Abstract

We present a closed-form analytical description of the early stages of spectral broadening of ultrashort laser pulses beyond the basic theory of self-phase modulation (SPM). In the limit of short propagation paths, approximate analytical expressions derived as a part of our treatment recover the canonical SPM-theory results for the nonlinear shift and spectral broadening. For longer propagation paths, these expressions shed light on how dispersion effects enter the scene, decelerating the spectral broadening in the regime of normal dispersion and giving rise to an explosion-like bandwidth growth in anomalous-dispersion high-soliton-number pulse evolution scenarios. Based on this formalism, we will provide an analytical derivation for the relation between the maximum soliton self-compression length and the soliton number, which has been previously treated as purely empirical.

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

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References

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  1. Y. R. Shen, The Principles of Nonlinear Optics (New York, Wiley-Interscience, 1984).
  2. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, 2001).
  3. F. X. Kärtner, ed., Few-Cycle Laser Pulse Generation and Its Applications (Springer, Berlin, 2004).
  4. C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S. W. Huang, K. H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards subcycle optical waveforms,” Laser Photonics Rev. 9(2), 129–171 (2015).
    [Crossref]
  5. S. O. Konorov, D. A. Akimov, E. E. Serebryannikov, A. A. Ivanov, M. V. Alfimov, and A. M. Zheltikov, “Cross-correlation FROG CARS with frequency-converting PCFs,” Phys. Rev. E 70, 057601 (2004).
    [Crossref]
  6. H. N. Paulsen, K. M. Hilligsøe, J. Thøgersen, S. R. Keiding, and J. J. Larsen, “Coherent anti-Stokes Raman scattering microscopy with a photonic crystal fiber based light source,” Opt. Lett. 28(13), 1123–1125 (2003).
    [Crossref] [PubMed]
  7. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
    [Crossref]
  8. A. M. Zheltikov, “Let there be white light: supercontinuum generation by ultrashort laser pulses,” Phys.- Usp. 49(6), 605–628 (2006).
    [Crossref]
  9. T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
    [Crossref] [PubMed]
  10. A. M. Zheltikov, A. L’Huillier, and F. Krausz, “Nonlinear Optics,” in Handbook of Lasers and Optics, ed. by F. Träger, New York, Springer, 2007, pp. 157 – 248.
  11. A. Hasegawa, Optical Solitons in Fibers (Heidelberg, Springer, 1990).
  12. V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–65 (1972).
  13. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45(13), 1095–1098 (1980).
    [Crossref]
  14. T. Balciunas, C. F. Dutin, G. Fan, T. Witting, A. A. Voronin, A. M. Zheltikov, G. Frédéric, G. G. Paulus, A. Baltuska, and F. Benabid, “Sub-cycle gigawatt peak power pulses self-compressed by optical shock waves,” Nat. Commun. 6, 6117 (2015).
    [Crossref] [PubMed]
  15. A. A. Voronin and A. M. Zheltikov, “Subcycle solitonic breathers,” Phys. Rev. A 90(4), 043807 (2014).
    [Crossref]
  16. J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88(17), 173901 (2002).
    [Crossref] [PubMed]
  17. A. A. Voronin, I. V. Fedotov, A. B. Fedotov, and A. M. Zheltikov, “Spectral interference of frequency-shifted solitons in a photonic-crystal fiber,” Opt. Lett. 34(5), 569–571 (2009).
    [Crossref] [PubMed]
  18. X. Fang, M. Hu, L. Huang, L. Chai, N. Dai, J. Li, A. Yu. Tashchilina, A. M. Zheltikov, and C. Wang, “Multiwatt octave-spanning supercontinuum generation in multicore PCF,” Opt. Lett. 37, 2292–2294 (2012).
    [Crossref] [PubMed]
  19. T. Südmeyer, F. Brunner, E. Innerhofer, R. Paschotta, K. Furusawa, J. C. Baggett, T. M. Monro, D. J. Richardson, and U. Keller, “Nonlinear femtosecond pulse compression at high average power levels by use of a large-mode-area holey fiber,” Opt. Lett. 28(20), 1951–1953 (2003).
    [Crossref] [PubMed]
  20. A. V. Mitrofanov, A. A. Ivanov, M. V. Alfimov, A. A. Podshivalov, and A. M. Zheltikov, “Microjoule supercontinuum generation by stretched megawatt femtosecond laser pulses in a large-mode-area photonic-crystal fiber,” Opt. Commun. 280(2), 453–456 (2007).
    [Crossref]
  21. G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4(1), 33–36 (2010).
    [Crossref]

2015 (2)

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S. W. Huang, K. H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards subcycle optical waveforms,” Laser Photonics Rev. 9(2), 129–171 (2015).
[Crossref]

T. Balciunas, C. F. Dutin, G. Fan, T. Witting, A. A. Voronin, A. M. Zheltikov, G. Frédéric, G. G. Paulus, A. Baltuska, and F. Benabid, “Sub-cycle gigawatt peak power pulses self-compressed by optical shock waves,” Nat. Commun. 6, 6117 (2015).
[Crossref] [PubMed]

2014 (1)

A. A. Voronin and A. M. Zheltikov, “Subcycle solitonic breathers,” Phys. Rev. A 90(4), 043807 (2014).
[Crossref]

2012 (1)

2010 (1)

G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4(1), 33–36 (2010).
[Crossref]

2009 (1)

2007 (1)

A. V. Mitrofanov, A. A. Ivanov, M. V. Alfimov, A. A. Podshivalov, and A. M. Zheltikov, “Microjoule supercontinuum generation by stretched megawatt femtosecond laser pulses in a large-mode-area photonic-crystal fiber,” Opt. Commun. 280(2), 453–456 (2007).
[Crossref]

2006 (2)

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

A. M. Zheltikov, “Let there be white light: supercontinuum generation by ultrashort laser pulses,” Phys.- Usp. 49(6), 605–628 (2006).
[Crossref]

2004 (1)

S. O. Konorov, D. A. Akimov, E. E. Serebryannikov, A. A. Ivanov, M. V. Alfimov, and A. M. Zheltikov, “Cross-correlation FROG CARS with frequency-converting PCFs,” Phys. Rev. E 70, 057601 (2004).
[Crossref]

2003 (2)

2002 (2)

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88(17), 173901 (2002).
[Crossref] [PubMed]

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[Crossref] [PubMed]

1980 (1)

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45(13), 1095–1098 (1980).
[Crossref]

1972 (1)

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–65 (1972).

Akimov, D. A.

S. O. Konorov, D. A. Akimov, E. E. Serebryannikov, A. A. Ivanov, M. V. Alfimov, and A. M. Zheltikov, “Cross-correlation FROG CARS with frequency-converting PCFs,” Phys. Rev. E 70, 057601 (2004).
[Crossref]

Alfimov, M. V.

A. V. Mitrofanov, A. A. Ivanov, M. V. Alfimov, A. A. Podshivalov, and A. M. Zheltikov, “Microjoule supercontinuum generation by stretched megawatt femtosecond laser pulses in a large-mode-area photonic-crystal fiber,” Opt. Commun. 280(2), 453–456 (2007).
[Crossref]

S. O. Konorov, D. A. Akimov, E. E. Serebryannikov, A. A. Ivanov, M. V. Alfimov, and A. M. Zheltikov, “Cross-correlation FROG CARS with frequency-converting PCFs,” Phys. Rev. E 70, 057601 (2004).
[Crossref]

Baggett, J. C.

Balciunas, T.

T. Balciunas, C. F. Dutin, G. Fan, T. Witting, A. A. Voronin, A. M. Zheltikov, G. Frédéric, G. G. Paulus, A. Baltuska, and F. Benabid, “Sub-cycle gigawatt peak power pulses self-compressed by optical shock waves,” Nat. Commun. 6, 6117 (2015).
[Crossref] [PubMed]

Baltuska, A.

T. Balciunas, C. F. Dutin, G. Fan, T. Witting, A. A. Voronin, A. M. Zheltikov, G. Frédéric, G. G. Paulus, A. Baltuska, and F. Benabid, “Sub-cycle gigawatt peak power pulses self-compressed by optical shock waves,” Nat. Commun. 6, 6117 (2015).
[Crossref] [PubMed]

Benabid, F.

T. Balciunas, C. F. Dutin, G. Fan, T. Witting, A. A. Voronin, A. M. Zheltikov, G. Frédéric, G. G. Paulus, A. Baltuska, and F. Benabid, “Sub-cycle gigawatt peak power pulses self-compressed by optical shock waves,” Nat. Commun. 6, 6117 (2015).
[Crossref] [PubMed]

Brunner, F.

Cerullo, G.

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S. W. Huang, K. H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards subcycle optical waveforms,” Laser Photonics Rev. 9(2), 129–171 (2015).
[Crossref]

Chai, L.

Cirmi, G.

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S. W. Huang, K. H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards subcycle optical waveforms,” Laser Photonics Rev. 9(2), 129–171 (2015).
[Crossref]

Coen, S.

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

Dai, N.

Dudley, J. M.

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

Dutin, C. F.

T. Balciunas, C. F. Dutin, G. Fan, T. Witting, A. A. Voronin, A. M. Zheltikov, G. Frédéric, G. G. Paulus, A. Baltuska, and F. Benabid, “Sub-cycle gigawatt peak power pulses self-compressed by optical shock waves,” Nat. Commun. 6, 6117 (2015).
[Crossref] [PubMed]

Eggert, S.

G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4(1), 33–36 (2010).
[Crossref]

Fan, G.

T. Balciunas, C. F. Dutin, G. Fan, T. Witting, A. A. Voronin, A. M. Zheltikov, G. Frédéric, G. G. Paulus, A. Baltuska, and F. Benabid, “Sub-cycle gigawatt peak power pulses self-compressed by optical shock waves,” Nat. Commun. 6, 6117 (2015).
[Crossref] [PubMed]

Fang, S.

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S. W. Huang, K. H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards subcycle optical waveforms,” Laser Photonics Rev. 9(2), 129–171 (2015).
[Crossref]

Fang, X.

Fedotov, A. B.

Fedotov, I. V.

Frédéric, G.

T. Balciunas, C. F. Dutin, G. Fan, T. Witting, A. A. Voronin, A. M. Zheltikov, G. Frédéric, G. G. Paulus, A. Baltuska, and F. Benabid, “Sub-cycle gigawatt peak power pulses self-compressed by optical shock waves,” Nat. Commun. 6, 6117 (2015).
[Crossref] [PubMed]

Furusawa, K.

Genty, G.

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

Gordon, J. P.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45(13), 1095–1098 (1980).
[Crossref]

Griebner, U.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88(17), 173901 (2002).
[Crossref] [PubMed]

Hanke, T.

G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4(1), 33–36 (2010).
[Crossref]

Hänsch, T. W.

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[Crossref] [PubMed]

Herrmann, J.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88(17), 173901 (2002).
[Crossref] [PubMed]

Hilligsøe, K. M.

Holzwarth, R.

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[Crossref] [PubMed]

Hong, K. H.

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S. W. Huang, K. H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards subcycle optical waveforms,” Laser Photonics Rev. 9(2), 129–171 (2015).
[Crossref]

Hu, M.

Huang, L.

Huang, S. W.

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S. W. Huang, K. H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards subcycle optical waveforms,” Laser Photonics Rev. 9(2), 129–171 (2015).
[Crossref]

Huber, R.

G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4(1), 33–36 (2010).
[Crossref]

Husakou, A.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88(17), 173901 (2002).
[Crossref] [PubMed]

Innerhofer, E.

Ivanov, A. A.

A. V. Mitrofanov, A. A. Ivanov, M. V. Alfimov, A. A. Podshivalov, and A. M. Zheltikov, “Microjoule supercontinuum generation by stretched megawatt femtosecond laser pulses in a large-mode-area photonic-crystal fiber,” Opt. Commun. 280(2), 453–456 (2007).
[Crossref]

S. O. Konorov, D. A. Akimov, E. E. Serebryannikov, A. A. Ivanov, M. V. Alfimov, and A. M. Zheltikov, “Cross-correlation FROG CARS with frequency-converting PCFs,” Phys. Rev. E 70, 057601 (2004).
[Crossref]

Kärtner, F. X.

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S. W. Huang, K. H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards subcycle optical waveforms,” Laser Photonics Rev. 9(2), 129–171 (2015).
[Crossref]

Keiding, S. R.

Keller, U.

Knight, J. C.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88(17), 173901 (2002).
[Crossref] [PubMed]

Konorov, S. O.

S. O. Konorov, D. A. Akimov, E. E. Serebryannikov, A. A. Ivanov, M. V. Alfimov, and A. M. Zheltikov, “Cross-correlation FROG CARS with frequency-converting PCFs,” Phys. Rev. E 70, 057601 (2004).
[Crossref]

Korn, G.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88(17), 173901 (2002).
[Crossref] [PubMed]

Krauss, G.

G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4(1), 33–36 (2010).
[Crossref]

Larsen, J. J.

Leitenstorfer, A.

G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4(1), 33–36 (2010).
[Crossref]

Li, J.

Lohss, S.

G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4(1), 33–36 (2010).
[Crossref]

Manzoni, C.

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S. W. Huang, K. H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards subcycle optical waveforms,” Laser Photonics Rev. 9(2), 129–171 (2015).
[Crossref]

Mitrofanov, A. V.

A. V. Mitrofanov, A. A. Ivanov, M. V. Alfimov, A. A. Podshivalov, and A. M. Zheltikov, “Microjoule supercontinuum generation by stretched megawatt femtosecond laser pulses in a large-mode-area photonic-crystal fiber,” Opt. Commun. 280(2), 453–456 (2007).
[Crossref]

Mollenauer, L. F.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45(13), 1095–1098 (1980).
[Crossref]

Monro, T. M.

Moses, J.

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S. W. Huang, K. H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards subcycle optical waveforms,” Laser Photonics Rev. 9(2), 129–171 (2015).
[Crossref]

Mücke, O. D.

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S. W. Huang, K. H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards subcycle optical waveforms,” Laser Photonics Rev. 9(2), 129–171 (2015).
[Crossref]

Nickel, D.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88(17), 173901 (2002).
[Crossref] [PubMed]

Paschotta, R.

Paulsen, H. N.

Paulus, G. G.

T. Balciunas, C. F. Dutin, G. Fan, T. Witting, A. A. Voronin, A. M. Zheltikov, G. Frédéric, G. G. Paulus, A. Baltuska, and F. Benabid, “Sub-cycle gigawatt peak power pulses self-compressed by optical shock waves,” Nat. Commun. 6, 6117 (2015).
[Crossref] [PubMed]

Podshivalov, A. A.

A. V. Mitrofanov, A. A. Ivanov, M. V. Alfimov, A. A. Podshivalov, and A. M. Zheltikov, “Microjoule supercontinuum generation by stretched megawatt femtosecond laser pulses in a large-mode-area photonic-crystal fiber,” Opt. Commun. 280(2), 453–456 (2007).
[Crossref]

Richardson, D. J.

Russell, P. St. J.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88(17), 173901 (2002).
[Crossref] [PubMed]

Sell, A.

G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4(1), 33–36 (2010).
[Crossref]

Serebryannikov, E. E.

S. O. Konorov, D. A. Akimov, E. E. Serebryannikov, A. A. Ivanov, M. V. Alfimov, and A. M. Zheltikov, “Cross-correlation FROG CARS with frequency-converting PCFs,” Phys. Rev. E 70, 057601 (2004).
[Crossref]

Shabat, A. B.

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–65 (1972).

Stolen, R. H.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45(13), 1095–1098 (1980).
[Crossref]

Südmeyer, T.

Tashchilina, A. Yu.

Thøgersen, J.

Udem, T.

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[Crossref] [PubMed]

Voronin, A. A.

T. Balciunas, C. F. Dutin, G. Fan, T. Witting, A. A. Voronin, A. M. Zheltikov, G. Frédéric, G. G. Paulus, A. Baltuska, and F. Benabid, “Sub-cycle gigawatt peak power pulses self-compressed by optical shock waves,” Nat. Commun. 6, 6117 (2015).
[Crossref] [PubMed]

A. A. Voronin and A. M. Zheltikov, “Subcycle solitonic breathers,” Phys. Rev. A 90(4), 043807 (2014).
[Crossref]

A. A. Voronin, I. V. Fedotov, A. B. Fedotov, and A. M. Zheltikov, “Spectral interference of frequency-shifted solitons in a photonic-crystal fiber,” Opt. Lett. 34(5), 569–571 (2009).
[Crossref] [PubMed]

Wadsworth, W. J.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88(17), 173901 (2002).
[Crossref] [PubMed]

Wang, C.

Witting, T.

T. Balciunas, C. F. Dutin, G. Fan, T. Witting, A. A. Voronin, A. M. Zheltikov, G. Frédéric, G. G. Paulus, A. Baltuska, and F. Benabid, “Sub-cycle gigawatt peak power pulses self-compressed by optical shock waves,” Nat. Commun. 6, 6117 (2015).
[Crossref] [PubMed]

Zakharov, V. E.

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–65 (1972).

Zhavoronkov, N.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88(17), 173901 (2002).
[Crossref] [PubMed]

Zheltikov, A. M.

T. Balciunas, C. F. Dutin, G. Fan, T. Witting, A. A. Voronin, A. M. Zheltikov, G. Frédéric, G. G. Paulus, A. Baltuska, and F. Benabid, “Sub-cycle gigawatt peak power pulses self-compressed by optical shock waves,” Nat. Commun. 6, 6117 (2015).
[Crossref] [PubMed]

A. A. Voronin and A. M. Zheltikov, “Subcycle solitonic breathers,” Phys. Rev. A 90(4), 043807 (2014).
[Crossref]

X. Fang, M. Hu, L. Huang, L. Chai, N. Dai, J. Li, A. Yu. Tashchilina, A. M. Zheltikov, and C. Wang, “Multiwatt octave-spanning supercontinuum generation in multicore PCF,” Opt. Lett. 37, 2292–2294 (2012).
[Crossref] [PubMed]

A. A. Voronin, I. V. Fedotov, A. B. Fedotov, and A. M. Zheltikov, “Spectral interference of frequency-shifted solitons in a photonic-crystal fiber,” Opt. Lett. 34(5), 569–571 (2009).
[Crossref] [PubMed]

A. V. Mitrofanov, A. A. Ivanov, M. V. Alfimov, A. A. Podshivalov, and A. M. Zheltikov, “Microjoule supercontinuum generation by stretched megawatt femtosecond laser pulses in a large-mode-area photonic-crystal fiber,” Opt. Commun. 280(2), 453–456 (2007).
[Crossref]

A. M. Zheltikov, “Let there be white light: supercontinuum generation by ultrashort laser pulses,” Phys.- Usp. 49(6), 605–628 (2006).
[Crossref]

S. O. Konorov, D. A. Akimov, E. E. Serebryannikov, A. A. Ivanov, M. V. Alfimov, and A. M. Zheltikov, “Cross-correlation FROG CARS with frequency-converting PCFs,” Phys. Rev. E 70, 057601 (2004).
[Crossref]

Laser Photonics Rev. (1)

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S. W. Huang, K. H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards subcycle optical waveforms,” Laser Photonics Rev. 9(2), 129–171 (2015).
[Crossref]

Nat. Commun. (1)

T. Balciunas, C. F. Dutin, G. Fan, T. Witting, A. A. Voronin, A. M. Zheltikov, G. Frédéric, G. G. Paulus, A. Baltuska, and F. Benabid, “Sub-cycle gigawatt peak power pulses self-compressed by optical shock waves,” Nat. Commun. 6, 6117 (2015).
[Crossref] [PubMed]

Nat. Photonics (1)

G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4(1), 33–36 (2010).
[Crossref]

Nature (1)

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[Crossref] [PubMed]

Opt. Commun. (1)

A. V. Mitrofanov, A. A. Ivanov, M. V. Alfimov, A. A. Podshivalov, and A. M. Zheltikov, “Microjoule supercontinuum generation by stretched megawatt femtosecond laser pulses in a large-mode-area photonic-crystal fiber,” Opt. Commun. 280(2), 453–456 (2007).
[Crossref]

Opt. Lett. (4)

Phys. Rev. A (1)

A. A. Voronin and A. M. Zheltikov, “Subcycle solitonic breathers,” Phys. Rev. A 90(4), 043807 (2014).
[Crossref]

Phys. Rev. E (1)

S. O. Konorov, D. A. Akimov, E. E. Serebryannikov, A. A. Ivanov, M. V. Alfimov, and A. M. Zheltikov, “Cross-correlation FROG CARS with frequency-converting PCFs,” Phys. Rev. E 70, 057601 (2004).
[Crossref]

Phys. Rev. Lett. (2)

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88(17), 173901 (2002).
[Crossref] [PubMed]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45(13), 1095–1098 (1980).
[Crossref]

Phys.- Usp. (1)

A. M. Zheltikov, “Let there be white light: supercontinuum generation by ultrashort laser pulses,” Phys.- Usp. 49(6), 605–628 (2006).
[Crossref]

Rev. Mod. Phys. (1)

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

Sov. Phys. JETP (1)

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–65 (1972).

Other (5)

A. M. Zheltikov, A. L’Huillier, and F. Krausz, “Nonlinear Optics,” in Handbook of Lasers and Optics, ed. by F. Träger, New York, Springer, 2007, pp. 157 – 248.

A. Hasegawa, Optical Solitons in Fibers (Heidelberg, Springer, 1990).

Y. R. Shen, The Principles of Nonlinear Optics (New York, Wiley-Interscience, 1984).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, 2001).

F. X. Kärtner, ed., Few-Cycle Laser Pulse Generation and Its Applications (Springer, Berlin, 2004).

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Figures (2)

Fig. 1
Fig. 1 Temporal dynamics of high-N NSE solitons found by numerically solving the NSE [Eq. (1)] with N = 5 (a) and 7 (b).
Fig. 2
Fig. 2 Spectral broadening in the regime of (a, b) normal (sgnβ2 = + 1) and (c - f) anomalous (sgnβ2 = −1) dispersion: (maps) numerical solution of the NSE [Eq. (1)] and (solid lines) calculation using Eq. (14) (a, b) and Eq. (13) (c - f) with N = 5 (a, c, d) and 7 (b, e, f). The spectral bandwidth is normalized to the spectral bandwidth Δω0 of the input pulse. The propagation coordinate z is normalized to the dispersion length ld.

Equations (14)

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i u z = β 2 2 2 u η 2 γ P 0 | u | 2 u,
u( z,η )=u( 0,η )exp[ i ϕ SPM ( z,η ) ],
ϕ SPM ( z,η )=γ P 0 | u( 0,η ) | 2 z.
Δ ω SPM ( z ) γ P 0 z/ τ 0 ,
α SPM = 2 ϕ SPM η 2 2γ P 0 z τ 0 2 .
z m 0.32π l d / ( 2N ) .
| u( z,η ) | 2 = 1 ψ( z ) exp{ η 2 [ τ(z) ] 2 },
ψ( z )= [ ( 1 α 0 β 2 z ) 2 + ( z/ l d ) 2 ] 1/2 ,
τ( z )= τ 0 ψ( z )= τ 0 [ ( 1 α 0 β 2 z ) 2 + ( z/ l d ) 2 ] 1/2 .
τ( z ) τ 0 [ ( 1+2sgn( β 2 )| β 2 | γ P 0 z 2 / τ 0 2 ) 2 + ( z/ l d ) 2 ] 1/2 .
z m ( l d l nl ) 1/2 2 = l d 2N .
Δω( z )( γ P 0 / τ 0 ) 0 z [ 1+sgn( β 2 ) ( ζ/ l c ) 2 ]dζ .
Δω( z ) 1 τ 0 l c l nl arcsin( z l c )
Δω( z ) 1 τ 0 l c l nl arctan( z l c )

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