Abstract

We demonstrate frequency redshifting and blueshifting of dispersive waves at group velocity horizons of solitons in fibers. The tunnelling probability of waves that cannot propagate through the fiber-optical solitons (horizons) is measured and described analytically. For shifts up to two times the soliton spectral width, the waves frequency shift with probability exceeding 90% rather than tunnelling through the soliton in our experiment. We also discuss key features of fiber optical Cherenkov radiation such as high efficiency and large bandwidth within this framework.

© 2012 OSA

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    [CrossRef]
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    [CrossRef]
  3. K. Kitayama, Y. Kimura, and S. Seikai, “Fiber-optic logic gate,” Appl. Phys. Lett. 46, 317–319 (1985).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  20. N. Nishizawa and T. Goto, “Characteristics of pulse trapping by ultrashort soliton pulse in optical fibers across zerodispersion wavelength,” Opt. Express 10, 1151–1159 (2002).
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    [CrossRef]
  22. A. Efimov, A. Yulin, D. Skryabin, J. C. Knight, N. Joly, F. Omenetto, A. J. Taylor, and P. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett. 95, 213902 (2005).
    [CrossRef] [PubMed]
  23. 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]
  24. S. Hill, C. E. Kuklewicz, U. Leonhardt, and F. König, “Evolution of light trapped by a soliton in a microstructured fiber,” Opt. Express 1713588–13600 (2009).
    [CrossRef] [PubMed]
  25. S. Robertson and U. Leonhardt, “Frequency shifting at fiber-optical event horizons: the effect of Raman deceleration,” Phys. Rev. A 81, 063835 (2010).
    [CrossRef]
  26. W. G. Unruh, “Experimental black-hole evaporation,” Phys. Rev. Lett. 46, 1351–1353 (1981).
    [CrossRef]
  27. S. M. Hawking, “Black-hole explosions,” Nature 248, 30–31 (1974).
    [CrossRef]
  28. S. M. Hawking, “Particle creation by black-holes,” Commun. Math. Phys. 43, 199–220 (1975).
    [CrossRef]
  29. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2006).
  30. 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]
  31. 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]
  32. N. N. Rosanov, N. V. Vysotina, and A. N. Shatsev, “Forward light reflection from a moving inhomogeneity,” JETP Lett. 93, 308–312 (2011).
    [CrossRef]
  33. L. D. Landau and E. M. Lifshitz, Quantum Mechanics3, (Butterworth-Heinemann, 1981).
  34. Details of this technique will be published elsewhere.
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  37. G. Q. Chang, L. J. Chen, and F. X. Kärtner, “Highly efficient Cherenkov radiation in photonic crystal fibers for broadband visible wavelength generation,” Opt.Lett. 35, 2361–2363, (2010).
    [CrossRef] [PubMed]
  38. G. Q. Chang, L. J. Chen, and F. X. Kärtner, “Fiber-optic Cherenkov radiation in the few-cycle regime,” Opt. Express 19, 6635–6647 (2011).
    [CrossRef] [PubMed]

2011

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

N. N. Rosanov, N. V. Vysotina, and A. N. Shatsev, “Forward light reflection from a moving inhomogeneity,” JETP Lett. 93, 308–312 (2011).
[CrossRef]

G. Q. Chang, L. J. Chen, and F. X. Kärtner, “Fiber-optic Cherenkov radiation in the few-cycle regime,” Opt. Express 19, 6635–6647 (2011).
[CrossRef] [PubMed]

2010

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]

G. Q. Chang, L. J. Chen, and F. X. Kärtner, “Highly efficient Cherenkov radiation in photonic crystal fibers for broadband visible wavelength generation,” Opt.Lett. 35, 2361–2363, (2010).
[CrossRef] [PubMed]

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. A. B. Miller, “Are optical transistors the logical next step?” Nat. Photonics 4, 3–5 (2010).
[CrossRef]

2009

2008

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

A. V. Gorbach and D. V. Skryabin, “Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic-crystal fibres,” Nat. Photonics 1, 653–656 (2007).
[CrossRef]

2005

A. Efimov, A. Yulin, D. Skryabin, J. C. Knight, N. Joly, F. Omenetto, A. J. Taylor, and P. 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]

2003

L. Tartara, I. Cristiani, and V. Degiorgio, “Blue light and infrared continuum generation by soliton fission in a microstructured fiber,” Appl. Phys. B 77, 307–311 (2003).
[CrossRef]

P. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
[CrossRef] [PubMed]

2002

1996

1995

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).
[CrossRef] [PubMed]

1992

1989

1988

1987

1986

1985

K. Kitayama, Y. Kimura, and S. Seikai, “Fiber-optic logic gate,” Appl. Phys. Lett. 46, 317–319 (1985).
[CrossRef]

1981

W. G. Unruh, “Experimental black-hole evaporation,” Phys. Rev. Lett. 46, 1351–1353 (1981).
[CrossRef]

1980

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

1975

S. M. Hawking, “Particle creation by black-holes,” Commun. Math. Phys. 43, 199–220 (1975).
[CrossRef]

1974

S. M. Hawking, “Black-hole explosions,” Nature 248, 30–31 (1974).
[CrossRef]

1973

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

1972

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, 62–69 (1972).

1969

S. Akhmanov, A. Sukhorukov, and A. Chirkin, “Nonstationary phenomena and spacetime analogy in nonlinear optics,” Sov. Phys. JETP 28, 748–757 (1969).

Agrawal, G. P.

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

Akhmanov, S.

S. Akhmanov, A. Sukhorukov, and A. Chirkin, “Nonstationary phenomena and spacetime analogy in nonlinear optics,” Sov. Phys. JETP 28, 748–757 (1969).

Akhmediev, N.

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).
[CrossRef] [PubMed]

Amiranashvili, Sh.

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

Atkin, D. M.

Birks, T. A.

Boppart, S. A.

Chang, G. Q.

G. Q. Chang, L. J. Chen, and F. X. Kärtner, “Fiber-optic Cherenkov radiation in the few-cycle regime,” Opt. Express 19, 6635–6647 (2011).
[CrossRef] [PubMed]

G. Q. Chang, L. J. Chen, and F. X. Kärtner, “Highly efficient Cherenkov radiation in photonic crystal fibers for broadband visible wavelength generation,” Opt.Lett. 35, 2361–2363, (2010).
[CrossRef] [PubMed]

Chen, H. H.

Chen, L. J.

G. Q. Chang, L. J. Chen, and F. X. Kärtner, “Fiber-optic Cherenkov radiation in the few-cycle regime,” Opt. Express 19, 6635–6647 (2011).
[CrossRef] [PubMed]

G. Q. Chang, L. J. Chen, and F. X. Kärtner, “Highly efficient Cherenkov radiation in photonic crystal fibers for broadband visible wavelength generation,” Opt.Lett. 35, 2361–2363, (2010).
[CrossRef] [PubMed]

Chirkin, A.

S. Akhmanov, A. Sukhorukov, and A. Chirkin, “Nonstationary phenomena and spacetime analogy in nonlinear optics,” Sov. Phys. JETP 28, 748–757 (1969).

Cristiani, I.

L. Tartara, I. Cristiani, and V. Degiorgio, “Blue light and infrared continuum generation by soliton fission in a microstructured fiber,” Appl. Phys. B 77, 307–311 (2003).
[CrossRef]

Degiorgio, V.

L. Tartara, I. Cristiani, and V. Degiorgio, “Blue light and infrared continuum generation by soliton fission in a microstructured fiber,” Appl. Phys. B 77, 307–311 (2003).
[CrossRef]

Demircan, A.

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

Doran, N. J.

Efimov, A.

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

Fischer, B.

Fujimoto, J. G.

Gorbach, A. V.

A. V. Gorbach and D. V. Skryabin, “Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic-crystal fibres,” Nat. Photonics 1, 653–656 (2007).
[CrossRef]

Gordon, J. G.

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

Gordon, J. P.

Goto, T.

Hasegawa, A.

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

Haus, H. A.

Hawking, S. M.

S. M. Hawking, “Particle creation by black-holes,” Commun. Math. Phys. 43, 199–220 (1975).
[CrossRef]

S. M. Hawking, “Black-hole explosions,” Nature 248, 30–31 (1974).
[CrossRef]

Hill, S.

S. Hill, C. E. Kuklewicz, U. Leonhardt, and F. König, “Evolution of light trapped by a soliton in a microstructured fiber,” Opt. Express 1713588–13600 (2009).
[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]

Islam, M. N.

Joly, N.

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

Karlsson, M.

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).
[CrossRef] [PubMed]

Kärtner, F. X.

G. Q. Chang, L. J. Chen, and F. X. Kärtner, “Fiber-optic Cherenkov radiation in the few-cycle regime,” Opt. Express 19, 6635–6647 (2011).
[CrossRef] [PubMed]

G. Q. Chang, L. J. Chen, and F. X. Kärtner, “Highly efficient Cherenkov radiation in photonic crystal fibers for broadband visible wavelength generation,” Opt.Lett. 35, 2361–2363, (2010).
[CrossRef] [PubMed]

Kimura, Y.

K. Kitayama, Y. Kimura, and S. Seikai, “Fiber-optic logic gate,” Appl. Phys. Lett. 46, 317–319 (1985).
[CrossRef]

Kitayama, K.

K. Kitayama, Y. Kimura, and S. Seikai, “Fiber-optic logic gate,” Appl. Phys. Lett. 46, 317–319 (1985).
[CrossRef]

Knight, J. C.

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

J. C. Knight, T. A. Birks, P. S. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996).
[CrossRef] [PubMed]

König, F.

S. Hill, C. E. Kuklewicz, U. Leonhardt, and F. König, “Evolution of light trapped by a soliton in a microstructured fiber,” Opt. Express 1713588–13600 (2009).
[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]

Kuklewicz, C. E.

LaGasse, M. J.

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics3, (Butterworth-Heinemann, 1981).

Larom, B.

Lee, Y. C.

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]

S. Hill, C. E. Kuklewicz, U. Leonhardt, and F. König, “Evolution of light trapped by a soliton in a microstructured fiber,” Opt. Express 1713588–13600 (2009).
[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]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics3, (Butterworth-Heinemann, 1981).

Liu-Wong, D.

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]

Menyuk, C. R.

Miller, D. A. B.

D. A. B. Miller, “Are optical transistors the logical next step?” Nat. Photonics 4, 3–5 (2010).
[CrossRef]

Mollenauer, L. F.

M. N. Islam, L. F. Mollenauer, R. H. Stolen, J. R. Simpson, and H. T. Shang, “Cross-phase modulation in optical fibers,” Opt. Lett. 12, 625–627 (1987).
[CrossRef] [PubMed]

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

Nazarathy, M.

Nevet, A.

Nishizawa, N.

Omenetto, F.

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

Orenstein, M.

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]

Rosanov, N. N.

N. N. Rosanov, N. V. Vysotina, and A. N. Shatsev, “Forward light reflection from a moving inhomogeneity,” JETP Lett. 93, 308–312 (2011).
[CrossRef]

Rudnitsky, A.

Russell, P.

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

P. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
[CrossRef] [PubMed]

Russell, P. S.

Seikai, S.

K. Kitayama, Y. Kimura, and S. Seikai, “Fiber-optic logic gate,” Appl. Phys. Lett. 46, 317–319 (1985).
[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, 62–69 (1972).

Shang, H. T.

Shatsev, A. N.

N. N. Rosanov, N. V. Vysotina, and A. N. Shatsev, “Forward light reflection from a moving inhomogeneity,” JETP Lett. 93, 308–312 (2011).
[CrossRef]

Simpson, J. R.

Skryabin, D.

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

Skryabin, D. V.

A. V. Gorbach and D. V. Skryabin, “Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic-crystal fibres,” Nat. Photonics 1, 653–656 (2007).
[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]

Stegeman, G. I.

Steinmeyer, G.

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

Stolen, R. H.

M. N. Islam, L. F. Mollenauer, R. H. Stolen, J. R. Simpson, and H. T. Shang, “Cross-phase modulation in optical fibers,” Opt. Lett. 12, 625–627 (1987).
[CrossRef] [PubMed]

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

Sukhorukov, A.

S. Akhmanov, A. Sukhorukov, and A. Chirkin, “Nonstationary phenomena and spacetime analogy in nonlinear optics,” Sov. Phys. JETP 28, 748–757 (1969).

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]

Tappert, F.

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

Tartara, L.

L. Tartara, I. Cristiani, and V. Degiorgio, “Blue light and infrared continuum generation by soliton fission in a microstructured fiber,” Appl. Phys. B 77, 307–311 (2003).
[CrossRef]

Taylor, A. J.

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

Taylor, J. R.

J. R. Taylor, Optical Solitons Theory and Experiment (Cambridge Press, 2005).

Trillo, S.

Tu, H.

Unruh, W. G.

W. G. Unruh, “Experimental black-hole evaporation,” Phys. Rev. Lett. 46, 1351–1353 (1981).
[CrossRef]

Vysotina, N. V.

N. N. Rosanov, N. V. Vysotina, and A. N. Shatsev, “Forward light reflection from a moving inhomogeneity,” JETP Lett. 93, 308–312 (2011).
[CrossRef]

Wabnitz, S.

Wai, P. K. A.

Wood, D.

Wright, E. M.

Yulin, A.

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Figures (5)

Fig. 1
Fig. 1

Probe waves reflecting off a soliton: Contours of constant reflectivity (10% increments) as a function of the Barrier height B and the detuning ΩT0. High reflectivity is not limited to small detunings (ΩT0 ≪ 1).

Fig. 2
Fig. 2

Contributions to the total mode conversion efficiency as a function of the frequency shift of the probe wave (Eq. (4) and (6)). Dashed: Reflectivity R of the soliton (Eq. (4)). Green: Fraction ηint of the probe light colliding with the soliton. Red: total efficiency η = Rηint.

Fig. 3
Fig. 3

Two spectra of the blue and the red shifted probe light, initially at λ = 532nm (notch-filtered in output, grey area). The soliton was tuned to 846 and 825nm, respectively. Spectral shifts of −12nm (blue) and +13nm (red) are observed. The expected reflectivities are 98% and 55%, respectively, according to Eq. (4).

Fig. 4
Fig. 4

Location of shifted probe spectra for different soliton wavelengths. The solid line is the prediction from the dispersion curve as shown in the inset. Wavelengths between which the integral (shaded area) of the dispersion parameter D vanishes are group velocity matched.

Fig. 5
Fig. 5

Measurement of mode conversion efficiency as a function of total frequency shift of probe wave. Red: tunnelling model η (Eq. (6)). Efficient conversion (R > 90%) occurs over more than ±12 THz and is described by the tunnelling model. The grey curve, for comparison, shows a typical input pulse spectrum.

Equations (6)

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A 1 z + β 1 A 1 t + i 2 β 2 2 A 1 t 2 = i γ ( | A 1 | 2 + r | A 2 | 2 ) A 1
2 A 1 τ 2 2 i β 1 β 2 A 1 ζ 2 r γ P 0 β 2 sech 2 ( τ / T 0 ) A 1 = 0.
2 A 1 τ 2 2 β 2 [ β 1 Ω + r γ P 0 sech 2 ( τ / T 0 ) ] A 1 = 0 ,
T = 1 1 + ξ R = ξ 1 + ξ , ξ = { cos 2 ( π / 2 1 B ) sinh 2 ( π Ω T 0 ) : B < 1 cosh 2 ( π / 2 B 1 ) sinh 2 ( π Ω T 0 ) : B 1
B = 1 + [ 2 π ln 3 + 2 Ω T 0 ] 2 .
η = R η int , η int = L c ν δ n g L ν β 2 Ω ,

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