Abstract

We propose and demonstrate a method for the adaptive phase correction of dynamic multimode fiber beams. The phase of incident beam is reconstructed in real-time based on the complete modal information, which obtained by using the modal decomposition of correlation filter method. For the proof of principle, both of the modal decomposition and the phase correction are implemented using the same computer-generated hologram, which was encoded into a phase-only spatial light modulator. We demonstrate the phase correction of dynamic multimode beam at a rate of 5 Hz and achieve a 1.73-fold improvement on the average power-in-the-bucket. The experimental results indicate the feasibility of the real-time phase correction for the large mode area fiber laser by adaptive optics.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
More Like This
Modal decomposition of fiber modes based on direct far-field measurements at two different distances with a multi-variable optimization algorithm

Byungho Kim, Jeongkyun Na, Juhwan Kim, Hansol Kim, and Yoonchan Jeong
Opt. Express 29(14) 21502-21520 (2021)

Wavefront reconstruction by modal decomposition

Christian Schulze, Darryl Naidoo, Daniel Flamm, Oliver A. Schmidt, Andrew Forbes, and Michael Duparré
Opt. Express 20(18) 19714-19725 (2012)

Multimode fiber modal decomposition based on hybrid genetic global optimization algorithm

Lei Li, Jinyong Leng, Pu Zhou, and Jinbao Chen
Opt. Express 25(17) 19680-19690 (2017)

View More...

References

  • View by:
  • Article Order
  • Year
  • Author
  • Publication
  1. M. N. Zervas and C. A. Codemard, “High power fiber lasers: A review,” IEEE J. Sel. Top. Quantum Electron. 20(5), 219–241 (2014).
    [Crossref]
  2. J. Nilsson and D. N. Payne, “Physics. High-power fiber lasers,” Science 332(6032), 921–922 (2011).
    [Crossref] [PubMed]
  3. H. Yoda, P. Polynkin, and M. Mansuripur, “Beam quality factor of higher order modes in a step-index fiber,” J. Lightwave Technol. 24(3), 1350–1355 (2006).
    [Crossref]
  4. S. Wielandy, “Implications of higher-order mode content in large mode area fibers with good beam quality,” Opt. Express 15(23), 15402–15409 (2007).
    [Crossref] [PubMed]
  5. C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7(11), 861–867 (2013).
    [Crossref]
  6. R. Tao, X. Wang, and P. Zhou, “Comprehensive theoretical study of mode instability in high-power fiber lasers by employing a universal model and its implications,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–19 (2018).
    [Crossref]
  7. M.-J. Li, X. Chen, A. Liu, S. Gray, J. Wang, D. T. Walton, and L. A. Zenteno, “Limit of effective area for single-mode operation in step-index large mode area laser fibers,” J. Lightwave Technol. 27(15), 3010–3016 (2009).
    [Crossref]
  8. B. Yang, H. Zhang, C. Shi, R. Tao, R. Su, P. Ma, X. Wang, P. Zhou, X. Xu, and Q. Lu, “3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated raman scattering and transverse mode instability,” J. Opt. 20(2), 025802 (2018).
    [Crossref]
  9. V. Scarnera, F. Ghiringhelli, A. Malinowski, C. A. Codemard, M. K. Durkin, and M. N. Zervas, “Modal instabilities in high power fiber laser oscillators,” Opt. Express 27(4), 4386–4403 (2019).
    [Crossref] [PubMed]
  10. F. Stutzki, F. Jansen, T. Eidam, A. Steinmetz, C. Jauregui, J. Limpert, and A. Tünnermann, “High average power large-pitch fiber amplifier with robust single-mode operation,” Opt. Lett. 36(5), 689–691 (2011).
    [Crossref] [PubMed]
  11. L. Dong, X. Peng, and J. Li, “Leakage channel optical fibers with large effective area,” J. Opt. Soc. Am. B 24(8), 1689–1697 (2007).
    [Crossref]
  12. X. Ma, C. Zhu, I. N. Hu, A. Kaplan, and A. Galvanauskas, “Single-mode chirally-coupled-core fibers with larger than 50 µm diameter cores,” Opt. Express 22(8), 9206–9219 (2014).
    [Crossref] [PubMed]
  13. L. W. Casperson, “Phase compensation of laser beam modes,” Opt. Quantum Electron. 8(6), 537–544 (1976).
    [Crossref]
  14. G. Machavariani, A. A. Ishaaya, L. Shimshi, N. Davidson, A. A. Friesem, and E. Hasman, “Efficient mode transformations of degenerate Laguerre-Gaussian beams,” Appl. Opt. 43(12), 2561–2567 (2004).
    [Crossref] [PubMed]
  15. K. Igarashi, D. Souma, T. Tsuritani, and I. Morita, “Performance evaluation of selective mode conversion based on phase plates for a 10-mode fiber,” Opt. Express 22(17), 20881–20893 (2014).
    [Crossref] [PubMed]
  16. Y.-S. Lee, K.-S. Lim, M. R. Islam, M.-H. Lai, and H. Ahmad, “Dynamic LP01–LP11 mode conversion by a tilted binary phase plate,” J. Lightwave Technol. 35(16), 3597–3603 (2017).
    [Crossref]
  17. A. A. Ishaaya, G. Machavariani, N. Davidson, A. A. Friesem, and E. Hasman, “Conversion of a high-order mode beam into a nearly Gaussian beam by use of a single interferometric element,” Opt. Lett. 28(7), 504–506 (2003).
    [Crossref] [PubMed]
  18. B. L. Boheng Lai, L. D. Lizhi Dong, S. C. Shanqiu Chen, G. T. Guomao Tang, W. L. Wenjin Liu, S. W. Shuai Wang, X. H. Xing He, K. Y. Kangjian Yang, P. Y. Ping Yang, B. X. Bing Xu, C. W. Chao Wang, X. L. Xianda Liu, Q. P. Qingsheng Pang, and Y. L. and Yang Liu, “Hybrid adaptive optics system for a solid-state zigzag masteroscillator power amplifier laser system,” Chin. Opt. Lett. 14(9), 091402 (2016).
    [Crossref]
  19. R. Li, M. Griffith, L. Laycock, and W. Lubeigt, “Controllable continuous-wave Nd:YVO4 self-Raman lasers using intracavity adaptive optics,” Opt. Lett. 39(16), 4762–4765 (2014).
    [Crossref] [PubMed]
  20. A. Alexandrov, V. Zavalova, A. Kudryashov, A. Rukosuev, Y. Sheldakova, V. Samarkin, and D. Dumitras, “Beam correction in TiS lasers by means of adaptive optics,” AIP Conf. Proc. 1228, 123–129 (2010).
    [Crossref]
  21. H. Ma, H. Zhao, P. Zhou, X. Wang, Y. Ma, X. Xu, and Z. Liu, “Adaptive conversion of multimode beam to near-diffraction-limited flattop beam based on dual-phase-only liquid-crystal spatial light modulators,” Opt. Express 18(26), 27723–27730 (2010).
    [Crossref] [PubMed]
  22. H.-C. Zhao, H.-T. Ma, P. Zhou, X.-L. Wang, Y.-X. Ma, X. Li, X.-J. Xu, and Y.-J. Zhao, “Multimode fiber laser beam cleanup based on stochastic parallel gradient descent algorithm,” Opt. Commun. 284(2), 613–615 (2011).
    [Crossref]
  23. H.-C. Zhao, X.-L. Wang, P. Zhou, H.-T. Ma, Y.-X. Ma, S.-H. Wang, X.-J. Xu, and Y.-J. Zhao, “Experimental explorations of the high-order gaussian mode transformation based on blind-optimization adaptive optics,” Opt. Commun. 284(19), 4654–4657 (2011).
    [Crossref]
  24. J. Li, H.-C. Zhao, Z.-L. Chen, and X.-J. Xu, “Beam cleanup of a multimode fiber seeded by an off-center single-mode laser source,” Optik (Stuttg.) 124(16), 2501–2503 (2013).
    [Crossref]
  25. L. Dong, W. Liu, P. Yang, H. Yan, X. Lei, S. Wang, and B. Xu, “Transformations of high-order mode Hermite–Gaussian beams using a deformable mirror,” Laser Phys. 23(3), 035004 (2013).
    [Crossref]
  26. Q. Bian, L. Huang, X. J. Wang, X. K. Ma, P. Yan, and M. L. Gong, “Experimental investigation on the beam quality improvement of the fiber laser by adaptive optics,” Laser Phys. 25(12), 125101 (2015).
    [Crossref]
  27. D. Malacara, Optical shop testing, 3rd ed. (John Wiley & Sons, Inc., 2007), Chap. 4.
  28. M. Paurisse, L. Lévèque, M. Hanna, F. Druon, and P. Georges, “Complete measurement of fiber modal content by wavefront analysis,” Opt. Express 20(4), 4074–4084 (2012).
    [Crossref] [PubMed]
  29. S. Mousset, C. Rouyer, G. Marre, N. Blanchot, S. Montant, and B. Wattellier, “Piston measurement by quadriwave lateral shearing interferometry,” Opt. Lett. 31(17), 2634–2636 (2006).
    [Crossref] [PubMed]
  30. K. Xie, W. Liu, Q. Zhou, H. Zhao, and X. Xu, “Numerical study of the measurement capability of quadriwave lateral shearing interferometry for multimode fiber laser (conference presentation),” presented at SPIE Security + Defence, (SPIE, 2017)
  31. L. Huang, S. Guo, J. Leng, H. Lü, P. Zhou, and X. Cheng, “Real-time mode decomposition for few-mode fiber based on numerical method,” Opt. Express 23(4), 4620–4629 (2015).
    [Crossref] [PubMed]
  32. O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94(14), 143902 (2005).
    [Crossref] [PubMed]
  33. R. Brüning, P. Gelszinnis, C. Schulze, D. Flamm, and M. Duparré, “Comparative analysis of numerical methods for the mode analysis of laser beams,” Appl. Opt. 52(32), 7769–7777 (2013).
    [Crossref] [PubMed]
  34. Y. An, L. Huang, J. Li, J. Leng, L. Yang, and P. Zhou, “Learning to decompose the modes in few-mode fibers with deep convolutional neural network,” Opt. Express 27(7), 10127–10137 (2019).
    [Crossref]
  35. D. R. Gray, S. R. Sandoghchi, N. V. Wheeler, G. T. Jasion, J. P. Wooler, M. N. Petrovich, F. Poletti, and D. J. Richardson, “Towards real-time mode content characterization of multimode fibers,” presented at 2014 The European Conference on Optical Communication (ECOC), 2014), 1–3.
    [Crossref]
  36. J. W. Nicholson, A. D. Yablon, S. Ramachandran, and S. Ghalmi, “Spatially and spectrally resolved imaging of modal content in large-mode-area fibers,” Opt. Express 16(10), 7233–7243 (2008).
    [Crossref] [PubMed]
  37. N. Andermahr, T. Theeg, and C. Fallnich, “Novel approach for polarization-sensitive measurements of transverse modes in few-mode optical fibers,” Appl. Phys. B 91(2), 353–357 (2008).
    [Crossref]
  38. M. Lyu, Z. Lin, G. Li, and G. Situ, “Fast modal decomposition for optical fibers using digital holography,” Sci. Rep. 7(1), 6556 (2017).
    [Crossref] [PubMed]
  39. D. R. Gray, M. N. Petrovich, S. R. Sandoghchi, N. V. Wheeler, N. K. Baddela, G. T. Jasion, T. Bradley, D. J. Richardson, and F. Poletti, “Real-time modal analysis via wavelength-swept spatial and spectral (S2) imaging,” IEEE Photonics Technol. Lett. 28, 1034–1037 (2016).
  40. F. Stutzki, H.-J. Otto, F. Jansen, C. Gaida, C. Jauregui, J. Limpert, and A. Tünnermann, “High-speed modal decomposition of mode instabilities in high-power fiber lasers,” Opt. Lett. 36(23), 4572–4574 (2011).
    [Crossref] [PubMed]
  41. L. Huang, T. Yao, J. Leng, S. Guo, R. Tao, P. Zhou, and X. Cheng, “Mode instability dynamics in high-power low-numerical-aperture step-index fiber amplifier,” Appl. Opt. 56(19), 5412–5417 (2017).
    [Crossref] [PubMed]
  42. T. Kaiser, D. Flamm, S. Schröter, and M. Duparré, “Complete modal decomposition for optical fibers using CGH-based correlation filters,” Opt. Express 17(11), 9347–9356 (2009).
    [Crossref] [PubMed]
  43. D. Flamm, D. Naidoo, C. Schulze, A. Forbes, and M. Duparré, “Mode analysis with a spatial light modulator as a correlation filter,” Opt. Lett. 37(13), 2478–2480 (2012).
    [Crossref] [PubMed]
  44. C. Schulze, D. Naidoo, D. Flamm, O. A. Schmidt, A. Forbes, and M. Duparré, “Wavefront reconstruction by modal decomposition,” Opt. Express 20(18), 19714–19725 (2012).
    [Crossref] [PubMed]
  45. C. Schulze, A. Dudley, D. Flamm, M. Duparré, and A. Forbes, “Reconstruction of laser beam wavefronts based on mode analysis,” Appl. Opt. 52(21), 5312–5317 (2013).
    [Crossref] [PubMed]
  46. D. Flamm, C. Schulze, R. Brüning, O. A. Schmidt, T. Kaiser, S. Schröter, and M. Duparré, “Fast M2 measurement for fiber beams based on modal analysis,” Appl. Opt. 51(7), 987–993 (2012).
    [Crossref] [PubMed]
  47. A. E. Siegman, “How to (maybe) measure laser beam quality,” in DPSS (Diode Pumped Solid State) Lasers: Applications and Issues, (Optical Society of America, 1998), p. MQ1.
  48. ISO, ISO 11146–1: 2005, “Lasers and laser-related equipment-test methods for laser beam widths, divergence angles and beam propagation ratios part 1: stigmatic and simple astigmatic beams,” (2005).
  49. S. A. Shakir, B. Culver, B. Nelson, Y. Starcher, G. M. Bates, and J. W. Hedrick, “Power scaling of passively phased fiber amplifier arrays,” Proc. SPIE 7070, 70700N (2008).
    [Crossref]
  50. J.-C. Sinquin, J.-M. Lurçon, and C. Guillemard, “Deformable mirror technologies for astronomy at CILAS,” presented at SPIE Astronomical Telescopes + Instrumentation, (SPIE, 2008), 12.

2019 (2)

2018 (2)

R. Tao, X. Wang, and P. Zhou, “Comprehensive theoretical study of mode instability in high-power fiber lasers by employing a universal model and its implications,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–19 (2018).
[Crossref]

B. Yang, H. Zhang, C. Shi, R. Tao, R. Su, P. Ma, X. Wang, P. Zhou, X. Xu, and Q. Lu, “3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated raman scattering and transverse mode instability,” J. Opt. 20(2), 025802 (2018).
[Crossref]

2017 (3)

2016 (2)

D. R. Gray, M. N. Petrovich, S. R. Sandoghchi, N. V. Wheeler, N. K. Baddela, G. T. Jasion, T. Bradley, D. J. Richardson, and F. Poletti, “Real-time modal analysis via wavelength-swept spatial and spectral (S2) imaging,” IEEE Photonics Technol. Lett. 28, 1034–1037 (2016).

B. L. Boheng Lai, L. D. Lizhi Dong, S. C. Shanqiu Chen, G. T. Guomao Tang, W. L. Wenjin Liu, S. W. Shuai Wang, X. H. Xing He, K. Y. Kangjian Yang, P. Y. Ping Yang, B. X. Bing Xu, C. W. Chao Wang, X. L. Xianda Liu, Q. P. Qingsheng Pang, and Y. L. and Yang Liu, “Hybrid adaptive optics system for a solid-state zigzag masteroscillator power amplifier laser system,” Chin. Opt. Lett. 14(9), 091402 (2016).
[Crossref]

2015 (2)

L. Huang, S. Guo, J. Leng, H. Lü, P. Zhou, and X. Cheng, “Real-time mode decomposition for few-mode fiber based on numerical method,” Opt. Express 23(4), 4620–4629 (2015).
[Crossref] [PubMed]

Q. Bian, L. Huang, X. J. Wang, X. K. Ma, P. Yan, and M. L. Gong, “Experimental investigation on the beam quality improvement of the fiber laser by adaptive optics,” Laser Phys. 25(12), 125101 (2015).
[Crossref]

2014 (4)

2013 (5)

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

R. Brüning, P. Gelszinnis, C. Schulze, D. Flamm, and M. Duparré, “Comparative analysis of numerical methods for the mode analysis of laser beams,” Appl. Opt. 52(32), 7769–7777 (2013).
[Crossref] [PubMed]

J. Li, H.-C. Zhao, Z.-L. Chen, and X.-J. Xu, “Beam cleanup of a multimode fiber seeded by an off-center single-mode laser source,” Optik (Stuttg.) 124(16), 2501–2503 (2013).
[Crossref]

L. Dong, W. Liu, P. Yang, H. Yan, X. Lei, S. Wang, and B. Xu, “Transformations of high-order mode Hermite–Gaussian beams using a deformable mirror,” Laser Phys. 23(3), 035004 (2013).
[Crossref]

C. Schulze, A. Dudley, D. Flamm, M. Duparré, and A. Forbes, “Reconstruction of laser beam wavefronts based on mode analysis,” Appl. Opt. 52(21), 5312–5317 (2013).
[Crossref] [PubMed]

2012 (4)

2011 (5)

H.-C. Zhao, H.-T. Ma, P. Zhou, X.-L. Wang, Y.-X. Ma, X. Li, X.-J. Xu, and Y.-J. Zhao, “Multimode fiber laser beam cleanup based on stochastic parallel gradient descent algorithm,” Opt. Commun. 284(2), 613–615 (2011).
[Crossref]

H.-C. Zhao, X.-L. Wang, P. Zhou, H.-T. Ma, Y.-X. Ma, S.-H. Wang, X.-J. Xu, and Y.-J. Zhao, “Experimental explorations of the high-order gaussian mode transformation based on blind-optimization adaptive optics,” Opt. Commun. 284(19), 4654–4657 (2011).
[Crossref]

F. Stutzki, H.-J. Otto, F. Jansen, C. Gaida, C. Jauregui, J. Limpert, and A. Tünnermann, “High-speed modal decomposition of mode instabilities in high-power fiber lasers,” Opt. Lett. 36(23), 4572–4574 (2011).
[Crossref] [PubMed]

J. Nilsson and D. N. Payne, “Physics. High-power fiber lasers,” Science 332(6032), 921–922 (2011).
[Crossref] [PubMed]

F. Stutzki, F. Jansen, T. Eidam, A. Steinmetz, C. Jauregui, J. Limpert, and A. Tünnermann, “High average power large-pitch fiber amplifier with robust single-mode operation,” Opt. Lett. 36(5), 689–691 (2011).
[Crossref] [PubMed]

2010 (2)

A. Alexandrov, V. Zavalova, A. Kudryashov, A. Rukosuev, Y. Sheldakova, V. Samarkin, and D. Dumitras, “Beam correction in TiS lasers by means of adaptive optics,” AIP Conf. Proc. 1228, 123–129 (2010).
[Crossref]

H. Ma, H. Zhao, P. Zhou, X. Wang, Y. Ma, X. Xu, and Z. Liu, “Adaptive conversion of multimode beam to near-diffraction-limited flattop beam based on dual-phase-only liquid-crystal spatial light modulators,” Opt. Express 18(26), 27723–27730 (2010).
[Crossref] [PubMed]

2009 (2)

2008 (3)

S. A. Shakir, B. Culver, B. Nelson, Y. Starcher, G. M. Bates, and J. W. Hedrick, “Power scaling of passively phased fiber amplifier arrays,” Proc. SPIE 7070, 70700N (2008).
[Crossref]

J. W. Nicholson, A. D. Yablon, S. Ramachandran, and S. Ghalmi, “Spatially and spectrally resolved imaging of modal content in large-mode-area fibers,” Opt. Express 16(10), 7233–7243 (2008).
[Crossref] [PubMed]

N. Andermahr, T. Theeg, and C. Fallnich, “Novel approach for polarization-sensitive measurements of transverse modes in few-mode optical fibers,” Appl. Phys. B 91(2), 353–357 (2008).
[Crossref]

2007 (2)

2006 (2)

2005 (1)

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94(14), 143902 (2005).
[Crossref] [PubMed]

2004 (1)

2003 (1)

1976 (1)

L. W. Casperson, “Phase compensation of laser beam modes,” Opt. Quantum Electron. 8(6), 537–544 (1976).
[Crossref]

Abouraddy, A. F.

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94(14), 143902 (2005).
[Crossref] [PubMed]

Ahmad, H.

Alexandrov, A.

A. Alexandrov, V. Zavalova, A. Kudryashov, A. Rukosuev, Y. Sheldakova, V. Samarkin, and D. Dumitras, “Beam correction in TiS lasers by means of adaptive optics,” AIP Conf. Proc. 1228, 123–129 (2010).
[Crossref]

An, Y.

and Yang Liu, Y. L.

Andermahr, N.

N. Andermahr, T. Theeg, and C. Fallnich, “Novel approach for polarization-sensitive measurements of transverse modes in few-mode optical fibers,” Appl. Phys. B 91(2), 353–357 (2008).
[Crossref]

Baddela, N. K.

D. R. Gray, M. N. Petrovich, S. R. Sandoghchi, N. V. Wheeler, N. K. Baddela, G. T. Jasion, T. Bradley, D. J. Richardson, and F. Poletti, “Real-time modal analysis via wavelength-swept spatial and spectral (S2) imaging,” IEEE Photonics Technol. Lett. 28, 1034–1037 (2016).

Bates, G. M.

S. A. Shakir, B. Culver, B. Nelson, Y. Starcher, G. M. Bates, and J. W. Hedrick, “Power scaling of passively phased fiber amplifier arrays,” Proc. SPIE 7070, 70700N (2008).
[Crossref]

Bian, Q.

Q. Bian, L. Huang, X. J. Wang, X. K. Ma, P. Yan, and M. L. Gong, “Experimental investigation on the beam quality improvement of the fiber laser by adaptive optics,” Laser Phys. 25(12), 125101 (2015).
[Crossref]

Bing Xu, B. X.

Blanchot, N.

Boheng Lai, B. L.

Bradley, T.

D. R. Gray, M. N. Petrovich, S. R. Sandoghchi, N. V. Wheeler, N. K. Baddela, G. T. Jasion, T. Bradley, D. J. Richardson, and F. Poletti, “Real-time modal analysis via wavelength-swept spatial and spectral (S2) imaging,” IEEE Photonics Technol. Lett. 28, 1034–1037 (2016).

Brüning, R.

Casperson, L. W.

L. W. Casperson, “Phase compensation of laser beam modes,” Opt. Quantum Electron. 8(6), 537–544 (1976).
[Crossref]

Chao Wang, C. W.

Chen, X.

Chen, Z.-L.

J. Li, H.-C. Zhao, Z.-L. Chen, and X.-J. Xu, “Beam cleanup of a multimode fiber seeded by an off-center single-mode laser source,” Optik (Stuttg.) 124(16), 2501–2503 (2013).
[Crossref]

Cheng, X.

Codemard, C. A.

Culver, B.

S. A. Shakir, B. Culver, B. Nelson, Y. Starcher, G. M. Bates, and J. W. Hedrick, “Power scaling of passively phased fiber amplifier arrays,” Proc. SPIE 7070, 70700N (2008).
[Crossref]

Davidson, N.

Dong, L.

L. Dong, W. Liu, P. Yang, H. Yan, X. Lei, S. Wang, and B. Xu, “Transformations of high-order mode Hermite–Gaussian beams using a deformable mirror,” Laser Phys. 23(3), 035004 (2013).
[Crossref]

L. Dong, X. Peng, and J. Li, “Leakage channel optical fibers with large effective area,” J. Opt. Soc. Am. B 24(8), 1689–1697 (2007).
[Crossref]

Druon, F.

Dudley, A.

Dumitras, D.

A. Alexandrov, V. Zavalova, A. Kudryashov, A. Rukosuev, Y. Sheldakova, V. Samarkin, and D. Dumitras, “Beam correction in TiS lasers by means of adaptive optics,” AIP Conf. Proc. 1228, 123–129 (2010).
[Crossref]

Duparré, M.

Durkin, M. K.

Eidam, T.

Fallnich, C.

N. Andermahr, T. Theeg, and C. Fallnich, “Novel approach for polarization-sensitive measurements of transverse modes in few-mode optical fibers,” Appl. Phys. B 91(2), 353–357 (2008).
[Crossref]

Fink, Y.

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94(14), 143902 (2005).
[Crossref] [PubMed]

Flamm, D.

Forbes, A.

Friesem, A. A.

Gaida, C.

Galvanauskas, A.

Gelszinnis, P.

Georges, P.

Ghalmi, S.

Ghiringhelli, F.

Gong, M. L.

Q. Bian, L. Huang, X. J. Wang, X. K. Ma, P. Yan, and M. L. Gong, “Experimental investigation on the beam quality improvement of the fiber laser by adaptive optics,” Laser Phys. 25(12), 125101 (2015).
[Crossref]

Gray, D. R.

D. R. Gray, M. N. Petrovich, S. R. Sandoghchi, N. V. Wheeler, N. K. Baddela, G. T. Jasion, T. Bradley, D. J. Richardson, and F. Poletti, “Real-time modal analysis via wavelength-swept spatial and spectral (S2) imaging,” IEEE Photonics Technol. Lett. 28, 1034–1037 (2016).

Gray, S.

Griffith, M.

Guo, S.

Guomao Tang, G. T.

Hanna, M.

Hasman, E.

Hedrick, J. W.

S. A. Shakir, B. Culver, B. Nelson, Y. Starcher, G. M. Bates, and J. W. Hedrick, “Power scaling of passively phased fiber amplifier arrays,” Proc. SPIE 7070, 70700N (2008).
[Crossref]

Hu, I. N.

Huang, L.

Igarashi, K.

Ishaaya, A. A.

Islam, M. R.

Jansen, F.

Jasion, G. T.

D. R. Gray, M. N. Petrovich, S. R. Sandoghchi, N. V. Wheeler, N. K. Baddela, G. T. Jasion, T. Bradley, D. J. Richardson, and F. Poletti, “Real-time modal analysis via wavelength-swept spatial and spectral (S2) imaging,” IEEE Photonics Technol. Lett. 28, 1034–1037 (2016).

Jauregui, C.

Joannopoulos, J. D.

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94(14), 143902 (2005).
[Crossref] [PubMed]

Kaiser, T.

Kangjian Yang, K. Y.

Kaplan, A.

Kudryashov, A.

A. Alexandrov, V. Zavalova, A. Kudryashov, A. Rukosuev, Y. Sheldakova, V. Samarkin, and D. Dumitras, “Beam correction in TiS lasers by means of adaptive optics,” AIP Conf. Proc. 1228, 123–129 (2010).
[Crossref]

Lai, M.-H.

Laycock, L.

Lee, Y.-S.

Lei, X.

L. Dong, W. Liu, P. Yang, H. Yan, X. Lei, S. Wang, and B. Xu, “Transformations of high-order mode Hermite–Gaussian beams using a deformable mirror,” Laser Phys. 23(3), 035004 (2013).
[Crossref]

Leng, J.

Lévèque, L.

Li, G.

M. Lyu, Z. Lin, G. Li, and G. Situ, “Fast modal decomposition for optical fibers using digital holography,” Sci. Rep. 7(1), 6556 (2017).
[Crossref] [PubMed]

Li, J.

Li, M.-J.

Li, R.

Li, X.

H.-C. Zhao, H.-T. Ma, P. Zhou, X.-L. Wang, Y.-X. Ma, X. Li, X.-J. Xu, and Y.-J. Zhao, “Multimode fiber laser beam cleanup based on stochastic parallel gradient descent algorithm,” Opt. Commun. 284(2), 613–615 (2011).
[Crossref]

Lim, K.-S.

Limpert, J.

Lin, Z.

M. Lyu, Z. Lin, G. Li, and G. Situ, “Fast modal decomposition for optical fibers using digital holography,” Sci. Rep. 7(1), 6556 (2017).
[Crossref] [PubMed]

Liu, A.

Liu, W.

L. Dong, W. Liu, P. Yang, H. Yan, X. Lei, S. Wang, and B. Xu, “Transformations of high-order mode Hermite–Gaussian beams using a deformable mirror,” Laser Phys. 23(3), 035004 (2013).
[Crossref]

Liu, Z.

Lizhi Dong, L. D.

Lu, Q.

B. Yang, H. Zhang, C. Shi, R. Tao, R. Su, P. Ma, X. Wang, P. Zhou, X. Xu, and Q. Lu, “3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated raman scattering and transverse mode instability,” J. Opt. 20(2), 025802 (2018).
[Crossref]

Lü, H.

Lubeigt, W.

Lyu, M.

M. Lyu, Z. Lin, G. Li, and G. Situ, “Fast modal decomposition for optical fibers using digital holography,” Sci. Rep. 7(1), 6556 (2017).
[Crossref] [PubMed]

Ma, H.

Ma, H.-T.

H.-C. Zhao, H.-T. Ma, P. Zhou, X.-L. Wang, Y.-X. Ma, X. Li, X.-J. Xu, and Y.-J. Zhao, “Multimode fiber laser beam cleanup based on stochastic parallel gradient descent algorithm,” Opt. Commun. 284(2), 613–615 (2011).
[Crossref]

H.-C. Zhao, X.-L. Wang, P. Zhou, H.-T. Ma, Y.-X. Ma, S.-H. Wang, X.-J. Xu, and Y.-J. Zhao, “Experimental explorations of the high-order gaussian mode transformation based on blind-optimization adaptive optics,” Opt. Commun. 284(19), 4654–4657 (2011).
[Crossref]

Ma, P.

B. Yang, H. Zhang, C. Shi, R. Tao, R. Su, P. Ma, X. Wang, P. Zhou, X. Xu, and Q. Lu, “3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated raman scattering and transverse mode instability,” J. Opt. 20(2), 025802 (2018).
[Crossref]

Ma, X.

Ma, X. K.

Q. Bian, L. Huang, X. J. Wang, X. K. Ma, P. Yan, and M. L. Gong, “Experimental investigation on the beam quality improvement of the fiber laser by adaptive optics,” Laser Phys. 25(12), 125101 (2015).
[Crossref]

Ma, Y.

Ma, Y.-X.

H.-C. Zhao, H.-T. Ma, P. Zhou, X.-L. Wang, Y.-X. Ma, X. Li, X.-J. Xu, and Y.-J. Zhao, “Multimode fiber laser beam cleanup based on stochastic parallel gradient descent algorithm,” Opt. Commun. 284(2), 613–615 (2011).
[Crossref]

H.-C. Zhao, X.-L. Wang, P. Zhou, H.-T. Ma, Y.-X. Ma, S.-H. Wang, X.-J. Xu, and Y.-J. Zhao, “Experimental explorations of the high-order gaussian mode transformation based on blind-optimization adaptive optics,” Opt. Commun. 284(19), 4654–4657 (2011).
[Crossref]

Machavariani, G.

Malinowski, A.

Mansuripur, M.

Marre, G.

Montant, S.

Morita, I.

Mousset, S.

Naidoo, D.

Nelson, B.

S. A. Shakir, B. Culver, B. Nelson, Y. Starcher, G. M. Bates, and J. W. Hedrick, “Power scaling of passively phased fiber amplifier arrays,” Proc. SPIE 7070, 70700N (2008).
[Crossref]

Nicholson, J. W.

Nilsson, J.

J. Nilsson and D. N. Payne, “Physics. High-power fiber lasers,” Science 332(6032), 921–922 (2011).
[Crossref] [PubMed]

Otto, H.-J.

Paurisse, M.

Payne, D. N.

J. Nilsson and D. N. Payne, “Physics. High-power fiber lasers,” Science 332(6032), 921–922 (2011).
[Crossref] [PubMed]

Peng, X.

Petrovich, M. N.

D. R. Gray, M. N. Petrovich, S. R. Sandoghchi, N. V. Wheeler, N. K. Baddela, G. T. Jasion, T. Bradley, D. J. Richardson, and F. Poletti, “Real-time modal analysis via wavelength-swept spatial and spectral (S2) imaging,” IEEE Photonics Technol. Lett. 28, 1034–1037 (2016).

Ping Yang, P. Y.

Poletti, F.

D. R. Gray, M. N. Petrovich, S. R. Sandoghchi, N. V. Wheeler, N. K. Baddela, G. T. Jasion, T. Bradley, D. J. Richardson, and F. Poletti, “Real-time modal analysis via wavelength-swept spatial and spectral (S2) imaging,” IEEE Photonics Technol. Lett. 28, 1034–1037 (2016).

Polynkin, P.

Qingsheng Pang, Q. P.

Ramachandran, S.

Richardson, D. J.

D. R. Gray, M. N. Petrovich, S. R. Sandoghchi, N. V. Wheeler, N. K. Baddela, G. T. Jasion, T. Bradley, D. J. Richardson, and F. Poletti, “Real-time modal analysis via wavelength-swept spatial and spectral (S2) imaging,” IEEE Photonics Technol. Lett. 28, 1034–1037 (2016).

Rouyer, C.

Rukosuev, A.

A. Alexandrov, V. Zavalova, A. Kudryashov, A. Rukosuev, Y. Sheldakova, V. Samarkin, and D. Dumitras, “Beam correction in TiS lasers by means of adaptive optics,” AIP Conf. Proc. 1228, 123–129 (2010).
[Crossref]

Samarkin, V.

A. Alexandrov, V. Zavalova, A. Kudryashov, A. Rukosuev, Y. Sheldakova, V. Samarkin, and D. Dumitras, “Beam correction in TiS lasers by means of adaptive optics,” AIP Conf. Proc. 1228, 123–129 (2010).
[Crossref]

Sandoghchi, S. R.

D. R. Gray, M. N. Petrovich, S. R. Sandoghchi, N. V. Wheeler, N. K. Baddela, G. T. Jasion, T. Bradley, D. J. Richardson, and F. Poletti, “Real-time modal analysis via wavelength-swept spatial and spectral (S2) imaging,” IEEE Photonics Technol. Lett. 28, 1034–1037 (2016).

Scarnera, V.

Schmidt, O. A.

Schröter, S.

Schulze, C.

Shakir, S. A.

S. A. Shakir, B. Culver, B. Nelson, Y. Starcher, G. M. Bates, and J. W. Hedrick, “Power scaling of passively phased fiber amplifier arrays,” Proc. SPIE 7070, 70700N (2008).
[Crossref]

Shanqiu Chen, S. C.

Shapira, O.

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94(14), 143902 (2005).
[Crossref] [PubMed]

Sheldakova, Y.

A. Alexandrov, V. Zavalova, A. Kudryashov, A. Rukosuev, Y. Sheldakova, V. Samarkin, and D. Dumitras, “Beam correction in TiS lasers by means of adaptive optics,” AIP Conf. Proc. 1228, 123–129 (2010).
[Crossref]

Shi, C.

B. Yang, H. Zhang, C. Shi, R. Tao, R. Su, P. Ma, X. Wang, P. Zhou, X. Xu, and Q. Lu, “3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated raman scattering and transverse mode instability,” J. Opt. 20(2), 025802 (2018).
[Crossref]

Shimshi, L.

Shuai Wang, S. W.

Situ, G.

M. Lyu, Z. Lin, G. Li, and G. Situ, “Fast modal decomposition for optical fibers using digital holography,” Sci. Rep. 7(1), 6556 (2017).
[Crossref] [PubMed]

Souma, D.

Starcher, Y.

S. A. Shakir, B. Culver, B. Nelson, Y. Starcher, G. M. Bates, and J. W. Hedrick, “Power scaling of passively phased fiber amplifier arrays,” Proc. SPIE 7070, 70700N (2008).
[Crossref]

Steinmetz, A.

Stutzki, F.

Su, R.

B. Yang, H. Zhang, C. Shi, R. Tao, R. Su, P. Ma, X. Wang, P. Zhou, X. Xu, and Q. Lu, “3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated raman scattering and transverse mode instability,” J. Opt. 20(2), 025802 (2018).
[Crossref]

Tao, R.

B. Yang, H. Zhang, C. Shi, R. Tao, R. Su, P. Ma, X. Wang, P. Zhou, X. Xu, and Q. Lu, “3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated raman scattering and transverse mode instability,” J. Opt. 20(2), 025802 (2018).
[Crossref]

R. Tao, X. Wang, and P. Zhou, “Comprehensive theoretical study of mode instability in high-power fiber lasers by employing a universal model and its implications,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–19 (2018).
[Crossref]

L. Huang, T. Yao, J. Leng, S. Guo, R. Tao, P. Zhou, and X. Cheng, “Mode instability dynamics in high-power low-numerical-aperture step-index fiber amplifier,” Appl. Opt. 56(19), 5412–5417 (2017).
[Crossref] [PubMed]

Theeg, T.

N. Andermahr, T. Theeg, and C. Fallnich, “Novel approach for polarization-sensitive measurements of transverse modes in few-mode optical fibers,” Appl. Phys. B 91(2), 353–357 (2008).
[Crossref]

Tsuritani, T.

Tünnermann, A.

Walton, D. T.

Wang, J.

Wang, S.

L. Dong, W. Liu, P. Yang, H. Yan, X. Lei, S. Wang, and B. Xu, “Transformations of high-order mode Hermite–Gaussian beams using a deformable mirror,” Laser Phys. 23(3), 035004 (2013).
[Crossref]

Wang, S.-H.

H.-C. Zhao, X.-L. Wang, P. Zhou, H.-T. Ma, Y.-X. Ma, S.-H. Wang, X.-J. Xu, and Y.-J. Zhao, “Experimental explorations of the high-order gaussian mode transformation based on blind-optimization adaptive optics,” Opt. Commun. 284(19), 4654–4657 (2011).
[Crossref]

Wang, X.

R. Tao, X. Wang, and P. Zhou, “Comprehensive theoretical study of mode instability in high-power fiber lasers by employing a universal model and its implications,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–19 (2018).
[Crossref]

B. Yang, H. Zhang, C. Shi, R. Tao, R. Su, P. Ma, X. Wang, P. Zhou, X. Xu, and Q. Lu, “3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated raman scattering and transverse mode instability,” J. Opt. 20(2), 025802 (2018).
[Crossref]

H. Ma, H. Zhao, P. Zhou, X. Wang, Y. Ma, X. Xu, and Z. Liu, “Adaptive conversion of multimode beam to near-diffraction-limited flattop beam based on dual-phase-only liquid-crystal spatial light modulators,” Opt. Express 18(26), 27723–27730 (2010).
[Crossref] [PubMed]

Wang, X. J.

Q. Bian, L. Huang, X. J. Wang, X. K. Ma, P. Yan, and M. L. Gong, “Experimental investigation on the beam quality improvement of the fiber laser by adaptive optics,” Laser Phys. 25(12), 125101 (2015).
[Crossref]

Wang, X.-L.

H.-C. Zhao, X.-L. Wang, P. Zhou, H.-T. Ma, Y.-X. Ma, S.-H. Wang, X.-J. Xu, and Y.-J. Zhao, “Experimental explorations of the high-order gaussian mode transformation based on blind-optimization adaptive optics,” Opt. Commun. 284(19), 4654–4657 (2011).
[Crossref]

H.-C. Zhao, H.-T. Ma, P. Zhou, X.-L. Wang, Y.-X. Ma, X. Li, X.-J. Xu, and Y.-J. Zhao, “Multimode fiber laser beam cleanup based on stochastic parallel gradient descent algorithm,” Opt. Commun. 284(2), 613–615 (2011).
[Crossref]

Wattellier, B.

Wenjin Liu, W. L.

Wheeler, N. V.

D. R. Gray, M. N. Petrovich, S. R. Sandoghchi, N. V. Wheeler, N. K. Baddela, G. T. Jasion, T. Bradley, D. J. Richardson, and F. Poletti, “Real-time modal analysis via wavelength-swept spatial and spectral (S2) imaging,” IEEE Photonics Technol. Lett. 28, 1034–1037 (2016).

Wielandy, S.

Xianda Liu, X. L.

Xing He, X. H.

Xu, B.

L. Dong, W. Liu, P. Yang, H. Yan, X. Lei, S. Wang, and B. Xu, “Transformations of high-order mode Hermite–Gaussian beams using a deformable mirror,” Laser Phys. 23(3), 035004 (2013).
[Crossref]

Xu, X.

B. Yang, H. Zhang, C. Shi, R. Tao, R. Su, P. Ma, X. Wang, P. Zhou, X. Xu, and Q. Lu, “3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated raman scattering and transverse mode instability,” J. Opt. 20(2), 025802 (2018).
[Crossref]

H. Ma, H. Zhao, P. Zhou, X. Wang, Y. Ma, X. Xu, and Z. Liu, “Adaptive conversion of multimode beam to near-diffraction-limited flattop beam based on dual-phase-only liquid-crystal spatial light modulators,” Opt. Express 18(26), 27723–27730 (2010).
[Crossref] [PubMed]

Xu, X.-J.

J. Li, H.-C. Zhao, Z.-L. Chen, and X.-J. Xu, “Beam cleanup of a multimode fiber seeded by an off-center single-mode laser source,” Optik (Stuttg.) 124(16), 2501–2503 (2013).
[Crossref]

H.-C. Zhao, H.-T. Ma, P. Zhou, X.-L. Wang, Y.-X. Ma, X. Li, X.-J. Xu, and Y.-J. Zhao, “Multimode fiber laser beam cleanup based on stochastic parallel gradient descent algorithm,” Opt. Commun. 284(2), 613–615 (2011).
[Crossref]

H.-C. Zhao, X.-L. Wang, P. Zhou, H.-T. Ma, Y.-X. Ma, S.-H. Wang, X.-J. Xu, and Y.-J. Zhao, “Experimental explorations of the high-order gaussian mode transformation based on blind-optimization adaptive optics,” Opt. Commun. 284(19), 4654–4657 (2011).
[Crossref]

Yablon, A. D.

Yan, H.

L. Dong, W. Liu, P. Yang, H. Yan, X. Lei, S. Wang, and B. Xu, “Transformations of high-order mode Hermite–Gaussian beams using a deformable mirror,” Laser Phys. 23(3), 035004 (2013).
[Crossref]

Yan, P.

Q. Bian, L. Huang, X. J. Wang, X. K. Ma, P. Yan, and M. L. Gong, “Experimental investigation on the beam quality improvement of the fiber laser by adaptive optics,” Laser Phys. 25(12), 125101 (2015).
[Crossref]

Yang, B.

B. Yang, H. Zhang, C. Shi, R. Tao, R. Su, P. Ma, X. Wang, P. Zhou, X. Xu, and Q. Lu, “3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated raman scattering and transverse mode instability,” J. Opt. 20(2), 025802 (2018).
[Crossref]

Yang, L.

Yang, P.

L. Dong, W. Liu, P. Yang, H. Yan, X. Lei, S. Wang, and B. Xu, “Transformations of high-order mode Hermite–Gaussian beams using a deformable mirror,” Laser Phys. 23(3), 035004 (2013).
[Crossref]

Yao, T.

Yoda, H.

Zavalova, V.

A. Alexandrov, V. Zavalova, A. Kudryashov, A. Rukosuev, Y. Sheldakova, V. Samarkin, and D. Dumitras, “Beam correction in TiS lasers by means of adaptive optics,” AIP Conf. Proc. 1228, 123–129 (2010).
[Crossref]

Zenteno, L. A.

Zervas, M. N.

Zhang, H.

B. Yang, H. Zhang, C. Shi, R. Tao, R. Su, P. Ma, X. Wang, P. Zhou, X. Xu, and Q. Lu, “3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated raman scattering and transverse mode instability,” J. Opt. 20(2), 025802 (2018).
[Crossref]

Zhao, H.

Zhao, H.-C.

J. Li, H.-C. Zhao, Z.-L. Chen, and X.-J. Xu, “Beam cleanup of a multimode fiber seeded by an off-center single-mode laser source,” Optik (Stuttg.) 124(16), 2501–2503 (2013).
[Crossref]

H.-C. Zhao, X.-L. Wang, P. Zhou, H.-T. Ma, Y.-X. Ma, S.-H. Wang, X.-J. Xu, and Y.-J. Zhao, “Experimental explorations of the high-order gaussian mode transformation based on blind-optimization adaptive optics,” Opt. Commun. 284(19), 4654–4657 (2011).
[Crossref]

H.-C. Zhao, H.-T. Ma, P. Zhou, X.-L. Wang, Y.-X. Ma, X. Li, X.-J. Xu, and Y.-J. Zhao, “Multimode fiber laser beam cleanup based on stochastic parallel gradient descent algorithm,” Opt. Commun. 284(2), 613–615 (2011).
[Crossref]

Zhao, Y.-J.

H.-C. Zhao, X.-L. Wang, P. Zhou, H.-T. Ma, Y.-X. Ma, S.-H. Wang, X.-J. Xu, and Y.-J. Zhao, “Experimental explorations of the high-order gaussian mode transformation based on blind-optimization adaptive optics,” Opt. Commun. 284(19), 4654–4657 (2011).
[Crossref]

H.-C. Zhao, H.-T. Ma, P. Zhou, X.-L. Wang, Y.-X. Ma, X. Li, X.-J. Xu, and Y.-J. Zhao, “Multimode fiber laser beam cleanup based on stochastic parallel gradient descent algorithm,” Opt. Commun. 284(2), 613–615 (2011).
[Crossref]

Zhou, P.

Y. An, L. Huang, J. Li, J. Leng, L. Yang, and P. Zhou, “Learning to decompose the modes in few-mode fibers with deep convolutional neural network,” Opt. Express 27(7), 10127–10137 (2019).
[Crossref]

B. Yang, H. Zhang, C. Shi, R. Tao, R. Su, P. Ma, X. Wang, P. Zhou, X. Xu, and Q. Lu, “3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated raman scattering and transverse mode instability,” J. Opt. 20(2), 025802 (2018).
[Crossref]

R. Tao, X. Wang, and P. Zhou, “Comprehensive theoretical study of mode instability in high-power fiber lasers by employing a universal model and its implications,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–19 (2018).
[Crossref]

L. Huang, T. Yao, J. Leng, S. Guo, R. Tao, P. Zhou, and X. Cheng, “Mode instability dynamics in high-power low-numerical-aperture step-index fiber amplifier,” Appl. Opt. 56(19), 5412–5417 (2017).
[Crossref] [PubMed]

L. Huang, S. Guo, J. Leng, H. Lü, P. Zhou, and X. Cheng, “Real-time mode decomposition for few-mode fiber based on numerical method,” Opt. Express 23(4), 4620–4629 (2015).
[Crossref] [PubMed]

H.-C. Zhao, X.-L. Wang, P. Zhou, H.-T. Ma, Y.-X. Ma, S.-H. Wang, X.-J. Xu, and Y.-J. Zhao, “Experimental explorations of the high-order gaussian mode transformation based on blind-optimization adaptive optics,” Opt. Commun. 284(19), 4654–4657 (2011).
[Crossref]

H.-C. Zhao, H.-T. Ma, P. Zhou, X.-L. Wang, Y.-X. Ma, X. Li, X.-J. Xu, and Y.-J. Zhao, “Multimode fiber laser beam cleanup based on stochastic parallel gradient descent algorithm,” Opt. Commun. 284(2), 613–615 (2011).
[Crossref]

H. Ma, H. Zhao, P. Zhou, X. Wang, Y. Ma, X. Xu, and Z. Liu, “Adaptive conversion of multimode beam to near-diffraction-limited flattop beam based on dual-phase-only liquid-crystal spatial light modulators,” Opt. Express 18(26), 27723–27730 (2010).
[Crossref] [PubMed]

Zhu, C.

AIP Conf. Proc. (1)

A. Alexandrov, V. Zavalova, A. Kudryashov, A. Rukosuev, Y. Sheldakova, V. Samarkin, and D. Dumitras, “Beam correction in TiS lasers by means of adaptive optics,” AIP Conf. Proc. 1228, 123–129 (2010).
[Crossref]

Appl. Opt. (5)

Appl. Phys. B (1)

N. Andermahr, T. Theeg, and C. Fallnich, “Novel approach for polarization-sensitive measurements of transverse modes in few-mode optical fibers,” Appl. Phys. B 91(2), 353–357 (2008).
[Crossref]

Chin. Opt. Lett. (1)

IEEE J. Sel. Top. Quantum Electron. (2)

M. N. Zervas and C. A. Codemard, “High power fiber lasers: A review,” IEEE J. Sel. Top. Quantum Electron. 20(5), 219–241 (2014).
[Crossref]

R. Tao, X. Wang, and P. Zhou, “Comprehensive theoretical study of mode instability in high-power fiber lasers by employing a universal model and its implications,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–19 (2018).
[Crossref]

IEEE Photonics Technol. Lett. (1)

D. R. Gray, M. N. Petrovich, S. R. Sandoghchi, N. V. Wheeler, N. K. Baddela, G. T. Jasion, T. Bradley, D. J. Richardson, and F. Poletti, “Real-time modal analysis via wavelength-swept spatial and spectral (S2) imaging,” IEEE Photonics Technol. Lett. 28, 1034–1037 (2016).

J. Lightwave Technol. (3)

J. Opt. (1)

B. Yang, H. Zhang, C. Shi, R. Tao, R. Su, P. Ma, X. Wang, P. Zhou, X. Xu, and Q. Lu, “3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated raman scattering and transverse mode instability,” J. Opt. 20(2), 025802 (2018).
[Crossref]

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

Laser Phys. (2)

L. Dong, W. Liu, P. Yang, H. Yan, X. Lei, S. Wang, and B. Xu, “Transformations of high-order mode Hermite–Gaussian beams using a deformable mirror,” Laser Phys. 23(3), 035004 (2013).
[Crossref]

Q. Bian, L. Huang, X. J. Wang, X. K. Ma, P. Yan, and M. L. Gong, “Experimental investigation on the beam quality improvement of the fiber laser by adaptive optics,” Laser Phys. 25(12), 125101 (2015).
[Crossref]

Nat. Photonics (1)

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

Opt. Commun. (2)

H.-C. Zhao, H.-T. Ma, P. Zhou, X.-L. Wang, Y.-X. Ma, X. Li, X.-J. Xu, and Y.-J. Zhao, “Multimode fiber laser beam cleanup based on stochastic parallel gradient descent algorithm,” Opt. Commun. 284(2), 613–615 (2011).
[Crossref]

H.-C. Zhao, X.-L. Wang, P. Zhou, H.-T. Ma, Y.-X. Ma, S.-H. Wang, X.-J. Xu, and Y.-J. Zhao, “Experimental explorations of the high-order gaussian mode transformation based on blind-optimization adaptive optics,” Opt. Commun. 284(19), 4654–4657 (2011).
[Crossref]

Opt. Express (11)

H. Ma, H. Zhao, P. Zhou, X. Wang, Y. Ma, X. Xu, and Z. Liu, “Adaptive conversion of multimode beam to near-diffraction-limited flattop beam based on dual-phase-only liquid-crystal spatial light modulators,” Opt. Express 18(26), 27723–27730 (2010).
[Crossref] [PubMed]

M. Paurisse, L. Lévèque, M. Hanna, F. Druon, and P. Georges, “Complete measurement of fiber modal content by wavefront analysis,” Opt. Express 20(4), 4074–4084 (2012).
[Crossref] [PubMed]

J. W. Nicholson, A. D. Yablon, S. Ramachandran, and S. Ghalmi, “Spatially and spectrally resolved imaging of modal content in large-mode-area fibers,” Opt. Express 16(10), 7233–7243 (2008).
[Crossref] [PubMed]

Y. An, L. Huang, J. Li, J. Leng, L. Yang, and P. Zhou, “Learning to decompose the modes in few-mode fibers with deep convolutional neural network,” Opt. Express 27(7), 10127–10137 (2019).
[Crossref]

L. Huang, S. Guo, J. Leng, H. Lü, P. Zhou, and X. Cheng, “Real-time mode decomposition for few-mode fiber based on numerical method,” Opt. Express 23(4), 4620–4629 (2015).
[Crossref] [PubMed]

X. Ma, C. Zhu, I. N. Hu, A. Kaplan, and A. Galvanauskas, “Single-mode chirally-coupled-core fibers with larger than 50 µm diameter cores,” Opt. Express 22(8), 9206–9219 (2014).
[Crossref] [PubMed]

K. Igarashi, D. Souma, T. Tsuritani, and I. Morita, “Performance evaluation of selective mode conversion based on phase plates for a 10-mode fiber,” Opt. Express 22(17), 20881–20893 (2014).
[Crossref] [PubMed]

V. Scarnera, F. Ghiringhelli, A. Malinowski, C. A. Codemard, M. K. Durkin, and M. N. Zervas, “Modal instabilities in high power fiber laser oscillators,” Opt. Express 27(4), 4386–4403 (2019).
[Crossref] [PubMed]

S. Wielandy, “Implications of higher-order mode content in large mode area fibers with good beam quality,” Opt. Express 15(23), 15402–15409 (2007).
[Crossref] [PubMed]

T. Kaiser, D. Flamm, S. Schröter, and M. Duparré, “Complete modal decomposition for optical fibers using CGH-based correlation filters,” Opt. Express 17(11), 9347–9356 (2009).
[Crossref] [PubMed]

C. Schulze, D. Naidoo, D. Flamm, O. A. Schmidt, A. Forbes, and M. Duparré, “Wavefront reconstruction by modal decomposition,” Opt. Express 20(18), 19714–19725 (2012).
[Crossref] [PubMed]

Opt. Lett. (6)

Opt. Quantum Electron. (1)

L. W. Casperson, “Phase compensation of laser beam modes,” Opt. Quantum Electron. 8(6), 537–544 (1976).
[Crossref]

Optik (Stuttg.) (1)

J. Li, H.-C. Zhao, Z.-L. Chen, and X.-J. Xu, “Beam cleanup of a multimode fiber seeded by an off-center single-mode laser source,” Optik (Stuttg.) 124(16), 2501–2503 (2013).
[Crossref]

Phys. Rev. Lett. (1)

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94(14), 143902 (2005).
[Crossref] [PubMed]

Proc. SPIE (1)

S. A. Shakir, B. Culver, B. Nelson, Y. Starcher, G. M. Bates, and J. W. Hedrick, “Power scaling of passively phased fiber amplifier arrays,” Proc. SPIE 7070, 70700N (2008).
[Crossref]

Sci. Rep. (1)

M. Lyu, Z. Lin, G. Li, and G. Situ, “Fast modal decomposition for optical fibers using digital holography,” Sci. Rep. 7(1), 6556 (2017).
[Crossref] [PubMed]

Science (1)

J. Nilsson and D. N. Payne, “Physics. High-power fiber lasers,” Science 332(6032), 921–922 (2011).
[Crossref] [PubMed]

Other (6)

D. R. Gray, S. R. Sandoghchi, N. V. Wheeler, G. T. Jasion, J. P. Wooler, M. N. Petrovich, F. Poletti, and D. J. Richardson, “Towards real-time mode content characterization of multimode fibers,” presented at 2014 The European Conference on Optical Communication (ECOC), 2014), 1–3.
[Crossref]

K. Xie, W. Liu, Q. Zhou, H. Zhao, and X. Xu, “Numerical study of the measurement capability of quadriwave lateral shearing interferometry for multimode fiber laser (conference presentation),” presented at SPIE Security + Defence, (SPIE, 2017)

D. Malacara, Optical shop testing, 3rd ed. (John Wiley & Sons, Inc., 2007), Chap. 4.

J.-C. Sinquin, J.-M. Lurçon, and C. Guillemard, “Deformable mirror technologies for astronomy at CILAS,” presented at SPIE Astronomical Telescopes + Instrumentation, (SPIE, 2008), 12.

A. E. Siegman, “How to (maybe) measure laser beam quality,” in DPSS (Diode Pumped Solid State) Lasers: Applications and Issues, (Optical Society of America, 1998), p. MQ1.

ISO, ISO 11146–1: 2005, “Lasers and laser-related equipment-test methods for laser beam widths, divergence angles and beam propagation ratios part 1: stigmatic and simple astigmatic beams,” (2005).

Supplementary Material (1)

NameDescription
Visualization 1       A demonstration of the adaptive correction of dynamic multimode LMA fiber laser beam.

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)
Fig. 1
Fig. 1 Simulation of the diffraction pattern of a MM beam. (a) + 1st Rank diffraction pattern on the Fourier plane. Corr., the corrected far-field intensity profile; Ori., the original far-field intensity profile. (b) Modal weight of the incident beam. (c) Near-field intensity profile of the incident beam. The spots in the red polygon are for modal weight analysis; the spots in the yellow polygon are for modal phase analysis; the spots in the white box are for far-field monitoring.

Download Full Size | PPT Slide | PDF

Fig. 2
Fig. 2 Simulated comparison of the far-field intensity profiles of six LP modes. The subgraphs in the first row indicate the original far-field intensity profiles without correction. The subgraphs in the second row indicate the corrected far-field intensity profiles. The white circle in each subgraph indicates a D = 97 μm bucket. Subgraphs in the third row indicate the PIB vs the bucket radius. The blue curve and red curve indicate the original and corrected PIB respectively.

Download Full Size | PPT Slide | PDF

Fig. 3
Fig. 3 Experimental setup. SMF, single-mode fiber; FC, fiber connector; LMA fiber, large-mode-area fiber; L1, L2, lenses; MO, microscopic objective; NPBS, non-polarizing beam splitter; PBS, polarizing beam splitter; SLM, spatial light modulator; 1st Rank, + 1st rank diffraction beam of CGH.

Download Full Size | PPT Slide | PDF

Fig. 4
Fig. 4 Workflow of the adaptive phase correction in the experiment. (a) The kth CGH displayed on the SLM; (b) the diffraction pattern in the kth frame of the Camera 2; (c) the modal components analyzed by MD; (d) the reconstructed near-field phase distribution; (e) the (k + 1) th CGH with conjugated phase of reconstructed field; (f) the far-field intensity profiles acquired from the diffraction pattern in the (k + 1) th frame of the Camera 2.

Download Full Size | PPT Slide | PDF

Fig. 5
Fig. 5 Typical example of the static correction. (a) The modal weight spectrum. (b) The measured near-field intensity profile. (c) The reconstructed near-field intensity profile. (d) The original far-field intensity profile. (e) The corrected far-field intensity profile. The white circle in each subgraph indicates a D = 97 μm bucket.

Download Full Size | PPT Slide | PDF

Fig. 6
Fig. 6 The far field intensity PIB vs time curves for the original beam without correction (blue) referred to the corrected beam (red). The black dashed curve represents the modal weight of FM. The yellow curve represents the PIB of the ideal corrected beam. The green curve represents the cross correlation between the reconstructed far-field intensity profile and the measured one. The near-field intensity profiles of correspond time are shown on the top of figure. Ori. PIB, the original far-field PIB; Corr. PIB, the corrected far-field PIB; Ideal Corr. PIB, the ideal corrected far-field PIB; FM weight, the modal weight of LP01 mode; FF CC, the far-field correlation coefficient.

Download Full Size | PPT Slide | PDF

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

T M e a s u r e ( r ) = ∑ n = 1 N T n ( r ) e i K n r + ∑ n = 2 N ( T n cos ( r ) e i K n cos r + T n sin ( r ) e i K n sin r )
C = | ∬ Δ I R e c ( x , y ) Δ I M e a ( x , y ) d x d y ∬ Δ I R e c 2 ( x , y ) d x d y ∬ Δ I M e a 2 ( x , y ) d x d y |
T C o r r e c t ( r ) = e − i ϕ R e c ( r ) ⋅ e i K C o r r e c t r
T O r i ( r ) = e i K O r i r
T F i n a l ( r , k + 1 ) = T M e a s u r e ( r ) + A O r i ⋅ T O r i ( r ) + A C o r r e c t ⋅ T C o r r e c t ( r , k )

Metrics