Abstract

In this manuscript, we report on coherent polarization beam combination (CPBC) of a four-channel pulsed amplifier array in the picosecond regime by using single frequency dithering technique. By employing a photo-detector with low-pass bandwidth (8.5 MHz at 10 dB gain) to filter the intensity fluctuation and obtain phase errors for feedback, a combined laser pulse with~480 ps pulse width at~60 MHz repetition rate is obtained with an average power of 88 W. By adjusting the optical path differences (OPDs) and controlling the pump power to ensure the synchronizations and alleviate the influence of nonlinear phases among each channel, more than 90% combining efficiency is achieved with excellent beam quality (M2~1.1). Finally, the efficiency loss of the system along with the power scaling process is discussed.

© 2014 Optical Society of America

1. Introduction

Pulsed fiber lasers and amplifiers have attracted considerable attention due to their great potential applications in remote sensing, material processing, nonlinear frequency generation and so forth. However, the achievable average and peak power of the monolithic amplifier/laser are currently limited by several issues, including mode instability, fiber damage, thermal effects and non-linear effects [1]. Coherent beam combination (CBC) of several individual amplifiers provides a promising approach to mitigate the limitations aforementioned. This technique is widely known in continuous wave (CW) laser system, and both passive phasing techniques and active phasing techniques had been adopted in different structures [212]. Nowadays, active CBC of continuous-wave configuration had been extended to 64-channel [6] and the 4 kW combined output power had been demonstrated [7]. Recently, CBC techniques were introduced into pulsed laser systems for further high power scalability, and intensive works had been performed continuously [1318]. However, the demonstrations in pulsed regime aforementioned mainly focused within two channels. As for experimental extendibility of CBC in the pulsed regime, five-channel system was demonstrated by active phasing in a tiled array, and an 800 W average power with a peak power of 21.5 kW had been reported in the nanosecond regime [19]. Nevertheless, in the tiled array configuration that without filled-aperture components, a portion of power will be encircled into the side-lobes in the far-field pattern, thus inevitably degrades the beam quality and power concentration of the coherently combined beam. Active coherent polarization beam combination (CPBC) was proposed and validated in CW regime [20], and this combination technique can avoid side-lobes due to that all the combined beams are coaxially superposed into one single beam. Also, some other active filled-aperture configurations can be employed to overcome side-lobes, such as CBC based on diffractive optical element (DOE) [21] and re-imaging waveguide [22]. High power CPBC of two CW fiber amplifier chains and low-power CPBC of eight fiber lasers had been demonstrated by our group [23,24]. This technique was also applied to the chirped-pulse regime quite recently [25,26], and the extendibility of this technique in the pulsed regime is analyzed theoretically [25]. Recently, all-fiber polarization-maintained and diffraction-limited picosecond amplifier had been reported with an average power of 200 W and a peak power of 107 kW in a common large-mode-area (LMA) active fiber [27], which offers a suitable source for CPBC system so that remarkable power enhancement can be expected for a range of applications including laser machining, material processing, and pumping of optical parametric oscillators.

Different from CW regime, some crucial issues should be intensively considered in the pulsed active CBC regime. Firstly, the intrinsic intensity fluctuation should be eliminated in the feedback signal for the phase controller to demodulate the actual phase errors among each amplifier. As for high repetition rate CBC configuration, due to that the frequency of phase noise in hundreds watt level is well below several kHz [7, 28], so low pass filter can be employed to extract the actual phase errors by filtering the high frequency intensity fluctuation in the feedback loop. Secondly, the requirement of temporal synchronization of each amplifier and the effective controlling of the nonlinear phase fluctuations among each channel is crucial for the system to operate with high combining efficiency. Fortunately, the effects of spectral phase shift and nonlinear phase shift on CBC is very tiny when the amplifiers have the same optical paths and approximately equal peak powers [29,30].

2. Principle and experimental setup

In principle, the implementation of active CPBC can be explained as follows. Generally, when two linear-polarized beams are combined by using a polarization beam combiner (PBC), the polarization state of the combined beam is not linearly polarized, and it is just a mixture of the two injected beams. Thus, it cannot completely permeate into the next PBC by rotating the half wavelength plate (HWP), as shown in Fig. 1(a). However, when the phase difference between the two orthogonal polarizations is locked and set to δ = nπ, where δ is the phase difference between the two channels and n is an integer, the combined beam is a new pure linear-polarized one (see Fig. 1(b)), thus it can be further combined with another linear-polarized beam by a PBC, so multi-channel system can be extended straightforwardly by phase locking [20].

 figure: Fig. 1

Fig. 1 Polarization state of the combined beam for (a) without phasing and (b) phase locked.

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The experimental configuration to implement four-channel CPBC system is shown in Fig. 2. The seed is a narrow-bandwidth mode-locked Yb-doped all fiber laser consisting of a fiber Bragg grating (FBG) and a LiNbO3 phase modulator (PM) in a linear cavity [31]. The output power of the seed laser is 10 mW with a central wavelength of 1064 nm. The seed laser is firstly amplified to be 200 mW by a preamplifier (P-A), and then split into four channels by a splitter. After the splitter, each channel is coupled into a LiNbO3 phase modulator with 150 MHz electro-optical bandwidth and 2.5 V half wavelength voltage. The output port of each phase modulator is about 10 mW, and the power loss is attributed to the insertion loss of the splitter and modulator. After the phase modulator, each channel is connected up a commercial fiber delay line (by OZ Optics Limited Company, Canada) with the resolution of 0.496 um and travel range of 50 mm. After the delay lines, each beam is amplified by a two stage amplifier chains. The first stage is a commercial all fiber single mode (SM) and polarization-maintained (PM) amplifier, and the output power of each beam can be scaled to be more than 3 W. The second stage is also an all fiber SM and PM fiber made by ourselves. In the second stage, the active fiber is double-clad single mode Yb-doped fiber with a 10 μm core diameter and 125 μm inner cladding diameter. The cladding absorption of the double-clad fiber is more than 5dB/m near 976 nm. After pumped by a laser diode (45 W maximum power) with 975 nm central wavelength, the output power of the four amplifiers can be scaled to be 20 W power level. After the second stages, the four laser beams are collimated by four isolator-embedded collimators, and sent to free space for polarization combination. By rotating the HWPs and coaxial adjusting the four beams, they can be combined in the following PBCs. In Fig. 2, M1~M4 are four all-reflected mirrors. Due to the limited polarization extinction ratios (PERs) of the four amplifiers, some leakage powers will be existed in dark-port 1 (DP1) and dark-port 2 (DP2). After polarization combination in the PBC1 and PBC2, the two combined beams are injected into PBC3 by two HWPs for further combination in PBC3. After a high-reflectance mirror (M5~99.9:0.1), a small portion of power is sent to a 96:4 beam splitter (M6). Small portion of the power (4%) reflected by M6 is collected by a measurable instrument (MI) (high-speed PD, CCD camera, optical spectrum analyzer, beam quality analyzer, et. al.), and 96% of the transmitted power is received by a photo detector (PD) through a linear polarizer (P). The photo detector is an InGaAs amplifier detector produced with a 700–1800nm response wavelength, which acts as a simple low pass filter to filter the high frequency intensity movement and extract the actual phase differences among the four channels. The extracted signal of the PD is transformed by our active phasing controller for compensating the phase differences among different channels.

 figure: Fig. 2

Fig. 2 Experimental configuration of the four-channel CPBC system. P-A: pre-amplifier; C1-C4: isolator-embedded collimators; HWP: half wavelength plate; M1-M4: all-reflectance mirrors; M5: high- reflectance mirror (99.9:0.1); M6: 96:4 splitter; PBC1-PBC3: polarization beam combiners; P: linear polarizer; DP1-DP2: dark ports; PD-photo-detector.

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3. Experimental results and discussions

3.1 Optical path differences compensation among different channels

In our CPBC system, optical path differences (OPDs) among different channels are the detrimental factors that should be compensated for obtaining high combining efficiency. This is mainly attributed to twofold: (i) due to that the linewidth of the amplifiers are narrowband, so enough coherence should be ensured by compensating the OPDs; (ii) the achievement of temporal synchronization and the effective controlling of the nonlinear phase shifts among the amplifiers need to compensate the OPDs. In our experiment, due to the travel range of the fiber delay lines is limited to 50 mm, so normally effective OPDs compensation should be achieved by three steps. Firstly, according to the pulses of the four channels in one cycle, the OPDs among the four channels can be coarsely estimated and compensated simply by cutting or fusing some parts of passive fibers. Secondly, the four pulses can be overlapped effectively by adjusting the displacements of the four collimators. Thirdly, more precise compensation obtains by adjusting the delay lines. Due to that the resolution (0.496 um) of the delay lines are limited and they are adjusted by manually selecting and setting the delay values through computer (not active controlled), so the optical paths of all the channels cannot adjust strictly equal ceaseless. Thus, the dynamical piston phase errors cannot compensate by optical delay lines. This is different from the functions of active delay lines in Ref [26]. In the experiment, the delay lines are adjusted to optimum state (namely the combining efficiency of the whole system is maximal when the phase control circuit performed) by continuously selecting and setting the optimal delay values through computer.

3.2 The validation of the feasibility of phase controller

The active CPBC of the four pulsed amplifier chains is performed based on our single-frequency dithering algorithm processor [8, 32]. The mathematical principle of the single frequency dithering technique can be found in Ref [32], which is similar to the analysis of chirp-pulsed CPBC system based on LOCSET (Locking of Optical Coherence by Single-detector Electronic-frequency Tagging) feedback technique [25]. The novelty of single frequency dithering technique is that time division multiplexing principle is incorporated into the phase controller so that only one modulation frequency is required to demodulate the phase differences among different channels. The metric function of the single frequency dithering technique is denoted by the amplitude of the voltage signal transformed by the PD. The voltage signal transformed by the PD includes the information of phase differences among the four amplifier chains, which can be used to generate the phase control signal by modulation and demodulation technique.

Firstly, we validate the feasibility of the active phase controller in the pulsed regime by the time series signal collected in the PD and the phase noise suppression process of the four amplifier chains. The time-dependent phasing process and the phase noise suppression results are shown in Fig. 3. Figure 3(a) shows that the normalized energy collected by the PD fluctuates randomly along with time in the circumstance of without phase controlling. This phenomenon ascribes to that the phase differences among the four amplifier chains change continuously with the influence of thermal effects, environmental vibrations and so forth. However, when the single frequency dithering algorithm processor performed, the normalized energy in the PD can be locked effectively both at maximum state and minimum state, which suggests that the phase differences among the four amplifier chains are also compensated effectively. From Fig. 3(b), we conclude that the spectral density of power of the phase noise below 1 kHz is efficiently suppressed both in phasing at maximum state and minimum state.

 figure: Fig. 3

Fig. 3 The time-dependent phasing process along with time and the spectral density of power of phase noise in open loop and closed loop. (a) Time series signals. (b) Spectral density.

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The feasibility of the single frequency dithering algorithm processor can be also investigated by the movement of intensity profiles collected by the CCD camera. In the circumstance of without phasing, the intensity profile at the camera changes along with time and the power values in power meter 1 and power meter 2 are instable due to the uncertain phase differences among the four beams. Figures 4(a)4(d) plot four snapshots of the intensity profiles without phasing. When the single frequency dithering algorithm performs at maximum or minimum metric state, the intensity profile of the combined beam and the combined output power collected by the power meters can be stable. The intensity profiles at maximum phasing state and minimum phasing state are shown in Figs. 4(e) and 4(f), respectively.

 figure: Fig. 4

Fig. 4 The combined intensity profiles of the system in the circumstance of without phasing ((a)-(d)), with phasing at maximum state (e), and with phasing at minimum state (f).

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In the experiment, when the system is performed with active phase controller and optimized by the delay lines controller, the average power values collected by DP1, DP2, power meter 1 and power meter 2 are measured to be 0.1 W, 0.13 W, 88 W and 9.4 W, respectively. The combining efficiency (η) of the whole system is calculated to be 90.1% by the formula

η=Pp1Pp1+Pp2+PDP1+PDP2

In Eq. (1), Pp1, Pp2, PDP1 and PDP2 are the average power values collected by power meter 1, power meter 2, DP1 and DP2, respectively.

Figure 5 shows the pulse shapes of a single channel and the coherently polarization combined beam. The pulse shape of the polarization combined beam is almost the same as that of a single amplifier chain. The FWHM (full width at half-maximum) of the combined pulse is measured to be 480 ps, and the peak power is approximately calculated to be 2.89 kW by employing the Gaussian-like pulse peak power formula [33]

 figure: Fig. 5

Fig. 5 Measured pulse shapes with (a) a single channel and combined beam in one cycle, and (b) combined beam in 6 cycles.

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Ppeak=2ln2πPaveτf

Where Ppeak and Pave are the peak power and average power of the combined pulse, respectively, τis the FWHM of the combined pulse, and f is the pulse repetition rate.

We also investigate the beam quality (M2 factor) and the spectrum of the coherently combined beam, which is shown in Fig. 6. The measurement of the beam quality is M2x~1.1 and M2y~1.1 (shown in Fig. 6(a)). Figure 6(b) indicates that no amplified spontaneous emission (ASE) and residual pump light are observed in the combined beam.

 figure: Fig. 6

Fig. 6 (a) The beam quality (M2 factor) of the coherently combined beam and (b) the spectrum of the coherently polarization combined beam at 12 W power-level and 88 W power-level.

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3.3 Efficiency loss along with the power scaling process

The relationship of the combining efficiency of the system and the total injected laser power is shown in Fig. 7 (solid line with cube marker), which shows that the combining efficiency of the whole system decreases from 94.3% (12 W coherently output power) to 90.1% (88 W coherently output power) along with the power scaling of the system. In order to investigate the influence of OPDs and nonlinear phases on combining efficiency, we replace the picosecond-pulsed seed laser by a single frequency CW seed to avoid the influence of OPDs and nonlinear phases among pulses. The combining efficiencies of the system are 95.1% at 12W coherently combined power and 91% at 78.5 W (limited by stimulated Brillouin scattering (SBS) effect) coherently combined power, which is also shown in Fig. 7 (dashed line with circle marker). According to Fig. 7, we conclude that efficiency loss caused by OPDs and nonlinear phases in the four-channel picosecond-pulsed system is within 1% along with the power scaling, and their influence is increased little along increase the injected power level.

 figure: Fig. 7

Fig. 7 The comparison results of combining efficiency between the picosecond-pulsed system and the single frequency CW system.

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In addition to the influence of OPDs and nonlinear phases, some imperfections, including depolarization errors of the injected beams, coaxial errors, residual phase error of the phase controller, mode size errors, beam pointing errors, and beam divergence errors, also exist in the present system [34]. As aforementioned, the limited PERs induced power loss is 0.23 W, so their influence on efficiency loss is calculated to be 0.24%. Assuming that δd is the precision of the adjustment apparatus and w is the beam width, δd/w is about 0.003 in our experiment. According to our previous theoretical analysis, the influence of static coaxial error on the combining efficiency of the whole system can be neglected [35].

The efficiency loss induced by residual phase error of the phase controller can be estimated by extending our previous analysis to four-channel system [35], which can be expressed by

Δη=1212(4P1P2cos2δ+(P1P2)2+4P3P4cos2δ+(P3P4)2)j=14Pj

Where Pj is the output power of beam j, and δ is the residual phase error (root-mean-square (RMS) value) of the phase controller.

By employing the normalized voltage collected by the PD when the phase controller performed, the residual phase error of the system is estimated to be λ/20 [36]. By calculation, the efficiency loss caused by residual phase error is within 3%. This influence increase little along with the power scaling in the experiment.

By the analysis above, we see that at 12 W power-level, the efficiency loss induced by mode size errors, beam pointing errors, and beam divergence errors is within 2%. And the residual piston phase error is the significant detrimental factor in this power level. However, at maximum power, the efficiency loss induced by mode size errors, beam pointing errors, and beam divergence errors is ~6%, which becomes the significant detrimental factors in this power level. This adverse issues may be alleviated by adopting self-adapting apparatus (tilt mirrors or deformation mirrors), which is crucial in high power CPBC system.

5. Conclusion

We demonstrate CPBC of a four-channel picosecond pulsed fiber amplifier array by using single frequency dithering technique. An average power of 88 W coherently combined laser pulse with~480 ps pulse width at 59.5238 MHz repetition rate is achieved with long-time stability. The peak power of the combined pulse is estimated to be 2.89 kW. More than 94% and 90% combining efficiencies are obtained at 12 W output power and 88 W output power. In the experiment, the residual phase error of the phase controller is within λ/20 and the beam quality (M2 factor) of the coherently polarization combined beam is measured to be 1.1. By the analysis, we conclude that the impact of OPDs and nonlinear phases on the combining efficiency of the system is less than 1%. We present that, at 12 W power level, the residual piston phasing error is the foremost detrimental factor of the CPBC system. However, along with the power scaling process, the influence of beam pointing errors, beam divergence errors, and beam size errors should also be considered carefully.

References and links

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References

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  1. C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7(11), 861–867 (2013).
    [Crossref]
  2. T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. J. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express 14(25), 12015–12021 (2006).
    [Crossref] [PubMed]
  3. G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
    [Crossref]
  4. M. A. Vorontsov and S. L. Lachinova, “Laser beam projection with adaptive array of fiber collimators. I. Basic considerations for analysis,” J. Opt. Soc. Am. A 25(8), 1949–1959 (2008).
    [Crossref] [PubMed]
  5. P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combination of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15(2), 248–256 (2009).
    [Crossref]
  6. J. Bourderionnet, C. Bellanger, J. Primot, and A. Brignon, “Collective coherent phase combining of 64 fibers,” Opt. Express 19(18), 17053–17058 (2011).
    [Crossref] [PubMed]
  7. C. X. Yu, S. J. Augst, S. M. Redmond, K. C. Goldizen, D. V. Murphy, A. Sanchez, and T. Y. Fan, “Coherent combining of a 4 kW, eight-element fiber amplifier array,” Opt. Lett. 36(14), 2686–2688 (2011).
    [Crossref] [PubMed]
  8. Y. Ma, X. Wang, J. Leng, H. Xiao, X. Dong, J. Zhu, W. Du, P. Zhou, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination of 1.08 kW fiber amplifier array using single frequency dithering technique,” Opt. Lett. 36(6), 951–953 (2011).
    [Crossref] [PubMed]
  9. X. L. Wang, P. Zhou, Y. X. Ma, J. Y. Leng, X. J. Xu, and Z. J. Liu, “Active phasing a nine-element 1.14 kW all-fiber two-tone MOPA array using SPGD algorithm,” Opt. Lett. 36(16), 3121–3123 (2011).
    [Crossref] [PubMed]
  10. C. J. Corcoran and F. Durville, “Experimental demonstration of a phase—locked laser array using a self-Fourier cavity,” Appl. Phys. Lett. 86, 201118 (2005).
  11. J. Lhermite, A. Desfarges-Berthelemot, V. Kermene, and A. Barthelemy, “Passive phase locking of an array of four fiber amplifiers by an all-optical feedback loop,” Opt. Lett. 32(13), 1842–1844 (2007).
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  12. P. C. Shardlow and M. J. Damzen, “Phase conjugate self-organized coherent beam combination: a passive technique for laser power scaling,” Opt. Lett. 35(7), 1082–1084 (2010).
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    [Crossref] [PubMed]
  14. L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5 μm fiber amplifiers in a long-pulse regime,” Opt. Lett. 36(4), 523–525 (2011).
    [Crossref] [PubMed]
  15. S. Palese, E. Cheung, G. Goodno, C. C. Shih, F. Di Teodoro, T. McComb, and M. Weber, “Coherent combining of pulsed fiber amplifiers in the nonlinear chirp regime with intra-pulse phase control,” Opt. Express 20(7), 7422–7435 (2012).
    [Crossref] [PubMed]
  16. Y. Zaouter, L. Daniault, M. Hanna, D. N. Papadopoulos, F. Morin, C. Hönninger, F. Druon, E. Mottay, and P. Georges, “Passive coherent combination of two ultrafast rod type fiber chirped pulse amplifiers,” Opt. Lett. 37(9), 1460–1462 (2012).
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  17. H. Liu, B. He, J. Zhou, J. Dong, Y. Wei, and Q. Lou, “Coherent beam combination of two nanosecond fiber amplifiers by an all-optical feedback loop,” Opt. Lett. 37(18), 3885–3887 (2012).
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  18. A. Brignon edited, Coherent Laser Beam Combining (Wiley, 2013).
  19. R. Su, P. Zhou, X. Wang, H. Zhang, and X. Xu, “Active coherent beam combining of a five-element, 800 W nanosecond fiber amplifier array,” Opt. Lett. 37(19), 3978–3980 (2012).
    [Crossref] [PubMed]
  20. R. Uberna, A. Bratcher, and B. G. Tiemann, “Coherent polarization beam combination,” IEEE J. Quantum Electron. 46, 1191–1196 (2010).
    [Crossref] [PubMed]
  21. S. M. Redmond, D. J. Ripin, C. X. Yu, S. J. Augst, T. Y. Fan, P. A. Thielen, J. E. Rothenberg, and G. D. Goodno, “Diffractive coherent combining of a 2.5 kW fiber laser array into a 1.9 kW Gaussian beam,” Opt. Lett. 37(14), 2832–2834 (2012).
    [Crossref] [PubMed]
  22. R. Uberna, A. Bratcher, T. G. Alley, A. D. Sanchez, A. S. Flores, and B. Pulford, “Coherent combination of high power fiber amplifiers in a two-dimensional re-imaging waveguide,” Opt. Express 18(13), 13547–13553 (2010).
    [Crossref] [PubMed]
  23. P. F. Ma, P. Zhou, H. Xiao, Y. X. Ma, R. T. Su, and Z. J. Liu, “Generation of a 481 W single frequency and linearly polarized beam by coherent polarization locking,” IEEE Photonics Technol. Lett. 25(19), 1936–1938 (2013).
    [Crossref]
  24. P. F. Ma, P. Zhou, R. T. Su, Y. X. Ma, and Z. J. Liu, “Coherent polarization beam combining of eight fiber lasers using single-frequency dithering technique,” Laser Phys. Lett. 9(6), 456–458 (2012).
    [Crossref]
  25. L. A. Siiman, W. Z. Chang, T. Zhou, and A. Galvanauskas, “Coherent femtosecond pulse combining of multiple parallel chirped pulse fiber amplifiers,” Opt. Express 20(16), 18097–18116 (2012).
    [Crossref] [PubMed]
  26. A. Klenke, S. Breitkopf, M. Kienel, T. Gottschall, T. Eidam, S. Hädrich, J. Rothhardt, J. Limpert, and A. Tünnermann, “530 W, 1.3 mJ, four-channel coherently combined femtosecond fiber chirped-pulse amplification system,” Opt. Lett. 38(13), 2283–2285 (2013).
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  27. P. S. Teh, R. J. Lewis, S. U. Alam, and D. J. Richardson, “200 W diffraction limited, single-polarization, all-fiber picosecond MOPA,” Opt. Express 21(22), 25883–25889 (2013).
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  28. D. C. Jones, C. D. Stacey, and A. M. Scott, “Phase stabilization of a large-mode-area ytterbium-doped fiber amplifier,” Opt. Lett. 32(5), 466–468 (2007).
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  29. A. Klenke, E. Seise, J. Limpert, and A. Tünnermann, “Basic considerations on coherent combining of ultrashort laser pulses,” Opt. Express 19(25), 25379–25387 (2011).
    [Crossref] [PubMed]
  30. R. Su, P. Zhou, X. Wang, H. Zhang, and X. Xu, “Impact of temporal and spectral aberrations on coherent beam combination of nanosecond fiber lasers,” Appl. Opt. 52(10), 2187–2193 (2013).
    [Crossref] [PubMed]
  31. R. Tao, X. Wang, P. Zhou, L. Si, and Z. Liu, “Widely tunable mode-locked all-fiberized Yb-doped fiber laser with near-transform-limited spectrum linewidth,” Appl. Phys. B, doi: (2013).
    [Crossref]
  32. Y. Ma, P. Zhou, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination with single frequency dithering technique,” Opt. Lett. 35(9), 1308–1310 (2010).
    [Crossref] [PubMed]
  33. M. Leigh, W. Shi, J. Zong, J. Wang, S. Jiang, and N. Peyghambarian, “Compact, single-frequency all-fiber Q-switched laser at 1 microm,” Opt. Lett. 32(8), 897–899 (2007).
    [Crossref] [PubMed]
  34. G. D. Goodno, C. C. Shih, and J. E. Rothenberg, “Perturbative analysis of coherent combining efficiency with mismatched lasers,” Opt. Express 18(24), 25403–25414 (2010).
    [Crossref] [PubMed]
  35. P. Ma, P. Zhou, Y. Ma, R. Su, and Z. Liu, “Analysis of the effects of aberrations on coherent polarization beam combining of fiber laser beams,” Appl. Opt. 51(16), 3546–3551 (2012).
    [Crossref] [PubMed]
  36. V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15(2), 257–268 (2009).
    [Crossref]

2013 (5)

2012 (8)

P. Ma, P. Zhou, Y. Ma, R. Su, and Z. Liu, “Analysis of the effects of aberrations on coherent polarization beam combining of fiber laser beams,” Appl. Opt. 51(16), 3546–3551 (2012).
[Crossref] [PubMed]

P. F. Ma, P. Zhou, R. T. Su, Y. X. Ma, and Z. J. Liu, “Coherent polarization beam combining of eight fiber lasers using single-frequency dithering technique,” Laser Phys. Lett. 9(6), 456–458 (2012).
[Crossref]

L. A. Siiman, W. Z. Chang, T. Zhou, and A. Galvanauskas, “Coherent femtosecond pulse combining of multiple parallel chirped pulse fiber amplifiers,” Opt. Express 20(16), 18097–18116 (2012).
[Crossref] [PubMed]

S. M. Redmond, D. J. Ripin, C. X. Yu, S. J. Augst, T. Y. Fan, P. A. Thielen, J. E. Rothenberg, and G. D. Goodno, “Diffractive coherent combining of a 2.5 kW fiber laser array into a 1.9 kW Gaussian beam,” Opt. Lett. 37(14), 2832–2834 (2012).
[Crossref] [PubMed]

S. Palese, E. Cheung, G. Goodno, C. C. Shih, F. Di Teodoro, T. McComb, and M. Weber, “Coherent combining of pulsed fiber amplifiers in the nonlinear chirp regime with intra-pulse phase control,” Opt. Express 20(7), 7422–7435 (2012).
[Crossref] [PubMed]

Y. Zaouter, L. Daniault, M. Hanna, D. N. Papadopoulos, F. Morin, C. Hönninger, F. Druon, E. Mottay, and P. Georges, “Passive coherent combination of two ultrafast rod type fiber chirped pulse amplifiers,” Opt. Lett. 37(9), 1460–1462 (2012).
[Crossref] [PubMed]

H. Liu, B. He, J. Zhou, J. Dong, Y. Wei, and Q. Lou, “Coherent beam combination of two nanosecond fiber amplifiers by an all-optical feedback loop,” Opt. Lett. 37(18), 3885–3887 (2012).
[Crossref] [PubMed]

R. Su, P. Zhou, X. Wang, H. Zhang, and X. Xu, “Active coherent beam combining of a five-element, 800 W nanosecond fiber amplifier array,” Opt. Lett. 37(19), 3978–3980 (2012).
[Crossref] [PubMed]

2011 (7)

M. Zhang, E. J. R. Kelleher, A. S. Pozharov, E. D. Obraztsova, S. V. Popov, and J. R. Taylor, “Passive synchronization of all-fiber lasers through a common saturable absorber,” Opt. Lett. 36(20), 3984–3986 (2011).
[Crossref] [PubMed]

L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5 μm fiber amplifiers in a long-pulse regime,” Opt. Lett. 36(4), 523–525 (2011).
[Crossref] [PubMed]

J. Bourderionnet, C. Bellanger, J. Primot, and A. Brignon, “Collective coherent phase combining of 64 fibers,” Opt. Express 19(18), 17053–17058 (2011).
[Crossref] [PubMed]

C. X. Yu, S. J. Augst, S. M. Redmond, K. C. Goldizen, D. V. Murphy, A. Sanchez, and T. Y. Fan, “Coherent combining of a 4 kW, eight-element fiber amplifier array,” Opt. Lett. 36(14), 2686–2688 (2011).
[Crossref] [PubMed]

Y. Ma, X. Wang, J. Leng, H. Xiao, X. Dong, J. Zhu, W. Du, P. Zhou, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination of 1.08 kW fiber amplifier array using single frequency dithering technique,” Opt. Lett. 36(6), 951–953 (2011).
[Crossref] [PubMed]

X. L. Wang, P. Zhou, Y. X. Ma, J. Y. Leng, X. J. Xu, and Z. J. Liu, “Active phasing a nine-element 1.14 kW all-fiber two-tone MOPA array using SPGD algorithm,” Opt. Lett. 36(16), 3121–3123 (2011).
[Crossref] [PubMed]

A. Klenke, E. Seise, J. Limpert, and A. Tünnermann, “Basic considerations on coherent combining of ultrashort laser pulses,” Opt. Express 19(25), 25379–25387 (2011).
[Crossref] [PubMed]

2010 (5)

2009 (2)

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combination of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15(2), 248–256 (2009).
[Crossref]

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15(2), 257–268 (2009).
[Crossref]

2008 (1)

2007 (4)

2006 (1)

2005 (1)

C. J. Corcoran and F. Durville, “Experimental demonstration of a phase—locked laser array using a self-Fourier cavity,” Appl. Phys. Lett. 86, 201118 (2005).

Alam, S. U.

Alley, T. G.

Anderegg, J.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Asman, C. P.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Augst, S. J.

Azarian, A.

Baker, J. T.

Barthelemy, A.

Bellanger, C.

Benham, V.

Bennaï, B.

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15(2), 257–268 (2009).
[Crossref]

Bourderionnet, J.

Bourdon, P.

L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5 μm fiber amplifiers in a long-pulse regime,” Opt. Lett. 36(4), 523–525 (2011).
[Crossref] [PubMed]

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15(2), 257–268 (2009).
[Crossref]

Bratcher, A.

Breitkopf, S.

Brignon, A.

Brosnan, S.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Cadoret, K.

Canat, G.

L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5 μm fiber amplifiers in a long-pulse regime,” Opt. Lett. 36(4), 523–525 (2011).
[Crossref] [PubMed]

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15(2), 257–268 (2009).
[Crossref]

Chang, W. Z.

Cheung, E.

Cheung, E. C.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Corcoran, C. J.

C. J. Corcoran and F. Durville, “Experimental demonstration of a phase—locked laser array using a self-Fourier cavity,” Appl. Phys. Lett. 86, 201118 (2005).

Culpepper, M. A.

Damzen, M. J.

Daniault, L.

Desfarges-Berthelemot, A.

Di Teodoro, F.

Dong, J.

Dong, X.

Druon, F.

Du, W.

Durville, F.

C. J. Corcoran and F. Durville, “Experimental demonstration of a phase—locked laser array using a self-Fourier cavity,” Appl. Phys. Lett. 86, 201118 (2005).

Eidam, T.

Fan, T. Y.

Flores, A. S.

Galvanauskas, A.

Georges, P.

Goldizen, K. C.

Goodno, G.

Goodno, G. D.

S. M. Redmond, D. J. Ripin, C. X. Yu, S. J. Augst, T. Y. Fan, P. A. Thielen, J. E. Rothenberg, and G. D. Goodno, “Diffractive coherent combining of a 2.5 kW fiber laser array into a 1.9 kW Gaussian beam,” Opt. Lett. 37(14), 2832–2834 (2012).
[Crossref] [PubMed]

G. D. Goodno, C. C. Shih, and J. E. Rothenberg, “Perturbative analysis of coherent combining efficiency with mismatched lasers,” Opt. Express 18(24), 25403–25414 (2010).
[Crossref] [PubMed]

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Gottschall, T.

Goular, D.

L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5 μm fiber amplifiers in a long-pulse regime,” Opt. Lett. 36(4), 523–525 (2011).
[Crossref] [PubMed]

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15(2), 257–268 (2009).
[Crossref]

Guo, S.

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combination of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15(2), 248–256 (2009).
[Crossref]

Hädrich, S.

Hammons, D.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Hanna, M.

He, B.

Hönninger, C.

Injeyan, H.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Jaouën, Y.

L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5 μm fiber amplifiers in a long-pulse regime,” Opt. Lett. 36(4), 523–525 (2011).
[Crossref] [PubMed]

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15(2), 257–268 (2009).
[Crossref]

Jauregui, C.

C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7(11), 861–867 (2013).
[Crossref]

Jiang, S.

Jolivet, V.

L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5 μm fiber amplifiers in a long-pulse regime,” Opt. Lett. 36(4), 523–525 (2011).
[Crossref] [PubMed]

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15(2), 257–268 (2009).
[Crossref]

Jones, D. C.

Kelleher, E. J. R.

Kermene, V.

Kienel, M.

Klenke, A.

Komine, H.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Lachinova, S. L.

Leigh, M.

Leng, J.

Leng, J. Y.

Lewis, R. J.

Lhermite, J.

Limpert, J.

Liu, H.

Liu, Z.

Liu, Z. J.

P. F. Ma, P. Zhou, H. Xiao, Y. X. Ma, R. T. Su, and Z. J. Liu, “Generation of a 481 W single frequency and linearly polarized beam by coherent polarization locking,” IEEE Photonics Technol. Lett. 25(19), 1936–1938 (2013).
[Crossref]

P. F. Ma, P. Zhou, R. T. Su, Y. X. Ma, and Z. J. Liu, “Coherent polarization beam combining of eight fiber lasers using single-frequency dithering technique,” Laser Phys. Lett. 9(6), 456–458 (2012).
[Crossref]

X. L. Wang, P. Zhou, Y. X. Ma, J. Y. Leng, X. J. Xu, and Z. J. Liu, “Active phasing a nine-element 1.14 kW all-fiber two-tone MOPA array using SPGD algorithm,” Opt. Lett. 36(16), 3121–3123 (2011).
[Crossref] [PubMed]

Lombard, L.

L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5 μm fiber amplifiers in a long-pulse regime,” Opt. Lett. 36(4), 523–525 (2011).
[Crossref] [PubMed]

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15(2), 257–268 (2009).
[Crossref]

Long, W. H.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Lou, Q.

Lu, C. A.

Ma, H.

Y. Ma, P. Zhou, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination with single frequency dithering technique,” Opt. Lett. 35(9), 1308–1310 (2010).
[Crossref] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combination of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15(2), 248–256 (2009).
[Crossref]

Ma, P.

Ma, P. F.

P. F. Ma, P. Zhou, H. Xiao, Y. X. Ma, R. T. Su, and Z. J. Liu, “Generation of a 481 W single frequency and linearly polarized beam by coherent polarization locking,” IEEE Photonics Technol. Lett. 25(19), 1936–1938 (2013).
[Crossref]

P. F. Ma, P. Zhou, R. T. Su, Y. X. Ma, and Z. J. Liu, “Coherent polarization beam combining of eight fiber lasers using single-frequency dithering technique,” Laser Phys. Lett. 9(6), 456–458 (2012).
[Crossref]

Ma, Y.

Ma, Y. X.

P. F. Ma, P. Zhou, H. Xiao, Y. X. Ma, R. T. Su, and Z. J. Liu, “Generation of a 481 W single frequency and linearly polarized beam by coherent polarization locking,” IEEE Photonics Technol. Lett. 25(19), 1936–1938 (2013).
[Crossref]

P. F. Ma, P. Zhou, R. T. Su, Y. X. Ma, and Z. J. Liu, “Coherent polarization beam combining of eight fiber lasers using single-frequency dithering technique,” Laser Phys. Lett. 9(6), 456–458 (2012).
[Crossref]

X. L. Wang, P. Zhou, Y. X. Ma, J. Y. Leng, X. J. Xu, and Z. J. Liu, “Active phasing a nine-element 1.14 kW all-fiber two-tone MOPA array using SPGD algorithm,” Opt. Lett. 36(16), 3121–3123 (2011).
[Crossref] [PubMed]

McClellan, M.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

McComb, T.

McNaught, S. J.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Moreau, B.

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15(2), 257–268 (2009).
[Crossref]

Morin, F.

Mottay, E.

Murphy, D. V.

Nelson, D. J.

Obraztsova, E. D.

Palese, S.

Papadopoulos, D. N.

Peyghambarian, N.

Pilkington, D.

Popov, S. V.

Pourtal, E.

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15(2), 257–268 (2009).
[Crossref]

Pozharov, A. S.

Primot, J.

Pulford, B.

Redmond, S.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Redmond, S. M.

Richardson, D. J.

Ripin, D. J.

Rothenberg, J. E.

Rothhardt, J.

Sanchez, A.

Sanchez, A. D.

Scott, A. M.

Seise, E.

Shardlow, P. C.

Shay, T. M.

Shi, W.

Shih, C. C.

Si, L.

Siiman, L. A.

Simpson, R.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Sollee, J.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Spring, J.

Stacey, C. D.

Su, R.

Su, R. T.

P. F. Ma, P. Zhou, H. Xiao, Y. X. Ma, R. T. Su, and Z. J. Liu, “Generation of a 481 W single frequency and linearly polarized beam by coherent polarization locking,” IEEE Photonics Technol. Lett. 25(19), 1936–1938 (2013).
[Crossref]

P. F. Ma, P. Zhou, R. T. Su, Y. X. Ma, and Z. J. Liu, “Coherent polarization beam combining of eight fiber lasers using single-frequency dithering technique,” Laser Phys. Lett. 9(6), 456–458 (2012).
[Crossref]

Tao, R.

R. Tao, X. Wang, P. Zhou, L. Si, and Z. Liu, “Widely tunable mode-locked all-fiberized Yb-doped fiber laser with near-transform-limited spectrum linewidth,” Appl. Phys. B, doi: (2013).
[Crossref]

Taylor, J. R.

Teh, P. S.

Thielen, P. A.

Tiemann, B. G.

R. Uberna, A. Bratcher, and B. G. Tiemann, “Coherent polarization beam combination,” IEEE J. Quantum Electron. 46, 1191–1196 (2010).
[Crossref] [PubMed]

Tünnermann, A.

Uberna, R.

Vasseur, O.

L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5 μm fiber amplifiers in a long-pulse regime,” Opt. Lett. 36(4), 523–525 (2011).
[Crossref] [PubMed]

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15(2), 257–268 (2009).
[Crossref]

Vorontsov, M. A.

Wang, J.

Wang, X.

Wang, X. L.

Ward, B.

Weber, M.

S. Palese, E. Cheung, G. Goodno, C. C. Shih, F. Di Teodoro, T. McComb, and M. Weber, “Coherent combining of pulsed fiber amplifiers in the nonlinear chirp regime with intra-pulse phase control,” Opt. Express 20(7), 7422–7435 (2012).
[Crossref] [PubMed]

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Wei, Y.

Weiss, S. B.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Wickham, M.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Xiao, H.

P. F. Ma, P. Zhou, H. Xiao, Y. X. Ma, R. T. Su, and Z. J. Liu, “Generation of a 481 W single frequency and linearly polarized beam by coherent polarization locking,” IEEE Photonics Technol. Lett. 25(19), 1936–1938 (2013).
[Crossref]

Y. Ma, X. Wang, J. Leng, H. Xiao, X. Dong, J. Zhu, W. Du, P. Zhou, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination of 1.08 kW fiber amplifier array using single frequency dithering technique,” Opt. Lett. 36(6), 951–953 (2011).
[Crossref] [PubMed]

Xu, X.

Xu, X. J.

Yu, C. X.

Zaouter, Y.

Zhang, H.

Zhang, M.

Zhao, Y.

Zhou, J.

Zhou, P.

P. F. Ma, P. Zhou, H. Xiao, Y. X. Ma, R. T. Su, and Z. J. Liu, “Generation of a 481 W single frequency and linearly polarized beam by coherent polarization locking,” IEEE Photonics Technol. Lett. 25(19), 1936–1938 (2013).
[Crossref]

R. Su, P. Zhou, X. Wang, H. Zhang, and X. Xu, “Impact of temporal and spectral aberrations on coherent beam combination of nanosecond fiber lasers,” Appl. Opt. 52(10), 2187–2193 (2013).
[Crossref] [PubMed]

P. Ma, P. Zhou, Y. Ma, R. Su, and Z. Liu, “Analysis of the effects of aberrations on coherent polarization beam combining of fiber laser beams,” Appl. Opt. 51(16), 3546–3551 (2012).
[Crossref] [PubMed]

P. F. Ma, P. Zhou, R. T. Su, Y. X. Ma, and Z. J. Liu, “Coherent polarization beam combining of eight fiber lasers using single-frequency dithering technique,” Laser Phys. Lett. 9(6), 456–458 (2012).
[Crossref]

R. Su, P. Zhou, X. Wang, H. Zhang, and X. Xu, “Active coherent beam combining of a five-element, 800 W nanosecond fiber amplifier array,” Opt. Lett. 37(19), 3978–3980 (2012).
[Crossref] [PubMed]

X. L. Wang, P. Zhou, Y. X. Ma, J. Y. Leng, X. J. Xu, and Z. J. Liu, “Active phasing a nine-element 1.14 kW all-fiber two-tone MOPA array using SPGD algorithm,” Opt. Lett. 36(16), 3121–3123 (2011).
[Crossref] [PubMed]

Y. Ma, X. Wang, J. Leng, H. Xiao, X. Dong, J. Zhu, W. Du, P. Zhou, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination of 1.08 kW fiber amplifier array using single frequency dithering technique,” Opt. Lett. 36(6), 951–953 (2011).
[Crossref] [PubMed]

Y. Ma, P. Zhou, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination with single frequency dithering technique,” Opt. Lett. 35(9), 1308–1310 (2010).
[Crossref] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combination of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15(2), 248–256 (2009).
[Crossref]

R. Tao, X. Wang, P. Zhou, L. Si, and Z. Liu, “Widely tunable mode-locked all-fiberized Yb-doped fiber laser with near-transform-limited spectrum linewidth,” Appl. Phys. B, doi: (2013).
[Crossref]

Zhou, T.

Zhu, J.

Zong, J.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

C. J. Corcoran and F. Durville, “Experimental demonstration of a phase—locked laser array using a self-Fourier cavity,” Appl. Phys. Lett. 86, 201118 (2005).

IEEE J. Quantum Electron. (1)

R. Uberna, A. Bratcher, and B. G. Tiemann, “Coherent polarization beam combination,” IEEE J. Quantum Electron. 46, 1191–1196 (2010).
[Crossref] [PubMed]

IEEE J. Sel. Top. Quantum Electron. (3)

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combination of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15(2), 248–256 (2009).
[Crossref]

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15(2), 257–268 (2009).
[Crossref]

IEEE Photonics Technol. Lett. (1)

P. F. Ma, P. Zhou, H. Xiao, Y. X. Ma, R. T. Su, and Z. J. Liu, “Generation of a 481 W single frequency and linearly polarized beam by coherent polarization locking,” IEEE Photonics Technol. Lett. 25(19), 1936–1938 (2013).
[Crossref]

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

Laser Phys. Lett. (1)

P. F. Ma, P. Zhou, R. T. Su, Y. X. Ma, and Z. J. Liu, “Coherent polarization beam combining of eight fiber lasers using single-frequency dithering technique,” Laser Phys. Lett. 9(6), 456–458 (2012).
[Crossref]

Nat. Photonics (1)

C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7(11), 861–867 (2013).
[Crossref]

Opt. Express (8)

T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. J. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express 14(25), 12015–12021 (2006).
[Crossref] [PubMed]

J. Bourderionnet, C. Bellanger, J. Primot, and A. Brignon, “Collective coherent phase combining of 64 fibers,” Opt. Express 19(18), 17053–17058 (2011).
[Crossref] [PubMed]

S. Palese, E. Cheung, G. Goodno, C. C. Shih, F. Di Teodoro, T. McComb, and M. Weber, “Coherent combining of pulsed fiber amplifiers in the nonlinear chirp regime with intra-pulse phase control,” Opt. Express 20(7), 7422–7435 (2012).
[Crossref] [PubMed]

L. A. Siiman, W. Z. Chang, T. Zhou, and A. Galvanauskas, “Coherent femtosecond pulse combining of multiple parallel chirped pulse fiber amplifiers,” Opt. Express 20(16), 18097–18116 (2012).
[Crossref] [PubMed]

R. Uberna, A. Bratcher, T. G. Alley, A. D. Sanchez, A. S. Flores, and B. Pulford, “Coherent combination of high power fiber amplifiers in a two-dimensional re-imaging waveguide,” Opt. Express 18(13), 13547–13553 (2010).
[Crossref] [PubMed]

P. S. Teh, R. J. Lewis, S. U. Alam, and D. J. Richardson, “200 W diffraction limited, single-polarization, all-fiber picosecond MOPA,” Opt. Express 21(22), 25883–25889 (2013).
[Crossref] [PubMed]

A. Klenke, E. Seise, J. Limpert, and A. Tünnermann, “Basic considerations on coherent combining of ultrashort laser pulses,” Opt. Express 19(25), 25379–25387 (2011).
[Crossref] [PubMed]

G. D. Goodno, C. C. Shih, and J. E. Rothenberg, “Perturbative analysis of coherent combining efficiency with mismatched lasers,” Opt. Express 18(24), 25403–25414 (2010).
[Crossref] [PubMed]

Opt. Lett. (15)

Y. Ma, P. Zhou, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination with single frequency dithering technique,” Opt. Lett. 35(9), 1308–1310 (2010).
[Crossref] [PubMed]

M. Leigh, W. Shi, J. Zong, J. Wang, S. Jiang, and N. Peyghambarian, “Compact, single-frequency all-fiber Q-switched laser at 1 microm,” Opt. Lett. 32(8), 897–899 (2007).
[Crossref] [PubMed]

D. C. Jones, C. D. Stacey, and A. M. Scott, “Phase stabilization of a large-mode-area ytterbium-doped fiber amplifier,” Opt. Lett. 32(5), 466–468 (2007).
[Crossref] [PubMed]

R. Su, P. Zhou, X. Wang, H. Zhang, and X. Xu, “Active coherent beam combining of a five-element, 800 W nanosecond fiber amplifier array,” Opt. Lett. 37(19), 3978–3980 (2012).
[Crossref] [PubMed]

S. M. Redmond, D. J. Ripin, C. X. Yu, S. J. Augst, T. Y. Fan, P. A. Thielen, J. E. Rothenberg, and G. D. Goodno, “Diffractive coherent combining of a 2.5 kW fiber laser array into a 1.9 kW Gaussian beam,” Opt. Lett. 37(14), 2832–2834 (2012).
[Crossref] [PubMed]

A. Klenke, S. Breitkopf, M. Kienel, T. Gottschall, T. Eidam, S. Hädrich, J. Rothhardt, J. Limpert, and A. Tünnermann, “530 W, 1.3 mJ, four-channel coherently combined femtosecond fiber chirped-pulse amplification system,” Opt. Lett. 38(13), 2283–2285 (2013).
[Crossref] [PubMed]

Y. Zaouter, L. Daniault, M. Hanna, D. N. Papadopoulos, F. Morin, C. Hönninger, F. Druon, E. Mottay, and P. Georges, “Passive coherent combination of two ultrafast rod type fiber chirped pulse amplifiers,” Opt. Lett. 37(9), 1460–1462 (2012).
[Crossref] [PubMed]

H. Liu, B. He, J. Zhou, J. Dong, Y. Wei, and Q. Lou, “Coherent beam combination of two nanosecond fiber amplifiers by an all-optical feedback loop,” Opt. Lett. 37(18), 3885–3887 (2012).
[Crossref] [PubMed]

J. Lhermite, A. Desfarges-Berthelemot, V. Kermene, and A. Barthelemy, “Passive phase locking of an array of four fiber amplifiers by an all-optical feedback loop,” Opt. Lett. 32(13), 1842–1844 (2007).
[Crossref] [PubMed]

P. C. Shardlow and M. J. Damzen, “Phase conjugate self-organized coherent beam combination: a passive technique for laser power scaling,” Opt. Lett. 35(7), 1082–1084 (2010).
[Crossref] [PubMed]

M. Zhang, E. J. R. Kelleher, A. S. Pozharov, E. D. Obraztsova, S. V. Popov, and J. R. Taylor, “Passive synchronization of all-fiber lasers through a common saturable absorber,” Opt. Lett. 36(20), 3984–3986 (2011).
[Crossref] [PubMed]

L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5 μm fiber amplifiers in a long-pulse regime,” Opt. Lett. 36(4), 523–525 (2011).
[Crossref] [PubMed]

C. X. Yu, S. J. Augst, S. M. Redmond, K. C. Goldizen, D. V. Murphy, A. Sanchez, and T. Y. Fan, “Coherent combining of a 4 kW, eight-element fiber amplifier array,” Opt. Lett. 36(14), 2686–2688 (2011).
[Crossref] [PubMed]

Y. Ma, X. Wang, J. Leng, H. Xiao, X. Dong, J. Zhu, W. Du, P. Zhou, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination of 1.08 kW fiber amplifier array using single frequency dithering technique,” Opt. Lett. 36(6), 951–953 (2011).
[Crossref] [PubMed]

X. L. Wang, P. Zhou, Y. X. Ma, J. Y. Leng, X. J. Xu, and Z. J. Liu, “Active phasing a nine-element 1.14 kW all-fiber two-tone MOPA array using SPGD algorithm,” Opt. Lett. 36(16), 3121–3123 (2011).
[Crossref] [PubMed]

Other (2)

A. Brignon edited, Coherent Laser Beam Combining (Wiley, 2013).

R. Tao, X. Wang, P. Zhou, L. Si, and Z. Liu, “Widely tunable mode-locked all-fiberized Yb-doped fiber laser with near-transform-limited spectrum linewidth,” Appl. Phys. B, doi: (2013).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 Polarization state of the combined beam for (a) without phasing and (b) phase locked.
Fig. 2
Fig. 2 Experimental configuration of the four-channel CPBC system. P-A: pre-amplifier; C1-C4: isolator-embedded collimators; HWP: half wavelength plate; M1-M4: all-reflectance mirrors; M5: high- reflectance mirror (99.9:0.1); M6: 96:4 splitter; PBC1-PBC3: polarization beam combiners; P: linear polarizer; DP1-DP2: dark ports; PD-photo-detector.
Fig. 3
Fig. 3 The time-dependent phasing process along with time and the spectral density of power of phase noise in open loop and closed loop. (a) Time series signals. (b) Spectral density.
Fig. 4
Fig. 4 The combined intensity profiles of the system in the circumstance of without phasing ((a)-(d)), with phasing at maximum state (e), and with phasing at minimum state (f).
Fig. 5
Fig. 5 Measured pulse shapes with (a) a single channel and combined beam in one cycle, and (b) combined beam in 6 cycles.
Fig. 6
Fig. 6 (a) The beam quality (M2 factor) of the coherently combined beam and (b) the spectrum of the coherently polarization combined beam at 12 W power-level and 88 W power-level.
Fig. 7
Fig. 7 The comparison results of combining efficiency between the picosecond-pulsed system and the single frequency CW system.

Equations (3)

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η= P p1 P p1 + P p2 + P DP1 + P DP2
P peak = 2 ln2 π P ave τf
Δη= 1 2 1 2 ( 4 P 1 P 2 cos 2 δ+ ( P 1 P 2 ) 2 + 4 P 3 P 4 cos 2 δ+ ( P 3 P 4 ) 2 ) j=1 4 P j

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