Abstract

We study experimentally and numerically the spectral and spatial dynamics of second harmonic generation in an all-optically poled multimode graded-index fiber. In contrast with poled single-mode fibers, in a multimode graded-index fiber a pump can generate a series of sharp sidebands around its second harmonic (SH) that originate from the sub-millimetric periodic evolution of the intensity at the fundamental frequency. The mutual interaction between the fundamental and its SH may also strongly affect the spatial distribution of guided light for both colors: when increasing the pump power, both fundamental and SH output beams evolve from disordered multimode speckles into two bell‐shaped beams.

© 2017 Optical Society of America

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References

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K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, Phys. Rev. Lett. 116, 183901 (2016).
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[Crossref]

2015 (4)

M. Conforti, S. Trillo, A. Mussot, and A. Kudlinski, Sci. Rep. 5, 9433 (2015).
[Crossref]

K. Krupa, A. Labruyère, A. Tonello, B. M. Shalaby, V. Couderc, F. Baronio, and A. B. Aceves, Optica 2, 1058 (2015).
[Crossref]

L. G. Wright, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 9, 306 (2015).
[Crossref]

L. G. Wright, S. Wabnitz, D. N. Christodoulides, and F. W. Wise, Phys. Rev. Lett. 115, 223902 (2015).
[Crossref]

2013 (2)

W. H. Renninger and F. W. Wise, Nat. Commun. 4, 1719 (2013).
[Crossref]

H. Al-Jibbouri, I. Vidanović, A. Balaž, and A. Pelster, J. Phys. B 46, 065303 (2013).
[Crossref]

2012 (1)

F. Baronio, M. Conforti, C. D. Angelis, M. Andreana, A. Tonello, and V. Couderc, Laser Phys. Lett. 9, 359 (2012).
[Crossref]

2010 (1)

2009 (1)

2008 (1)

2003 (1)

1999 (1)

1996 (1)

1995 (1)

1994 (2)

1987 (2)

1986 (1)

Aceves, A. B.

Al-Jibbouri, H.

H. Al-Jibbouri, I. Vidanović, A. Balaž, and A. Pelster, J. Phys. B 46, 065303 (2013).
[Crossref]

Andreana, M.

F. Baronio, M. Conforti, C. D. Angelis, M. Andreana, A. Tonello, and V. Couderc, Laser Phys. Lett. 9, 359 (2012).
[Crossref]

Angelis, C. D.

F. Baronio, M. Conforti, C. D. Angelis, M. Andreana, A. Tonello, and V. Couderc, Laser Phys. Lett. 9, 359 (2012).
[Crossref]

Balaž, A.

H. Al-Jibbouri, I. Vidanović, A. Balaž, and A. Pelster, J. Phys. B 46, 065303 (2013).
[Crossref]

Baronio, F.

K. Krupa, A. Labruyère, A. Tonello, B. M. Shalaby, V. Couderc, F. Baronio, and A. B. Aceves, Optica 2, 1058 (2015).
[Crossref]

F. Baronio, M. Conforti, C. D. Angelis, M. Andreana, A. Tonello, and V. Couderc, Laser Phys. Lett. 9, 359 (2012).
[Crossref]

Barthélémy, A.

K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, Phys. Rev. Lett. 116, 183901 (2016).
[Crossref]

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self‐cleaning in multimode fiber,” arXiv:1603.02972 (2016).

Bendahmane, A.

K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, Phys. Rev. Lett. 116, 183901 (2016).
[Crossref]

Bonfrate, G.

Broderick, N. G.

Buy-Lesvigne, C.

Canagasabey, A.

Chernov, P. V.

Christodoulides, D. N.

L. G. Wright, Z. Liu, D. A. Nolan, M.-J. Li, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 10, 771 (2016).
[Crossref]

L. G. Wright, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 9, 306 (2015).
[Crossref]

L. G. Wright, S. Wabnitz, D. N. Christodoulides, and F. W. Wise, Phys. Rev. Lett. 115, 223902 (2015).
[Crossref]

Conforti, M.

M. Conforti, S. Trillo, A. Mussot, and A. Kudlinski, Sci. Rep. 5, 9433 (2015).
[Crossref]

F. Baronio, M. Conforti, C. D. Angelis, M. Andreana, A. Tonello, and V. Couderc, Laser Phys. Lett. 9, 359 (2012).
[Crossref]

Corbari, C.

Couderc, V.

K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, Phys. Rev. Lett. 116, 183901 (2016).
[Crossref]

K. Krupa, A. Labruyère, A. Tonello, B. M. Shalaby, V. Couderc, F. Baronio, and A. B. Aceves, Optica 2, 1058 (2015).
[Crossref]

F. Baronio, M. Conforti, C. D. Angelis, M. Andreana, A. Tonello, and V. Couderc, Laser Phys. Lett. 9, 359 (2012).
[Crossref]

V. Couderc, A. Tonello, C. Buy-Lesvigne, P. Leproux, and L. Grossard, Opt. Lett. 35, 145 (2010).
[Crossref]

V. Tombelaine, C. Buy-Lesvigne, P. Leproux, V. Couderc, and G. Mélin, Opt. Lett. 33, 2011 (2008).
[Crossref]

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self‐cleaning in multimode fiber,” arXiv:1603.02972 (2016).

de Sandro, J. P.

Dianov, E. M.

Dong, L.

Fabert, M.

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self‐cleaning in multimode fiber,” arXiv:1603.02972 (2016).

Gladyshev, A. V.

Grossard, L.

Guillemet, S.

Hernandez, Y.

Ibsen, M.

Kazansky, P. G.

Kornienko, L. S.

Kosolapov, A.

Krupa, K.

K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, Phys. Rev. Lett. 116, 183901 (2016).
[Crossref]

K. Krupa, A. Labruyère, A. Tonello, B. M. Shalaby, V. Couderc, F. Baronio, and A. B. Aceves, Optica 2, 1058 (2015).
[Crossref]

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self‐cleaning in multimode fiber,” arXiv:1603.02972 (2016).

Kudlinski, A.

M. Conforti, S. Trillo, A. Mussot, and A. Kudlinski, Sci. Rep. 5, 9433 (2015).
[Crossref]

Kyung, J. H.

Labruyère, A.

Lawandy, N. M.

Leproux, P.

Levenson, J. A.

Li, M.-J.

L. G. Wright, Z. Liu, D. A. Nolan, M.-J. Li, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 10, 771 (2016).
[Crossref]

Liegeois, F.

Liu, Z.

L. G. Wright, Z. Liu, D. A. Nolan, M.-J. Li, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 10, 771 (2016).
[Crossref]

Longhi, S.

Margulis, W.

Mélin, G.

Millot, G.

K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, Phys. Rev. Lett. 116, 183901 (2016).
[Crossref]

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self‐cleaning in multimode fiber,” arXiv:1603.02972 (2016).

Mussot, A.

M. Conforti, S. Trillo, A. Mussot, and A. Kudlinski, Sci. Rep. 5, 9433 (2015).
[Crossref]

Nolan, D. A.

L. G. Wright, Z. Liu, D. A. Nolan, M.-J. Li, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 10, 771 (2016).
[Crossref]

Österberg, U.

Pelster, A.

H. Al-Jibbouri, I. Vidanović, A. Balaž, and A. Pelster, J. Phys. B 46, 065303 (2013).
[Crossref]

Pruneri, V.

Renninger, W. H.

W. H. Renninger and F. W. Wise, Nat. Commun. 4, 1719 (2013).
[Crossref]

Richardson, D. J.

Rybaltovsky, A. O.

Sauvain, E.

Shalaby, B. M.

K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, Phys. Rev. Lett. 116, 183901 (2016).
[Crossref]

K. Krupa, A. Labruyère, A. Tonello, B. M. Shalaby, V. Couderc, F. Baronio, and A. B. Aceves, Optica 2, 1058 (2015).
[Crossref]

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self‐cleaning in multimode fiber,” arXiv:1603.02972 (2016).

Simonneau, C.

St.J. Russell, P.

Stolen, R. H.

Tom, H. W. K.

Tombelaine, V.

Tonello, A.

K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, Phys. Rev. Lett. 116, 183901 (2016).
[Crossref]

K. Krupa, A. Labruyère, A. Tonello, B. M. Shalaby, V. Couderc, F. Baronio, and A. B. Aceves, Optica 2, 1058 (2015).
[Crossref]

F. Baronio, M. Conforti, C. D. Angelis, M. Andreana, A. Tonello, and V. Couderc, Laser Phys. Lett. 9, 359 (2012).
[Crossref]

V. Couderc, A. Tonello, C. Buy-Lesvigne, P. Leproux, and L. Grossard, Opt. Lett. 35, 145 (2010).
[Crossref]

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self‐cleaning in multimode fiber,” arXiv:1603.02972 (2016).

Trillo, S.

M. Conforti, S. Trillo, A. Mussot, and A. Kudlinski, Sci. Rep. 5, 9433 (2015).
[Crossref]

Vidakovic, P.

Vidanovic, I.

H. Al-Jibbouri, I. Vidanović, A. Balaž, and A. Pelster, J. Phys. B 46, 065303 (2013).
[Crossref]

Wabnitz, S.

K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, Phys. Rev. Lett. 116, 183901 (2016).
[Crossref]

L. G. Wright, S. Wabnitz, D. N. Christodoulides, and F. W. Wise, Phys. Rev. Lett. 115, 223902 (2015).
[Crossref]

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self‐cleaning in multimode fiber,” arXiv:1603.02972 (2016).

Wise, F. W.

L. G. Wright, Z. Liu, D. A. Nolan, M.-J. Li, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 10, 771 (2016).
[Crossref]

L. G. Wright, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 9, 306 (2015).
[Crossref]

L. G. Wright, S. Wabnitz, D. N. Christodoulides, and F. W. Wise, Phys. Rev. Lett. 115, 223902 (2015).
[Crossref]

W. H. Renninger and F. W. Wise, Nat. Commun. 4, 1719 (2013).
[Crossref]

Wright, L. G.

L. G. Wright, Z. Liu, D. A. Nolan, M.-J. Li, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 10, 771 (2016).
[Crossref]

L. G. Wright, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 9, 306 (2015).
[Crossref]

L. G. Wright, S. Wabnitz, D. N. Christodoulides, and F. W. Wise, Phys. Rev. Lett. 115, 223902 (2015).
[Crossref]

Yashkov, M. V.

Yatsenko, Y. P.

J. Phys. B (1)

H. Al-Jibbouri, I. Vidanović, A. Balaž, and A. Pelster, J. Phys. B 46, 065303 (2013).
[Crossref]

Laser Phys. Lett. (1)

F. Baronio, M. Conforti, C. D. Angelis, M. Andreana, A. Tonello, and V. Couderc, Laser Phys. Lett. 9, 359 (2012).
[Crossref]

Nat. Commun. (1)

W. H. Renninger and F. W. Wise, Nat. Commun. 4, 1719 (2013).
[Crossref]

Nat. Photonics (2)

L. G. Wright, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 9, 306 (2015).
[Crossref]

L. G. Wright, Z. Liu, D. A. Nolan, M.-J. Li, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 10, 771 (2016).
[Crossref]

Opt. Lett. (12)

Optica (1)

Phys. Rev. Lett. (2)

L. G. Wright, S. Wabnitz, D. N. Christodoulides, and F. W. Wise, Phys. Rev. Lett. 115, 223902 (2015).
[Crossref]

K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, Phys. Rev. Lett. 116, 183901 (2016).
[Crossref]

Sci. Rep. (1)

M. Conforti, S. Trillo, A. Mussot, and A. Kudlinski, Sci. Rep. 5, 9433 (2015).
[Crossref]

Other (1)

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self‐cleaning in multimode fiber,” arXiv:1603.02972 (2016).

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Figures (8)

Fig. 1.
Fig. 1.

Experimental setup to pole and test the MM-GRIN fiber. HWP, half-wave plate; QWP, quarter-wave plate; BPF, bandpass filter with a 10 nm bandwidth at 532 nm.

Fig. 2.
Fig. 2.

Evolution of the SH average power versus time (after removing the KTP crystal) measured at the output of the 6 m long MM-GRIN fiber for an injected FF peak power of 37.5 kW.

Fig. 3.
Fig. 3.

Spectra measured along the poled MM-GRIN fiber by the cut-back method (in the absence of GPI); the logarithmic scale and the use of the frequency on the x-axis emphasize the spectral lines around 532 nm. The insets show a photo of the output beam (a) without and (b) with GPI.

Fig. 4.
Fig. 4.

Top panel: QPM diagram considering a poling period Λ=48  μm and a self-imaging period ΛS=0.615  mm; the horizontal lines show the momenta due to ΛS (for different values of q). Bottom panel: spectrum measured at the 6 m long poled MM-GRIN fiber output. The dashed vertical lines show the predicted SH wavelengths.

Fig. 5.
Fig. 5.

Numerically calculated spectra (on a logarithmic scale) as a function of the propagation distance.

Fig. 6.
Fig. 6.

Calculated output spectrum around the FF pump at 1064 nm (top panel) and around the most intense SH peak at 532 nm (bottom panel). The dashed vertical lines show the theoretical positions of the additional SH peaks.

Fig. 7.
Fig. 7.

Measured beam shapes and corresponding profiles (for x=0, y=0) at the output of the 6 m long MM-GRIN fiber. FF beam for an injected peak power of (a) 3.75 kW and (b) 25.9 kW; SH beam for an injected peak power of (c) 3.75 kW [as in (a)] and (d) 40.5 kW.

Fig. 8.
Fig. 8.

Measured FF and SH beam shapes at the output of a 2 m long poled MM-GRIN fiber. The pump peak powers are: (a, c) 0.94 kW and (b, d) 39 kW. The reference horizontal bars are 10 μm wide.

Equations (3)

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

Δβ=β(2ω)2β(ω)2πΛ=0,
Δβq2πΛS=0,
χ(2)(z)=χ0(2)cos(2πΛz)q=15{1+cos(q2πΛSz)}.

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