Crossref]

2005 (2)

H. J. Kong, S. K. Lee, D. W. Lee, and H. Guo, “Phase control of a stimulated Brillouin scattering phase conjugate mirror,” Appl. Phys. Lett. 86(5), 051111 (2005).
[Crossref]

T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11(3), 567–577 (2005).
[Crossref]

2004 (1)

H. Yoshida, M. Nakatsuka, T. Hatae, S. Kitamura, T. Sakuma, and T. Hamano, “Two-beam-combined 7.4 J, 50 Hz Q-switch pulsed YAG laser system based on SBS phase conjugation mirror for plasma diagnostics,” Jpn. J. Appl. Phys. 43(No. 8A), L1038–L1040 (2004).
[Crossref]

2001 (1)

H. Yoshida, A. Ohkubo, H. Fujita, and M. Nakatsuka, “Thermally induced effects of stimulated Brillouin scattering via phase-conjugation mirror for repetitive laser pulse,” Rev. Laser Eng. 29(2), 109–114 (2001).
[Crossref]

1990 (1)

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42(9), 5514–5521 (1990).
[Crossref] [PubMed]

1988 (1)

1986 (1)

D. Lowenthal and J. M. Eggleston, “ASE effects in small aspect ratio laser oscillators and amplifiers with nonsaturable absorption,” IEEE J. Quantum Electron. 22(8), 1165–1173 (1986).
[Crossref]

Ahmed, M. A.

Banerjee, S.

Bauer, D.

Beak, D. H.

H. J. Kong, J. S. Shin, J. W. Yoon, and D. H. Beak, “Phase stabilization of the amplitude dividing four-beam combined laser system using stimulated Brillouin scattering phase conjugate mirrors,” Laser Part. Beams 27(01), 179–184 (2009).
[Crossref]

Boyd, R. W.

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42(9), 5514–5521 (1990).
[Crossref] [PubMed]

Chen, J.

L. Tong, Z. Zhao, L. Cui, C. Liu, J. Chen, Q. Gao, and C. Tang, “400-Hz pulsed single-longitudinal-mode Nd:YAG laser with more than 100-mJ pulse energy and good beam quality,” Laser Phys. 21(1), 52–56 (2011).
[Crossref]

Chvykov, V.

V. Chvykov, J. Nees, and K. Krushelnick, “Transverse amplified spontaneous emission: The limiting factor for output energy of ultra-high power lasers,” Opt. Commun. 312, 216–221 (2014).
[Crossref]

Cimolino, M. C.

Collier, J. L.

Cui, L.

L. Tong, Z. Zhao, L. Cui, C. Liu, J. Chen, Q. Gao, and C. Tang, “400-Hz pulsed single-longitudinal-mode Nd:YAG laser with more than 100-mJ pulse energy and good beam quality,” Laser Phys. 21(1), 52–56 (2011).
[Crossref]

Divoky, M.

M. Divoky, P. Sikocinski, J. Pilar, A. Lucianetti, M. Sawicka, O. Slezak, and T. Mocek, “Design of high-energy-class cryogenically cooled Yb3+:YAG multislab laser system with low wavefront distortion,” Opt. Eng. 52(6), 064201 (2013).
[Crossref]

Eggleston, J. M.

D. Lowenthal and J. M. Eggleston, “ASE effects in small aspect ratio laser oscillators and amplifiers with nonsaturable absorption,” IEEE J. Quantum Electron. 22(8), 1165–1173 (1986).
[Crossref]

Ertel, K.

Fan, T. Y.

T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11(3), 567–577 (2005).
[Crossref]

Fujita, H.

H. Yoshida, A. Ohkubo, H. Fujita, and M. Nakatsuka, “Thermally induced effects of stimulated Brillouin scattering via phase-conjugation mirror for repetitive laser pulse,” Rev. Laser Eng. 29(2), 109–114 (2001).
[Crossref]

Gao, Q.

L. Tong, Z. Zhao, L. Cui, C. Liu, J. Chen, Q. Gao, and C. Tang, “400-Hz pulsed single-longitudinal-mode Nd:YAG laser with more than 100-mJ pulse energy and good beam quality,” Laser Phys. 21(1), 52–56 (2011).
[Crossref]

Graf, T.

Guo, H.

H. J. Kong, S. K. Lee, D. W. Lee, and H. Guo, “Phase control of a stimulated Brillouin scattering phase conjugate mirror,” Appl. Phys. Lett. 86(5), 051111 (2005).
[Crossref]

Hamano, T.

H. Yoshida, M. Nakatsuka, T. Hatae, S. Kitamura, T. Sakuma, and T. Hamano, “Two-beam-combined 7.4 J, 50 Hz Q-switch pulsed YAG laser system based on SBS phase conjugation mirror for plasma diagnostics,” Jpn. J. Appl. Phys. 43(No. 8A), L1038–L1040 (2004).
[Crossref]

Hatae, T.

H. Yoshida, M. Nakatsuka, T. Hatae, S. Kitamura, T. Sakuma, and T. Hamano, “Two-beam-combined 7.4 J, 50 Hz Q-switch pulsed YAG laser system based on SBS phase conjugation mirror for plasma diagnostics,” Jpn. J. Appl. Phys. 43(No. 8A), L1038–L1040 (2004).
[Crossref]

Hernandez-Gomez, C.

Killi, A.

Kitamura, S.

H. Yoshida, M. Nakatsuka, T. Hatae, S. Kitamura, T. Sakuma, and T. Hamano, “Two-beam-combined 7.4 J, 50 Hz Q-switch pulsed YAG laser system based on SBS phase conjugation mirror for plasma diagnostics,” Jpn. J. Appl. Phys. 43(No. 8A), L1038–L1040 (2004).
[Crossref]

Kong, H. J.

J. S. Shin, S. Park, H. J. Kong, and J. W. Yoon, “Phase stabilization of a wave-front dividing four-beam combined amplifier with stimulated Brillouin scattering phase conjugate mirrors,” Appl. Phys. Lett. 96(13), 131116 (2010).
[Crossref]

H. J. Kong, J. S. Shin, J. W. Yoon, and D. H. Beak, “Phase stabilization of the amplitude dividing four-beam combined laser system using stimulated Brillouin scattering phase conjugate mirrors,” Laser Part. Beams 27(01), 179–184 (2009).
[Crossref]

H. J. Kong, S. K. Lee, D. W. Lee, and H. Guo, “Phase control of a stimulated Brillouin scattering phase conjugate mirror,” Appl. Phys. Lett. 86(5), 051111 (2005).
[Crossref]

Krushelnick, K.

V. Chvykov, J. Nees, and K. Krushelnick, “Transverse amplified spontaneous emission: The limiting factor for output energy of ultra-high power lasers,” Opt. Commun. 312, 216–221 (2014).
[Crossref]

Lee, D. W.

H. J. Kong, S. K. Lee, D. W. Lee, and H. Guo, “Phase control of a stimulated Brillouin scattering phase conjugate mirror,” Appl. Phys. Lett. 86(5), 051111 (2005).
[Crossref]

Lee, S. K.

H. J. Kong, S. K. Lee, D. W. Lee, and H. Guo, “Phase control of a stimulated Brillouin scattering phase conjugate mirror,” Appl. Phys. Lett. 86(5), 051111 (2005).
[Crossref]

Lim, C.

H. Park, C. Lim, H. Yoshida, and M. Nakatsuka, “Measurement of stimulated brillouin scattering characteristics in heavy fluorocarbon liquids and perfluoropolyether liquids,” Jpn. J. Appl. Phys. 45(6A), 5073–5075 (2006).
[Crossref]

Liu, C.

L. Tong, Z. Zhao, L. Cui, C. Liu, J. Chen, Q. Gao, and C. Tang, “400-Hz pulsed single-longitudinal-mode Nd:YAG laser with more than 100-mJ pulse energy and good beam quality,” Laser Phys. 21(1), 52–56 (2011).
[Crossref]

Loescher, A.

Loeser, M.

Lowenthal, D.

D. Lowenthal and J. M. Eggleston, “ASE effects in small aspect ratio laser oscillators and amplifiers with nonsaturable absorption,” IEEE J. Quantum Electron. 22(8), 1165–1173 (1986).
[Crossref]

Lucianetti, A.

M. Divoky, P. Sikocinski, J. Pilar, A. Lucianetti, M. Sawicka, O. Slezak, and T. Mocek, “Design of high-energy-class cryogenically cooled Yb3+:YAG multislab laser system with low wavefront distortion,” Opt. Eng. 52(6), 064201 (2013).
[Crossref]

Mason, P. D.

Mocek, T.

M. Divoky, P. Sikocinski, J. Pilar, A. Lucianetti, M. Sawicka, O. Slezak, and T. Mocek, “Design of high-energy-class cryogenically cooled Yb3+:YAG multislab laser system with low wavefront distortion,” Opt. Eng. 52(6), 064201 (2013).
[Crossref]

Moyer, R. H.

Nakatsuka, M.

H. Park, C. Lim, H. Yoshida, and M. Nakatsuka, “Measurement of stimulated brillouin scattering characteristics in heavy fluorocarbon liquids and perfluoropolyether liquids,” Jpn. J. Appl. Phys. 45(6A), 5073–5075 (2006).
[Crossref]

H. Yoshida, M. Nakatsuka, T. Hatae, S. Kitamura, T. Sakuma, and T. Hamano, “Two-beam-combined 7.4 J, 50 Hz Q-switch pulsed YAG laser system based on SBS phase conjugation mirror for plasma diagnostics,” Jpn. J. Appl. Phys. 43(No. 8A), L1038–L1040 (2004).
[Crossref]

H. Yoshida, A. Ohkubo, H. Fujita, and M. Nakatsuka, “Thermally induced effects of stimulated Brillouin scattering via phase-conjugation mirror for repetitive laser pulse,” Rev. Laser Eng. 29(2), 109–114 (2001).
[Crossref]

Narum, P.

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42(9), 5514–5521 (1990).
[Crossref] [PubMed]

Nees, J.

V. Chvykov, J. Nees, and K. Krushelnick, “Transverse amplified spontaneous emission: The limiting factor for output energy of ultra-high power lasers,” Opt. Commun. 312, 216–221 (2014).
[Crossref]

Negel, J.-P.

Ohkubo, A.

H. Yoshida, A. Ohkubo, H. Fujita, and M. Nakatsuka, “Thermally induced effects of stimulated Brillouin scattering via phase-conjugation mirror for repetitive laser pulse,” Rev. Laser Eng. 29(2), 109–114 (2001).
[Crossref]

Park, H.

H. Park, C. Lim, H. Yoshida, and M. Nakatsuka, “Measurement of stimulated brillouin scattering characteristics in heavy fluorocarbon liquids and perfluoropolyether liquids,” Jpn. J. Appl. Phys. 45(6A), 5073–5075 (2006).
[Crossref]

Park, S.

J. S. Shin, S. Park, H. J. Kong, and J. W. Yoon, “Phase stabilization of a wave-front dividing four-beam combined amplifier with stimulated Brillouin scattering phase conjugate mirrors,” Appl. Phys. Lett. 96(13), 131116 (2010).
[Crossref]

Phillips, P. J.

Pilar, J.

M. Divoky, P. Sikocinski, J. Pilar, A. Lucianetti, M. Sawicka, O. Slezak, and T. Mocek, “Design of high-energy-class cryogenically cooled Yb3+:YAG multislab laser system with low wavefront distortion,” Opt. Eng. 52(6), 064201 (2013).
[Crossref]

Rzaewski, K.

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42(9), 5514–5521 (1990).
[Crossref] [PubMed]

Sakuma, T.

H. Yoshida, M. Nakatsuka, T. Hatae, S. Kitamura, T. Sakuma, and T. Hamano, “Two-beam-combined 7.4 J, 50 Hz Q-switch pulsed YAG laser system based on SBS phase conjugation mirror for plasma diagnostics,” Jpn. J. Appl. Phys. 43(No. 8A), L1038–L1040 (2004).
[Crossref]

Sawicka, M.

M. Divoky, P. Sikocinski, J. Pilar, A. Lucianetti, M. Sawicka, O. Slezak, and T. Mocek, “Design of high-energy-class cryogenically cooled Yb3+:YAG multislab laser system with low wavefront distortion,” Opt. Eng. 52(6), 064201 (2013).
[Crossref]

Shin, J. S.

J. S. Shin, S. Park, H. J. Kong, and J. W. Yoon, “Phase stabilization of a wave-front dividing four-beam combined amplifier with stimulated Brillouin scattering phase conjugate mirrors,” Appl. Phys. Lett. 96(13), 131116 (2010).
[Crossref]

H. J. Kong, J. S. Shin, J. W. Yoon, and D. H. Beak, “Phase stabilization of the amplitude dividing four-beam combined laser system using stimulated Brillouin scattering phase conjugate mirrors,” Laser Part. Beams 27(01), 179–184 (2009).
[Crossref]

Siebold, M.

Sikocinski, P.

M. Divoky, P. Sikocinski, J. Pilar, A. Lucianetti, M. Sawicka, O. Slezak, and T. Mocek, “Design of high-energy-class cryogenically cooled Yb3+:YAG multislab laser system with low wavefront distortion,” Opt. Eng. 52(6), 064201 (2013).
[Crossref]

Slezak, O.

M. Divoky, P. Sikocinski, J. Pilar, A. Lucianetti, M. Sawicka, O. Slezak, and T. Mocek, “Design of high-energy-class cryogenically cooled Yb3+:YAG multislab laser system with low wavefront distortion,” Opt. Eng. 52(6), 064201 (2013).
[Crossref]

Sutter, D.

Tang, C.

L. Tong, Z. Zhao, L. Cui, C. Liu, J. Chen, Q. Gao, and C. Tang, “400-Hz pulsed single-longitudinal-mode Nd:YAG laser with more than 100-mJ pulse energy and good beam quality,” Laser Phys. 21(1), 52–56 (2011).
[Crossref]

Tong, L.

L. Tong, Z. Zhao, L. Cui, C. Liu, J. Chen, Q. Gao, and C. Tang, “400-Hz pulsed single-longitudinal-mode Nd:YAG laser with more than 100-mJ pulse energy and good beam quality,” Laser Phys. 21(1), 52–56 (2011).
[Crossref]

Valley, M.

Voss, A.

Yoon, J. W.

J. S. Shin, S. Park, H. J. Kong, and J. W. Yoon, “Phase stabilization of a wave-front dividing four-beam combined amplifier with stimulated Brillouin scattering phase conjugate mirrors,” Appl. Phys. Lett. 96(13), 131116 (2010).
[Crossref]

H. J. Kong, J. S. Shin, J. W. Yoon, and D. H. Beak, “Phase stabilization of the amplitude dividing four-beam combined laser system using stimulated Brillouin scattering phase conjugate mirrors,” Laser Part. Beams 27(01), 179–184 (2009).
[Crossref]

Yoshida, H.

H. Park, C. Lim, H. Yoshida, and M. Nakatsuka, “Measurement of stimulated brillouin scattering characteristics in heavy fluorocarbon liquids and perfluoropolyether liquids,” Jpn. J. Appl. Phys. 45(6A), 5073–5075 (2006).
[Crossref]

H. Yoshida, M. Nakatsuka, T. Hatae, S. Kitamura, T. Sakuma, and T. Hamano, “Two-beam-combined 7.4 J, 50 Hz Q-switch pulsed YAG laser system based on SBS phase conjugation mirror for plasma diagnostics,” Jpn. J. Appl. Phys. 43(No. 8A), L1038–L1040 (2004).
[Crossref]

H. Yoshida, A. Ohkubo, H. Fujita, and M. Nakatsuka, “Thermally induced effects of stimulated Brillouin scattering via phase-conjugation mirror for repetitive laser pulse,” Rev. Laser Eng. 29(2), 109–114 (2001).
[Crossref]

Zhao, Z.

L. Tong, Z. Zhao, L. Cui, C. Liu, J. Chen, Q. Gao, and C. Tang, “400-Hz pulsed single-longitudinal-mode Nd:YAG laser with more than 100-mJ pulse energy and good beam quality,” Laser Phys. 21(1), 52–56 (2011).
[Crossref]

Appl. Phys. Lett. (2)

H. J. Kong, S. K. Lee, D. W. Lee, and H. Guo, “Phase control of a stimulated Brillouin scattering phase conjugate mirror,” Appl. Phys. Lett. 86(5), 051111 (2005).
[Crossref]

J. S. Shin, S. Park, H. J. Kong, and J. W. Yoon, “Phase stabilization of a wave-front dividing four-beam combined amplifier with stimulated Brillouin scattering phase conjugate mirrors,” Appl. Phys. Lett. 96(13), 131116 (2010).
[Crossref]

IEEE J. Quantum Electron. (1)

D. Lowenthal and J. M. Eggleston, “ASE effects in small aspect ratio laser oscillators and amplifiers with nonsaturable absorption,” IEEE J. Quantum Electron. 22(8), 1165–1173 (1986).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11(3), 567–577 (2005).
[Crossref]

J. Opt. Soc. Am. B (1)

Jpn. J. Appl. Phys. (2)

H. Park, C. Lim, H. Yoshida, and M. Nakatsuka, “Measurement of stimulated brillouin scattering characteristics in heavy fluorocarbon liquids and perfluoropolyether liquids,” Jpn. J. Appl. Phys. 45(6A), 5073–5075 (2006).
[Crossref]

H. Yoshida, M. Nakatsuka, T. Hatae, S. Kitamura, T. Sakuma, and T. Hamano, “Two-beam-combined 7.4 J, 50 Hz Q-switch pulsed YAG laser system based on SBS phase conjugation mirror for plasma diagnostics,” Jpn. J. Appl. Phys. 43(No. 8A), L1038–L1040 (2004).
[Crossref]

Laser Part. Beams (1)

H. J. Kong, J. S. Shin, J. W. Yoon, and D. H. Beak, “Phase stabilization of the amplitude dividing four-beam combined laser system using stimulated Brillouin scattering phase conjugate mirrors,” Laser Part. Beams 27(01), 179–184 (2009).
[Crossref]

Laser Phys. (1)

L. Tong, Z. Zhao, L. Cui, C. Liu, J. Chen, Q. Gao, and C. Tang, “400-Hz pulsed single-longitudinal-mode Nd:YAG laser with more than 100-mJ pulse energy and good beam quality,” Laser Phys. 21(1), 52–56 (2011).
[Crossref]

Opt. Commun. (1)

V. Chvykov, J. Nees, and K. Krushelnick, “Transverse amplified spontaneous emission: The limiting factor for output energy of ultra-high power lasers,” Opt. Commun. 312, 216–221 (2014).
[Crossref]

Opt. Eng. (1)

M. Divoky, P. Sikocinski, J. Pilar, A. Lucianetti, M. Sawicka, O. Slezak, and T. Mocek, “Design of high-energy-class cryogenically cooled Yb3+:YAG multislab laser system with low wavefront distortion,” Opt. Eng. 52(6), 064201 (2013).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (1)

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42(9), 5514–5521 (1990).
[Crossref] [PubMed]

Rev. Laser Eng. (1)

H. Yoshida, A. Ohkubo, H. Fujita, and M. Nakatsuka, “Thermally induced effects of stimulated Brillouin scattering via phase-conjugation mirror for repetitive laser pulse,” Rev. Laser Eng. 29(2), 109–114 (2001).
[Crossref]

Other (1)

J. Hecht, Understanding Lasers: An Entry-Level Guide, 3rd Edition (John Wiley & Sons, Inc., 2008), Chap. 12.

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Figures (6)

Fig. 1
Fig. 1 Rotating wedge SPL-SBS-PCM; (a) a schematic diagram of the optical design principle, (b) a picture of the rotating wedge SPL-SBS-PCM. A wedge is driven by a servo motor.
Fig. 2
Fig. 2 Simulation result for the path length fluctuation (peak to peak); the wedge is translated by 0.3 mm and 0.5 mm in the x and y directions, respectively, when z-axis is the optic axis; the rotation axis of the wedge is tilted by 0.015 deg. in the y direction; and the front glass of the cell is tilted by −0.03 deg. and 0.02 deg. in the x and y directions, respectively.
Fig. 3
Fig. 3 Experimental setup of the four-beam combination experiment using the RW-SSP; ISO, optical isolator; HWP, half wave plate; PBS, polarizing beam splitter; W, wedge; PZT, 45 degree mirror attached piezoelectric transducer; RW, rotating wedge device; Cell, SBS cell; QWP, quarter wave plate; and EM, energymeter.
Fig. 4
Fig. 4 Experimental results of two beam combination; (a) the rms values of relative phase with different values of C; (b), (c), and (d), typical phase measurement signals during 120 s when C is 0.05, 0.2, and 0.5, respectively.
Fig. 5
Fig. 5 Experimental results of a four-beam combination; (a) the relative phases between combining beams during 10 min shows an rms fluctuation of λ/26.7 (beam 1 & 2), λ/28.8 (beam 3 & 4), and λ/24.7 (beam 12 & 34), and (b) detailed results during the first minute.
Fig. 6
Fig. 6 Applied voltages of 3 PZTs during the four-beam combination experiment.

Equations (1)

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Δ V 1 [ V ]=C [ V/rad ]*Δ Φ 12 [ rad ],

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