- Email: [email protected]
Coherent beam combination of two thulium-doped fiber laser beams with the multi-ditheringtechnique
Optics & Laser Technology 43 (2011) 721–724
Contents lists available at ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Coherent beam combination of two thulium-doped fiber laser beams with the multi-dithering technique Yanxing Ma, Pu Zhou, Xiaolin Wang, Kai Han, Haotong Ma, Xiaojun Xu, Lei Si, Zejin Liu n, Yijun Zhao College of Opticelectric Science and Engineering, National University of Defense Technology, Changsha 410073, China
a r t i c l e in fo
abstract
Article history: Received 12 July 2010 Received in revised form 26 September 2010 Accepted 29 September 2010 Available online 16 October 2010
Coherent beam combination of two thulium-doped fiber laser beams using a multi-dithering technique is presented for the first time. In the experiment, two fiber lasers centered at 1948.6 nm are coherently combined, and a phase modulator based on piezoelectric ceramics transducer is connected in one beam path to compensate for the phase errors between the two beams. When the phase control system is closed loop, the fringe contrast of the far-field intensity pattern is improved to be more than 75%, from 15% in open-loop, and the residual phase error is less than l/20. The experimental results show that the performance of the phase control system is robust and the control bandwidth is more than 1 kHz, which indicates that the above approach can be scaled to facilitate the coherent beam combination of kilo-watt level thulium-doped fiber laser. & 2010 Elsevier Ltd. All rights reserved.
Keywords: Fiber laser Coherent beam combination Multi-dithering technique
High power fiber lasers, particularly Yb-doped fiber lasers centered at 1 mm, have been widely utilized in scientific research and in industrial and martial applications. At present, the maximum output power of a single-mode Yb-doped fiber laser is about 10 kW [1], and that from a multi-mode one is more than 50 kW [2]. Compared with 1 mm fiber laser, the output power of 2 mm fiber laser is lower and the maximum output power is about 1 kW [3]. Nevertheless, due to the rapid development of highbrightness fiber-coupled pump diodes at 790–800 nm and Tm-doped and Ho-doped fibers, the speed of power scaling of 2 mm fiber lasers exceeds Er-fiber or Yb-fiber three-fold [4]. In addition, 2 mm fiber laser has many other advantages [5–10]. Firstly, 2 mm lasers fall into the eye-safe catergory can be used in the medical treatment. Secondly, the permissible power of 2 mm laser transmission in free space can be several orders of magnitude greater than at 1 mm. Thirdly, the power scaling capability of 2 mm fiber lasers is better than their 1 mm counterpart due to higher stimulated Brillouin scattering threshold induced by the longer wavelength [7,10]. Additionally, 2 mm lasers can provide an excellent starting point for nonlinear frequency conversion to the mid-infrared spectral region [8]. The development of 2 mm fiber lasers is gaining momentum. Further increase in the output power of 2 mm fiber lasers will be limited by nonlinear effects, thermal loading and fiber damage. Coherent beam combination (CBC) with active phase-locking is a promising approach to solve this problem. Active phase-locking
n
Corresponding author. E-mail address: [email protected] (Z. Liu).
0030-3992/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2010.09.015
has been successfully used in coherent beam combination of a 1 mm fiber laser array. Anderegg et al. [11] reported 470 W output power from a four-element fiber array with heterodyne detection in 2006, and Shay et al. [12] reported 725 W output power from a five-element array using a multi-dithering technique in 2009, but as far as we know, coherent beam combination of 2 mm fiber laser arrays with active phase-locking has not been reported up to now. The reason can be attributed to the fact that the passive components, i.e., fiber-pigtailed frequency shifter, fiber-coupled electro-optical phase modulator, which are often used in previous coherent beam combination schemes, are not readily available in 2 mm band. The multi-dithering technique is a promising approach for the coherent beam combination of 2 mm fiber lasers due to free of frequency shifters, besides, this technique is robust [12–14] and the requirement of the performance of phase modulator is relatively low, such that a passive fiber wrapped around a cylindrical piezoelectric ceramic transducer (PZT) could be a good replacement for an electro-optical phase modulator. In this manuscript, we report the active phase-locking of Tm-doped fiber lasers based on the multi-dithering technique. To the best of our knowledge, this is the first demonstration of coherent beam combination using active phase-locking of fiber lasers in midinfrared band. The scheme of the experiment is shown in Fig. 1. The beam from the thulium-doped fiber laser is split into two beams and one beam is coupled into the phase modulator and then sent into free-space via a collimator. Another beam is directly coupled to a collimator. The radius of the collimator is 2 mm, the radius of laser beam from collimator is about 1 mm, and the distance
722
Y. Ma et al. / Optics & Laser Technology 43 (2011) 721–724
Thulium fiber laser
Splitter
Collimator
Sampler Lens
CCD
Lens
Phase Modulator
Pinhole Photodetector
Near Field Beam 2mm 6mm
Oscilloscope
Signal Processing
Fig. 1. Scheme of coherent beam combination of two thulium-doped lasers with multi-dithering technique.
Fig. 2. Spectrum of the thulium-doped fiber laser.
between the two collimators is about 6 mm (as an inset shown in Fig. 1). The output beams from collimators travel 3 m and are sampled by a cubic beam splitter. After the splitter, a part of the combined beam is sent to a focusing lens with 1 m focal length that images the central lobe of the far-field onto a home-made pinhole with 50 mm radius. A PDA10CS amplified photodetector (THORLABS) is located immediately behind the pinhole. The wavelength range of the photodetector, indicated in the operating manual, is from 700 to 1800 nm, but it still can be used detect radiation in the 2 mm band laser. The output from the photodetector is used to produce the phase control signal in the signal processor based on a field programmable gate array (FPGA) where the multi-dithering algorithm is implemented. Another part of the combined beam after the splitter is also focused by a lens onto a infrared CCD camera, and is used to diagnose the farfield beam profile of the combined beam. 20 mW thulium-doped fiber laser with a 1948.6 nm center wavelength is an all-fiber configuration pumped by 1580 nm Er-fiber laser. Its optical spectrum is shown in Fig. 2. The output power of the Tm-doped fiber laser is not high, but the motivation of this manuscript is to demonstrate the validity of scaling coherent beam combination using the multi-dithering technique to the midinfrared laser band and tom show that the laser power can be
boosted by incorporating Tm-doped fiber amplifiers in each fiber channel [8,15]. The phase modulator is shown in Fig. 3. Optical fiber is wrapped around a PZT cylinder with 14 mm diameter and 15 mm height. The first resonance frequency of the phase modulator is about 70 kHz and the half-wave voltage far from the resonance frequency is about 2.5 V. It is to be noted that the stability of halfwave voltage is constant with increase in modulation frequency. Nevertheless, due to the robust performance of the multi-dithering technique, it is found that stable coherent beam combination can be achieved. In the experiment, a 60 kHz, 0.2 V sine-wave phase modulation signal is applied to the phase modulator. When the control system is open-loop, the multi-dithering technique is not performed and the phases of beams randomly fluctuate due thermal gardients and mechanical vibrations. The power encircled in the targetpinhole fluctuates and the intensity pattern at the observing plane keeps shifting. The long-exposure far-field intensity distribution is shown in Fig. 3(a), and its fringe contrast is calculated to be less than 15%, where the fringe contrast is defined by the formula (Imax Imin)/(Imax + Imin), where Imax and Imin are the maximum optical intensity and the adjacent minimum on the intensity pattern, respectively. When the control system is close-loop, the phase controlling algorithm is implemented and the phase
Y. Ma et al. / Optics & Laser Technology 43 (2011) 721–724
modulation and control signal are added to the modulator, and the phase noises are compensated efficiently. The intensity pattern at the observing plane is clear and steady and the long-exposure
Fig. 3. PZT phase modulator.
723
far-field intensity distribution is shown in Fig. 4(b) and its fringe contrast is calculated to be more than 75%. The fidelity of coherent beam combination and the phase fluctuation suppression can be further studied using the time series signals and the spectral density of energy encircled in the pinhole shown in Fig. 5. When the control loop is open, the normalized energy encircled in the pinhole fluctuates between 0 and 1 randomly. When the control loop is closed, the energy encircled in the pinhole can be locked steadily to be more than 0.9 for most of the time and the residual phase error is less than l/20 (shown in Fig. 5(a)), and the spectral density lowers by about 10 dB than in open-loop below 100 Hz (shown in Fig. 5(b)), which denotes a large increase in energy encircled in the main lobe. Phase fluctuations less than l/20 are not compensated because they go below the noise floor of the phase control system. It is to be noted that about 1 kHz phase noises in open-loop have been also effectively compensated (encircled by the black ellipse in Fig. 5(b)), which indicates that the bandwidth of the phase control system is more than 1 kHz. The measured phase fluctuation frequency of a thulium-doped fiber amplifier at 608 W output power in a relatively quiet lab environment is well below 1 kHz [15]. Thus it can be concluded that coherent beam combination of thulium-doped fiber lasers can be straightforwardly scaled to kW level using the multi-dithering technique. In summary, we present coherent beam combination of two thulium-doped fiber lasers with the multi-dithering technique. The fringe contrast of the long-exposure coherent combined beam profile is improved to 75% in close-loop from 15% in open-loop.
Fig. 4. Long-exposure far-field intensity pattern of the combined laser beam (a) open-loop (b) close-loop.
Fig. 5. Time series signals of energy encircled in the pinhole in open-loop and close-loop (a) time series signals (b) spectral density.
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Y. Ma et al. / Optics & Laser Technology 43 (2011) 721–724
It is found that the PZT phase modulator can be easily utilized in coherent beam combination of any wavelength lasers with the multi-dithering technique if only the relevant fiber is available. Finally, the robust performance of coherent beam combination based on the multi-dithering technique is demonstrated again. References [1] IPG photonics successfully tests world’s first 10 kW single-mode production laser, available on /www.ipgphotonics.com/Collateral/Documents/English-US/ PR_Final_10kW_SM_laser.pdfS. [2] YLR-HP Series: 1–50 kW ytterbium fiber lasers, available on /http://www. ipgphotonics.com/products_1micron_lasers_cw_ylr-hpseries.htmS. [3] Ehrenreich T, Leveille R, Majid I, Tankala K, 1 kW, all-glass Tm:fiber laser, SPIE Photonics West 2010: LASE Fiber Lasers VII: Technology, System and Applicaitons, available on /http://www.qpeak.comS. [4] Christensen.S, Frith.G, Samson.B, Developments in thulium-doped fiber lasers offer higher power, Newsroom of SPIE, available on /http://www.nufern. comS. [5] Geng J, Wang Q, Luo T, Jiang S, Amzajerdian F. Single-frequency narrowlinewidth Tm-doped fiber laser using silicate glass fiber. Opt Lett 2009;34: 3493–95.
[6] Wang Q, Geng J, Luo T, Jiang S. Mode-locked 2 mm laser with highly thuliumdoped silicate fiber. Opt Lett 2009;34:3616–18. [7] Moulton P.F., Power scaling of high-efficiency, Tm-doped fiber lasers. In: Proceedings of the SPRC 2008 annual symposium, available on /http://www. qpeak.comS. [8] Pearson L, Kim JW, Zhang Z, Ibsen M, Sahu JK, Clarkson WA. High-power linearly-polarized single-frequency thulium-doped fiber master-oscillator power-amplifier. Opt Express 2010;18:1607–12. [9] Dergachev A, Armstrong D, Smith A, Drake T, Dubois M. 3.4 mm ZGP RISTRA nanosecond optical parametric oscillator pumped by a 2.05 mm Ho: YLF MOPA system. Opt Express 2007;15:14404–13. [10] Kurkov AS, Dvoyrin VV, Marakulin AV. All-fiber 10 W holmium lasers pumped at l 1.15 mm. Opt Lett 2010;35:490–2. [11] Anderegg J, Brosnan S, Cheung E, Epp P, Hammons D, Komine H, et al. Coherently coupled high power fiber arrays. Proc SPIE 2006;6102. 6102U-1–5. [12] Shay TM, Baker JT, Sanchez AD, Robin CA, Vergien CL, Zeringue C, et al. High power phase locking of a fiber amplifier array. Proc SPIE 2009;7195. 71951M-1–8. [13] Shay TM. Theory of electronically phased coherent beam combination without a reference beam. Opt Express 2006;14:12188–95. [14] Shay TM, Benham V, Baker JT, Ward CB, Sanchez AD, Culpepper MA, et al. First experimental demonstration of self-synchronous phase locking of an optical array. Opt Express 2006;14:12015–21. [15] Goodno GD, Book LD, Rothenberg JE. Low-phase-noise, single-frequency, single-mode 608 W thulium fiber amplifier. Opt Lett 2009;34:1204–6.
Contents lists available at ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Coherent beam combination of two thulium-doped fiber laser beams with the multi-dithering technique Yanxing Ma, Pu Zhou, Xiaolin Wang, Kai Han, Haotong Ma, Xiaojun Xu, Lei Si, Zejin Liu n, Yijun Zhao College of Opticelectric Science and Engineering, National University of Defense Technology, Changsha 410073, China
a r t i c l e in fo
abstract
Article history: Received 12 July 2010 Received in revised form 26 September 2010 Accepted 29 September 2010 Available online 16 October 2010
Coherent beam combination of two thulium-doped fiber laser beams using a multi-dithering technique is presented for the first time. In the experiment, two fiber lasers centered at 1948.6 nm are coherently combined, and a phase modulator based on piezoelectric ceramics transducer is connected in one beam path to compensate for the phase errors between the two beams. When the phase control system is closed loop, the fringe contrast of the far-field intensity pattern is improved to be more than 75%, from 15% in open-loop, and the residual phase error is less than l/20. The experimental results show that the performance of the phase control system is robust and the control bandwidth is more than 1 kHz, which indicates that the above approach can be scaled to facilitate the coherent beam combination of kilo-watt level thulium-doped fiber laser. & 2010 Elsevier Ltd. All rights reserved.
Keywords: Fiber laser Coherent beam combination Multi-dithering technique
High power fiber lasers, particularly Yb-doped fiber lasers centered at 1 mm, have been widely utilized in scientific research and in industrial and martial applications. At present, the maximum output power of a single-mode Yb-doped fiber laser is about 10 kW [1], and that from a multi-mode one is more than 50 kW [2]. Compared with 1 mm fiber laser, the output power of 2 mm fiber laser is lower and the maximum output power is about 1 kW [3]. Nevertheless, due to the rapid development of highbrightness fiber-coupled pump diodes at 790–800 nm and Tm-doped and Ho-doped fibers, the speed of power scaling of 2 mm fiber lasers exceeds Er-fiber or Yb-fiber three-fold [4]. In addition, 2 mm fiber laser has many other advantages [5–10]. Firstly, 2 mm lasers fall into the eye-safe catergory can be used in the medical treatment. Secondly, the permissible power of 2 mm laser transmission in free space can be several orders of magnitude greater than at 1 mm. Thirdly, the power scaling capability of 2 mm fiber lasers is better than their 1 mm counterpart due to higher stimulated Brillouin scattering threshold induced by the longer wavelength [7,10]. Additionally, 2 mm lasers can provide an excellent starting point for nonlinear frequency conversion to the mid-infrared spectral region [8]. The development of 2 mm fiber lasers is gaining momentum. Further increase in the output power of 2 mm fiber lasers will be limited by nonlinear effects, thermal loading and fiber damage. Coherent beam combination (CBC) with active phase-locking is a promising approach to solve this problem. Active phase-locking
n
Corresponding author. E-mail address: [email protected] (Z. Liu).
0030-3992/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2010.09.015
has been successfully used in coherent beam combination of a 1 mm fiber laser array. Anderegg et al. [11] reported 470 W output power from a four-element fiber array with heterodyne detection in 2006, and Shay et al. [12] reported 725 W output power from a five-element array using a multi-dithering technique in 2009, but as far as we know, coherent beam combination of 2 mm fiber laser arrays with active phase-locking has not been reported up to now. The reason can be attributed to the fact that the passive components, i.e., fiber-pigtailed frequency shifter, fiber-coupled electro-optical phase modulator, which are often used in previous coherent beam combination schemes, are not readily available in 2 mm band. The multi-dithering technique is a promising approach for the coherent beam combination of 2 mm fiber lasers due to free of frequency shifters, besides, this technique is robust [12–14] and the requirement of the performance of phase modulator is relatively low, such that a passive fiber wrapped around a cylindrical piezoelectric ceramic transducer (PZT) could be a good replacement for an electro-optical phase modulator. In this manuscript, we report the active phase-locking of Tm-doped fiber lasers based on the multi-dithering technique. To the best of our knowledge, this is the first demonstration of coherent beam combination using active phase-locking of fiber lasers in midinfrared band. The scheme of the experiment is shown in Fig. 1. The beam from the thulium-doped fiber laser is split into two beams and one beam is coupled into the phase modulator and then sent into free-space via a collimator. Another beam is directly coupled to a collimator. The radius of the collimator is 2 mm, the radius of laser beam from collimator is about 1 mm, and the distance
722
Y. Ma et al. / Optics & Laser Technology 43 (2011) 721–724
Thulium fiber laser
Splitter
Collimator
Sampler Lens
CCD
Lens
Phase Modulator
Pinhole Photodetector
Near Field Beam 2mm 6mm
Oscilloscope
Signal Processing
Fig. 1. Scheme of coherent beam combination of two thulium-doped lasers with multi-dithering technique.
Fig. 2. Spectrum of the thulium-doped fiber laser.
between the two collimators is about 6 mm (as an inset shown in Fig. 1). The output beams from collimators travel 3 m and are sampled by a cubic beam splitter. After the splitter, a part of the combined beam is sent to a focusing lens with 1 m focal length that images the central lobe of the far-field onto a home-made pinhole with 50 mm radius. A PDA10CS amplified photodetector (THORLABS) is located immediately behind the pinhole. The wavelength range of the photodetector, indicated in the operating manual, is from 700 to 1800 nm, but it still can be used detect radiation in the 2 mm band laser. The output from the photodetector is used to produce the phase control signal in the signal processor based on a field programmable gate array (FPGA) where the multi-dithering algorithm is implemented. Another part of the combined beam after the splitter is also focused by a lens onto a infrared CCD camera, and is used to diagnose the farfield beam profile of the combined beam. 20 mW thulium-doped fiber laser with a 1948.6 nm center wavelength is an all-fiber configuration pumped by 1580 nm Er-fiber laser. Its optical spectrum is shown in Fig. 2. The output power of the Tm-doped fiber laser is not high, but the motivation of this manuscript is to demonstrate the validity of scaling coherent beam combination using the multi-dithering technique to the midinfrared laser band and tom show that the laser power can be
boosted by incorporating Tm-doped fiber amplifiers in each fiber channel [8,15]. The phase modulator is shown in Fig. 3. Optical fiber is wrapped around a PZT cylinder with 14 mm diameter and 15 mm height. The first resonance frequency of the phase modulator is about 70 kHz and the half-wave voltage far from the resonance frequency is about 2.5 V. It is to be noted that the stability of halfwave voltage is constant with increase in modulation frequency. Nevertheless, due to the robust performance of the multi-dithering technique, it is found that stable coherent beam combination can be achieved. In the experiment, a 60 kHz, 0.2 V sine-wave phase modulation signal is applied to the phase modulator. When the control system is open-loop, the multi-dithering technique is not performed and the phases of beams randomly fluctuate due thermal gardients and mechanical vibrations. The power encircled in the targetpinhole fluctuates and the intensity pattern at the observing plane keeps shifting. The long-exposure far-field intensity distribution is shown in Fig. 3(a), and its fringe contrast is calculated to be less than 15%, where the fringe contrast is defined by the formula (Imax Imin)/(Imax + Imin), where Imax and Imin are the maximum optical intensity and the adjacent minimum on the intensity pattern, respectively. When the control system is close-loop, the phase controlling algorithm is implemented and the phase
Y. Ma et al. / Optics & Laser Technology 43 (2011) 721–724
modulation and control signal are added to the modulator, and the phase noises are compensated efficiently. The intensity pattern at the observing plane is clear and steady and the long-exposure
Fig. 3. PZT phase modulator.
723
far-field intensity distribution is shown in Fig. 4(b) and its fringe contrast is calculated to be more than 75%. The fidelity of coherent beam combination and the phase fluctuation suppression can be further studied using the time series signals and the spectral density of energy encircled in the pinhole shown in Fig. 5. When the control loop is open, the normalized energy encircled in the pinhole fluctuates between 0 and 1 randomly. When the control loop is closed, the energy encircled in the pinhole can be locked steadily to be more than 0.9 for most of the time and the residual phase error is less than l/20 (shown in Fig. 5(a)), and the spectral density lowers by about 10 dB than in open-loop below 100 Hz (shown in Fig. 5(b)), which denotes a large increase in energy encircled in the main lobe. Phase fluctuations less than l/20 are not compensated because they go below the noise floor of the phase control system. It is to be noted that about 1 kHz phase noises in open-loop have been also effectively compensated (encircled by the black ellipse in Fig. 5(b)), which indicates that the bandwidth of the phase control system is more than 1 kHz. The measured phase fluctuation frequency of a thulium-doped fiber amplifier at 608 W output power in a relatively quiet lab environment is well below 1 kHz [15]. Thus it can be concluded that coherent beam combination of thulium-doped fiber lasers can be straightforwardly scaled to kW level using the multi-dithering technique. In summary, we present coherent beam combination of two thulium-doped fiber lasers with the multi-dithering technique. The fringe contrast of the long-exposure coherent combined beam profile is improved to 75% in close-loop from 15% in open-loop.
Fig. 4. Long-exposure far-field intensity pattern of the combined laser beam (a) open-loop (b) close-loop.
Fig. 5. Time series signals of energy encircled in the pinhole in open-loop and close-loop (a) time series signals (b) spectral density.
724
Y. Ma et al. / Optics & Laser Technology 43 (2011) 721–724
It is found that the PZT phase modulator can be easily utilized in coherent beam combination of any wavelength lasers with the multi-dithering technique if only the relevant fiber is available. Finally, the robust performance of coherent beam combination based on the multi-dithering technique is demonstrated again. References [1] IPG photonics successfully tests world’s first 10 kW single-mode production laser, available on /www.ipgphotonics.com/Collateral/Documents/English-US/ PR_Final_10kW_SM_laser.pdfS. [2] YLR-HP Series: 1–50 kW ytterbium fiber lasers, available on /http://www. ipgphotonics.com/products_1micron_lasers_cw_ylr-hpseries.htmS. [3] Ehrenreich T, Leveille R, Majid I, Tankala K, 1 kW, all-glass Tm:fiber laser, SPIE Photonics West 2010: LASE Fiber Lasers VII: Technology, System and Applicaitons, available on /http://www.qpeak.comS. [4] Christensen.S, Frith.G, Samson.B, Developments in thulium-doped fiber lasers offer higher power, Newsroom of SPIE, available on /http://www.nufern. comS. [5] Geng J, Wang Q, Luo T, Jiang S, Amzajerdian F. Single-frequency narrowlinewidth Tm-doped fiber laser using silicate glass fiber. Opt Lett 2009;34: 3493–95.
[6] Wang Q, Geng J, Luo T, Jiang S. Mode-locked 2 mm laser with highly thuliumdoped silicate fiber. Opt Lett 2009;34:3616–18. [7] Moulton P.F., Power scaling of high-efficiency, Tm-doped fiber lasers. In: Proceedings of the SPRC 2008 annual symposium, available on /http://www. qpeak.comS. [8] Pearson L, Kim JW, Zhang Z, Ibsen M, Sahu JK, Clarkson WA. High-power linearly-polarized single-frequency thulium-doped fiber master-oscillator power-amplifier. Opt Express 2010;18:1607–12. [9] Dergachev A, Armstrong D, Smith A, Drake T, Dubois M. 3.4 mm ZGP RISTRA nanosecond optical parametric oscillator pumped by a 2.05 mm Ho: YLF MOPA system. Opt Express 2007;15:14404–13. [10] Kurkov AS, Dvoyrin VV, Marakulin AV. All-fiber 10 W holmium lasers pumped at l 1.15 mm. Opt Lett 2010;35:490–2. [11] Anderegg J, Brosnan S, Cheung E, Epp P, Hammons D, Komine H, et al. Coherently coupled high power fiber arrays. Proc SPIE 2006;6102. 6102U-1–5. [12] Shay TM, Baker JT, Sanchez AD, Robin CA, Vergien CL, Zeringue C, et al. High power phase locking of a fiber amplifier array. Proc SPIE 2009;7195. 71951M-1–8. [13] Shay TM. Theory of electronically phased coherent beam combination without a reference beam. Opt Express 2006;14:12188–95. [14] Shay TM, Benham V, Baker JT, Ward CB, Sanchez AD, Culpepper MA, et al. First experimental demonstration of self-synchronous phase locking of an optical array. Opt Express 2006;14:12015–21. [15] Goodno GD, Book LD, Rothenberg JE. Low-phase-noise, single-frequency, single-mode 608 W thulium fiber amplifier. Opt Lett 2009;34:1204–6.