# Towards Ultimate High-Power Scaling: Coherent Beam Combining of Fiber Lasers

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## Abstract

**:**

## 1. Introduction

#### 1.1. Power Scaling Limitations of Fiber Lasers and Amplifiers

#### 1.1.1. Nonlinear Effects (NLEs)

- Stimulated Raman Scattering effect

^{−13}m/W, which is nearly three orders of magnitude smaller than the Brillouin gain coefficient discussed next. Therefore, SRS is more prominent in pulsed systems, however, can also occur in kW-level CW systems.

- Stimulated Brillouin Scattering effect:

^{−11}m/W and it has the lowest power threshold among the NLEs in single-frequency CW fiber amplifiers. The main approach to mitigating the SBS is broadening the spectral linewidth via external phase modulation [34,35]. To realize the SBS suppression, the change in phase modulation should be less than the phonon lifetime. This is also why SBS does not typically occur for pulsed systems with pulse durations below the ~10 ns phonon lifetime. Numerous theoretical and experimental studies on mitigating the SBS effect in fiber lasers and amplifiers has been conducted to prevent instability and physical damage to the laser system [36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53]. As a case in point, in 2020, Wang et al. demonstrated a 2.5 kW narrow linewidth linearly polarized MOPA by efficient suppressing of SBS-induced self-pulsing (SP) via implementing cascade phase modulation [54]. In the same year, they presented the first 3 kW all-fiber narrow linewidth linearly polarized MOPA via a bi-directional pumping scheme [55]. In the case of non-polarized MOPA, in 2019, a 3.7 kW monolithic narrow-linewidth single-mode fiber amplifier was reported by suppressing the NLEs [56].

- Self-phase modulation effect

- Self-focusing effect

- Four-wave mixing effect

- Transverse mode instability effect

#### 1.1.2. Thermal Issues

#### 1.1.3. Optical Damage

#### 1.1.4. Pumping Limitations

^{2}factor of ∼1.3 [11], and 10.6 kW with the beam quality M

^{2}factor of ∼2 [85]. Even if the technical challenges for fabricating high-power YDFLs could be overcome, the highest theoretical achievable output power through diode pumping is calculated as 28–38 kW via a diode pumping scheme [20]. Therefore the need for new power-scaling approaches beyond the fundamental limitation has been recognized and is an active field of research.

#### 1.2. Methods for Power Scaling

#### 1.2.1. Tandem Pumping

#### 1.2.2. Beam Combining

## 2. Incoherent Beam Combining

#### 2.1. Side-by-Side Beam Combining

#### 2.2. Passive Components

#### 2.3. Spectral Beam Combining (SBC)

## 3. Coherent Beam Combining (CBC)

^{2}factor) of the output laser beam. Combining efficiency is typically calculated by dividing the power of the combined beam by the sum of the output power of amplified laser beams. However, for CBC systems, two key metrics are employed for assessing the function of CBC, which are brightness (B) and Strehl ratio (S). The brightness of each optical beam, which considers the output power and the quality of the beam (${M}^{2}\mathrm{factor}$), can be defined as:

#### 3.1. The Geometry of Combining/Splitting in Space and Time

#### 3.1.1. Tiled Aperture (TA)

- Multicore fibers and photonic crystal fibers (MCFs and MC-PCFs);

#### 3.1.2. Filled Aperture (FA)

- Polarization beam combiners and thin-film polarizer

- Intensity beam combiners

- Diffractive optical elements

- Segment mirrors (SM)

#### 3.1.3. Mixed Aperture (MA)

#### 3.2. Laser Sources and Amplifiers

#### 3.2.1. Seed Lasers

#### 3.2.2. Laser Amplifiers

- Large mode area (LMA) fibers

- Photonic crystal fibers (PCFs)

- Taper double-clad fibers (T-DCF)

#### 3.3. Phase-Locking Systems

#### 3.3.1. Passive Phase Control

- Common resonator

- Optical phase conjugate

- Evanescent (leaky) wave coupling

- Self-organized

#### 3.3.2. Active Phase Control

- Hansch–Couillaud (HC) polarization detection

- Hill Climbing

- Optical Heterodyne Detection (OHD)

- Frequency dithering

- Collective phase-intensity technique

- Collective phase measurement technique

- 2.
- Phase-intensity mapping (PIM)

#### 3.4. Optical Path Difference Control

#### 3.5. Channel Scaling

## 4. Coherent Beam Combining of Ultrafast Fiber Lasers

#### 4.1. Spatial CBC

#### 4.2. Temporal CBC

#### 4.3. Multidimensional (Spatial + Temporal) CBC

#### 4.4. Spectral CBC (Spectral Pulse Synthesis)

## 5. Coherent Beam Combining of CW Fiber Lasers

#### 5.1. Tiled Aperture

- Directed-energy applications

- Power scaling

#### 5.2. Filled Aperture

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Zervas, M.N.; Codemard, C.A. High Power Fiber Lasers: A Review. IEEE J. Sel. Top. Quantum Electron.
**2014**, 20, 219–241. [Google Scholar] [CrossRef] - Moulton, P.F.; Rines, G.A.; Slobodtchikov, E.V.; Wall, K.F.; Frith, G.; Samson, B.; Carter, A.L.G. Tm-Doped Fiber Lasers: Fundamentals and Power Scaling. IEEE J. Sel. Top. Quantum Electron.
**2009**, 15, 85–92. [Google Scholar] [CrossRef] - Richardson, D.J.; Nilsson, J.; Clarkson, W.A. High power fiber lasers: Current status and future perspectives [Invited]. J. Opt. Soc. Am. B
**2010**, 27, B63. [Google Scholar] [CrossRef] - Jauregui, C.; Limpert, J.; Tünnermann, A. High-power fibre lasers. Nat. Photonics
**2013**, 7, 861–867. [Google Scholar] [CrossRef] - Fang, Q.; Li, J.; Shi, W.; Qin, Y.; Xu, Y.; Meng, X.; Norwood, R.A.; Peyghambarian, N. 5 kW near-Diffraction-limited and 8 kW High-Brightness Monolithic Continuous Wave Fiber lasers Directly Pumped by laser Diodes. IEEE Photonics J.
**2017**, 9, 1–7. [Google Scholar] [CrossRef][Green Version] - Liu, Z.; Jin, X.; Su, R.; Ma, P.; Zhou, P. Development status of high power fiber lasers and their coherent beam combination. Sci. China Inf. Sci.
**2019**, 62, 41301. [Google Scholar] [CrossRef][Green Version] - Chang, G.; Wei, Z. Ultrafast Fiber Lasers: An Expanding Versatile Toolbox. iScience
**2020**, 23, 101101. [Google Scholar] [CrossRef] - Fermann, M.E.; Hartl, I. Ultrafast Fiber Laser Technology. IEEE J. Sel. Top. Quantum Electron.
**2009**, 15, 191–206. [Google Scholar] [CrossRef] - Lim, J.J.; Sujecki, S.; Lang, L.; Zhang, Z.; Paboeuf, D.; Pauliat, G.; Lucas-Leclin, G.; Georges, P.; MacKenzie, R.; Bream, P.; et al. Design and Simulation of Next-Generation High-Power, High-Brightness Laser Diodes. IEEE J. Sel. Top. Quantum Electron.
**2009**, 15, 993–1008. [Google Scholar] [CrossRef][Green Version] - Snitzer, E.; Po, H.; Hakimi, F.; Tumminelli, R.; McCollum, B.C. Double Clad, Offset Core Nd Fiber Laser. In Proceedings of the Optical Fiber Sensors, OSA, New Orleans, LO, USA, 27 January 1988; p. PD5. [Google Scholar]
- Yang, B.; Wang, P.; Zhang, H.; Xi, X.; Shi, C.; Wang, X.; Xu, X. 6 kW single mode monolithic fiber laser enabled by effective mitigation of the transverse mode instability. Opt. Express
**2021**, 29, 26366. [Google Scholar] [CrossRef] - Shcherbakov, E.A.; Fomin, V.V.; Abramov, A.A.; Ferin, A.A.; Mochalov, D.V.; Gapontsev, V.P. Industrial Grade 100 kW Power CW Fiber Laser. In Proceedings of the Advanced Solid-State Lasers Congress, OSA, Paris, France, 27 October–1 November 2013; Volume 5, p. ATh4A.2. [Google Scholar]
- Shiner, B. The Impact of Fiber Laser Technology on the World Wide Material Processing Market. In Proceedings of the CLEO, OSA, San Jose, CA, USA, 9–14 June 2013; p. AF2J.1. [Google Scholar]
- Strickland, D.; Mourou, G. Compression of amplified chirped optical pulses. Opt. Commun.
**1985**, 56, 219–221. [Google Scholar] [CrossRef] - Eidam, T.; Hanf, S.; Seise, E.; Andersen, T.V.; Gabler, T.; Wirth, C.; Schreiber, T.; Limpert, J.; Tünnermann, A. Femtosecond fiber CPA system emitting 830 W average output power. Opt. Lett.
**2010**, 35, 94. [Google Scholar] [CrossRef] - Klenke, A.; Hädrich, S.; Eidam, T.; Rothhardt, J.; Kienel, M.; Demmler, S.; Gottschall, T.; Limpert, J.; Tünnermann, A. 22 GW peak-power fiber chirped-pulse-amplification system. Opt. Lett.
**2014**, 39, 6875. [Google Scholar] [CrossRef] - Dawson, J.W.; Messerly, M.J.; Beach, R.J.; Shverdin, M.Y.; Stappaerts, E.A.; Sridharan, A.K.; Pax, P.H.; Heebner, J.E.; Siders, C.W.; Barty, C.P.J. Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power. Opt. Express
**2008**, 16, 13240. [Google Scholar] [CrossRef] - Zervas, M.N. Power Scaling Limits in High Power Fiber Amplifiers due to Transverse Mode Instability, Thermal Lensing, and Fiber Mechanical Reliability. In Fiber Lasers XV: Technology and Systems; SPIE LASE 10512; SPIE Digital Library: San Francisco, CA, USA, 2018; p. 1051205. [Google Scholar]
- Zhu, J.; Zhou, P.; Ma, Y.; Xu, X.; Liu, Z. Power scaling analysis of tandem-pumped Yb-doped fiber lasers and amplifiers. Opt. Express
**2011**, 19, 18645. [Google Scholar] [CrossRef] - Zervas, M.N. Transverse mode instability, thermal lensing and power scaling in Yb
^{3+}-doped high-power fiber amplifiers. Opt. Express**2019**, 27, 19019. [Google Scholar] [CrossRef] [PubMed] - Agrawal, G. Nonlinear Fiber Optics, 6th ed.; Academic Press: London, UK, 2019; ISBN 9780128170427. [Google Scholar]
- Boyd, R.W. Nonlinear Optics, 4th ed.; Academic Press: Cambrigde, MA, USA, 2020; ISBN 9780128110027. [Google Scholar]
- Jauregui, C.; Stihler, C.; Limpert, J. Transverse mode instability. Adv. Opt. Photonics
**2020**, 12, 429. [Google Scholar] [CrossRef] - Hejaz, K.; Shayganmanesh, M.; Rezaei-Nasirabad, R.; Roohforouz, A.; Azizi, S.; Abedinajafi, A.; Vatani, V. Modal instability induced by stimulated Raman scattering in high-power Yb-doped fiber amplifiers. Opt. Lett.
**2017**, 42, 5274. [Google Scholar] [CrossRef] [PubMed] - Li, Z.; Jing, F.; Li, C.; Liu, Y.; Luo, Q.; Lin, H.; Huang, Z.; Xu, S.; Yang, Z.; Wang, J. Impact of Stimulated Raman Scattering on the Transverse Mode Instability Threshold. IEEE Photonics J.
**2018**, 10, 1–9. [Google Scholar] [CrossRef] - Kim, J.; Dupriez, P.; Codemard, C.; Nilsson, J.; Sahu, J.K. Suppression of stimulated Raman scattering in a high power Yb-doped fiber amplifier using a W-type core with fundamental mode cut-off. Opt. Express
**2006**, 14, 5103. [Google Scholar] [CrossRef] [PubMed] - Jansen, F.; Nodop, D.; Jauregui, C.; Limpert, J.; Tünnermann, A. Modeling the inhibition of stimulated Raman scattering in passive and active fibers by lumped spectral filters in high power fiber laser systems. Opt. Express
**2009**, 17, 16255. [Google Scholar] [CrossRef] [PubMed] - Xu, H.; Jiang, M.; Shi, C.; Zhou, P.; Zhao, G.; Gu, X. Spectral shaping for suppressing stimulated-Raman-scattering in a fiber laser. Appl. Opt.
**2017**, 56, 3538. [Google Scholar] [CrossRef] - Shi, C.; Su, R.T.; Zhang, H.W.; Yang, B.L.; Wang, X.L.; Zhou, P.; Xu, X.J.; Lu, Q.S. Experimental Study of Output Characteristics of Bi-Directional Pumping High Power Fiber Amplifier in Different Pumping Schemes. IEEE Photonics J.
**2017**, 9, 1–10. [Google Scholar] [CrossRef][Green Version] - Zenteno, L.A.; Wang, J.; Walton, D.T.; Ruffin, B.A.; Li, M.J.; Gray, S.; Crowley, A.; Chen, X. Suppression of Raman gain in single-transverse-mode dual-hole-assisted fiber. Opt. Express
**2005**, 13, 8921. [Google Scholar] [CrossRef] - Liu, A.; Chen, X.; Li, M.-J.; Wang, J.; Walton, D.T.; Zenteno, L.A. Suppressing nonlinear effects for power scaling of high power fiber lasers. Passiv Compon. Fiber-Based Devices IV
**2007**, 6781, 67810H. [Google Scholar] [CrossRef] - Li, T.; Ke, W.; Ma, Y.; Sun, Y.; Gao, Q. Suppression of stimulated Raman scattering in a high-power fiber amplifier by inserting long transmission fibers in a seed laser. J. Opt. Soc. Am. B
**2019**, 36, 1457. [Google Scholar] [CrossRef] - Jiao, K.; Shen, H.; Guan, Z.; Yang, F.; Zhu, R. Suppressing stimulated Raman scattering in kW-level continuous-wave MOPA fiber laser based on long-period fiber gratings. Opt. Express
**2020**, 28, 6048. [Google Scholar] [CrossRef] [PubMed] - Hadjifotiou, A.; Hill, G.A. Suppression of stimulated brillouin backscattering by psk modulation for high-power optical transmission. IEE Proc. J Optoelectron.
**1986**, 133, 256. [Google Scholar] [CrossRef] - Willems, F.W.; Muys, W.; Leong, J.S. Simultaneous suppression of stimulated Brillouin scattering and interferometric noise in externally modulated lightwave AM-SCM systems. IEEE Photonics Technol. Lett.
**1994**, 6, 1476–1478. [Google Scholar] [CrossRef] - Broderick, N.G.R.; Offerhaus, H.L.; Richardson, D.J.; Sammut, R.A.; Caplen, J.; Dong, L. Large Mode Area Fibers for High Power Applications. Opt. Fiber Technol.
**1999**, 5, 185–196. [Google Scholar] [CrossRef] - Koyamada, Y.; Sato, S.; Nakamura, S.; Sotobayashi, H.; Chujo, W. Simulating and designing Brillouin gain spectrum in single-mode fibers. J. Light. Technol.
**2004**, 22, 631–639. [Google Scholar] [CrossRef] - Lee, J.; Lee, K.H.; Jeong, H.; Park, M.; Seung, J.H.; Lee, J.H. 2.05 kW all-fiber high-beam-quality fiber amplifier with stimulated Brillouin scattering suppression incorporating a narrow-linewidth fiber-Bragg-grating-stabilized laser diode seed source. Appl. Opt.
**2019**, 58, 6251. [Google Scholar] [CrossRef] [PubMed] - Tian, X.; Zhao, X.; Wang, M.; Wang, Z. Suppression of stimulated Brillouin scattering in optical fibers by tilted fiber Bragg gratings. Opt. Lett.
**2020**, 45, 4802. [Google Scholar] [CrossRef] [PubMed] - Prakash, R.; Vikram, B.S.; Supradeepa, V.R. Polarization Maintaining, Narrow Linewidth Fiber Laser with >1 kW Output Power Using a Novel Dual Sine and Noise Modulation for Enhanced SBS Suppression. In Fiber Lasers XVIII Technology and Systems; Zervas, M.N., Jauregui-Misas, C., Eds.; SPIE: Bellingham, WA, USA, 2021; Volume 11665, p. 3. [Google Scholar]
- Anderson, B.M.; MacDonald, K.; Taliaferro, A.; Flores, A. SBS Suppression Techniques in High-Power, Narrow-Linewidth Fiber Amplifiers. In Fiber Lasers XVIII: Technology and Systems; Zervas, M.N., Jauregui-Misas, C., Eds.; SPIE: Bellingham, WA, USA, 2021; Volume 11665, p. 12. [Google Scholar]
- Zeringue, C.; Dajani, I.; Naderi, S.; Moore, G.T.; Robin, C. A theoretical study of transient stimulated Brillouin scattering in optical fibers seeded with phase-modulated light. Opt. Express
**2012**, 20, 21196. [Google Scholar] [CrossRef] [PubMed] - Flores, A.; Robin, C.; Lanari, A.; Dajani, I. Pseudo-random binary sequence phase modulation for narrow linewidth, kilowatt, monolithic fiber amplifiers. Opt. Express
**2014**, 22, 17735. [Google Scholar] [CrossRef] [PubMed][Green Version] - Yang, Y.; Li, B.; Liu, M.; Huang, X.; Feng, Y.; Cheng, D.; He, B.; Zhou, J.; Nilsson, J. Optimization and visualization of phase modulation with filtered and amplified maximal-length sequence for SBS suppression in a short fiber system: A theoretical treatment. Opt. Express
**2021**, 29, 16781. [Google Scholar] [CrossRef] - Beier, F.; Hupel, C.; Kuhn, S.; Hein, S.; Nold, J.; Proske, F.; Sattler, B.; Liem, A.; Jauregui, C.; Limpert, J.; et al. Single mode 43 kW output power from a diode-pumped Yb-doped fiber amplifier. Opt. Express
**2017**, 25, 14892. [Google Scholar] [CrossRef] - Kobyakov, A.; Kumar, S.; Chowdhury, D.Q.; Ruffin, A.B.; Sauer, M.; Bickham, S.R.; Mishra, R. Design concept for optical fibers with enhanced SBS threshold. Opt. Express
**2005**, 13, 5338. [Google Scholar] [CrossRef] - Ruffin, A.B.; Li, M.-J.; Chen, X.; Kobyakov, A.; Annunziata, F. Brillouin gain analysis for fibers with different refractive indices. Opt. Lett.
**2005**, 30, 3123. [Google Scholar] [CrossRef] - Fini, J.M. Bend-resistant design of conventional and microstructure fibers with very large mode area. Opt. Express
**2006**, 14, 69. [Google Scholar] [CrossRef] - Liu, A. Novel SBS Suppression Scheme for High-Power Fiber Amplifiers. In Fiber Lasers III: Technology, Systems, and Applications; SPIE: San Jose, CA, USA, 2006; Volume 6102, p. 61021R. [Google Scholar]
- Li, M.-J.; Chen, X.; Wang, J.; Gray, S.; Liu, A.; Demeritt, J.A.; Ruffin, A.B.; Crowley, A.M.; Walton, D.T.; Zenteno, L.A. Al/Ge co-doped large mode area fiber with high SBS threshold. Opt. Express
**2007**, 15, 8290. [Google Scholar] [CrossRef] - Mermelstein, M.D.; Andrejco, M.J.; Fini, J.; Yablon, A.; Headley, C., III; DiGiovanni, D.J.; McCurdy, A.H. 11.2 dB SBS Gain Suppression in a Large Mode Area Yb-Doped Optical Fiber. In Fiber Lasers V: Technology, Systems, and Applications; Broeng, J., Headley, C., III, Eds.; SPIE: San Jose, CA, USA, 2008; Volume 6873, p. 68730N. [Google Scholar]
- Harish, A.V.; Nilsson, J. Suppression of Stimulated Brillouin Scattering in Single-Frequency Fiber Raman Amplifier Through Pump Modulation. J. Light. Technol.
**2019**, 37, 3280–3289. [Google Scholar] [CrossRef] - Huang, Y.; Yan, P.; Wang, Z.; Tian, J.; Li, D.; Xiao, Q.; Gong, M. 2.19 kW narrow linewidth FBG-based MOPA configuration fiber laser. Opt. Express
**2019**, 27, 3136. [Google Scholar] [CrossRef] - Wang, Y.; Feng, Y.; Ma, Y.; Chang, Z.; Peng, W.; Sun, Y.; Gao, Q.; Zhu, R.; Tang, C. 2.5 kW Narrow Linewidth Linearly Polarized All-Fiber MOPA With Cascaded Phase-Modulation to Suppress SBS Induced Self-Pulsing. IEEE Photonics J.
**2020**, 12, 1–15. [Google Scholar] [CrossRef] - Wang, Y.; Ke, W.; Peng, W.; Chang, Z.; Feng, Y.; Sun, Y.; Gao, Q.; Ma, Y.; Zhu, R.; Tang, C. 3 kW, 0.2 nm narrow linewidth linearly polarized all-fiber laser based on a compact MOPA structure. Laser Phys. Lett.
**2020**, 17, 075101. [Google Scholar] [CrossRef] - Lin, H.; Tao, R.; Li, C.; Wang, B.; Guo, C.; Shu, Q.; Zhao, P.; Xu, L.; Wang, J.; Jing, F.; et al. 3.7 kW monolithic narrow linewidth single mode fiber laser through simultaneously suppressing nonlinear effects and mode instability. Opt. Express
**2019**, 27, 9716. [Google Scholar] [CrossRef] [PubMed] - Stolen, R.H.; Lin, C. Self-phase-modulation in silica optical fibers. Phys. Rev. A
**1978**, 17, 1448–1453. [Google Scholar] [CrossRef] - Shimizu, F. Frequency Broadening in Liquids by a Short Light Pulse. Phys. Rev. Lett.
**1967**, 19, 1097–1100. [Google Scholar] [CrossRef] - Hasegawa, A.; Tappert, F. Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion. Appl. Phys. Lett.
**1973**, 23, 142–144. [Google Scholar] [CrossRef] - Farrow, R.L.; Kliner, D.A.V.; Hadley, G.R.; Smith, A.V. Peak-power limits on fiber amplifiers imposed by self-focusing. Opt. Lett.
**2006**, 31, 3423. [Google Scholar] [CrossRef] - Dong, L. Approximate Treatment of the Nonlinear Waveguide Equation in the Regime of Nonlinear Self-Focus. J. Light. Technol.
**2008**, 26, 3476–3485. [Google Scholar] [CrossRef] - Schimpf, D.N.; Eidam, T.; Seise, E.; Hädrich, S.; Limpert, J.; Tünnermann, A. Circular versus linear polarization in laser-amplifiers with Kerr-nonlinearity. Opt. Express
**2009**, 17, 18774. [Google Scholar] [CrossRef] - Smith, A.V.; Do, B.T.; Hadley, G.R.; Farrow, R.L. Optical Damage Limits to Pulse Energy from Fibers. IEEE J. Sel. Top. Quantum Electron.
**2009**, 15, 153–158. [Google Scholar] [CrossRef] - Zheng, J.; Zhao, W.; Zhao, B.; Li, Z.; Li, G.; Gao, Q.; Ju, P.; Gao, W.; She, S.; Wu, P. Four-wave mixing effect on high-power continuous-wave all-fiber lasers. Mod. Phys. Lett. B
**2018**, 32, 1850275. [Google Scholar] [CrossRef] - Eidam, T.; Wirth, C.; Jauregui, C.; Stutzki, F.; Jansen, F.; Otto, H.-J.; Schmidt, O.; Schreiber, T.; Limpert, J.; Tünnermann, A. Experimental observations of the threshold-like onset of mode instabilities in high power fiber amplifiers. Opt. Express
**2011**, 19, 13218. [Google Scholar] [CrossRef] - Smith, A.V.; Smith, J.J. Influence of pump and seed modulation on the mode instability thresholds of fiber amplifiers. Opt. Express
**2012**, 20, 24545. [Google Scholar] [CrossRef] - Smith, A.V.; Smith, J.J. Mode instability in high power fiber amplifiers. Opt. Express
**2011**, 19, 10180. [Google Scholar] [CrossRef] [PubMed] - Jauregui, C.; Eidam, T.; Otto, H.-J.; Stutzki, F.; Jansen, F.; Limpert, J.; Tünnermann, A. Physical origin of mode instabilities in high-power fiber laser systems. Opt. Express
**2012**, 20, 12912. [Google Scholar] [CrossRef] [PubMed] - Ward, B.; Robin, C.; Dajani, I. Origin of thermal modal instabilities in large mode area fiber amplifiers. Opt. Express
**2012**, 20, 11407. [Google Scholar] [CrossRef] [PubMed] - Hejaz, K.; Shayganmanesh, M.; Azizi, S.; Abedinajafi, A.; Roohforouz, A.; Rezaei-Nasirabad, R.; Vatani, V. Transverse mode instability of fiber oscillators in comparison with fiber amplifiers. Laser Phys. Lett.
**2018**, 15, 055102. [Google Scholar] [CrossRef] - Roohforouz, A.; Eyni Chenar, R.; Rezaei-Nasirabad, R.; Azizi, S.; Hejaz, K.; Hamedani Golshan, A.; Abedinajafi, A.; Vatani, V.; Nabavi, S.H. The effect of population inversion saturation on the transverse mode instability threshold in high power fiber laser oscillators. Sci. Rep.
**2021**, 11, 21116. [Google Scholar] [CrossRef] [PubMed] - Ke, W.-W.; Wang, X.-J.; Bao, X.-F.; Shu, X.-J. Thermally induced mode distortion and its limit to power scaling of fiber lasers. Opt. Express
**2013**, 21, 14272. [Google Scholar] [CrossRef] - Zervas, M.N. Power Scalability in High Power Fibre Amplifiers. In Proceedings of the 2017 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC), Munich, Germany, 25–29 June 2017; Volume 82, p. 1. [Google Scholar]
- Brown, D.C.; Hoffman, H.J. Thermal, stress, and thermo-optic effects in high average power double-clad silica fiber lasers. IEEE J. Quantum Electron.
**2001**, 37, 207–217. [Google Scholar] [CrossRef] - Lapointe, M.-A.; Chatigny, S.; Piché, M.; Cain-Skaff, M.; Maran, J.-N. Thermal Effects in High-Power CW Fiber Lasers. In Fiber Lasers VI: Technology, Systems, and Applications; Gapontsev, D.V., Kliner, D.A., Dawson, J.W., Tankala, K., Eds.; SPIE: San Jose, CA, USA, 2009; Volume 7195, p. 71951U. [Google Scholar]
- Stuart, B.C.; Feit, M.D.; Rubenchik, A.M.; Shore, B.W.; Perry, M.D. Laser-Induced Damage in Dielectrics with Nanosecond to Subpicosecond Pulses. Phys. Rev. Lett.
**1995**, 74, 2248–2251. [Google Scholar] [CrossRef][Green Version] - Smith, A.; Do, B.; Soderlund, M. Deterministic Nanosecond Laser-Induced Breakdown Thresholds in Pure and Yb 3+ Doped Fused Silica. In Fiber Lasers IV: Technology, Systems and Applications; SPIE: San Jose, CA, USA, 2007; Volume 6453, p. 645317. [Google Scholar] [CrossRef]
- Gapontsev, V.; Gapontsev, D.; Platonov, N.; Shkurikhin, O.; Fomin, V.; Mashkin, A.; Abramov, M.; Ferin, S. 2 kW CW Ytterbium Fiber Laser with Record Diffraction-Limited Brightness. In Proceedings of the CLEO/Europe Conference on Lasers and Electro-Optics Europe, Munich, Germany, 12–17 June 2005; Volume 12, p. 508. [Google Scholar]
- Jain, D.; Jung, Y.; Barua, P.; Alam, S.; Sahu, J.K. Demonstration of ultra-low NA rare-earth doped step index fiber for applications in high power fiber lasers. Opt. Express
**2015**, 23, 7407. [Google Scholar] [CrossRef][Green Version] - Midilli, Y.; Ortaç, B. An All-Fiber Ultra-Low Numerical Aperture High Power Fiber MOPA System with an Output Power above 500 W. In Proceedings of the European Conference on Lasers and Electro-Optics, Munich, Germany, 23–27 June 2019; Volume 140, p. 14892. [Google Scholar]
- Lim, K.-J.; Kai-Wen Seah, S.; Yong’En Ye, J.; Lim, W.W.; Seah, C.-P.; Tan, Y.-B.; Tan, S.; Lim, H.; Sidharthan, R.; Prasadh, A.R.; et al. High absorption large-mode area step-index fiber for tandem-pumped high-brightness high-power lasers. Photonics Res.
**2020**, 8, 1599. [Google Scholar] [CrossRef] - Paschotta, R.; Nilsson, J.; Barber, P.R.; Caplen, J.E.; Tropper, A.C.; Hanna, D.C. Lifetime quenching in Yb-doped fibres. Opt. Commun.
**1997**, 136, 375–378. [Google Scholar] [CrossRef][Green Version] - Huang, L.; Yao, T.; Leng, J.; Guo, S.; Tao, R.; Zhou, P.; Cheng, X. Mode instability dynamics in high-power low-numerical-aperture step-index fiber amplifier. Appl. Opt.
**2017**, 56, 5412. [Google Scholar] [CrossRef] [PubMed] - Midilli, Y.; Ortac, B. Demonstration of an All-Fiber Ultra-Low Numerical Aperture Ytterbium-Doped Large Mode Area Fiber in a Master Oscillator Power Amplifier Configuration Above 1 kW Power Level. J. Light. Technol.
**2020**, 38, 1915–1920. [Google Scholar] [CrossRef] - Lin, H.; Xu, L.; Li, C.; Shu, Q.; Chu, Q.; Xie, L.; Guo, C.; Zhao, P.; Li, Z.; Wang, J.; et al. 10.6 kW high-brightness cascade-end-pumped monolithic fiber lasers directly pumped by laser diodes in step-index large mode area double cladding fiber. Results Phys.
**2019**, 14, 102479. [Google Scholar] [CrossRef] - Codemard, C.A.; Sahu, J.K.; Nilsson, J. Tandem Cladding-Pumping for Control of Excess Gain in Ytterbium-Doped Fiber Amplifiers. IEEE J. Quantum Electron.
**2010**, 46, 1860–1869. [Google Scholar] [CrossRef] - Dai, J.; Li, F.; Liu, N.; Shen, C.; Zhang, L.; Li, H.; Li, Y.; Sun, S.; Li, Y.; Lv, J.; et al. Extraction of More than 10 kW from Yb-Doped Tandem-Pumping Aluminophosphosilicate Fiber. In Global Intelligent Industry Conference 2020; Wang, L., Ed.; SPIE: Bellingham, WA, USA, 2021; Volume 11780, p. 76. [Google Scholar]
- Zhou, P.; Xiao, H.; Leng, J.; Xu, J.; Chen, Z.; Zhang, H.; Liu, Z. High-power fiber lasers based on tandem pumping. J. Opt. Soc. Am. B
**2017**, 34, A29. [Google Scholar] [CrossRef] - Glick, Y.; Sintov, Y.; Zuitlin, R.; Pearl, S.; Shamir, Y.; Feldman, R.; Horvitz, Z.; Shafir, N. Single-mode 230 W output power 1018 nm fiber laser and ASE competition suppression. J. Opt. Soc. Am. B
**2016**, 33, 1392. [Google Scholar] [CrossRef] - Khitrov, V.; Samson, B.; Machewirth, D.; Tankala, K. 242W Single-Mode CW Fiber Laser Operating at 1030nm Lasing Wavelength and with 0.35 nm Spectral Width. In Proceedings of the Advanced Solid-State Photonics, OSA, Incline Village, NV, USA, 29 January–1 February 2006; p. WD5. [Google Scholar]
- Ottenhues, C.; Theeg, T.; Hausmann, K.; Wysmolek, M.; Sayinc, H.; Neumann, J.; Kracht, D. Single-mode monolithic fiber laser with 200 W output power at a wavelength of 1018 nm. Opt. Lett.
**2015**, 40, 4851. [Google Scholar] [CrossRef] - Wang, X.; Yan, P.; Wang, Z.; Huang, Y.; Tian, J.; Li, D.; Xiao, Q. The 5.4 kW Output Power of the Ytterbium-Doped Tandem-Pumping Fiber Amplifier. In Proceedings of the Conference on Lasers and Electro Optics, San Jose, CA, USA, 13–18 May 2018; pp. 4–5. [Google Scholar]
- Lafouti, M.; Latifi, H.; Sarabi, H.; Fathi, H.; Ebrahimzadeh, S.; Sarikhani, S. 407 W specially-designed fiber laser at 1018 nm using a gain fiber with a low core/cladding ratio of 20/400 μ m. Laser Phys.
**2018**, 28, 115102. [Google Scholar] [CrossRef] - Lafouti, M.; Latifi, H.; Fathi, H.; Ebrahimzadeh, S.; Sarikhani, S.; Sarabi, H. Experimental investigation of a high-power 1018 nm fiber laser using a 20/400 μm ytterbium-doped fiber. Appl. Opt.
**2019**, 58, 729. [Google Scholar] [CrossRef] [PubMed] - Yan, P.; Wang, X.; Wang, Z.; Huang, Y.; Li, D.; Xiao, Q.; Gong, M. A 1150-W 1018-nm Fiber Laser Bidirectional Pumped by Wavelength-Stabilized Laser Diodes. IEEE J. Sel. Top. Quantum Electron.
**2018**, 24, 1–6. [Google Scholar] [CrossRef] - Fomin, V.; Abramov, M.; Ferin, A.; Abramov, A.; Mochalov, D.; Platonov, N.V.G. 10 kW Single-Mode Fiber Laser. In Proceedings of the 5th International Symposium on High-Power Fiber Lasers and Their Applications, St. Petersburg, Russia, 28 July 2010. [Google Scholar]
- Ferin, A.; Gapontsev, V.; Fomin, V.; Abramov, A.; Avramov, M.; Mochalov, D. 17 kW CW Laser with 50 µm Delivery Fiber. In Proceedings of the 15th Internation Conference on Laser Optics, St. Petersburg, Russia, 25–29 June 2012; p. 12AD. [Google Scholar]
- Yao, T.; Ji, J.; Nilsson, J. Ultra-Low Quantum-Defect Heating in Ytterbium-Doped Aluminosilicate Fibers. J. Light. Technol.
**2014**, 32, 429–434. [Google Scholar] [CrossRef] - Naderi, S.; Dajani, I.; Grosek, J.; Madden, T.; Dinh, T.-N. Theoretical Analysis of Effect of Pump and Signal Wavelengths on Modal Instabilities in Yb-Doped Fiber Amplifiers. In Nonlinear Frequency Generation and Conversion: Material, Devices and Applications XIII; SPIE: San Francisco, CA, USA, 2014; Volume 8964, pp. 264–270. [Google Scholar] [CrossRef]
- Fu, S.; Feng, X.; Si, L.; Guo, Z.; Jia, X.; Zhao, Y.; Yuan, S.; Dong, X. Self-pulsing dynamics of high-power Yb-doped fiber lasers. Microw. Opt. Technol. Lett.
**2006**, 48, 2282–2285. [Google Scholar] [CrossRef] - Limpert, J.; Klenke, A.; Kienel, M.; Breitkopf, S.; Eidam, T.; Hadrich, S.; Jauregui, C.; Tunnermann, A. Performance Scaling of Ultrafast Laser Systems by Coherent Addition of Femtosecond Pulses. IEEE J. Sel. Top. Quantum Electron.
**2014**, 20, 268–277. [Google Scholar] [CrossRef] - Klenke, A.; Muller, M.; Stark, H.; Kienel, M.; Jauregui, C.; Tunnermann, A.; Limpert, J. Coherent Beam Combination of Ultrafast Fiber Lasers. IEEE J. Sel. Top. Quantum Electron.
**2018**, 24, 1–9. [Google Scholar] [CrossRef] - Klenke, A.; Seise, E.; Limpert, J.; Tünnermann, A. Basic considerations on coherent combining of ultrashort laser pulses. Opt. Express
**2011**, 19, 25379. [Google Scholar] [CrossRef] [PubMed] - Uberna, R.; Bratcher, A.; Tiemann, B.G. Coherent Polarization Beam Combination. IEEE J. Quantum Electron.
**2010**, 46, 1191–1196. [Google Scholar] [CrossRef] - Fan, T.Y. Laser beam combining for high-power, high-radiance sources. IEEE J. Sel. Top. Quantum Electron.
**2005**, 11, 567–577. [Google Scholar] [CrossRef] - Augst, S.J.; Ranka, J.K.; Fan, T.Y.; Sanchez, A. Beam combining of ytterbium fiber amplifiers. J. Opt. Soc. Am. B
**2007**, 24, 1707. [Google Scholar] [CrossRef] - Liu, Z.; Zhou, P.; Xu, X.; Wang, X.; Ma, Y. Coherent beam combining of high power fiber lasers: Progress and prospect. Sci. China Technol. Sci.
**2013**, 56, 1597–1606. [Google Scholar] [CrossRef] - Liu, Z.; Ma, P.; Su, R.; Tao, R.; Ma, Y.; Wang, X.; Zhou, P. High-power coherent beam polarization combination of fiber lasers: Progress and prospect. J. Opt. Soc. Am. B
**2017**, 34, A7. [Google Scholar] [CrossRef] - Bourdon, P.; Le Gouet, J.; Goular, D.; Lombard, L.; Durecu, A. Coherent Combining with Active Phase Control: A Practical Tool for Adaptive and Nonlinear Optics. In Proceedings of the 2017 Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR), Singapore, 31 July–4 August 2017; Volume 122, pp. 1–3. [Google Scholar]
- Hanna, M.; Guichard, F.; Zaouter, Y.; Papadopoulos, D.N.; Druon, F.; Georges, P. Coherent combination of ultrafast fiber amplifiers. J. Phys. B At. Mol. Opt. Phys.
**2016**, 49, 062004. [Google Scholar] [CrossRef] - Sprangle, P.; Ting, A.; Penano, J.; Fischer, R.; Hafizi, B. Incoherent Combining and Atmospheric Propagation of High-Power Fiber Lasers for Directed-Energy Applications. IEEE J. Quantum Electron.
**2009**, 45, 138–148. [Google Scholar] [CrossRef] - Sprangle, P.; Hafizi, B.; Ting, A.; Fischer, R. High-power lasers for directed-energy applications. Appl. Opt.
**2015**, 54, F201. [Google Scholar] [CrossRef] - Lockheed Martin Demonstrates 30 kW Weapons-Grade Fiber Laser. Available online: https://www.laserfocusworld.com/lasers-sources/article/16564243/lockheed-martin-demonstrates-30-kw-weaponsgrade-fiber-laser (accessed on 30 January 2014).
- Zhu, Y.; Li, P.; Li, C.; Wang, L.; Yao, C.; Zhang, X.; Li, S.; Zhou, Y. Quantizing the Coherent Polarization Beam Combination from Temporal, Spatial, and Spectral Domains. In Fourth International Symposium on High Power Laser Science and Engineering (HPLSE 2021); Zhu, J., Ed.; SPIE: Bellingham, WA, USA, 2021; Volume 11849, p. 18. [Google Scholar]
- Lei, C.; Gu, Y.; Chen, Z.; Wang, Z.; Zhou, P.; Ma, Y.; Xiao, H.; Leng, J.; Wang, X.; Hou, J.; et al. Incoherent beam combining of fiber lasers by an all-fiber 7 × 1 signal combiner at a power level of 14 kW. Opt. Express
**2018**, 26, 10421. [Google Scholar] [CrossRef] - Goodno, G.D.; Asman, C.P.; Anderegg, J.; Brosnan, S.; Cheung, E.C.; Hammons, D.; Injeyan, H.; Komine, H.; Long, W.H.; McClellan, M.; et al. Brightness-Scaling Potential of Actively Phase-Locked Solid-State Laser Arrays. IEEE J. Sel. Top. Quantum Electron.
**2007**, 13, 460–472. [Google Scholar] [CrossRef] - Augst, S.J.; Goyal, A.K.; Aggarwal, R.L.; Fan, T.Y.; Sanchez, A. Wavelength beam combining of ytterbium fiber lasers. Opt. Lett.
**2003**, 28, 331. [Google Scholar] [CrossRef] [PubMed] - Sevian, A.; Andrusyak, O.; Ciapurin, I.; Smirnov, V.; Venus, G.; Glebov, L. Efficient power scaling of laser radiation by spectral-beam combining: Erratum. Opt. Lett.
**2008**, 33, 760. [Google Scholar] [CrossRef] - Zhu, Z.; Gou, L.; Jiang, M.; Hui, Y.; Lei, H.; Li, Q. High Beam Quality in Two Directions and High Efficiency Output of a Diode Laser Array by Spectral-Beam-Combining. Opt. Express
**2014**, 22, 17804. [Google Scholar] [CrossRef] - Sanchez-Rubio, A.; Fan, T.Y.; Augst, S.J.; Goyal, A.K.; Creedon, K.J.; Gopinath, J.T.; Daneu, V.; Chann, B.; Hung, R. Wavelength Beam Combining for Power and Brightness Scaling of Laser Systems. MIT-Lincoln Lab. J.
**2014**, 20, 52–66. [Google Scholar] - Wirth, C.; Schmidt, O.; Tsybin, I.; Schreiber, T.; Eberhardt, R.; Limpert, J.; Tünnermann, A.; Ludewigt, K.; Gowin, M.; ten Have, E.; et al. High average power spectral beam combining of four fiber amplifiers to 82 kW. Opt. Lett.
**2011**, 36, 3118. [Google Scholar] [CrossRef] - Schmidt, O.; Rekas, M.; Wirth, C.; Rothhardt, J.; Rhein, S.; Kliner, A.; Strecker, M.; Schreiber, T.; Limpert, J.; Eberhardt, R.; et al. High power narrow-band fiber-based ASE source. Opt. Express
**2011**, 19, 4421. [Google Scholar] [CrossRef] [PubMed] - Xu, J.; Liu, W.; Leng, J.; Xiao, H.; Guo, S.; Zhou, P.; Chen, J. Power scaling of narrowband high-power all-fiber superfluorescent fiber source to 1.87 kW. Opt. Lett.
**2015**, 40, 2973. [Google Scholar] [CrossRef] - Zheng, Y.; Yang, Y.; Wang, J.; Hu, M.; Liu, G.; Zhao, X.; Chen, X.; Liu, K.; Zhao, C.; He, B.; et al. 10.8 kW spectral beam combination of eight all-fiber superfluorescent sources and their dispersion compensation. Opt. Express
**2016**, 24, 12063. [Google Scholar] [CrossRef] - Zheng, Y.; Zhu, Z.; Liu, X.; Yu, M.; Li, S.; Zhang, L.; Ni, Q.; Wang, J.; Wang, X. High-power, high-beam-quality spectral beam combination of six narrow-linewidth fiber amplifiers with two transmission diffraction gratings. Appl. Opt.
**2019**, 58, 8339. [Google Scholar] [CrossRef] [PubMed] - Chen, F.; Ma, J.; Wei, C.; Zhu, R.; Zhou, W.; Yuan, Q.; Pan, S.; Zhang, J.; Wen, Y.; Dou, J. 10 kW-level spectral beam combination of two high power broad-linewidth fiber lasers by means of edge filters. Opt. Express
**2017**, 25, 32783. [Google Scholar] [CrossRef] - Wirth, C.; Schmidt, O.; Tsybin, I.; Schreiber, T.; Peschel, T.; Brückner, F.; Clausnitzer, T.; Limpert, J.; Eberhardt, R.; Tünnermann, A.; et al. 2 kW incoherent beam combining of four narrow-linewidth photonic crystal fiber amplifiers. Opt. Express
**2009**, 17, 1178. [Google Scholar] [CrossRef] [PubMed] - Madasamy, P.; Loftus, T.; Thomas, A.; Jones, P.; Honea, E. Comparison of Spectral Beam Combining Approaches for High Power Fiber Laser Systems. In Laser Source Technology for Defense and Security IV; Dubinskii, M., Wood, G.L., Eds.; SPIE: Orlando, FL, USA, 2008; Volume 6952, p. 695207. [Google Scholar]
- Shi, C.; Zhang, H.; Wang, X.; Zhou, P.; Xu, X. kW-class high power fiber laser enabled by active long tapered fiber. High Power Laser Sci. Eng.
**2018**, 6, e16. [Google Scholar] [CrossRef][Green Version] - Ma, J.; Chen, F.; Wei, C.; Zhu, R. Modeling and Analysis of the Influence of an Edge Filter on the Combining Efficiency and Beam Quality of a 10-kW-Class Spectral Beam-Combining System. Appl. Sci.
**2019**, 9, 2152. [Google Scholar] [CrossRef][Green Version] - Lockheed Martin to Deliver World Record-Setting 60kW Laser to U.S. Army. 2017. Available online: https://news.lockheedmartin.com/2017-03-16-Lockheed-Martin-to-Deliver-World-Record-Setting-60kW-Laser-to-U-S-Army (accessed on 28 May 2021).
- Honea, E.; Afzal, R.S.; Savage-Leuchs, M.; Henrie, J.; Brar, K.; Kurz, N.; Jander, D.; Gitkind, N.; Hu, D.; Robin, C.; et al. Advances in Fiber Laser Spectral Beam Combining for Power Scaling. In Components and Packaging for Laser Systems II; Glebov, A.L., Leisher, P.O., Eds.; SPIE: San Francisco, CA, USA, 2016; Volume 9730, p. 97300Y. [Google Scholar]
- Team Dynetics Receives Contract for Next Phase of 100 KW-Class Laser Weapon System for U.S. Army. 2018. Available online: https://news.lockheedmartin.com/2018-08-06-Team-Dynetics-Receives-Contract-for-Next-Phase-of-100-kW-Class-Laser-Weapon-System-for-U-S-Army (accessed on 4 December 2021).
- Brignon, A. Coherent Laser Beam Combining. Wiley-VCH: Veinheim, Germany, 2013; p. 481. [Google Scholar]
- Ripper, J.E.; Paoli, T.L. Optical coupling of adjacent stripe-geometry junction lasers. Appl. Phys. Lett.
**1970**, 17, 371–373. [Google Scholar] [CrossRef] - Kozlov, V.A.; Hernández-Cordero, J.; Morse, T.F. All-fiber coherent beam combining of fiber lasers. Opt. Lett.
**1999**, 24, 1814. [Google Scholar] [CrossRef][Green Version] - Cheung, E.C.; Weber, M.; Rice, R.R. Phase Locking of a Pulsed Fiber Amplifier. In Proceedings of the Advanced Solid-State Photonics, OSA, Nara, Japan, 27–30 January 2008; p. WA2. [Google Scholar]
- McNaught, S.J.; Asman, C.P.; Injeyan, H.; Jankevics, A.; Johnson, A.M.F.; Jones, G.C.; Komine, H.; Machan, J.; Marmo, J.; McClellan, M.; et al. 100-kW Coherently Combined Nd:YAG MOPA Laser Array. In Proceedings of the Frontiers in Optics 2009/Laser Science XXV/Fall 2009 OSA Optics & Photonics Technical Digest, San Jose, CA, USA, 11–15 October 2009; p. FThD2. [Google Scholar]
- Goodno, G.D.; Shih, C.; Rothenberg, J.E. Perturbative analysis of coherent combining efficiency with mismatched lasers. Opt. Express
**2010**, 18, 25403. [Google Scholar] [CrossRef] [PubMed] - Leshchenko, V.E. Coherent combining efficiency in tiled and filled aperture approaches. Opt. Express
**2015**, 23, 15944. [Google Scholar] [CrossRef] - Prossotowicz, M.; Heimes, A.; Flamm, D.; Jansen, F.; Otto, H.-J.; Budnicki, A.; Killi, A.; Morgner, U. Coherent beam combining with micro-lens arrays. Opt. Lett.
**2020**, 45, 6728. [Google Scholar] [CrossRef] [PubMed] - Zhi, D.; Zhang, Z.; Ma, Y.; Wang, X.; Chen, Z.; Wu, W.; Zhou, P.; Si, L. Realization of large energy proportion in the central lobe by coherent beam combination based on conformal projection system. Sci. Rep.
**2017**, 7, 2199. [Google Scholar] [CrossRef] - Scifres, D.R.; Streifer, W.; Burnham, R.D. High-power coupled-multiple-stripe phase-locked injection laser. Appl. Phys. Lett.
**1979**, 34, 259–261. [Google Scholar] [CrossRef] - Tan, Y.; Li, X. Impact of Filling Factor on Correction of Piston and Tip/Tilt in Coherent Beam Combination. In 14th National Conference on Laser Technology and Optoelectronics (LTO 2019); Xu, H.-L., Chen, F., Ji, L., Li, B., Xie, X., Leng, Y., Sheng, Z., Yang, Y., Zhao, J., Zhu, J., Eds.; SPIE: Shanghai, China, 2019; Volume 11170, p. 215. [Google Scholar]
- Lachinova, S.L.; Vorontsov, M.A. Laser beam projection with adaptive array of fiber collimators II Analysis of atmospheric compensation efficiency. J. Opt. Soc. Am. A
**2008**, 25, 1960. [Google Scholar] [CrossRef] [PubMed] - Le Dortz, J.; Heilmann, A.; Antier, M.; Bourderionnet, J.; Larat, C.; Fsaifes, I.; Daniault, L.; Bellanger, S.; Simon Boisson, C.; Chanteloup, J.-C.; et al. Highly scalable femtosecond coherent beam combining demonstrated with 19 fibers. Opt. Lett.
**2017**, 42, 1887. [Google Scholar] [CrossRef] - Yu, C.X.; Augst, S.J.; Redmond, S.M.; Goldizen, K.C.; Murphy, D.V.; Sanchez, A.; Fan, T.Y. Coherent combining of a 4 kW, eight-element fiber amplifier array. Opt. Lett.
**2011**, 36, 2686. [Google Scholar] [CrossRef] - Bourderionnet, J.; Bellanger, C.; Primot, J.; Brignon, A. Coherent Phase Combining of 64 Fibers. In Proceedings of the Conference on Lasers and Electro-Optics Europe and 12th European Quantum Electronics Conference (CLEO EUROPE/EQEC), Munich, Germany, 22–26 May 2011; Volume 19, p. 1. [Google Scholar]
- Weyrauch, T.; Vorontsov, M.A.; Carhart, G.W.; Beresnev, L.A.; Rostov, A.P.; Polnau, E.E.; Liu, J.J. Experimental demonstration of coherent beam combining over a 7 km propagation path. Opt. Lett.
**2011**, 36, 4455. [Google Scholar] [CrossRef] [PubMed] - Huang, Z.; Tang, X.; Luo, Y.; Liu, C.; Li, J.; Zhang, D.; Wang, X.; Chen, T.; Han, M. Active phase locking of thirty fiber channels using multilevel phase dithering method. Rev. Sci. Instrum.
**2016**, 87, 033109. [Google Scholar] [CrossRef] [PubMed] - Kabeya, D.; Kermène, V.; Fabert, M.; Benoist, J.; Saucourt, J.; Desfarges-Berthelemot, A.; Barthélémy, A. Efficient phase-locking of 37 fiber amplifiers by phase-intensity mapping in an optimization loop. Opt. Express
**2017**, 25, 13816. [Google Scholar] [CrossRef] - Fsaifes, I.; Daniault, L.; Bellanger, S.; Veinhard, M.; Bourderionnet, J.; Larat, C.; Lallier, E.; Durand, E.; Brignon, A.; Chanteloup, J.-C. Coherent beam combining of 61 femtosecond fiber amplifiers. Opt. Express
**2020**, 28, 20152. [Google Scholar] [CrossRef] [PubMed] - Du, Q.; Wang, D.; Zhou, T.; Li, D.; Wilcox, R. Characterization and Control of 81-beam Diffractive Coherent Combining. In Proceedings of the Laser Congress 2020 (ASSL, LAC), Washington, DC, USA, 13–16 October 2020; p. ATu4A.5. [Google Scholar]
- Chang, H.; Chang, Q.; Xi, J.; Hou, T.; Su, R.; Ma, P.; Wu, J.; Li, C.; Jiang, M.; Ma, Y.; et al. First experimental demonstration of coherent beam combining of more than 100 beams. Photonics Res.
**2020**, 8, 1943. [Google Scholar] [CrossRef] - Klenke, A.; Müller, M.; Stark, H.; Stutzki, F.; Hupel, C.; Schreiber, T.; Tünnermann, A.; Limpert, J. Coherently combined 16-channel multicore fiber laser system. Opt. Lett.
**2018**, 43, 1519. [Google Scholar] [CrossRef] [PubMed] - Ramirez, L.P.; Hanna, M.; Bouwmans, G.; El Hamzaoui, H.; Bouazaoui, M.; Labat, D.; Delplace, K.; Pouysegur, J.; Guichard, F.; Rigaud, P.; et al. Coherent beam combining with an ultrafast multicore Yb-doped fiber amplifier. Opt. Express
**2015**, 23, 5406. [Google Scholar] [CrossRef] [PubMed][Green Version] - Elkin, N.N.; Napartovich, A.P.; Sukharev, A.G.; Troschieva, V.N.; Vysotsky, D.V. Direct numerical simulation of radiation propagation in a multicore fiber. Opt. Commun.
**2000**, 177, 207–217. [Google Scholar] [CrossRef] - Wrage, M.; Glas, P.; Fischer, D.; Leitner, M.; Vysotsky, D.V.; Napartovich, A.P. Phase locking in a multicore fiber laser by means of a Talbot resonator. Opt. Lett.
**2000**, 25, 1436. [Google Scholar] [CrossRef] - Gorton, E.K.; Jenkins, R.M. Theory of 1-N-way phase-locked resonators. Appl. Opt.
**2001**, 40, 916. [Google Scholar] [CrossRef] - Vysotsky, D.V.; Napartovich, A.P. Coherent beam combining in optically coupled laser arrays. Quantum Electron.
**2019**, 49, 989–1007. [Google Scholar] [CrossRef] - Michaille, L.; Bennett, C.R.; Taylor, D.M.; Shepherd, T.J.; Broeng, J.; Simonsen, H.R.; Petersson, A. Phase locking and supermode selection in multicore photonic crystal fiber lasers with a large doped area. Opt. Lett.
**2005**, 30, 1668. [Google Scholar] [CrossRef] - Fang, X.-H.; Hu, M.-L.; Liu, B.-W.; Chai, L.; Wang, C.-Y.; Zheltikov, A.M. Generation of 150 MW, 110 fs pulses by phase-locked amplification in multicore photonic crystal fiber. Opt. Lett.
**2010**, 35, 2326. [Google Scholar] [CrossRef] [PubMed] - Paurisse, M.; Hanna, M.; Druon, F.; Georges, P. Wavefront Control by Digital Holography in an Yb-Doped Multi-Core Fiber Amplifier. In Proceedings of the Conference on Lasers and Electro-Optics, San Jose, CA, USA, 16–21 May 2010; Volume 35, p. CThO4. [Google Scholar]
- Steinkopff, A.; Jauregui, C.; Aleshire, C.; Klenke, A.; Limpert, J. Optimizing the Design of Coherently Combined Multicore Fiber Amplifiers. In Fiber Lasers XVIII: Technology and Systems; Zervas, M.N., Jauregui-Misas, C., Eds.; SPIE: Bellingham, WA, USA, 2021; Volume 11665, p. 58. [Google Scholar]
- Lin, D.; Carpenter, J.; Feng, Y.; Jain, S.; Jung, Y.; Feng, Y.; Zervas, M.N.; Richardson, D.J. Reconfigurable structured light generation in a multicore fibre amplifier. Nat. Commun.
**2020**, 11, 3986. [Google Scholar] [CrossRef] - Weyrauch, T.; Vorontsov, M.; Mangano, J.; Ovchinnikov, V.; Bricker, D.; Polnau, E.; Rostov, A. Deep turbulence effects mitigation with coherent combining of 21 laser beams over 7 km. Opt. Lett.
**2016**, 41, 840. [Google Scholar] [CrossRef] [PubMed] - Shekel, E.; Vidne, Y.; Urbach, B. 16 kW Single Mode CW Laser with Dynamic Beam for Material Processing. In Fiber Lasers XVII: Technology and Systems; Dong, L., Zervas, M.N., Eds.; SPIE: San Francisco, CA, USA, 2020; Volume 11260, p. 73. [Google Scholar]
- Ma, P.; Chang, H.; Ma, Y.; Su, R.; Qi, Y.; Wu, J.; Li, C.; Long, J.; Lai, W.; Chang, Q.; et al. 7.1 kW coherent beam combining system based on a seven-channel fiber amplifier array. Opt. Laser Technol.
**2021**, 140, 107016. [Google Scholar] [CrossRef] - Müller, M.; Aleshire, C.; Klenke, A.; Haddad, E.; Légaré, F.; Tünnermann, A.; Limpert, J. 10.4 kW coherently combined ultrafast fiber laser. Opt. Lett.
**2020**, 45, 3083. [Google Scholar] [CrossRef] - Regelskis, K.; Gavrilinas, N.; Trusovas, R.; Račiukaitis, G. Coherent addition of orthogonally polarized fibre lasers with high combining efficiency. Lith. J. Phys.
**2010**, 50, 209–214. [Google Scholar] [CrossRef] - Seise, E.; Klenke, A.; Limpert, J.; Tünnermann, A. Coherent addition of fiber-amplified ultrashort laser pulses. Opt. Express
**2010**, 18, 27827. [Google Scholar] [CrossRef] [PubMed] - Klenke, A.; Breitkopf, S.; Kienel, M.; Gottschall, T.; Eidam, T.; Hädrich, S.; Rothhardt, J.; Limpert, J.; Tünnermann, A. 530 W, 13 mJ, four-channel coherently combined femtosecond fiber chirped-pulse amplification system. Opt. Lett.
**2013**, 38, 2283. [Google Scholar] [CrossRef] - Kienel, M.; Müller, M.; Klenke, A.; Limpert, J.; Tünnermann, A. 12 mJ kW-class ultrafast fiber laser system using multidimensional coherent pulse addition. Opt. Lett.
**2016**, 41, 3343. [Google Scholar] [CrossRef] [PubMed] - Müller, M.; Kienel, M.; Klenke, A.; Gottschall, T.; Shestaev, E.; Plötner, M.; Limpert, J.; Tünnermann, A. 1 kW 1 mJ eight-channel ultrafast fiber laser. Opt. Lett.
**2016**, 41, 3439. [Google Scholar] [CrossRef] [PubMed] - Stark, H.; Buldt, J.; Müller, M.; Klenke, A.; Tünnermann, A.; Limpert, J. 23 mJ high-power fiber CPA system using electro-optically controlled divided-pulse amplification. Opt. Lett.
**2019**, 44, 5529. [Google Scholar] [CrossRef] - Stark, H.; Buldt, J.; Müller, M.; Klenke, A.; Limpert, J. 1 kW, 10 mJ, 120 fs coherently combined fiber CPA laser system. Opt. Lett.
**2021**, 46, 969. [Google Scholar] [CrossRef] - Müller, M.; Aleshire, C.; Buldt, J.; Stark, H.; Grebing, C.; Klenke, A.; Limpert, J. Scaling potential of beam-splitter-based coherent beam combination. Opt. Express
**2021**, 29, 27900. [Google Scholar] [CrossRef] - Veldkamp, W.B.; Leger, J.R.; Swanson, G.J. Coherent summation of laser beams using binary phase gratings. Opt. Lett.
**1986**, 11, 303. [Google Scholar] [CrossRef] - Ehbets, P.; Gale, M.T.; Herzig, H.P.; Prongué, D. High-efficiency continuous surface-relief gratings for two-dimensional array generation. Opt. Lett.
**1992**, 17, 908. [Google Scholar] [CrossRef][Green Version] - Coherent Laser Beam Combining. Available online: https://books.google.fi/books/about/Coherent_Laser_Beam_Combining.html?id=OccZAgAAQBAJ&source=kp_book_description&redir_esc=y (accessed on 8 June 2021).
- Flores, A.; Dajani, I.; Holten, R.; Ehrenreich, T.; Anderson, B. Multi-kilowatt diffractive coherent combining of pseudorandom-modulated fiber amplifiers. Opt. Eng.
**2016**, 55, 096101. [Google Scholar] [CrossRef][Green Version] - Hebling, J. Derivation of the pulse front tilt caused by angular dispersion. Opt. Quantum Electron.
**1996**, 28, 1759–1763. [Google Scholar] [CrossRef] - Zhou, T.; Sano, T.; Wilcox, R. Coherent combination of ultrashort pulse beams using two diffractive optics. Opt. Lett.
**2017**, 42, 4422. [Google Scholar] [CrossRef] - Cheung, E.C.; Ho, J.G.; Goodno, G.D.; Rice, R.R.; Rothenberg, J.; Thielen, P.; Weber, M.; Wickham, M. Diffractive-optics-based beam combination of a phase-locked fiber laser array. Opt. Lett.
**2008**, 33, 354. [Google Scholar] [CrossRef] [PubMed] - Redmond, S.M.; Ripin, D.J.; Yu, C.X.; Augst, S.J.; Fan, T.Y.; Thielen, P.A.; Rothenberg, J.E.; Goodno, G.D. Diffractive coherent combining of a 25 kW fiber laser array into a 19 kW Gaussian beam. Opt. Lett.
**2012**, 37, 2832. [Google Scholar] [CrossRef] - Thielen, P.A.; Ho, J.G.; Burchman, D.A.; Goodno, G.D.; Rothenberg, J.E.; Wickham, M.G.; Flores, A.; Lu, C.A.; Pulford, B.; Robin, C.; et al. Two-dimensional diffractive coherent combining of 15 fiber amplifiers into a 600 W beam. Opt. Lett.
**2012**, 37, 3741. [Google Scholar] [CrossRef] [PubMed] - McNaught, S.J.; Thielen, P.A.; Adams, L.N.; Ho, J.G.; Johnson, A.M.; Machan, J.P.; Rothenberg, J.E.; Shih, C.-C.; Shimabukuro, D.M.; Wacks, M.P.; et al. Scalable Coherent Combining of Kilowatt Fiber Amplifiers Into a 2.4-kW Beam. IEEE J. Sel. Top. Quantum Electron.
**2014**, 20, 174–181. [Google Scholar] [CrossRef] - Wilcox, R.; Dahlen, D.; Sano, T. Femtosecond Beam Combination Using Diffractive Optic Pairs. In Proceedings of the Conference on Lasers and Electro-Optics, San Jose, CA, USA, 14–19 May 2017; Volume 2017, p. SM4I.2. [Google Scholar]
- Zhou, T.; Du, Q.; Sano, T.; Wilcox, R.; Leemans, W. Two-dimensional combination of eight ultrashort pulsed beams using a diffractive optic pair. Opt. Lett.
**2018**, 43, 3269. [Google Scholar] [CrossRef] - Du, Q.; Zhou, T.; Doolittle, L.R.; Huang, G.; Li, D.; Wilcox, R. Deterministic stabilization of eight-way 2D diffractive beam combining using pattern recognition. Opt. Lett.
**2019**, 44, 4554. [Google Scholar] [CrossRef] - Liu, M.; Shen, H.; Yang, Y.; Xian, Y.; Zhang, J.; Wang, H.; Li, B.; Niu, X.; He, B. Investigation of combining-efficiency loss induced by a diffractive optical element in a single-aperture coherent beam combining system. Opt. Express
**2021**, 29, 5179. [Google Scholar] [CrossRef] - Klenke, A.; Müller, M.; Stark, H.; Tünnermann, A.; Limpert, J. Sequential phase locking scheme for a filled aperture intensity coherent combination of beam arrays. Opt. Express
**2018**, 26, 12072. [Google Scholar] [CrossRef] - Aleshire, C.; Steinkopff, A.; Jauregui, C.; Klenke, A.; Tünnermann, A.; Limpert, J. Simplified design of optical elements for filled-aperture coherent beam combination. Opt. Express
**2020**, 28, 21035. [Google Scholar] [CrossRef] - Harder, I.; Lano, M.; Lindlein, N.; Schwider, J. Homogenization and Beam Shaping with Microlens Arrays. In Photon Management; Photonics Europe: Strasbourg, France, 2004; Volume 5456, p. 99. [Google Scholar]
- Zimmermann, M.; Lindlein, N.; Voelkel, R.; Weible, K.J. Microlens laser beam homogenizer: From theory to application. Laser Beam Shap. VIII
**2007**, 6663, 666302. [Google Scholar] [CrossRef] - Jin, Y.; Hassan, A.; Jiang, Y. Freeform microlens array homogenizer for excimer laser beam shaping. Opt. Express
**2016**, 24, 24846. [Google Scholar] [CrossRef] - Streibl, N.; Nölscher, U.; Jahns, J.; Walker, S. Array generation with lenslet arrays. Appl. Opt.
**1991**, 30, 2739. [Google Scholar] [CrossRef] - Prossotowicz, M.; Heimes, A.; Flamm, D.; Jansen, F.; Otto, H.-J.; Budnicki, A.; Morgner, U.; Killi, A. Dynamic Coherent Beam Combining based on a Setup of Microlens Arrays. In Laser Resonators, Microresonators, and Beam Control XXII; Armani, A.M., Kudryashov, A.V., Paxton, A.H., Ilchenko, V.S., Eds.; SPIE: San Francisco, CA, USA, 2020; Volume 1126612, p. 38. [Google Scholar]
- Prossotowicz, M.; Flamm, D.; Heimes, A.; Jansen, F.; Otto, H.-J.; Budnicki, A.; Killi, A.; Morgner, U. Dynamic focus shaping with mixed-aperture coherent beam combining. Opt. Lett.
**2021**, 46, 1660. [Google Scholar] [CrossRef] - Kringlebotn, J.T.; Archambault, J.-L.; Reekie, L.; Payne, D.N. Er
^{3+}:Yb^{3+}-codoped fiber distributed-feedback laser. Opt. Lett.**1994**, 19, 2101. [Google Scholar] [CrossRef] - Yelen, K.; Zervas, M.N.; Hickey, L.M.B. Fibre DFB lasers with ultimate efficiency. OSA Trends Opt. Photonics Ser.
**2004**, 95, 703–705. [Google Scholar] - Bjarklev, A.; Broeng, J.; Bjarklev, A.S. Photonic Crystal Fibres; Springer: Boston, MA, USA, 2003; ISBN 9781461350958. [Google Scholar]
- Limpert, J.; Liem, A.; Reich, M.; Schreiber, T.; Nolte, S.; Zellmer, H.; Tunnermann, A.; Broeng, J.; Petersson, A.; Jakobsen, C. Low-nonlinearity single-transverse-mode ytterbium-doped photonic crystal fiber amplifier. Opt. Express
**2004**, 12, 1313. [Google Scholar] [CrossRef] - Kawamura, T.; Shirakawa, A.; Saito, K. Phase-locked and mode-locked multicore photonic crystal fiber laser with a saturable absorber. Opt. Express
**2021**, 29, 17023. [Google Scholar] [CrossRef] - Limpert, J.; Stutzki, F.; Jansen, F.; Otto, H.-J.; Eidam, T.; Jauregui, C.; Tünnermann, A. Yb-doped large-pitch fibres: Effective single-mode operation based on higher-order mode delocalisation. Light Sci. Appl.
**2012**, 1, e8. [Google Scholar] [CrossRef][Green Version] - Filippov, V.; Chamorovskii, Y.; Kerttula, J.; Golant, K.; Pessa, M.; Okhotnikov, O.G. Double clad tapered fiber for high power applications. Opt. Express
**2008**, 16, 1929. [Google Scholar] [CrossRef] [PubMed] - Filippov, V.; Chamorovskii, Y.K.; Golant, K.M.; Vorotynskii, A.; Okhotnikov, O.G. Optical Amplifiers and Lasers based on Tapered Fiber Geometry for Power and Energy Scaling with Low Signal Distortion. In Fiber Lasers XIII: Technology, Systems, and Applications; Ballato, J., Ed.; SPIE: San Francisco, CA, USA, 2016; Volume 9728, p. 97280V. [Google Scholar]
- Kerttula, J.; Filippov, V.; Chamorovskii, Y.; Ustimchik, V.; Golant, K.; Okhotnikov, O.G. Principles and performance of tapered fiber lasers: From uniform to flared geometry. Appl. Opt.
**2012**, 51, 7025. [Google Scholar] [CrossRef] - Huang, L.; Ma, P.; Su, R.; Lai, W.; Ma, Y.; Zhou, P. Comprehensive investigation on the power scaling of a tapered Yb-doped fiber-based monolithic linearly polarized high-peak-power near-transform-limited nanosecond fiber laser. Opt. Express
**2021**, 29, 761. [Google Scholar] [CrossRef] [PubMed] - Bobkov, K.K.; Aleshkina, S.S.; Khudyakov, M.M.; Lipatov, D.S.; Likhachev, M.E. Active Tapered Fibers for High Peak Power Fiber Lasers. In Micro-structured and Specialty Optical Fibres VII; Peterka, P., Kalli, K., Mendez, A., Eds.; SPIE: Bellingham, WA, USA, 2021; Volume 11773, p. 7. [Google Scholar]
- Guesmi, K.; Mugnier, A.; Canat, G.; Canal, C.; Maine, P. Simple Design for High Energy Femtosecond Tapered Double Clad Fiber Amplifier. In Fiber Lasers XVIII: Technology and Systems; Zervas, M.N., Jauregui-Misas, C., Eds.; SPIE: Bellingham, WA, USA, 2021; Volume 11665, p. 39. [Google Scholar]
- Ye, Y.; Xi, X.; Shi, C.; Yang, B.; Wang, X.; Zhang, H.; Zhou, P.; Xu, X. Comparative study on transverse mode instability of fiber amplifiers based on long tapered fiber and conventional uniform fiber. Laser Phys. Lett.
**2019**, 16, 085109. [Google Scholar] [CrossRef] - Fedotov, A.; Noronen, T.; Gumenyuk, R.; Ustimchik, V.; Chamorovskii, Y.; Golant, K.; Odnoblyudov, M.; Rissanen, J.; Niemi, T.; Filippov, V. Ultra-large core birefringent Yb-doped tapered double clad fiber for high power amplifiers. Opt. Express
**2018**, 26, 6581. [Google Scholar] [CrossRef] [PubMed][Green Version] - Filippov, V.; Chamorovskii, Y.; Kerttula, J.; Kholodkov, A.; Okhotnikov, O.G. 600 W power scalable single transverse mode tapered double-clad fiber laser. Opt. Express
**2009**, 17, 1203. [Google Scholar] [CrossRef] - Filippov, V.; Kerttula, J.; Chamorovskii, Y.; Golant, K.; Okhotnikov, O.G. Highly efficient 750 W tapered double-clad ytterbium fiber laser. Opt. Express
**2010**, 18, 12499. [Google Scholar] [CrossRef] - An, Y.; Yang, H.; Chen, X.; Xiao, H.; Huang, L.; Ma, P.; Xi, X.; Wang, X.; Zhou, P.; Pan, Z.; et al. 4 kW Single-Mode Laser Output Assisted by a Double-Tapered Double-Clad Fiber. In Fiber Lasers XVIII: Technology and Systems; Zervas, M.N., Jauregui-Misas, C., Eds.; SPIE: Bellingham, WA, USA, 2021; Volume 11665, p. 2. [Google Scholar]
- Zeng, L.; Pan, Z.; Xi, X.; Yang, H.; Ye, Y.; Huang, L.; Zhang, H.; Wang, X.; Wang, Z.; Zhou, P.; et al. 5 kW monolithic fiber amplifier employing homemade spindle-shaped ytterbium-doped fiber. Opt. Lett.
**2021**, 46, 1393. [Google Scholar] [CrossRef] - Yang, B.; Zhang, H.; Shi, C.; Wang, X.; Pan, Z.; Wang, Z.; Zhou, P.; Xu, X. High power monolithic tapered ytterbium-doped fiber laser oscillator. Opt. Express
**2019**, 27, 7585. [Google Scholar] [CrossRef] [PubMed] - Patokoski, K.; Rissanen, J.; Noronen, T.; Gumenyuk, R.; Chamorovskii, Y.; Filippov, V.; Toivonen, J. Single-frequency 100 ns/05 mJ laser pulses from all-fiber double clad ytterbium doped tapered fiber amplifier. Opt. Express
**2019**, 27, 31532. [Google Scholar] [CrossRef] - Kerttula, J.; Filippov, V.; Chamorovskii, Y.; Golant, K.; Okhotnikov, O.G. Actively Q-switched 16-mJ tapered double-clad ytterbium-doped fiber laser. Opt. Express
**2010**, 18, 18543. [Google Scholar] [CrossRef] - Ustimchik, V.E.; Stoliarov, D.A.; Korobko, D.A.; Chamorovskii, Y.K.; Filippov, V.N. Passively Q-switched 0.24 mJ ring laser based on anisotropic tapered fiber. Results Phys.
**2021**, 20, 103640. [Google Scholar] [CrossRef] - Bobkov, K.; Levchenko, A.; Kashaykina, T.; Aleshkina, S.; Bubnov, M.; Lipatov, D.; Laptev, A.; Guryanov, A.; Leventoux, Y.; Granger, G.; et al. Scaling of average power in sub-MW peak power Yb-doped tapered fiber picosecond pulse amplifiers. Opt. Express
**2021**, 29, 1722. [Google Scholar] [CrossRef] - Petrov, A.; Odnoblyudov, M.; Gumenyuk, R.; Minyonok, L.; Chumachenko, A.; Filippov, V. Picosecond Yb-doped tapered fiber laser system with 1.26 MW peak power and 200 W average output power. Sci. Rep.
**2020**, 10, 17781. [Google Scholar] [CrossRef] - Andrianov, A.V.; Kim, A.V.; Anashkina, E.A.; Meyerov, I.B.; Lebedev, S.A.; Sergeev, A.M.; Koenig, K.; Mourou, G. Modeling of coherent beam combining from multimillijoule chirped pulse tapered fiber amplifiers. Eur. Phys. J. Spec. Top.
**2015**, 224, 2579–2583. [Google Scholar] [CrossRef] - Bruesselbach, H.; Jones, D.C.; Mangir, M.S.; Minden, M.; Rogers, J.L. Self-organized coherence in fiber laser arrays. Opt. Lett.
**2005**, 30, 1339. [Google Scholar] [CrossRef] - Rothenberg, J.E. Passive coherent phasing of fiber laser arrays. In Lasers and Applications in Science and Engineering; SPIE: San Jose, CA, USA, 2008; Volume 6873, p. 6873151-9. [Google Scholar]
- Wang, B.; Sanchez, A. All-fiber Passive Coherent Beam Combining of Fiber Lasers and Challenges. In Proceedings of the Lasers, Sources, and Related Photonic Devices, San Diego, CA, USA, 29 January–1 February 2012; p. FTh3A.2. [Google Scholar]
- Wu, T.; Chang, W.; Galvanauskas, A.; Winful, H.G. Dynamical, bidirectional model for coherent beam combining in passive fiber laser arrays. Opt. Express
**2010**, 18, 25873. [Google Scholar] [CrossRef] - Jeux, F.; Desfarges-Berthelemot, A.; Kermène, V.; Barthelemy, A. Experimental demonstration of passive coherent combining of fiber lasers by phase contrast filtering. Opt. Express
**2012**, 20, 28941. [Google Scholar] [CrossRef] [PubMed] - Napartovich, A.P.; Vysotsky, D.V. Phase-locking of multicore fibre laser due to talbot self-reproduction. J. Mod. Opt.
**2003**, 50, 2715–2725. [Google Scholar] [CrossRef] - Huo, Y.; Cheo, P.K.; King, G.G. Fundamental mode operation of a 19-core phase-locked Yb-doped fiber amplifier. Opt. Express
**2004**, 12, 6230. [Google Scholar] [CrossRef] [PubMed] - He, B.; Lou, Q.; Wang, W.; Zhou, J.; Zheng, Y.; Dong, J.; Wei, Y.; Chen, W. Experimental demonstration of phase locking of a two-dimensional fiber laser array using a self-imaging resonator. Appl. Phys. Lett.
**2008**, 92, 251115. [Google Scholar] [CrossRef] - Corcoran, C.J.; Durville, F. Experimental demonstration of a phase-locked laser array using a self-Fourier cavity. Appl. Phys. Lett.
**2005**, 86, 201118. [Google Scholar] [CrossRef] - Kong, H.J.; Yoon, J.W.; Shin, J.S.; Beak, D.H. Long-term stabilized two-beam combination laser amplifier with stimulated Brillouin scattering mirrors. Appl. Phys. Lett.
**2008**, 92, 021120. [Google Scholar] [CrossRef][Green Version] - Zhou, P.; Liu, Z.; Wang, X.; Ma, Y.; Ma, H.; Xu, X.; Guo, S. Coherent Beam Combining of Fiber Amplifiers Using Stochastic Parallel Gradient Descent Algorithm and Its Application. IEEE J. Sel. Top. Quantum Electron.
**2009**, 15, 248–256. [Google Scholar] [CrossRef] - Yang, Y.; Hu, M.; He, B.; Zhou, J.; Liu, H.; Dai, S.; Wei, Y.; Lou, Q. Passive coherent beam combining of four Yb-doped fiber amplifier chains with injection-locked seed source. Opt. Lett.
**2013**, 38, 854. [Google Scholar] [CrossRef][Green Version] - Fridman, M.; Nixon, M.; Davidson, N.; Friesem, A.A. Passive phase locking of 25 fiber lasers. Opt. Lett.
**2010**, 35, 1434. [Google Scholar] [CrossRef] - Cao, J.; Hou, J.; Lu, Q.; Xu, X. Numerical research on self-organized coherent fiber laser arrays with circulating field theory. J. Opt. Soc. Am. B
**2008**, 25, 1187. [Google Scholar] [CrossRef] - Chang, W.-Z.; Wu, T.-W.; Winful, H.G.; Galvanauskas, A. Array size scalability of passively coherently phased fiber laser arrays. Opt. Express
**2010**, 18, 9634. [Google Scholar] [CrossRef] [PubMed] - Bruesselbach, H.; Minden, M.; Rogers, J.L.; Jones, D.C.; Mangir, M.S. 200 W Self-Organized Coherent Fiber Arrays. In Proceedings of the Conference on Lasers and Electro-Optics, Baltimore, MD, USA, 22–27 May 2005; Volume CMDD, pp. 532–534. [Google Scholar]
- Loftus, T.H.; Thomas, A.M.; Norsen, M.; Minelly, J.D.; Jones, P.; Honea, E.; Shakir, S.A.; Hendow, S.; Culver, W.; Nelson, B.; et al. Four-Channel, High Power, Passively Phase Locked Fiber Array. In Proceedings of the Advanced Solid-State Photonics, Nara, Japan, 27–30 January 2008; p. WA4. [Google Scholar]
- Jeux, F.; Desfarges-Berthelemot, A.; Kermene, V.; Barthelemy, A. Passive Coherent Combining of 15 Fiber Lasers by Phase Contrast Filtering. In Proceedings of the 2013 Conference on Lasers & Electro-Optics Europe & International Quantum Electronics Conference CLEO EUROPE/IQEC, Munich, Germany, 12–16 May 2013; p. 1. [Google Scholar]
- Zaouter, Y.; Daniault, L.; Hanna, M.; Papadopoulos, D.N.; Morin, F.; Hönninger, C.; Druon, F.; Mottay, E.; Georges, P. 2 GW Peak Power Ultrafast Fiber System Using Passive Coherent Beam Combining. In Proceedings of the Lasers, Sources, and Related Photonic Devices, San Diego, CA, USA, 29 January–1 February 2012; p. AM6A.1. [Google Scholar]
- Daniault, L.; Hanna, M.; Papadopoulos, D.N.; Zaouter, Y.; Mottay, E.; Druon, F.; Georges, P. Coherent Combining of Two Femtosecond Chirped-Pulse Amplifiers in a Passive Architecture. In Proceedings of the Lasers, Sources, and Related Photonic Devices, San Diego, CA, USA, 29 January–1 February 2012; p. AT4A.29. [Google Scholar]
- Zaouter, Y.; Daniault, L.; Hanna, M.; Papadopoulos, D.N.; Morin, F.; Hönninger, C.; Druon, F.; Mottay, E.; Georges, P. Passive coherent combination of two ultrafast rod type fiber chirped pulse amplifiers. Opt. Lett.
**2012**, 37, 1460. [Google Scholar] [CrossRef] - Bai, G.; Shen, H.; Liu, M.; Liu, K.; Zhang, H.; Niu, X.; Yang, Y.; He, B.; Zhou, J. Single-Aperture Passive Coherent Beam Combining of Fiber Lasers Based on Diffractive Optical Element. In Proceedings of the Conference on Lasers and Electro-Optics, San Jose, CA, USA, 5–10 May 2019; p. JW2A.95. [Google Scholar]
- Tilseth, E.; Kunkel, W.M.; Leger, J.R. Demonstration of Spatial Mode Selection in a Coherently Combined Fiber Laser. In Proceedings of the 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC), Munich, Germany, 23–27 June 2019; p. 1. [Google Scholar]
- Liu, H.; He, B.; Zhou, J.; Yang, Y.; Zheng, Y.; Hu, M.; Lou, Q. Experiments and Perturbative Analysis of Dammann-Grating-Based Aperture Filling in a Passive Coherent Beam Combination. J. Light. Technol.
**2014**, 32, 2220–2227. [Google Scholar] [CrossRef] - Yang, Y.; Zheng, Y.; Hu, M.; Zhao, C.; Chen, X.; Liu, K.; He, B.; Zhou, J. Coherent Beam Combining of Fiber Amplifiers by means of Dammann Grating Spatial Filter. In Proceedings of the Advanced Solid State Lasers, Shanghai, China, 16–21 November 2014; p. AM5A.51. [Google Scholar]
- Jain, A.; Spiegelberg, C.; Smirnov, V.; Bochove, E.; Glebov, L. Efficient Coherent Beam Combining of Fiber Lasers Using Multiplexed Volume Bragg Gratings. In Proceedings of the Conference on Lasers and Electro-Optics, San Jose, CA, USA, 6–11 May 2012; p. CF2N.8. [Google Scholar]
- Bochove, E.J.; Shakir, S.A. Analysis of a Spatial-Filtering Passive Fiber Laser Beam Combining System. IEEE J. Sel. Top. Quantum Electron.
**2009**, 15, 320–327. [Google Scholar] [CrossRef] - Shakir, S.A.; Culver, B.; Nelson, B.; Starcher, Y.; Bates, G.M.; Hedrick, J.W., Jr. Power Scaling of Passively Phased Fiber Amplifier Arrays. In Optical Technologies for Arming, Safing, Fuzing, and Firing IV; Dickey, F.M., Beyer, R.A., Eds.; SPIE: San Diego, CA, USA, 2008; Volume 7070, p. 70700N. [Google Scholar]
- Li, L.; Schülzgen, A.; Chen, S.; Temyanko, V.L.; Moloney, J.V.; Peyghambarian, N. Phase locking and in-phase supermode selection in monolithic multicore fiber lasers. Opt. Lett.
**2006**, 31, 2577. [Google Scholar] [CrossRef] - Steinhausser, B.; Brignon, A.; Lallier, E.; Huignard, J.P.; Georges, P. High energy, single-mode, narrow-linewidth fiber laser source using stimulated Brillouin scattering beam cleanup. Opt. Express
**2007**, 15, 6464. [Google Scholar] [CrossRef][Green Version] - Chiang, H.-S.; Leger, J.R.; Nilsson, J.; Sahu, J. Passive Coherent Beam Combining of Fiber Lasers: Accurate Measurements of Phase Error Tolerance. In Proceedings of the CLEO, San Jose, CA, USA, 9–14 June 2013; p. CW3M.6. [Google Scholar]
- Wu, T.; Chang, W.; Galvanauskas, A.; Winful, H.G. Model for passive coherent beam combining in fiber laser arrays. Opt. Express
**2009**, 17, 19509. [Google Scholar] [CrossRef] - Wang, B.; Mies, E.; Minden, M.; Sanchez, A. All-fiber 50 W coherently combined passive laser array. Opt. Lett.
**2009**, 34, 863. [Google Scholar] [CrossRef] [PubMed] - Bloom, G.; Larat, C.; Lallier, E.; Lehoucq, G.; Bansropun, S.; Lee-Bouhours, M.-S.L.; Loiseaux, B.; Carras, M.; Marcadet, X.; Lucas-Leclin, G.; et al. Passive coherent beam combining of quantum-cascade lasers with a Dammann grating. Opt. Lett.
**2011**, 36, 3810. [Google Scholar] [CrossRef][Green Version] - Corcoran, C.J.; Durville, F. Passive Phasing in a Coherent Laser Array. IEEE J. Sel. Top. Quantum Electron.
**2009**, 15, 294–300. [Google Scholar] [CrossRef] - Bloom, G.; Larat, C.; Lallier, E.; Carras, M.; Marcadet, X. Coherent combining of two quantum-cascade lasers in a Michelson cavity. Opt. Lett.
**2010**, 35, 1917. [Google Scholar] [CrossRef] [PubMed] - Zhao, P.; Dong, Z.; Zhang, J.; Lin, X. Passive coherent beam combination of three Nd:YAG lasers using cascaded Michelson-type compound cavities. Opt. Express
**2018**, 26, 18019. [Google Scholar] [CrossRef] - Golubentsev, A.A.; Likhanskii, V.V.; Napartovich, A.P. Theory of Phase Locking of an Array of Lasers. In proceding of High-Power Multibeam Lasers and Their Phase Locking; SPIE: St. Petersburg, Russian, 7 October 1993; Volume 2109, pp. 205–218. [Google Scholar]
- Rockwell, D.A.; Giuliano, C.R. Coherent coupling of laser gain media using phase conjugation. Opt. Lett.
**1986**, 11, 147. [Google Scholar] [CrossRef] [PubMed] - Carroll, D.L.; Johnson, R.; Pfeifer, S.J.; Moyer, R.H. Experimental investigations of stimulated Brillouin scattering beam combination. J. Opt. Soc. Am. B
**1992**, 9, 2214. [Google Scholar] [CrossRef] - Eggleston, J. Steady-state coherent Raman beam combining with multiaxial mode lasers. IEEE J. Quantum Electron.
**1986**, 22, 1942–1952. [Google Scholar] [CrossRef] - Park, S.; Cha, S.; Oh, J.; Lee, H.; Ahn, H.; Churn, K.S.; Kong, H.J. Coherent beam combination using self-phase locked stimulated Brillouin scattering phase conjugate mirrors with a rotating wedge for high power laser generation. Opt. Express
**2016**, 24, 8641. [Google Scholar] [CrossRef] - Botez, D. Monolithic Phase-Locked Semiconductor Laser Arrays. In Diode Laser Arrays; Cambridge University Press: Cambridge, UK, 1994; pp. 1–71. [Google Scholar]
- Bochove, E.J.; Cheo, P.K.; King, G.G. Self-organization in a multicore fiber laser array. Opt. Lett.
**2003**, 28, 1200. [Google Scholar] [CrossRef] - Cheo, P.K.; Liu, A.; King, G.G. A high-brightness laser beam from a phase-locked multicore Yb-doped fiber laser array. IEEE Photonics Technol. Lett.
**2001**, 13, 439–441. [Google Scholar] [CrossRef] - Cheo, P.K. Clad Pumped, Eye-Safe and Multi-Core Phase-Locked Fiber Lasers. U.S. Patent 6,031,850, 29 February 2000. [Google Scholar]
- Minden, M.L.; Bruesselbach, H.W.; Rogers, J.L.; Mangir, M.S.; Jones, D.C.; Dunning, G.J.; Hammon, D.L.; Solis, A.J.; Vaughan, L. Self-Organized Coherence in Fiber Laser Arrays. In Fiber Lasers: Technology, Systems, and Applications; Durvasula, L.N., Ed.; SPIE: San Jose, CA, USA, 7 June 2004; Volume 5335, p. 89. [Google Scholar]
- Zhou, P.; Chen, Z.; Xu, X.; Hou, J.; Liu, Z. Modeling Self-Organized Coherent Fiber Laser Array. In Proceedings of the High-Power Lasers and Applications IV, Beijing, China, 6 February 2008; SPIE: Beijing, China, 2008; Volume 6823, p. 68230G. [Google Scholar]
- Chen, Z.; Hou, J.; Zhou, P.; Wang, X.; Xu, X.; Jiang, Z.; Liu, Z. Mutual injection locking and coherent combining of three individual fiber lasers. Opt. Commun.
**2009**, 282, 60–63. [Google Scholar] [CrossRef] - Chen, Z.; Hou, J.; Wang, Z.; Chen, S. Self-Organized Coherence in Fiber Laser Arrays by Mutual Injection Locking. In Laser Optics 2010; Rosanov, N.N., Venediktov, V.Y., Eds.; SPIE: St. Petersburg, Russian, 22 March 2011; Volume 7822, p. 7822031-7. [Google Scholar]
- Hansch, T.W.; Couillaud, B. Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity. Opt. Commun.
**1980**, 35, 441–444. [Google Scholar] [CrossRef][Green Version] - Anderegg, J.; Brosnan, S.; Cheung, E.; Epp, P.; Hammons, D.; Komine, H.; Weber, M.; Wickham, M. Coherently Coupled High-Power Fiber Arrays. In Fiber Lasers III: Technology, Systems and Applications; Brown, A.J.W., Nilsson, J., Harter, D.J., Tünnermann, A., Eds.; SPIE: San Jose, CA, USA, 2006; Volume 6102, p. 61020U. [Google Scholar]
- O’Meara, T.R. The multidither principle in adaptive optics. J. Opt. Soc. Am.
**1977**, 67, 306. [Google Scholar] [CrossRef] - Ma, Y.; Zhou, P.; Wang, X.; Ma, H.; Xu, X.; Si, L.; Liu, Z.; Zhao, Y. Coherent beam combination with single frequency dithering technique. Opt. Lett.
**2010**, 35, 1308. [Google Scholar] [CrossRef] - Ma, Y.; Wang, X.; Leng, J.; Xiao, H.; Dong, X.; Zhu, J.; Du, W.; Zhou, P.; Xu, X.; Si, L.; et al. Coherent beam combination of 1.08 kW fiber amplifier array using single frequency dithering technique. Opt. Lett.
**2011**, 36, 951. [Google Scholar] [CrossRef] - Ma, P.F.; Zhou, P.; Su, R.T.; Ma, Y.X.; Liu, Z.J. Coherent polarization beam combining of eight fiber lasers using single-frequency dithering technique. Laser Phys. Lett.
**2012**, 9, 456–458. [Google Scholar] [CrossRef][Green Version] - Tang, X.; Huang, Z.; Zhang, D.; Wang, X.; Li, J.; Liu, C. An active phase locking of multiple fiber channels via square wave dithering algorithm. Opt. Commun.
**2014**, 321, 198–204. [Google Scholar] [CrossRef] - Shay, T.M.; Benham, V.; Baker, J.T.; Sanchez, A.D.; Pilkington, D.; Lu, C.A. Self-Synchronous and Self-Referenced Coherent Beam Combination for Large Optical Arrays. IEEE J. Sel. Top. Quantum Electron.
**2007**, 13, 480–486. [Google Scholar] [CrossRef] - Shay, T.M. Theory of electronically phased coherent beam combination without a reference beam. Opt. Express
**2006**, 14, 12188. [Google Scholar] [CrossRef] [PubMed] - Daniault, L.; Hanna, M.; Lombard, L.; Zaouter, Y.; Mottay, E.; Goular, D.; Bourdon, P.; Druon, F.; Georges, P. Coherent beam combining of two femtosecond fiber chirped-pulse amplifiers. Opt. Lett.
**2011**, 36, 621. [Google Scholar] [CrossRef][Green Version] - Wagner, T.J. Fiber Laser Beam Combining and Power Scaling Progress: Air Force Research Laboratory Laser Division. In Fiber Lasers IX: Technology, Systems, and Applications; SPIE: San Francisco, CA, USA, 15 February 2012; Volume 8237, p. 823718. [Google Scholar]
- Bourdon, P.; Jacqmin, H.; Augère, B.; Durécu, A.; Goular, D.; Rouzé, B.; Domel, R.; Fleury, D.; Planchat, C.; Lombard, L. Target-in-the-Loop Frequency-Tagging Coherent Combining of 7 Fiber Lasers up to 1 km Range. In Fiber Lasers XVIII: Technology and Systems; Zervas, M.N., Jauregui-Misas, C., Eds.; SPIE: Bellingham, WA, USA, 2021; p. 50. [Google Scholar]
- Kabeya, D.; Kermene, V.; Fabert, M.; Benoist, J.; Desfarges-Berthelemot, A.; Barthelemy, A. Active coherent combining of laser beam arrays by means of phase-intensity mapping in an optimization loop. Opt. Express
**2015**, 23, 31059. [Google Scholar] [CrossRef] - Wang, D.; Du, Q.; Zhou, T.; Li, D.; Wilcox, R. Stabilization of the 81-channel coherent beam combination using machine learning. Opt. Express
**2021**, 29, 5694. [Google Scholar] [CrossRef] - Du, Q.; Wang, D.; Zhou, T.; Li, D.; Wilcox, R. 81-beam coherent combination using a programmable array generator. Opt. Express
**2021**, 29, 5407. [Google Scholar] [CrossRef] [PubMed] - Su, R.; Zhou, P.; Wang, X.; Zhang, H.; Xu, X. Impact of temporal and spectral aberrations on coherent beam combination of nanosecond fiber lasers. Appl. Opt.
**2013**, 52, 2187. [Google Scholar] [CrossRef] [PubMed] - Yu, H.L.; Ma, P.F.; Wang, X.L.; Su, R.T.; Zhou, P.; Chen, J.B. Influence of temporal–spectral effects on ultrafast fiber coherent polarization beam combining system. Laser Phys. Lett.
**2015**, 12, 105301. [Google Scholar] [CrossRef] - Ma, P.; Tao, R.; Wang, X.; Ma, Y.; Su, R.; Zhou, P. Coherent polarization beam combination of four mode-locked fiber MOPAs in picosecond regime. Opt. Express
**2014**, 22, 4123. [Google Scholar] [CrossRef] [PubMed] - Yu, C.X.; Kansky, J.E.; Shaw, S.E.J.; Murphy, D.V.; Higgs, C. Coherent beam combining of large number of PM fibres in 2-D fibre array. Electron. Lett.
**2006**, 42, 1024. [Google Scholar] [CrossRef] - Lombard, L.; Azarian, A.; Cadoret, K.; Bourdon, P.; Goular, D.; Canat, G.; Jolivet, V.; Jaouën, Y.; Vasseur, O. Coherent beam combination of narrow-linewidth 15μm fiber amplifiers in a long-pulse regime. Opt. Lett.
**2011**, 36, 523. [Google Scholar] [CrossRef] - Siiman, L.A.; Chang, W.; Zhou, T.; Galvanauskas, A. Coherent femtosecond pulse combining of multiple parallel chirped pulse fiber amplifiers. Opt. Express
**2012**, 20, 18097. [Google Scholar] [CrossRef] - Müller, M.; Klenke, A.; Steinkopff, A.; Stark, H.; Tünnermann, A.; Limpert, J. 3.5 kW coherently combined ultrafast fiber laser. Opt. Lett.
**2018**, 43, 6037. [Google Scholar] [CrossRef] [PubMed] - Zhou, S.; Wise, F.W.; Ouzounov, D.G. Divided-pulse amplification of ultrashort pulses. Opt. Lett.
**2007**, 32, 871. [Google Scholar] [CrossRef] - Stark, H.; Müller, M.; Kienel, M.; Klenke, A.; Limpert, J.; Tünnermann, A. Electro-optically controlled divided-pulse amplification. Opt. Express
**2017**, 25, 13494. [Google Scholar] [CrossRef] - Guichard, F.; Lavenu, L.; Hanna, M.; Zaouter, Y.; Georges, P. Coherent combining efficiency in strongly saturated divided-pulse amplification systems. Opt. Express
**2016**, 24, 25329. [Google Scholar] [CrossRef] [PubMed] - Zaouter, Y.; Guichard, F.; Daniault, L.; Hanna, M.; Morin, F.; Hönninger, C.; Mottay, E.; Druon, F.; Georges, P. Femtosecond fiber chirped- and divided-pulse amplification system. Opt. Lett.
**2013**, 38, 106. [Google Scholar] [CrossRef] [PubMed] - Kienel, M.; Klenke, A.; Eidam, T.; Hädrich, S.; Limpert, J.; Tünnermann, A. Energy scaling of femtosecond amplifiers using actively controlled divided-pulse amplification. Opt. Lett.
**2014**, 39, 1049. [Google Scholar] [CrossRef] - Guichard, F.; Zaouter, Y.; Hanna, M.; Mai, K.-L.; Morin, F.; Hönninger, C.; Mottay, E.; Georges, P. High-energy chirped- and divided-pulse Sagnac femtosecond fiber amplifier. Opt. Lett.
**2015**, 40, 89. [Google Scholar] [CrossRef] - Daniault, L.; Hanna, M.; Papadopoulos, D.N.; Zaouter, Y.; Mottay, E.; Druon, F.; Georges, P. High peak-power stretcher-free femtosecond fiber amplifier using passive spatio-temporal coherent combining. Opt. Express
**2012**, 20, 21627. [Google Scholar] [CrossRef] [PubMed][Green Version] - Kienel, M.; Müller, M.; Klenke, A.; Eidam, T.; Limpert, J.; Tünnermann, A. Multidimensional coherent pulse addition of ultrashort laser pulses. Opt. Lett.
**2015**, 40, 522. [Google Scholar] [CrossRef] - Loftus, T.H.; Liu, A.; Hoffman, P.R.; Thomas, A.M.; Norsen, M.; Royse, R.; Honea, E. 522 W average power, spectrally beam-combined fiber laser with near-diffraction-limited beam quality. Opt. Lett.
**2007**, 32, 349. [Google Scholar] [CrossRef] - Andrusyak, O.; Smirnov, V.; Venus, G.; Vorobiev, N.; Glebov, L. Applications of Volume Bragg Gratings for Spectral Control and Beam Combining of High Power Fiber Lasers. In Fiber Lasers VI: Technology, Systems, and Applications; Gapontsev, D.V., Kliner, D.A., Dawson, J.W., Tankala, K., Eds.; SPIE: San Jose, CA, USA, 19 February 2009; Volume 7195, p. 71951Q. [Google Scholar]
- Regelskis, K.; Hou, K.-C.; Raciukaitis, G.; Galvanauskas, A. Spatial-Dispersion-Free Spectral Beam Combining of High Power Pulsed Yb-Doped Fiber Lasers. In Proceedings of the 2008 Conference on Lasers and Electro-Optics, San Jose, CA, USA, 4–9 May 2008; pp. 1–2. [Google Scholar]
- Chang, W.-Z.; Zhou, T.; Siiman, L.A.; Galvanauskas, A. Femtosecond pulse spectral synthesis in coherently-spectrally combined multi-channel fiber chirped pulse amplifiers. Opt. Express
**2013**, 21, 3897. [Google Scholar] [CrossRef] - Guichard, F.; Hanna, M.; Lombard, L.; Zaouter, Y.; Hönninger, C.; Morin, F.; Druon, F.; Mottay, E.; Georges, P. Two-channel pulse synthesis to overcome gain narrowing in femtosecond fiber amplifiers. Opt. Lett.
**2013**, 38, 5430. [Google Scholar] [CrossRef] [PubMed] - Rigaud, P.; Kermene, V.; Bouwmans, G.; Bigot, L.; Desfarges-Berthelemot, A.; Labat, D.; Le Rouge, A.; Mansuryan, T.; Barthélémy, A. Spatially dispersive amplification in a 12-core fiber and femtosecond pulse synthesis by coherent spectral combining. Opt. Express
**2013**, 21, 13555. [Google Scholar] [CrossRef] - Guichard, F.; Hanna, M.; Lombard, L.; Zaouter, Y.; Hönninger, C.; Morin, F.; Druon, F.; Mottay, E.; Georges, P. Spectral pulse synthesis in large-scale ultrafast coherent combining systems. Eur. Phys. J. Spec. Top.
**2015**, 224, 2545–2549. [Google Scholar] [CrossRef] - Goodno, G.D.; McNaught, S.J.; Rothenberg, J.E.; McComb, T.S.; Thielen, P.A.; Wickham, M.G.; Weber, M.E. Active phase and polarization locking of a 1.4 kW fiber amplifier. Opt. Lett.
**2010**, 35, 1542. [Google Scholar] [CrossRef] - Prieto, C.; Vaamonde, E.; Diego-Vallejo, D.; Jimenez, J.; Urbach, B.; Vidne, Y.; Shekel, E. Dynamic laser beam shaping for laser aluminium welding in e-mobility applications. Procedia CIRP
**2020**, 94, 596–600. [Google Scholar] [CrossRef] - Montoya, J.; Hwang, C.; Martz, D.; Aleshire, C.; Fan, T.Y.; Ripin, D.J. Photonic lantern kW-class fiber amplifier. Opt. Express
**2017**, 25, 27543. [Google Scholar] [CrossRef] [PubMed] - Uberna, R.; Bratcher, A.; Alley, T.G.; Sanchez, A.D.; Flores, A.S.; Pulford, B. Coherent combination of high power fiber amplifiers in a two-dimensional re-imaging waveguide. Opt. Express
**2010**, 18, 13547. [Google Scholar] [CrossRef] [PubMed] - Gerstner, E. Extreme light. Nat. Mater.
**2016**, 15, 1. [Google Scholar] [CrossRef]

**Figure 2.**Schematic representation of four main methods of incoherent beam combining (

**a**) side-by-side beam combining, (

**b**) beam combining using all-fiber passive signal components, (

**c**) SBC with volume Bragg gratings (VBG) as a wavelength-dependent transmission element, and (

**d**) SBC with reflection diffraction grating as a dispersive optical element.

**Figure 4.**Intensity patterns of the coherent combination of seven beams in tiled-apperture geometry at different distances. The beam profiles are shown in the same frame scale.

**Figure 5.**Impact of fill factor on the far-field intensity patterns of the coherent combination of seven beams in tiled-apperture geometry. The 2D beam profiles shown in the insets are illustrated in the same frame scale.

**Figure 6.**Schematic of tiled aperture coherent beam combination; (

**a**) CBC of multiple laser array in far field due to propagation and (

**b**) CBC of multiple laser beam emitted from multicore fiber in far field by implementing an optical lens.

**Figure 7.**Schematic of filled aperture CBC systems by the four most popular optical elements; (

**a**) CBC with polarization beam splitter (PBS), (

**b**) CBC with intensity beam splitter (IBS), (

**c**) CBC with diffractive optical element (DOE), and (

**d**) and CBC with segment mirror.

**Figure 8.**Schematic concept of mixed aperture CBC based on MLAs as a splitting and combining sections along with spatial light modulator as a phase shifter.

**Figure 9.**Far-field intensity patterns of coherent beam combination of seven laser beams, (

**a**) when the phase-locking system is on and (

**b**) when the phase-locking system is off. The 2D beam profiles shown in the insets are illustrated in the same frame scale.

**Figure 13.**Schematic representation of spatial coherent beam combining; (

**a**) PCBC with PBSs as splitters, TFPs as combiners, and phase-locking system by implementing Hansch–Couillaud detectors; (

**b**) CBC using fiber coupler as a splitter, IBSs as combining elements, and phase-locking systems by utilizing a single detector.

**Figure 15.**Schematic representation of multidimentional coherent beam combination of ultrafast pulsed laser.

**Figure 16.**Schematic representation of spectral coherent beam combination of ultrafast pulsed laser.

Year | Channel | Geometry | Operation Mode | Combining Efficiency | Controlling System | Institution | Ref. |
---|---|---|---|---|---|---|---|

2006 | 48 | Tiled | CW | RMS erorr < λ/30 | SPGD | MIT | [293] |

2011 | 64 | Tiled | CW | RMS erorr < λ/10 | PIM | TRT | [148] |

2017 | 37 | Tiled | CW | 96% | PIM | UNILIM | [151] |

2020 | 61 | Tiled | Pulsed | 50%, RMS erorr < λ/10 | SPGD | IPP | [152] |

2020 | 81 | Filled | Pulsed | RMS error < 1% | PIM | LBNL | [153] |

2020 | 107 | Tiled | CW | 96% * | SPGD | NUDT | [154] |

Combining Configuration | Year | Average Power | Peak Power | Pulse Energy | Pulse Duration | Beam Quality (M^{2}) | Combining Efficiency (%) | Channel Number/Replicas | Configuration | Institution | Ref. |
---|---|---|---|---|---|---|---|---|---|---|---|

Spatial | 2014 | 230 W | 22 GW | 5.7 mJ | 200 fs | ≤1.3 | 88 | 4 | CPA, HC detection, PBS | Jena | [16] |

2020 | 10.4 kW | 0.5 GW | 130 µJ | 254 fs | ≤1.2 | 96 | 12 | CPA, LOCSET, IBS | Jena | [169] | |

2021 | 1 kW | 68 GW | 10 mJ | 120 fs | ≤1.2 | 94 | 16 | CPA, HC detection, PBS and TFP | Jena | [176] | |

Temporal | 2013 | 77 W | 1.3 GW | 430 µJ | 320 fs | ≤1.3 | 97 | 2 | CPA + DPA, TFP, passive | Amplitude &CNRS | [300] |

2014 | 37.5 W | 2.9 GW | 1.25 mJ | 380 fs | NA | 75 | 4 | DPA, LOCSET, PBS | Jena | [301] | |

Spatio-temporal | 2015 | 55 W | 3.1 GW | 1.1 mJ | 300 fs | ≤1.3 | 90 | 2×2 | CPA + DPA, passive | Amplitude &CNRS | [302] |

2015 | NA | NA | 37 µJ | 50 ps | NA | 75 | 2 × 4 | DPA, LOCSET, PBS | Jena | [304] | |

2016 | 700 W | 45 GW | 12 mJ | 262 fs | ≤1.2 | 78 | 8 × 4 | CPA + DPA, LOCSET, PBS and TFP | Jena | [173] | |

2019 | 674 W | 80 GW | 23 mJ | 235 fs | NA | 71 | 12 × 8 | CPA + DPA, LOCSET, PBS and TFP | Jena | [175] | |

Spectral synthesis | 2013 | 273 mW | NA | NA | 403 fs | NA | 85.8 | 3 | Spectral filters, LOCSET | UMich | [308] |

2013 | 10 W | 2 MW | 0.29 µJ | 130 fs | ≤1.4 | 86 | 3 | LMA fiber, dichroic mirror | CNRS | [309] | |

2013 | 370 mW | NA | NA | 290fs | NA | NA | 12 | MCF, Grating and MLA twin pulses with 1.75 ps separation | CNRS | [310] |

Tiled aperture | Directed Energy | Year | Distance | Channel number | Tip/Tilt Correction | Phase Control Method | Institution | Ref. |

2011 | 7 km | 7 | √ | SPGD | UD | [149] | ||

2015 | 7 km | 21 | √ | SPGD | UD | [166] | ||

Power scaling | Year | Power (kW) | Channel number | Combining efficiency (%) | Phase control method | Institution | Ref. | |

2011 | 1.08 | 9 | 85 * | SFD | NUDT | [279] | ||

2011 | 4 | 8 | 78 | SPGD | MIT | [147] | ||

2020 | 16 | 32 | >95 | OPA | CIVAN | [167] | ||

2021 | 7.1 | 7 | 86 * | SPGD | NUDT | [168] | ||

Filled aperture | Combining technique | Year | Power (kW) | Channel number | Combining efficiency (%) | Phase control method | Institution | Ref. |

DOE | 2016 | 5 | 5 | 82 | LOCSET | AFRL | [181] | |

PBS | 2017 | 2.16 | 4 | 94.5 | SFD | NUDT | [108] | |

AFPL | 2017 | 1.27 | 3 | NA | SPGD | MIT | [314] | |

RIW | 2010 | 0.1 | 4 | 80 | LOCSET | LM Corp | [315] |

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**MDPI and ACS Style**

Fathi, H.; Närhi, M.; Gumenyuk, R. Towards Ultimate High-Power Scaling: Coherent Beam Combining of Fiber Lasers. *Photonics* **2021**, *8*, 566.
https://doi.org/10.3390/photonics8120566

**AMA Style**

Fathi H, Närhi M, Gumenyuk R. Towards Ultimate High-Power Scaling: Coherent Beam Combining of Fiber Lasers. *Photonics*. 2021; 8(12):566.
https://doi.org/10.3390/photonics8120566

**Chicago/Turabian Style**

Fathi, Hossein, Mikko Närhi, and Regina Gumenyuk. 2021. "Towards Ultimate High-Power Scaling: Coherent Beam Combining of Fiber Lasers" *Photonics* 8, no. 12: 566.
https://doi.org/10.3390/photonics8120566