Abstract

We report the experimental observation of Kerr beam self-cleaning in a graded-index multimode fiber, leading to output beam profiles different from a bell shape, close to the LP01 mode. For specific light injection conditions, nonlinear coupling among the guided modes can reshape the output speckle pattern generated by a pulsed beam into the low order LP11 mode. This effect was observed in a few meters-long multimode fiber with 750 ps pulses at 1064 nm in the normal dispersion regime. The power threshold for LP11 mode self-cleaning was about three times larger than that required for Kerr nonlinear self-cleaning into the LP01 mode.

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

Full Article  |  PDF Article
OSA Recommended Articles
Wavefront shaping for optimized many-mode Kerr beam self-cleaning in graded-index multimode fiber

E. Deliancourt, M. Fabert, A. Tonello, K. Krupa, A. Desfarges-Berthelemot, V. Kermene, G. Millot, A. Barthélémy, S. Wabnitz, and V. Couderc
Opt. Express 27(12) 17311-17321 (2019)

Kerr self-cleaning of pulsed beam in an ytterbium doped multimode fiber

R. Guenard, K. Krupa, R. Dupiol, M. Fabert, A. Bendahmane, V. Kermene, A. Desfarges-Berthelemot, J. L. Auguste, A. Tonello, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc
Opt. Express 25(5) 4783-4792 (2017)

Spatial beam self-cleaning and supercontinuum generation with Yb-doped multimode graded-index fiber taper based on accelerating self-imaging and dissipative landscape

A. Niang, T. Mansuryan, K. Krupa, A. Tonello, M. Fabert, P. Leproux, D. Modotto, O. N. Egorova, A. E. Levchenko, D. S. Lipatov, S. L. Semjonov, G. Millot, V. Couderc, and S. Wabnitz
Opt. Express 27(17) 24018-24028 (2019)

References

  • View by:
  • |
  • |
  • |

  1. A. Hasegawa, “Self-confinement of multimode optical pulse in a glass fiber,” Opt. Lett. 5(10), 416–417 (1980).
    [Crossref]
  2. S. Longhi, “Modulational instability and space–time dynamics in nonlinear parabolic-index optical fibers,” Opt. Lett. 28(23), 2363–2365 (2003).
    [Crossref]
  3. S. A. Ponomarenko and G. P. Agrawal, “Do Solitonlike Self-Similar Waves Exist in Nonlinear Optical Media?” Phys. Rev. Lett. 97(1), 013901 (2006).
    [Crossref]
  4. P. Ascheri, G. Garnier, C. Michel, V. Doya, and A. Picozzi, “Condensation and thermalization of classical optical waves in a waveguide,” Phys. Rev. A 83(3), 033838 (2011).
    [Crossref]
  5. A. Mecozzi, C. Antonelli, and M. Shtaif, “Nonlinear propagation in multi-mode fibers in the strong coupling regime,” Opt. Express 20(11), 11673 (2012).
    [Crossref]
  6. Z. Zhu, L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Observation of multimode solitons in few-mode fiber,” Opt. Lett. 41(20), 4819–4822 (2016).
    [Crossref]
  7. K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, “Observation of Geometric Parametric Instability Induced by the Periodic Spatial Self-Imaging of Multimode Waves,” Phys. Rev. Lett. 116(18), 183901 (2016).
    [Crossref]
  8. K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self-cleaning n multimode fibres,” Nat. Photonics 11(4), 237–241 (2017).
    [Crossref]
  9. Z. Liu, L.G. Wright, D.N. Christodoulides, and F. W. Wise, “Kerr self-cleaning of femtosecond-pulsed beams in graded-index multimode fiber,” Opt. Lett. 41(16), 3675–3678 (2016).
    [Crossref]
  10. L. G. Wright, Z. Liu, D. A. Nolan, M.-J. Li, D. N. Christodoulides, and F. W. Wise, “Self-organized instability in graded index multimode fibres,” Nat. Photonics 10(12), 771–776 (2016).
    [Crossref]
  11. A. Mafi, “Pulse Propagation in a Short Nonlinear Graded-Index Multimode Optical Fiber,” J. Lightwave Technol. 30(17), 2803–2811 (2012).
    [Crossref]
  12. S. Trillo and S. Wabnitz, “Nonlinear nonreciprocity in a coherent mismatched directional coupler,” Appl. Phys. Lett. 49(13), 752–754 (1986).
    [Crossref]
  13. R. W. Gerchberg and W. O. Saxton, “Practical algorithm for determination of phase from image and diffraction plane pictures,” Optik 35(2), 237–246 (1972).
  14. S. Skupin, U. Peschel, L. Bergé, and F. Lederer, “Stability of weakly nonlinear localized states in attractive potentials,” Phys. Rev. E 70(1), 016614 (2004).
    [Crossref]
  15. D. Mandelik, Y. Lahini, and Y. Silberberg, “Nonlinearly Induced Relaxation to the Ground State in a Two-Level System,” Phys. Rev. Lett. 95(7), 073902 (2005).
    [Crossref]

2017 (1)

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self-cleaning n multimode fibres,” Nat. Photonics 11(4), 237–241 (2017).
[Crossref]

2016 (4)

Z. Liu, L.G. Wright, D.N. Christodoulides, and F. W. Wise, “Kerr self-cleaning of femtosecond-pulsed beams in graded-index multimode fiber,” Opt. Lett. 41(16), 3675–3678 (2016).
[Crossref]

L. G. Wright, Z. Liu, D. A. Nolan, M.-J. Li, D. N. Christodoulides, and F. W. Wise, “Self-organized instability in graded index multimode fibres,” Nat. Photonics 10(12), 771–776 (2016).
[Crossref]

Z. Zhu, L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Observation of multimode solitons in few-mode fiber,” Opt. Lett. 41(20), 4819–4822 (2016).
[Crossref]

K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, “Observation of Geometric Parametric Instability Induced by the Periodic Spatial Self-Imaging of Multimode Waves,” Phys. Rev. Lett. 116(18), 183901 (2016).
[Crossref]

2012 (2)

2011 (1)

P. Ascheri, G. Garnier, C. Michel, V. Doya, and A. Picozzi, “Condensation and thermalization of classical optical waves in a waveguide,” Phys. Rev. A 83(3), 033838 (2011).
[Crossref]

2006 (1)

S. A. Ponomarenko and G. P. Agrawal, “Do Solitonlike Self-Similar Waves Exist in Nonlinear Optical Media?” Phys. Rev. Lett. 97(1), 013901 (2006).
[Crossref]

2005 (1)

D. Mandelik, Y. Lahini, and Y. Silberberg, “Nonlinearly Induced Relaxation to the Ground State in a Two-Level System,” Phys. Rev. Lett. 95(7), 073902 (2005).
[Crossref]

2004 (1)

S. Skupin, U. Peschel, L. Bergé, and F. Lederer, “Stability of weakly nonlinear localized states in attractive potentials,” Phys. Rev. E 70(1), 016614 (2004).
[Crossref]

2003 (1)

1986 (1)

S. Trillo and S. Wabnitz, “Nonlinear nonreciprocity in a coherent mismatched directional coupler,” Appl. Phys. Lett. 49(13), 752–754 (1986).
[Crossref]

1980 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “Practical algorithm for determination of phase from image and diffraction plane pictures,” Optik 35(2), 237–246 (1972).

Agrawal, G. P.

S. A. Ponomarenko and G. P. Agrawal, “Do Solitonlike Self-Similar Waves Exist in Nonlinear Optical Media?” Phys. Rev. Lett. 97(1), 013901 (2006).
[Crossref]

Antonelli, C.

Ascheri, P.

P. Ascheri, G. Garnier, C. Michel, V. Doya, and A. Picozzi, “Condensation and thermalization of classical optical waves in a waveguide,” Phys. Rev. A 83(3), 033838 (2011).
[Crossref]

Barthélémy, A.

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self-cleaning n multimode fibres,” Nat. Photonics 11(4), 237–241 (2017).
[Crossref]

K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, “Observation of Geometric Parametric Instability Induced by the Periodic Spatial Self-Imaging of Multimode Waves,” Phys. Rev. Lett. 116(18), 183901 (2016).
[Crossref]

Bendahmane, A.

K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, “Observation of Geometric Parametric Instability Induced by the Periodic Spatial Self-Imaging of Multimode Waves,” Phys. Rev. Lett. 116(18), 183901 (2016).
[Crossref]

Bergé, L.

S. Skupin, U. Peschel, L. Bergé, and F. Lederer, “Stability of weakly nonlinear localized states in attractive potentials,” Phys. Rev. E 70(1), 016614 (2004).
[Crossref]

Christodoulides, D. N.

L. G. Wright, Z. Liu, D. A. Nolan, M.-J. Li, D. N. Christodoulides, and F. W. Wise, “Self-organized instability in graded index multimode fibres,” Nat. Photonics 10(12), 771–776 (2016).
[Crossref]

Z. Zhu, L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Observation of multimode solitons in few-mode fiber,” Opt. Lett. 41(20), 4819–4822 (2016).
[Crossref]

Christodoulides, D.N.

Couderc, V.

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self-cleaning n multimode fibres,” Nat. Photonics 11(4), 237–241 (2017).
[Crossref]

K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, “Observation of Geometric Parametric Instability Induced by the Periodic Spatial Self-Imaging of Multimode Waves,” Phys. Rev. Lett. 116(18), 183901 (2016).
[Crossref]

Doya, V.

P. Ascheri, G. Garnier, C. Michel, V. Doya, and A. Picozzi, “Condensation and thermalization of classical optical waves in a waveguide,” Phys. Rev. A 83(3), 033838 (2011).
[Crossref]

Fabert, M.

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self-cleaning n multimode fibres,” Nat. Photonics 11(4), 237–241 (2017).
[Crossref]

Garnier, G.

P. Ascheri, G. Garnier, C. Michel, V. Doya, and A. Picozzi, “Condensation and thermalization of classical optical waves in a waveguide,” Phys. Rev. A 83(3), 033838 (2011).
[Crossref]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “Practical algorithm for determination of phase from image and diffraction plane pictures,” Optik 35(2), 237–246 (1972).

Hasegawa, A.

Krupa, K.

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self-cleaning n multimode fibres,” Nat. Photonics 11(4), 237–241 (2017).
[Crossref]

K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, “Observation of Geometric Parametric Instability Induced by the Periodic Spatial Self-Imaging of Multimode Waves,” Phys. Rev. Lett. 116(18), 183901 (2016).
[Crossref]

Lahini, Y.

D. Mandelik, Y. Lahini, and Y. Silberberg, “Nonlinearly Induced Relaxation to the Ground State in a Two-Level System,” Phys. Rev. Lett. 95(7), 073902 (2005).
[Crossref]

Lederer, F.

S. Skupin, U. Peschel, L. Bergé, and F. Lederer, “Stability of weakly nonlinear localized states in attractive potentials,” Phys. Rev. E 70(1), 016614 (2004).
[Crossref]

Li, M.-J.

L. G. Wright, Z. Liu, D. A. Nolan, M.-J. Li, D. N. Christodoulides, and F. W. Wise, “Self-organized instability in graded index multimode fibres,” Nat. Photonics 10(12), 771–776 (2016).
[Crossref]

Liu, Z.

Z. Liu, L.G. Wright, D.N. Christodoulides, and F. W. Wise, “Kerr self-cleaning of femtosecond-pulsed beams in graded-index multimode fiber,” Opt. Lett. 41(16), 3675–3678 (2016).
[Crossref]

L. G. Wright, Z. Liu, D. A. Nolan, M.-J. Li, D. N. Christodoulides, and F. W. Wise, “Self-organized instability in graded index multimode fibres,” Nat. Photonics 10(12), 771–776 (2016).
[Crossref]

Longhi, S.

Mafi, A.

Mandelik, D.

D. Mandelik, Y. Lahini, and Y. Silberberg, “Nonlinearly Induced Relaxation to the Ground State in a Two-Level System,” Phys. Rev. Lett. 95(7), 073902 (2005).
[Crossref]

Mecozzi, A.

Michel, C.

P. Ascheri, G. Garnier, C. Michel, V. Doya, and A. Picozzi, “Condensation and thermalization of classical optical waves in a waveguide,” Phys. Rev. A 83(3), 033838 (2011).
[Crossref]

Millot, G.

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self-cleaning n multimode fibres,” Nat. Photonics 11(4), 237–241 (2017).
[Crossref]

K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, “Observation of Geometric Parametric Instability Induced by the Periodic Spatial Self-Imaging of Multimode Waves,” Phys. Rev. Lett. 116(18), 183901 (2016).
[Crossref]

Nolan, D. A.

L. G. Wright, Z. Liu, D. A. Nolan, M.-J. Li, D. N. Christodoulides, and F. W. Wise, “Self-organized instability in graded index multimode fibres,” Nat. Photonics 10(12), 771–776 (2016).
[Crossref]

Peschel, U.

S. Skupin, U. Peschel, L. Bergé, and F. Lederer, “Stability of weakly nonlinear localized states in attractive potentials,” Phys. Rev. E 70(1), 016614 (2004).
[Crossref]

Picozzi, A.

P. Ascheri, G. Garnier, C. Michel, V. Doya, and A. Picozzi, “Condensation and thermalization of classical optical waves in a waveguide,” Phys. Rev. A 83(3), 033838 (2011).
[Crossref]

Ponomarenko, S. A.

S. A. Ponomarenko and G. P. Agrawal, “Do Solitonlike Self-Similar Waves Exist in Nonlinear Optical Media?” Phys. Rev. Lett. 97(1), 013901 (2006).
[Crossref]

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “Practical algorithm for determination of phase from image and diffraction plane pictures,” Optik 35(2), 237–246 (1972).

Shalaby, B. M.

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self-cleaning n multimode fibres,” Nat. Photonics 11(4), 237–241 (2017).
[Crossref]

K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, “Observation of Geometric Parametric Instability Induced by the Periodic Spatial Self-Imaging of Multimode Waves,” Phys. Rev. Lett. 116(18), 183901 (2016).
[Crossref]

Shtaif, M.

Silberberg, Y.

D. Mandelik, Y. Lahini, and Y. Silberberg, “Nonlinearly Induced Relaxation to the Ground State in a Two-Level System,” Phys. Rev. Lett. 95(7), 073902 (2005).
[Crossref]

Skupin, S.

S. Skupin, U. Peschel, L. Bergé, and F. Lederer, “Stability of weakly nonlinear localized states in attractive potentials,” Phys. Rev. E 70(1), 016614 (2004).
[Crossref]

Tonello, A.

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self-cleaning n multimode fibres,” Nat. Photonics 11(4), 237–241 (2017).
[Crossref]

K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, “Observation of Geometric Parametric Instability Induced by the Periodic Spatial Self-Imaging of Multimode Waves,” Phys. Rev. Lett. 116(18), 183901 (2016).
[Crossref]

Trillo, S.

S. Trillo and S. Wabnitz, “Nonlinear nonreciprocity in a coherent mismatched directional coupler,” Appl. Phys. Lett. 49(13), 752–754 (1986).
[Crossref]

Wabnitz, S.

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self-cleaning n multimode fibres,” Nat. Photonics 11(4), 237–241 (2017).
[Crossref]

K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, “Observation of Geometric Parametric Instability Induced by the Periodic Spatial Self-Imaging of Multimode Waves,” Phys. Rev. Lett. 116(18), 183901 (2016).
[Crossref]

S. Trillo and S. Wabnitz, “Nonlinear nonreciprocity in a coherent mismatched directional coupler,” Appl. Phys. Lett. 49(13), 752–754 (1986).
[Crossref]

Wise, F. W.

Wright, L. G.

Z. Zhu, L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Observation of multimode solitons in few-mode fiber,” Opt. Lett. 41(20), 4819–4822 (2016).
[Crossref]

L. G. Wright, Z. Liu, D. A. Nolan, M.-J. Li, D. N. Christodoulides, and F. W. Wise, “Self-organized instability in graded index multimode fibres,” Nat. Photonics 10(12), 771–776 (2016).
[Crossref]

Wright, L.G.

Zhu, Z.

Appl. Phys. Lett. (1)

S. Trillo and S. Wabnitz, “Nonlinear nonreciprocity in a coherent mismatched directional coupler,” Appl. Phys. Lett. 49(13), 752–754 (1986).
[Crossref]

J. Lightwave Technol. (1)

Nat. Photonics (2)

L. G. Wright, Z. Liu, D. A. Nolan, M.-J. Li, D. N. Christodoulides, and F. W. Wise, “Self-organized instability in graded index multimode fibres,” Nat. Photonics 10(12), 771–776 (2016).
[Crossref]

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self-cleaning n multimode fibres,” Nat. Photonics 11(4), 237–241 (2017).
[Crossref]

Opt. Express (1)

Opt. Lett. (4)

Optik (1)

R. W. Gerchberg and W. O. Saxton, “Practical algorithm for determination of phase from image and diffraction plane pictures,” Optik 35(2), 237–246 (1972).

Phys. Rev. A (1)

P. Ascheri, G. Garnier, C. Michel, V. Doya, and A. Picozzi, “Condensation and thermalization of classical optical waves in a waveguide,” Phys. Rev. A 83(3), 033838 (2011).
[Crossref]

Phys. Rev. E (1)

S. Skupin, U. Peschel, L. Bergé, and F. Lederer, “Stability of weakly nonlinear localized states in attractive potentials,” Phys. Rev. E 70(1), 016614 (2004).
[Crossref]

Phys. Rev. Lett. (3)

D. Mandelik, Y. Lahini, and Y. Silberberg, “Nonlinearly Induced Relaxation to the Ground State in a Two-Level System,” Phys. Rev. Lett. 95(7), 073902 (2005).
[Crossref]

K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, “Observation of Geometric Parametric Instability Induced by the Periodic Spatial Self-Imaging of Multimode Waves,” Phys. Rev. Lett. 116(18), 183901 (2016).
[Crossref]

S. A. Ponomarenko and G. P. Agrawal, “Do Solitonlike Self-Similar Waves Exist in Nonlinear Optical Media?” Phys. Rev. Lett. 97(1), 013901 (2006).
[Crossref]

Supplementary Material (2)

NameDescription
» Visualization 1       Decay of the LP11 transverse mode into a speckled output pattern versus input power decreasing
» Visualization 2       Robustness versus fiber squeezing of the spatial kerr-beam self-cleaning on the LP11 mode

Cited By

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

Alert me when this article is cited.


Figures (8)

Fig. 1.
Fig. 1. (a) Experimental condition used for axial power coupling in the GRIN-MMF fiber, (b) Corresponding experimental and numerical near field intensity patterns after 1 cm of propagation in the GRIN-MMF, (c) Fraction of power coupled into the guided modes (Hermite-Gauss basis); (d) Iso-intensity surface (at 50% of the local maximum) upon the propagation distance z.
Fig. 2.
Fig. 2. Intensity patterns at the GRIN-MMF output recorded (a) for standard Kerr self-cleaning on a bell-shaped beam at 2 kW peak power, and (b) for Kerr self-cleaning on a LP11 profile, for specific beam coupling conditions and 4.5 kW peak power.
Fig. 3.
Fig. 3. (a) Experimental condition used for power coupling in the GRIN-MMF fiber with an input incidence angle of 2.5°; (b) Corresponding experimental and numerical near field intensity patterns after 1 cm of propagation in the GRIN-MMF, (c) Fraction of power coupled into the guided modes (Hermite-Gauss basis), (d) Iso-intensity surface at 50% of the local maximum along the propagation distance z.
Fig. 4.
Fig. 4. Near field intensity patterns at the GRIN-MMF output recorded for increasing peak power values at the input. Laser beam coupling into the MMF was appropriate for Kerr self-cleaning on a LP11 profile.
Fig. 5.
Fig. 5. Near field (a),(b) and far field (c),(d) intensity patterns at the GRIN-MMF output recorded in linear propagation regime (a, c) and in the nonlinear self-cleaning regime (b, d) for appropriate settings of the input coupling, in order to get self-cleaning of a LP11 mode. The white line corresponds to the core boundary in the near field images and to the NA in the far field images.
Fig. 6.
Fig. 6. Correlation between the experimental patterns at the GRIN-MMF output and the LP11 theoretical shape, upon the launched laser power, in the near-field (blue curve) and far-field (red curve), respectively.
Fig. 7.
Fig. 7. Time-averaged numerical results (Iso-intensity surfaces at 50% of the local maximum) of beam propagation in a GRIN MMF. (a) absence of Kerr effect. (b) Kerr effect enabled. The insets show the beam intensities at three different positions along the propagation. White segment: 10 μm.
Fig. 8.
Fig. 8. Experimental output spectrum for the maximum input peak power (50 kW) coupled in the GRIN MMF within a 2.5° input angle. (a) output beam profile of the main intermodal FWM process at 728 nm, (b) output self-cleaned beam at 1064 nm before Raman and intermodal FWM generation (38 kW), (c) output pump beam pattern at 1064 nm after Raman and intermodal FWM generation; fiber length: 6 m.

Equations (1)

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

C S = I e x p I t h d S I e x p 2 d S I t h 2 d S

Metrics