Abstract

Intermodal four-wave mixing (IMFWM) is demonstrated in a standard SMF-28e + fiber through pumping in the normal dispersion regime by a Q-switched nanosecond pulsed laser. A new IMFWM process where two pump photons in LP01 mode are completely annihilated to give rise to Stokes and anti-Stokes photons, both in LP02 mode, has been observed. Discrete ultraviolet peaks at 390.7 nm and 396.7 nm are also observed in this communication fiber through a complex cascaded process.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
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  5. G. Lopez-Galmiche, Z. Sanjabi Eznaveh, M. A. Eftekhar, J. Antonio Lopez, L. G. Wright, F. Wise, D. Christodoulides, and R. Amezcua Correa, “Visible supercontinuum generation in a graded index multimode fiber pumped at 1064 nm,” Opt. Lett. 41(11), 2553–2556 (2016).
    [Crossref] [PubMed]
  6. K. Krupa, C. Louot, V. Couderc, M. Fabert, R. Guenard, B. M. Shalaby, A. Tonello, D. Pagnoux, P. Leproux, A. Bendahmane, R. Dupiol, G. Millot, S. Wabnitz, and S. Wabnitz, “Spatiotemporal characterization of supercontinuum extending from the visible to the mid-infrared in a multimode graded-index optical fiber,” Opt. Lett. 41(24), 5785–5788 (2016).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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2018 (1)

2017 (2)

2016 (5)

2015 (4)

2013 (1)

W. H. Renninger and F. W. Wise, “Optical solitons in graded-index multimode fibres,” Nat. Commun. 4(1), 1719 (2013).
[Crossref] [PubMed]

2012 (2)

J. Cheng, M. E. V. Pedersen, K. Charan, K. Wang, C. Xu, L. Grüner-Nielsen, and D. Jakobsen, “Intermodal four-wave mixing in a higher-order-mode fiber,” Appl. Phys. Lett. 101(16), 161106 (2012).
[Crossref] [PubMed]

A. Mafi, “Pulse Propagation in a Short Nonlinear Graded-Index Multimode Optical Fiber,” J. Lightwave Technol. 30(17), 2803–2811 (2012).
[Crossref]

2010 (1)

2009 (1)

H. Tu, Z. Jiang, D. L. Marks, and S. A. Boppart, “Intermodal four-wave mixing from femtosecond pulse-pumped photonic crystal fiber,” Appl. Phys. Lett. 94(10), 101109 (2009).
[Crossref] [PubMed]

2006 (1)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

2005 (1)

I. A. Walmsley and M. G. Raymer, “Toward Quantum-Information Processing with Photons,” Science 307(5716), 1733–1734 (2005).
[Crossref] [PubMed]

2004 (1)

2003 (1)

2002 (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

1987 (1)

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59(8), 880–883 (1987).
[Crossref] [PubMed]

1974 (1)

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24(7), 308–310 (1974).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59(8), 880–883 (1987).
[Crossref] [PubMed]

Amezcua Correa, R.

Andermahr, N.

Antonio Lopez, J.

Ashkin, A.

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24(7), 308–310 (1974).
[Crossref]

Barthelemy, A.

Barthélémy, 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] [PubMed]

Bendahmane, A.

Biancalana, F.

Birks, T.

Bjorkholm, J. E.

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24(7), 308–310 (1974).
[Crossref]

Boppart, S. A.

H. Tu, Z. Jiang, D. L. Marks, and S. A. Boppart, “Intermodal four-wave mixing from femtosecond pulse-pumped photonic crystal fiber,” Appl. Phys. Lett. 94(10), 101109 (2009).
[Crossref] [PubMed]

Charan, K.

J. Cheng, M. E. V. Pedersen, K. Charan, K. Wang, C. Xu, L. Grüner-Nielsen, and D. Jakobsen, “Intermodal four-wave mixing in a higher-order-mode fiber,” Appl. Phys. Lett. 101(16), 161106 (2012).
[Crossref] [PubMed]

Chen, Y.

Cheng, J.

J. Cheng, M. E. V. Pedersen, K. Charan, K. Wang, C. Xu, L. Grüner-Nielsen, and D. Jakobsen, “Intermodal four-wave mixing in a higher-order-mode fiber,” Appl. Phys. Lett. 101(16), 161106 (2012).
[Crossref] [PubMed]

Christodoulides, D.

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

Couderc, V.

Demas, J.

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

Dupiol, R.

Eftekhar, M. A.

Fabert, M.

Fallnich, C.

Farrell, G.

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

Gisin, N.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

Grüner-Nielsen, L.

J. Cheng, M. E. V. Pedersen, K. Charan, K. Wang, C. Xu, L. Grüner-Nielsen, and D. Jakobsen, “Intermodal four-wave mixing in a higher-order-mode fiber,” Appl. Phys. Lett. 101(16), 161106 (2012).
[Crossref] [PubMed]

Guenard, R.

Han, Y.

Jakobsen, D.

J. Cheng, M. E. V. Pedersen, K. Charan, K. Wang, C. Xu, L. Grüner-Nielsen, and D. Jakobsen, “Intermodal four-wave mixing in a higher-order-mode fiber,” Appl. Phys. Lett. 101(16), 161106 (2012).
[Crossref] [PubMed]

Jiang, Z.

H. Tu, Z. Jiang, D. L. Marks, and S. A. Boppart, “Intermodal four-wave mixing from femtosecond pulse-pumped photonic crystal fiber,” Appl. Phys. Lett. 94(10), 101109 (2009).
[Crossref] [PubMed]

Joly, N.

Kang, Z.

Kibler, B.

Knight, J.

Krupa, K.

Leproux, P.

Li, F.

Longhi, S.

Lopez-Galmiche, G.

Louot, C.

Lu, C.

Mafi, A.

Marks, D. L.

H. Tu, Z. Jiang, D. L. Marks, and S. A. Boppart, “Intermodal four-wave mixing from femtosecond pulse-pumped photonic crystal fiber,” Appl. Phys. Lett. 94(10), 101109 (2009).
[Crossref] [PubMed]

Mei, C.

Millot, G.

Modotto, D.

Nazemosadat, E.

Pagnoux, D.

Pedersen, M. E. V.

J. Cheng, M. E. V. Pedersen, K. Charan, K. Wang, C. Xu, L. Grüner-Nielsen, and D. Jakobsen, “Intermodal four-wave mixing in a higher-order-mode fiber,” Appl. Phys. Lett. 101(16), 161106 (2012).
[Crossref] [PubMed]

Picozzi, A.

A. Picozzi, G. Millot, and S. Wabnitz, “Nonlinear virtues of multimode fibre,” Nat. Commun. 9, 289–291 (2015).

Pourbeyram, H.

Ramachandran, S.

Raymer, M. G.

I. A. Walmsley and M. G. Raymer, “Toward Quantum-Information Processing with Photons,” Science 307(5716), 1733–1734 (2005).
[Crossref] [PubMed]

Renninger, W. H.

W. H. Renninger and F. W. Wise, “Optical solitons in graded-index multimode fibres,” Nat. Commun. 4(1), 1719 (2013).
[Crossref] [PubMed]

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

Rishoj, L.

Russell, P.

Sang, X.

Sanjabi Eznaveh, Z.

Shalaby, B. M.

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] [PubMed]

K. Krupa, C. Louot, V. Couderc, M. Fabert, R. Guenard, B. M. Shalaby, A. Tonello, D. Pagnoux, P. Leproux, A. Bendahmane, R. Dupiol, G. Millot, S. Wabnitz, and S. Wabnitz, “Spatiotemporal characterization of supercontinuum extending from the visible to the mid-infrared in a multimode graded-index optical fiber,” Opt. Lett. 41(24), 5785–5788 (2016).
[Crossref] [PubMed]

Steinvurzel, P.

Stolen, R. H.

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24(7), 308–310 (1974).
[Crossref]

Sylvestre, T.

Tai, B.

Tam, H. Y.

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

Tonello, A.

Tu, H.

H. Tu, Z. Jiang, D. L. Marks, and S. A. Boppart, “Intermodal four-wave mixing from femtosecond pulse-pumped photonic crystal fiber,” Appl. Phys. Lett. 94(10), 101109 (2009).
[Crossref] [PubMed]

Wabnitz, S.

A. Bendahmane, K. Krupa, A. Tonello, D. Modotto, T. Sylvestre, V. Couderc, S. Wabnitz, and G. Millot, “Seeded intermodal four-wave mixing in a highly multimode fiber,” J. Opt. Soc. Am. B 35(2), 295–301 (2018).
[Crossref]

R. Dupiol, A. Bendahmane, K. Krupa, A. Tonello, M. Fabert, B. Kibler, T. Sylvestre, A. Barthelemy, V. Couderc, S. Wabnitz, and G. Millot, “Far-detuned cascaded intermodal four-wave mixing in a multimode fiber,” Opt. Lett. 42(7), 1293–1296 (2017).
[Crossref] [PubMed]

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] [PubMed]

K. Krupa, C. Louot, V. Couderc, M. Fabert, R. Guenard, B. M. Shalaby, A. Tonello, D. Pagnoux, P. Leproux, A. Bendahmane, R. Dupiol, G. Millot, S. Wabnitz, and S. Wabnitz, “Spatiotemporal characterization of supercontinuum extending from the visible to the mid-infrared in a multimode graded-index optical fiber,” Opt. Lett. 41(24), 5785–5788 (2016).
[Crossref] [PubMed]

K. Krupa, C. Louot, V. Couderc, M. Fabert, R. Guenard, B. M. Shalaby, A. Tonello, D. Pagnoux, P. Leproux, A. Bendahmane, R. Dupiol, G. Millot, S. Wabnitz, and S. Wabnitz, “Spatiotemporal characterization of supercontinuum extending from the visible to the mid-infrared in a multimode graded-index optical fiber,” Opt. Lett. 41(24), 5785–5788 (2016).
[Crossref] [PubMed]

A. Picozzi, G. Millot, and S. Wabnitz, “Nonlinear virtues of multimode fibre,” Nat. Commun. 9, 289–291 (2015).

Wadsworth, W.

Wai, P. K. A.

Walmsley, I. A.

I. A. Walmsley and M. G. Raymer, “Toward Quantum-Information Processing with Photons,” Science 307(5716), 1733–1734 (2005).
[Crossref] [PubMed]

Wang, K.

Wise, F.

Wise, F. W.

W. H. Renninger and F. W. Wise, “Optical solitons in graded-index multimode fibres,” Nat. Commun. 4(1), 1719 (2013).
[Crossref] [PubMed]

Wright, L. G.

Wu, Q.

Xu, C.

J. Cheng, M. E. V. Pedersen, K. Charan, K. Wang, C. Xu, L. Grüner-Nielsen, and D. Jakobsen, “Intermodal four-wave mixing in a higher-order-mode fiber,” Appl. Phys. Lett. 101(16), 161106 (2012).
[Crossref] [PubMed]

Yan, B.

Yu, C.

Yuan, J.

Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

Zhang, X.

Zhong, K.

Zhou, G.

Zhou, X.

Appl. Phys. Lett. (3)

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24(7), 308–310 (1974).
[Crossref]

H. Tu, Z. Jiang, D. L. Marks, and S. A. Boppart, “Intermodal four-wave mixing from femtosecond pulse-pumped photonic crystal fiber,” Appl. Phys. Lett. 94(10), 101109 (2009).
[Crossref] [PubMed]

J. Cheng, M. E. V. Pedersen, K. Charan, K. Wang, C. Xu, L. Grüner-Nielsen, and D. Jakobsen, “Intermodal four-wave mixing in a higher-order-mode fiber,” Appl. Phys. Lett. 101(16), 161106 (2012).
[Crossref] [PubMed]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (2)

Mod. Phys. (1)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

Nat. Commun. (2)

W. H. Renninger and F. W. Wise, “Optical solitons in graded-index multimode fibres,” Nat. Commun. 4(1), 1719 (2013).
[Crossref] [PubMed]

A. Picozzi, G. Millot, and S. Wabnitz, “Nonlinear virtues of multimode fibre,” Nat. Commun. 9, 289–291 (2015).

Opt. Express (3)

Opt. Lett. (6)

J. Yuan, X. Sang, Q. Wu, G. Zhou, F. Li, X. Zhou, C. Yu, K. Wang, B. Yan, Y. Han, H. Y. Tam, and P. K. A. Wai, “Enhanced intermodal four-wave mixing for visible and near-infrared wavelength generation in a photonic crystal fiber,” Opt. Lett. 40(7), 1338–1341 (2015).
[Crossref] [PubMed]

G. Lopez-Galmiche, Z. Sanjabi Eznaveh, M. A. Eftekhar, J. Antonio Lopez, L. G. Wright, F. Wise, D. Christodoulides, and R. Amezcua Correa, “Visible supercontinuum generation in a graded index multimode fiber pumped at 1064 nm,” Opt. Lett. 41(11), 2553–2556 (2016).
[Crossref] [PubMed]

K. Krupa, C. Louot, V. Couderc, M. Fabert, R. Guenard, B. M. Shalaby, A. Tonello, D. Pagnoux, P. Leproux, A. Bendahmane, R. Dupiol, G. Millot, S. Wabnitz, and S. Wabnitz, “Spatiotemporal characterization of supercontinuum extending from the visible to the mid-infrared in a multimode graded-index optical fiber,” Opt. Lett. 41(24), 5785–5788 (2016).
[Crossref] [PubMed]

S. Longhi, “Modulational instability and space-time dynamics in nonlinear parabolic-index optical fibers,” Opt. Lett. 28(23), 2363–2365 (2003).
[Crossref] [PubMed]

R. Dupiol, A. Bendahmane, K. Krupa, A. Tonello, M. Fabert, B. Kibler, T. Sylvestre, A. Barthelemy, V. Couderc, S. Wabnitz, and G. Millot, “Far-detuned cascaded intermodal four-wave mixing in a multimode fiber,” Opt. Lett. 42(7), 1293–1296 (2017).
[Crossref] [PubMed]

J. Yuan, Z. Kang, F. Li, X. Zhang, C. Mei, G. Zhou, X. Sang, Q. Wu, B. Yan, X. Zhou, K. Zhong, K. Wang, C. Yu, G. Farrell, C. Lu, H. Y. Tam, and P. K. A. Wai, “Experimental generation of discrete ultraviolet wavelength by cascaded intermodal four-wave mixing in a multimode photonic crystal fiber,” Opt. Lett. 42(18), 3537–3540 (2017).
[Crossref] [PubMed]

Optica (1)

Phys. Rev. A (1)

H. Pourbeyram and A. Mafi, “Photon pair generation in multimode optical fibers via intermodal phase matching,” Phys. Rev. A 94(2), 023815 (2016).
[Crossref]

Phys. Rev. Lett. (2)

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] [PubMed]

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59(8), 880–883 (1987).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

Science (1)

I. A. Walmsley and M. G. Raymer, “Toward Quantum-Information Processing with Photons,” Science 307(5716), 1733–1734 (2005).
[Crossref] [PubMed]

Other (2)

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, Boston, 2007).

H. Pourbeyram and A. Mafi, “Apparent non-conservation of momentum of light due to strongly coupled nonlinear dynamics in a multimode optical fiber,” arXiv: 1701.05606 (2017).

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Figures (5)

Fig. 1
Fig. 1 Illustration of experimental setup for degenerate IMFWM. M′: High reflecting mirror at 1064 nm; D: Beam Dump; λ/2: Half-wave plate; MO: Microscope objective with magnification of 20X; 3D Translational stage; SMF-28e + : Fiber under test; BPF: Band pass filter; M: High reflecting mirror at 532 nm; USB4000: Ocean Optics Spectrometer; L1: Lens; CCD: camera.
Fig. 2
Fig. 2 Observed output spectra for a 28 cm long SMF-28 fiber at a peak input power of (a) 4.61 kW, (b) 5.65 kW, and (c) 6.71 kW. Here, A1−A3 and S1−S3 denote the observed anti-Stokes and Stokes waves respectively. Inset of Fig. 2c shows the spectrum of the residual pump at 6.71 kW.
Fig. 3
Fig. 3 Observed output spectra for a 51 cm long SMF-28 fiber at a peak input power of (a) 2.17 kW, (b) 2.67 kW, and (c) 4.61 kW. Here, A1−A6 and S1−S4 denote the observed anti-Stokes and Stokes waves respectively.
Fig. 4
Fig. 4 Phase matching curve for the IMFWM#1, IMFWM#2 and U-IMFWM process for initial pump pulses at 532 nm. The points with Δβ = 0 depict the perfect phase matching condition.
Fig. 5
Fig. 5 Output beam profiles imaged at (a) 447.5 nm, (b) 532 nm, and (c) 655.3 nm using a 10 nm band pass filter along with the respective intensity of spatial profile in (d), (e) and (f). Inset in Fig. 5b depicts transverse field profile consisting of a mixture of LP02 (80%) and LP21 (20%) mode at 655.3 nm.

Tables (1)

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Table 1 Experimental (Ex.) vs Theoretically (Th.) calculated parametric wavelengths, i.e. Stokes (S), Anti-Stokes (A) of different intermodal phase matching configurations

Equations (7)

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2 λ P = 1 λ S + 1 λ A
Δβ=2 β 01 P ( λ P ) β lm S ( λ S ) β l m A ( λ A )=0
σ=| dxdy | F P ( λ P ) | 2 F S ( λ S ) F A ( λ A ) |
Δβ( Ω )=δ β ( 0 ) δ β ( 1 ) Ω+ β ( 2 ) Ω 2
δ β ( 0 ) =2 β 01 P ( λ P ) β lm S ( λ P ) β l m A ( λ P )
δ β ( 1 ) =2πc[ β lm S ( 1 ) ( λ P ) β l m A ( 1 ) ( λ P ) ]
Σ β ( 2 ) =4 π 2 c 2 1 2 [ β lm S ( 2 ) ( λ P )+ β l m A ( 2 ) ( λ P ) ]

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