Abstract

In optical analogy of the event horizon, temporal pulse collision and mutual interactions are mainly between an intense solitary wave (soliton) and a dispersive probe wave. In such a regime, here we numerically investigate the probe-controlled soliton frequency shift as well as the soliton self-compression. In particular, in the dispersion landscape with multiple zero dispersion wavelengths, bi-directional soliton spectral tunneling effects is possible. Moreover, we propose a mid-infrared soliton self-compression to the generation of few-cycle ultrashort pulses, in a bulk of quadratic nonlinear crystals in contrast to optical fibers or cubic nonlinear media, which could contribute to the community with a simple and flexible method to experimental implementations

© 2015 Optical Society of America

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References

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  1. T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
    [Crossref] [PubMed]
  2. A. V. Yulin, D. V. Skryabin, P. St, and J. Russell, “Four-wave mixing of linear waves and solitons in fibers with higher-order dispersion,” Opt. Lett. 29, 2411–2413 (2004).
    [Crossref] [PubMed]
  3. D. V. Skryabin and A. V. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E 72, 016619 (2005).
    [Crossref]
  4. A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. S. J. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett. 95, 213902 (2005).
    [Crossref] [PubMed]
  5. A. V. Gorbach and D. V. Skryabin, “Bouncing of a dispersive pulse on an accelerating soliton and stepwise frequency conversion in optical fibers,” Opt. Express 15, 14560–14565 (2007).
    [Crossref] [PubMed]
  6. K. E. Webb, M. Erkintalo, Y. Xu, N. G. R. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, “Nonlinear optics of fibre event horizons,” Nat. Commun. 5, 4969 (2014).
    [Crossref] [PubMed]
  7. S. Robertson and U. Leonhardt, “Frequency shifting at fiber optical event horizons: the effect of Raman deceleration,” Phys. Rev. A 81, 063835 (2010).
    [Crossref]
  8. D. V. Skryabin and A. V. Gorbach, “Colloquium: Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010).
    [Crossref]
  9. V. E. Lobanov and A. P. Sukhorukov, “Total reflection, frequency, and velocity tuning in optical pulse collision in nonlinear dispersive media,” Phys. Rev. A 82, 033809(2010).
    [Crossref]
  10. A. Choudhary and F. König, “Efficient frequency shifting of dispersive waves at solitons,” Opt. Express 20, 5538–5546 (2012).
    [Crossref] [PubMed]
  11. A. V. Yulin, R. Driben, B. A. Malomed, and D. V. Skryabin, “Soliton interaction mediated by cascaded four wave mixing with dispersive waves,” Opt. Express 21, 14481–14486 (2013).
    [Crossref]
  12. L. Tartara, “Soliton control by a weak dispersive pulse,” J. Opt. Soc. Am. B 32, 395–399 (2015).
    [Crossref]
  13. A. Demircan, S. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett. 106. 163901(2011).
    [Crossref] [PubMed]
  14. A. Demircan, S. Amiranashvili, C. Brée, and G. Steinmeyer, “Compressible octave spanning supercontinuum generation by two-pulse collisions,” Phys. Rev. Lett. 110. 233901 (2013).
    [Crossref] [PubMed]
  15. A. Demircan, S. Amiranashvili, C. Brée, U. Morgner, and G. Steinmeyer, “Adjustable pulse compression scheme for generation of few-cycle pulses in the midinfrared,” Opt. Lett. 39, 2735–2738 (2014).
    [Crossref] [PubMed]
  16. X. Liu, B. Zhou, H. Guo, and M. Bache, “Mid-IR femtosecond frequency conversion by soliton-probe collision in phase-mismatched quadratic nonlinear crystals,” Opt. Lett. 40, 3798–3801 (2015).
    [Crossref]
  17. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2006).
  18. V. N. Serkin, V. A. Vysloukh, and J. M. Taylor, “Soliton spectral tunnelling effect,” Electron. Lett. 29, 12–13 (1993).
    [Crossref]
  19. H. Guo, S. F. Wang, X. Zeng, and M. Bache, “Understanding soliton spectral tunneling as a spectral coupling effect,” IEEE Photonics Technol. Lett. 25, 1928–1931 (2013).
    [Crossref]
  20. M. Bache, H. Guo, B. Zhou, and X. Zeng, “The anisotropic Kerr nonlinear refractive index of the beta-barium borate (β-BaB2O4) nonlinear crystal,” Opt. Mater. Express 3, 357–382 (2013).
    [Crossref]
  21. M. Bache, H. Guo, and B. Zhou, “Generating mid-IR octave-spanning supercontinua and few-cycle pulses with solitons in phase-mismatched quadratic nonlinear crystals,” Opt. Mater. Express 3, 1647–1657 (2013).
    [Crossref]
  22. H. Guo, X. Zeng, and M. Bache, “Generalized nonlinear wave equation in frequency domain,” arXiv:1301.1473 (2013).

2015 (2)

2014 (2)

K. E. Webb, M. Erkintalo, Y. Xu, N. G. R. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, “Nonlinear optics of fibre event horizons,” Nat. Commun. 5, 4969 (2014).
[Crossref] [PubMed]

A. Demircan, S. Amiranashvili, C. Brée, U. Morgner, and G. Steinmeyer, “Adjustable pulse compression scheme for generation of few-cycle pulses in the midinfrared,” Opt. Lett. 39, 2735–2738 (2014).
[Crossref] [PubMed]

2013 (5)

2012 (1)

2011 (1)

A. Demircan, S. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett. 106. 163901(2011).
[Crossref] [PubMed]

2010 (3)

S. Robertson and U. Leonhardt, “Frequency shifting at fiber optical event horizons: the effect of Raman deceleration,” Phys. Rev. A 81, 063835 (2010).
[Crossref]

D. V. Skryabin and A. V. Gorbach, “Colloquium: Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010).
[Crossref]

V. E. Lobanov and A. P. Sukhorukov, “Total reflection, frequency, and velocity tuning in optical pulse collision in nonlinear dispersive media,” Phys. Rev. A 82, 033809(2010).
[Crossref]

2008 (1)

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref] [PubMed]

2007 (1)

2005 (2)

D. V. Skryabin and A. V. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E 72, 016619 (2005).
[Crossref]

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. S. J. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref] [PubMed]

2004 (1)

1993 (1)

V. N. Serkin, V. A. Vysloukh, and J. M. Taylor, “Soliton spectral tunnelling effect,” Electron. Lett. 29, 12–13 (1993).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2006).

Amiranashvili, S.

A. Demircan, S. Amiranashvili, C. Brée, U. Morgner, and G. Steinmeyer, “Adjustable pulse compression scheme for generation of few-cycle pulses in the midinfrared,” Opt. Lett. 39, 2735–2738 (2014).
[Crossref] [PubMed]

A. Demircan, S. Amiranashvili, C. Brée, and G. Steinmeyer, “Compressible octave spanning supercontinuum generation by two-pulse collisions,” Phys. Rev. Lett. 110. 233901 (2013).
[Crossref] [PubMed]

A. Demircan, S. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett. 106. 163901(2011).
[Crossref] [PubMed]

Bache, M.

Brée, C.

A. Demircan, S. Amiranashvili, C. Brée, U. Morgner, and G. Steinmeyer, “Adjustable pulse compression scheme for generation of few-cycle pulses in the midinfrared,” Opt. Lett. 39, 2735–2738 (2014).
[Crossref] [PubMed]

A. Demircan, S. Amiranashvili, C. Brée, and G. Steinmeyer, “Compressible octave spanning supercontinuum generation by two-pulse collisions,” Phys. Rev. Lett. 110. 233901 (2013).
[Crossref] [PubMed]

Broderick, N. G. R.

K. E. Webb, M. Erkintalo, Y. Xu, N. G. R. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, “Nonlinear optics of fibre event horizons,” Nat. Commun. 5, 4969 (2014).
[Crossref] [PubMed]

Choudhary, A.

Demircan, A.

A. Demircan, S. Amiranashvili, C. Brée, U. Morgner, and G. Steinmeyer, “Adjustable pulse compression scheme for generation of few-cycle pulses in the midinfrared,” Opt. Lett. 39, 2735–2738 (2014).
[Crossref] [PubMed]

A. Demircan, S. Amiranashvili, C. Brée, and G. Steinmeyer, “Compressible octave spanning supercontinuum generation by two-pulse collisions,” Phys. Rev. Lett. 110. 233901 (2013).
[Crossref] [PubMed]

A. Demircan, S. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett. 106. 163901(2011).
[Crossref] [PubMed]

Driben, R.

Dudley, J. M.

K. E. Webb, M. Erkintalo, Y. Xu, N. G. R. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, “Nonlinear optics of fibre event horizons,” Nat. Commun. 5, 4969 (2014).
[Crossref] [PubMed]

Efimov, A.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. S. J. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref] [PubMed]

Erkintalo, M.

K. E. Webb, M. Erkintalo, Y. Xu, N. G. R. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, “Nonlinear optics of fibre event horizons,” Nat. Commun. 5, 4969 (2014).
[Crossref] [PubMed]

Genty, G.

K. E. Webb, M. Erkintalo, Y. Xu, N. G. R. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, “Nonlinear optics of fibre event horizons,” Nat. Commun. 5, 4969 (2014).
[Crossref] [PubMed]

Gorbach, A. V.

D. V. Skryabin and A. V. Gorbach, “Colloquium: Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010).
[Crossref]

A. V. Gorbach and D. V. Skryabin, “Bouncing of a dispersive pulse on an accelerating soliton and stepwise frequency conversion in optical fibers,” Opt. Express 15, 14560–14565 (2007).
[Crossref] [PubMed]

Guo, H.

Hill, S.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref] [PubMed]

Joly, N.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. S. J. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref] [PubMed]

Knight, J. C.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. S. J. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref] [PubMed]

König, F.

A. Choudhary and F. König, “Efficient frequency shifting of dispersive waves at solitons,” Opt. Express 20, 5538–5546 (2012).
[Crossref] [PubMed]

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref] [PubMed]

Kuklewicz, C.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref] [PubMed]

Leonhardt, U.

S. Robertson and U. Leonhardt, “Frequency shifting at fiber optical event horizons: the effect of Raman deceleration,” Phys. Rev. A 81, 063835 (2010).
[Crossref]

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref] [PubMed]

Liu, X.

Lobanov, V. E.

V. E. Lobanov and A. P. Sukhorukov, “Total reflection, frequency, and velocity tuning in optical pulse collision in nonlinear dispersive media,” Phys. Rev. A 82, 033809(2010).
[Crossref]

Malomed, B. A.

Morgner, U.

Murdoch, S. G.

K. E. Webb, M. Erkintalo, Y. Xu, N. G. R. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, “Nonlinear optics of fibre event horizons,” Nat. Commun. 5, 4969 (2014).
[Crossref] [PubMed]

Omenetto, F. G.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. S. J. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref] [PubMed]

Philbin, T. G.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref] [PubMed]

Robertson, S.

S. Robertson and U. Leonhardt, “Frequency shifting at fiber optical event horizons: the effect of Raman deceleration,” Phys. Rev. A 81, 063835 (2010).
[Crossref]

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref] [PubMed]

Russell, J.

Russell, P. S. J.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. S. J. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref] [PubMed]

Serkin, V. N.

V. N. Serkin, V. A. Vysloukh, and J. M. Taylor, “Soliton spectral tunnelling effect,” Electron. Lett. 29, 12–13 (1993).
[Crossref]

Skryabin, D. V.

A. V. Yulin, R. Driben, B. A. Malomed, and D. V. Skryabin, “Soliton interaction mediated by cascaded four wave mixing with dispersive waves,” Opt. Express 21, 14481–14486 (2013).
[Crossref]

D. V. Skryabin and A. V. Gorbach, “Colloquium: Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010).
[Crossref]

A. V. Gorbach and D. V. Skryabin, “Bouncing of a dispersive pulse on an accelerating soliton and stepwise frequency conversion in optical fibers,” Opt. Express 15, 14560–14565 (2007).
[Crossref] [PubMed]

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. S. J. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref] [PubMed]

D. V. Skryabin and A. V. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E 72, 016619 (2005).
[Crossref]

A. V. Yulin, D. V. Skryabin, P. St, and J. Russell, “Four-wave mixing of linear waves and solitons in fibers with higher-order dispersion,” Opt. Lett. 29, 2411–2413 (2004).
[Crossref] [PubMed]

St, P.

Steinmeyer, G.

A. Demircan, S. Amiranashvili, C. Brée, U. Morgner, and G. Steinmeyer, “Adjustable pulse compression scheme for generation of few-cycle pulses in the midinfrared,” Opt. Lett. 39, 2735–2738 (2014).
[Crossref] [PubMed]

A. Demircan, S. Amiranashvili, C. Brée, and G. Steinmeyer, “Compressible octave spanning supercontinuum generation by two-pulse collisions,” Phys. Rev. Lett. 110. 233901 (2013).
[Crossref] [PubMed]

A. Demircan, S. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett. 106. 163901(2011).
[Crossref] [PubMed]

Sukhorukov, A. P.

V. E. Lobanov and A. P. Sukhorukov, “Total reflection, frequency, and velocity tuning in optical pulse collision in nonlinear dispersive media,” Phys. Rev. A 82, 033809(2010).
[Crossref]

Tartara, L.

Taylor, A. J.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. S. J. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref] [PubMed]

Taylor, J. M.

V. N. Serkin, V. A. Vysloukh, and J. M. Taylor, “Soliton spectral tunnelling effect,” Electron. Lett. 29, 12–13 (1993).
[Crossref]

Vysloukh, V. A.

V. N. Serkin, V. A. Vysloukh, and J. M. Taylor, “Soliton spectral tunnelling effect,” Electron. Lett. 29, 12–13 (1993).
[Crossref]

Wang, S. F.

H. Guo, S. F. Wang, X. Zeng, and M. Bache, “Understanding soliton spectral tunneling as a spectral coupling effect,” IEEE Photonics Technol. Lett. 25, 1928–1931 (2013).
[Crossref]

Webb, K. E.

K. E. Webb, M. Erkintalo, Y. Xu, N. G. R. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, “Nonlinear optics of fibre event horizons,” Nat. Commun. 5, 4969 (2014).
[Crossref] [PubMed]

Xu, Y.

K. E. Webb, M. Erkintalo, Y. Xu, N. G. R. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, “Nonlinear optics of fibre event horizons,” Nat. Commun. 5, 4969 (2014).
[Crossref] [PubMed]

Yulin, A. V.

A. V. Yulin, R. Driben, B. A. Malomed, and D. V. Skryabin, “Soliton interaction mediated by cascaded four wave mixing with dispersive waves,” Opt. Express 21, 14481–14486 (2013).
[Crossref]

D. V. Skryabin and A. V. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E 72, 016619 (2005).
[Crossref]

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. S. J. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref] [PubMed]

A. V. Yulin, D. V. Skryabin, P. St, and J. Russell, “Four-wave mixing of linear waves and solitons in fibers with higher-order dispersion,” Opt. Lett. 29, 2411–2413 (2004).
[Crossref] [PubMed]

Zeng, X.

H. Guo, S. F. Wang, X. Zeng, and M. Bache, “Understanding soliton spectral tunneling as a spectral coupling effect,” IEEE Photonics Technol. Lett. 25, 1928–1931 (2013).
[Crossref]

M. Bache, H. Guo, B. Zhou, and X. Zeng, “The anisotropic Kerr nonlinear refractive index of the beta-barium borate (β-BaB2O4) nonlinear crystal,” Opt. Mater. Express 3, 357–382 (2013).
[Crossref]

H. Guo, X. Zeng, and M. Bache, “Generalized nonlinear wave equation in frequency domain,” arXiv:1301.1473 (2013).

Zhou, B.

Electron. Lett. (1)

V. N. Serkin, V. A. Vysloukh, and J. M. Taylor, “Soliton spectral tunnelling effect,” Electron. Lett. 29, 12–13 (1993).
[Crossref]

IEEE Photonics Technol. Lett. (1)

H. Guo, S. F. Wang, X. Zeng, and M. Bache, “Understanding soliton spectral tunneling as a spectral coupling effect,” IEEE Photonics Technol. Lett. 25, 1928–1931 (2013).
[Crossref]

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

Nat. Commun. (1)

K. E. Webb, M. Erkintalo, Y. Xu, N. G. R. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, “Nonlinear optics of fibre event horizons,” Nat. Commun. 5, 4969 (2014).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lett. (3)

Opt. Mater. Express (2)

Phys. Rev. A (2)

S. Robertson and U. Leonhardt, “Frequency shifting at fiber optical event horizons: the effect of Raman deceleration,” Phys. Rev. A 81, 063835 (2010).
[Crossref]

V. E. Lobanov and A. P. Sukhorukov, “Total reflection, frequency, and velocity tuning in optical pulse collision in nonlinear dispersive media,” Phys. Rev. A 82, 033809(2010).
[Crossref]

Phys. Rev. E (1)

D. V. Skryabin and A. V. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E 72, 016619 (2005).
[Crossref]

Phys. Rev. Lett. (3)

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. S. J. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref] [PubMed]

A. Demircan, S. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett. 106. 163901(2011).
[Crossref] [PubMed]

A. Demircan, S. Amiranashvili, C. Brée, and G. Steinmeyer, “Compressible octave spanning supercontinuum generation by two-pulse collisions,” Phys. Rev. Lett. 110. 233901 (2013).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

D. V. Skryabin and A. V. Gorbach, “Colloquium: Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010).
[Crossref]

Science (1)

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref] [PubMed]

Other (2)

H. Guo, X. Zeng, and M. Bache, “Generalized nonlinear wave equation in frequency domain,” arXiv:1301.1473 (2013).

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2006).

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Figures (4)

Fig. 1
Fig. 1 Simulation of two-pulse collision by using fiber dispersion coefficients ( β ¯ 1 = 0, β ¯ 2 = 1, β ¯ 3 = 0.1) at the FS and the nonlinear coefficients are set to 1. Raman effect is not included. (a) Corresponds relative group delay β1 = 1/Vg1. (b,c) Temporal and spectral evolution of pulse collision when Td = 20, and FS has a process of spectral blue-shift. (d,e) Td = 20, FS has a process of spectral red-shift. FS is centred at 0 and DW is centred at 20, P1 = 4, P2 = 1, T1 = 0.5, T2 = 4.
Fig. 2
Fig. 2 (a) Two-pulse collision with group velocity mismatch (input FS is centred at 0 and DW is centred at 17). (b,c) Temporal and spectral evolutions with same parameters of Fig. 1(d,e). (d) spectrograms at different propagation lengths. (e) Wavenumber D ^ ( ω ω s ) = k 2 β k / k ! ( ω ω s ).
Fig. 3
Fig. 3 Simulation by using fiber dispersion coefficients ( β ¯ 1 = 0, β ¯ 2 = 1, β ¯ 3 = 0.3, β ¯ 4 = 0.04, β ¯ 5 = 0.0019) at the FS. (a) Group velocity dispersion (GVD) curve. (b) Blue side SST effect evoked by collision induced blue-shift of the FS. (c) Red side SST effect evoked by collision induced red-shift of the FS.
Fig. 4
Fig. 4 Evolution of two-pulse collision in the BBO crystal (θ = 30°) by nonlinear wave equation in frequency domain (NWEF) [22]. (a) Relative group delay β1. (b) n2 of both the cascaded quadratic nonlinearity and the Kerr nonlinearity. (c) Temporal and (d) spectral evolution of two-pulse collision in the BBO crystal, the time delay between two initial pulses is −200 fs. (e) The envelope profile of the pulses at z= 0 and z= 38 mm. (f) The spectral profile of the pulses at z= 38 mm.

Equations (2)

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A ( z , T ) z = 1 ( D ( ω ) A ˜ ( z , ω ) ) + i γ ( 1 + i ω 0 T ) A ( z , T ) + R ( T T ) | A ( z , T ) | 2 d T ,
δ ω ( T ) = γ 1 L π T | A 2 ( L , T ) | 2 .

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