Abstract

Raman effect in gases can generate an extremely long-living wave of coherence that can lead to the establishment of an almost perfect temporal periodic variation of the medium refractive index. We show theoretically and numerically that the equations, regulate the pulse propagation in hollow-core photonic crystal fibers filled by Raman-active gas, are exactly identical to a classical problem in quantum condensed matter physics – but with the role of space and time reversed – namely an electron in a periodic potential subject to a constant electric field. We are therefore able to infer the existence of Wannier-Stark ladders, Bloch oscillations, and Zener tunneling, phenomena that are normally associated with condensed matter physics, using purely optical means.

© 2015 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref]
  3. J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B 28, A11–A26 (2011).
    [Crossref]
  4. P. St.J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278–286 (2014).
    [Crossref]
  5. F. Benabid, J. C. Knight, G. Antonopoulos, and P. St.J. Russell, “Stimulated raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
    [Crossref] [PubMed]
  6. O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
    [Crossref]
  7. N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source in ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
    [Crossref]
  8. W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018–21027 (2011).
    [Crossref] [PubMed]
  9. P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
    [Crossref] [PubMed]
  10. M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Soliton self-frequency blue-shift in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
    [Crossref]
  11. W. Chang, P. Hölzer, J. C. Travers, and P. St.J. Russell, “Combined soliton pulse compression and plasma-related frequency upconversion in gas-filled photonic crystal fiber,” Opt. Lett 38, 2984–2987 (2013).
    [Crossref] [PubMed]
  12. M. F. Saleh, W. Chang, J. C. Travers, P. St.J. Russell, and F. Biancalana, “Plasma-induced asymmetric self-phase modulation and modulational instability in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 109, 113902 (2012).
    [Crossref] [PubMed]
  13. M. F. Saleh, A. Marini, and F. Biancalana, “Shock-induced 𝒫𝒯 -symmetric potentials in gas-filled photonic crystal fibers,” Phys. Rev. A 89, 023801 (2014).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  20. G. Korn, O. Dühr, and A. Nazarkin, “Observation of raman self-conversion of fs-pulse frequency due to impulsive excitation of molecular vibrations,” Phys. Rev. Lett. 81, 1215–1218 (1998).
    [Crossref]
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    [Crossref]
  22. M. Wittmann, A. Nazarkin, and G. Korn, “fs-pulse synthesis using phase modulation by impulsively excited molecular vibrations,” Phys. Rev. Lett. 84, 5508–5511 (2000).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  25. C. Zener, “A theory of electrical breakdown of solid dielectrics,” R. Soc. Lond. A 145, 523 (1934).
    [Crossref]
  26. T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752 (1999).
    [Crossref]
  27. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756 (1999).
    [Crossref]
  28. M. Ghulinyan, C. J. Oton, Z. Gaburro, L. Pavesi, C. Toninelli, and D. S. Wiersma, “Zener tunneling of light waves in an optical superlattice,” Phys. Rev. Lett. 94, 127401 (2005).
    [Crossref] [PubMed]
  29. A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
    [Crossref] [PubMed]
  30. V. S. Butylkin, A. E. Kaplan, Y. G. Khronopulo, and E. I. Yakubovich, Resonant Nonlinear Interaction of Light with Matter (Springer-Verlag, 1989), 1st ed.
    [Crossref]
  31. P. Kinsler, “Optical pulse propagation with minimal approximations,” Phys. Rev. A 81, 013819 (2010).
    [Crossref]
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  35. V. Mizrahi and D. P. Shelton, “Nonlinear susceptibility of h2 and d2 accurately measured over a wide range of wavelengths,” Phys. Rev. A 32, 3454–3460 (1985).
    [Crossref] [PubMed]
  36. W. K. Bischel and M. J. Dyer, “Temperature dependence of the raman linewidth and line shift for the q(1) and q(0) transitions in normal and para-H2,” Phys. Rev. A 33, 3113–3123 (1986).
    [Crossref] [PubMed]
  37. R. A. Bartels, S. Backus, M. Murnane, and H. Kapteyn, “Impulsive stimulated raman scattering excitation of molecular vibrations via nonlinear pulse shaping,” Chem. Phys. Lett. 374, 326–333 (2003).
    [Crossref]
  38. L. Gagnon and P. A. Bélanger, “Soliton self-frequency shift versus Galilean-like symmetry,” Opt. Lett 15, 466–468 (1990).
    [Crossref] [PubMed]
  39. A. M. Bouchard and M. Luban, “Bloch oscillations and other dynamical phenomena of electrons in semiconductor superlattices,” Phys. Rev. B 52, 5105 (1995).
    [Crossref]
  40. G. J. Iafrate, J. P. Reynolds, J. He, and J. B. Krieger, “Bloch electron dynamics in spatially homogeneous electric fields,” Int. J. of High Speed Electr. 9, 223 (1998).
    [Crossref]

2015 (1)

2014 (2)

M. F. Saleh, A. Marini, and F. Biancalana, “Shock-induced 𝒫𝒯 -symmetric potentials in gas-filled photonic crystal fibers,” Phys. Rev. A 89, 023801 (2014).
[Crossref]

P. St.J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278–286 (2014).
[Crossref]

2013 (1)

W. Chang, P. Hölzer, J. C. Travers, and P. St.J. Russell, “Combined soliton pulse compression and plasma-related frequency upconversion in gas-filled photonic crystal fiber,” Opt. Lett 38, 2984–2987 (2013).
[Crossref] [PubMed]

2012 (2)

M. F. Saleh, W. Chang, J. C. Travers, P. St.J. Russell, and F. Biancalana, “Plasma-induced asymmetric self-phase modulation and modulational instability in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 109, 113902 (2012).
[Crossref] [PubMed]

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
[Crossref] [PubMed]

2011 (5)

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B 28, A11–A26 (2011).
[Crossref]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source in ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
[Crossref]

W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018–21027 (2011).
[Crossref] [PubMed]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[Crossref] [PubMed]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Soliton self-frequency blue-shift in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[Crossref]

2010 (1)

P. Kinsler, “Optical pulse propagation with minimal approximations,” Phys. Rev. A 81, 013819 (2010).
[Crossref]

2009 (1)

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
[Crossref]

2006 (2)

P. St.J. Russell, “Photonic-crystal fibers,” J. Light. Technol. 24, 4729–4749 (2006).
[Crossref]

K. Ihara, C. Eshima, S. Zaitsu, S. Kamitomo, K. Shinzen, Y. Hirakawa, and T. Imasaka, “Molecular-optic modulator,” Appl. Phys. Lett. 88, 074101 (2006).
[Crossref]

2005 (1)

M. Ghulinyan, C. J. Oton, Z. Gaburro, L. Pavesi, C. Toninelli, and D. S. Wiersma, “Zener tunneling of light waves in an optical superlattice,” Phys. Rev. Lett. 94, 127401 (2005).
[Crossref] [PubMed]

2003 (2)

R. A. Bartels, S. Backus, M. Murnane, and H. Kapteyn, “Impulsive stimulated raman scattering excitation of molecular vibrations via nonlinear pulse shaping,” Chem. Phys. Lett. 374, 326–333 (2003).
[Crossref]

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

2002 (1)

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St.J. Russell, “Stimulated raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[Crossref] [PubMed]

2000 (2)

M. Wittmann, A. Nazarkin, and G. Korn, “fs-pulse synthesis using phase modulation by impulsively excited molecular vibrations,” Phys. Rev. Lett. 84, 5508–5511 (2000).
[Crossref] [PubMed]

V. P. Kalosha and J. Herrmann, “Phase relations, quasicontinuous spectra and subfemtosecond pulses in high-order stimulated raman scattering with short-pulse excitation,” Phys. Rev. Lett. 85, 1226–1229 (2000).
[Crossref] [PubMed]

1999 (3)

A. Nazarkin, G. Korn, M. Wittmann, and T. Elsaesser, “Generation of multiple phase-locked stokes and anti-stokes components in an impulsively excited raman medium,” Phys. Rev. Lett. 83, 2560–2563 (1999).
[Crossref]

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752 (1999).
[Crossref]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756 (1999).
[Crossref]

1998 (3)

H. Kawano, Y. Hirakawa, and T. Imasaka, “Generation of high-order rotational lines in hydrogen by four-wave raman mixing in the femtosecond regime,” IEEE. J. Quantum Electron. 34, 260–268 (1998).
[Crossref]

G. Korn, O. Dühr, and A. Nazarkin, “Observation of raman self-conversion of fs-pulse frequency due to impulsive excitation of molecular vibrations,” Phys. Rev. Lett. 81, 1215–1218 (1998).
[Crossref]

G. J. Iafrate, J. P. Reynolds, J. He, and J. B. Krieger, “Bloch electron dynamics in spatially homogeneous electric fields,” Int. J. of High Speed Electr. 9, 223 (1998).
[Crossref]

1995 (1)

A. M. Bouchard and M. Luban, “Bloch oscillations and other dynamical phenomena of electrons in semiconductor superlattices,” Phys. Rev. B 52, 5105 (1995).
[Crossref]

1994 (1)

A. E. Kaplan, “Subfemtosecond pulses in mode-locked 2π solitons of the cascade stimulated raman scattering,” Phys. Rev. Lett. 73, 1243–1246 (1994).
[Crossref] [PubMed]

1993 (1)

S. Yoshikawa and T. Imasaka, “A new approach for the generation of ultrashort optical pulses,” Opt. Comm. 96, 94–98 (1993).
[Crossref]

1990 (1)

L. Gagnon and P. A. Bélanger, “Soliton self-frequency shift versus Galilean-like symmetry,” Opt. Lett 15, 466–468 (1990).
[Crossref] [PubMed]

1986 (1)

W. K. Bischel and M. J. Dyer, “Temperature dependence of the raman linewidth and line shift for the q(1) and q(0) transitions in normal and para-H2,” Phys. Rev. A 33, 3113–3123 (1986).
[Crossref] [PubMed]

1985 (1)

V. Mizrahi and D. P. Shelton, “Nonlinear susceptibility of h2 and d2 accurately measured over a wide range of wavelengths,” Phys. Rev. A 32, 3454–3460 (1985).
[Crossref] [PubMed]

1960 (1)

G. H. Wannier, “Wave functions and effective Hamiltonian for Bloch electrons in an electric field,” Phys. Rev. 117, 432 (1960).
[Crossref]

1934 (1)

C. Zener, “A theory of electrical breakdown of solid dielectrics,” R. Soc. Lond. A 145, 523 (1934).
[Crossref]

1928 (1)

F. Bloch, “Über die Quantenmechanik der Electronen in Kristallgittern,” Z. Phys. 52, 555 (1928).
[Crossref]

Abdolvand, A.

F. Belli, A. Abdolvand, W. Chang, J. C. Travers, and P. St.J. Russell, “Vacuum-ultraviolet to infrared supercontinuum in hydrogen-filled photonic crystal fiber,” Optica 2, 292–300 (2015).
[Crossref]

P. St.J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278–286 (2014).
[Crossref]

F. Belli, A. Abdolvand, W. Chang, J. C. Travers, and P. St.J. Russell, “Vacuum UV to IR supercontinuum generation by impulsive Raman self-scattering in hydrogen-filled PCF,” in CLEO: 2014, OSA Technical Digest (online) (Optical Society of America, 2014), p. paper FW1D.1.

Agrawal, G. P.

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

Aitchison, J. S.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756 (1999).
[Crossref]

Antonopoulos, G.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St.J. Russell, “Stimulated raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[Crossref] [PubMed]

Backus, S.

R. A. Bartels, S. Backus, M. Murnane, and H. Kapteyn, “Impulsive stimulated raman scattering excitation of molecular vibrations via nonlinear pulse shaping,” Chem. Phys. Lett. 374, 326–333 (2003).
[Crossref]

Baer, C. R. E.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
[Crossref]

Bartels, R. A.

R. A. Bartels, S. Backus, M. Murnane, and H. Kapteyn, “Impulsive stimulated raman scattering excitation of molecular vibrations via nonlinear pulse shaping,” Chem. Phys. Lett. 374, 326–333 (2003).
[Crossref]

Bélanger, P. A.

L. Gagnon and P. A. Bélanger, “Soliton self-frequency shift versus Galilean-like symmetry,” Opt. Lett 15, 466–468 (1990).
[Crossref] [PubMed]

Belli, F.

F. Belli, A. Abdolvand, W. Chang, J. C. Travers, and P. St.J. Russell, “Vacuum-ultraviolet to infrared supercontinuum in hydrogen-filled photonic crystal fiber,” Optica 2, 292–300 (2015).
[Crossref]

F. Belli, A. Abdolvand, W. Chang, J. C. Travers, and P. St.J. Russell, “Vacuum UV to IR supercontinuum generation by impulsive Raman self-scattering in hydrogen-filled PCF,” in CLEO: 2014, OSA Technical Digest (online) (Optical Society of America, 2014), p. paper FW1D.1.

Benabid, F.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
[Crossref]

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St.J. Russell, “Stimulated raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[Crossref] [PubMed]

Bersch, C.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
[Crossref] [PubMed]

Biancalana, F.

M. F. Saleh, A. Marini, and F. Biancalana, “Shock-induced 𝒫𝒯 -symmetric potentials in gas-filled photonic crystal fibers,” Phys. Rev. A 89, 023801 (2014).
[Crossref]

M. F. Saleh, W. Chang, J. C. Travers, P. St.J. Russell, and F. Biancalana, “Plasma-induced asymmetric self-phase modulation and modulational instability in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 109, 113902 (2012).
[Crossref] [PubMed]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[Crossref] [PubMed]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Soliton self-frequency blue-shift in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[Crossref]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source in ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
[Crossref]

Bischel, W. K.

W. K. Bischel and M. J. Dyer, “Temperature dependence of the raman linewidth and line shift for the q(1) and q(0) transitions in normal and para-H2,” Phys. Rev. A 33, 3113–3123 (1986).
[Crossref] [PubMed]

Bloch, F.

F. Bloch, “Über die Quantenmechanik der Electronen in Kristallgittern,” Z. Phys. 52, 555 (1928).
[Crossref]

Bouchard, A. M.

A. M. Bouchard and M. Luban, “Bloch oscillations and other dynamical phenomena of electrons in semiconductor superlattices,” Phys. Rev. B 52, 5105 (1995).
[Crossref]

Bräuer, A.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752 (1999).
[Crossref]

Butylkin, V. S.

V. S. Butylkin, A. E. Kaplan, Y. G. Khronopulo, and E. I. Yakubovich, Resonant Nonlinear Interaction of Light with Matter (Springer-Verlag, 1989), 1st ed.
[Crossref]

Chang, W.

F. Belli, A. Abdolvand, W. Chang, J. C. Travers, and P. St.J. Russell, “Vacuum-ultraviolet to infrared supercontinuum in hydrogen-filled photonic crystal fiber,” Optica 2, 292–300 (2015).
[Crossref]

P. St.J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278–286 (2014).
[Crossref]

W. Chang, P. Hölzer, J. C. Travers, and P. St.J. Russell, “Combined soliton pulse compression and plasma-related frequency upconversion in gas-filled photonic crystal fiber,” Opt. Lett 38, 2984–2987 (2013).
[Crossref] [PubMed]

M. F. Saleh, W. Chang, J. C. Travers, P. St.J. Russell, and F. Biancalana, “Plasma-induced asymmetric self-phase modulation and modulational instability in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 109, 113902 (2012).
[Crossref] [PubMed]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Soliton self-frequency blue-shift in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[Crossref]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[Crossref] [PubMed]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source in ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
[Crossref]

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B 28, A11–A26 (2011).
[Crossref]

W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018–21027 (2011).
[Crossref] [PubMed]

F. Belli, A. Abdolvand, W. Chang, J. C. Travers, and P. St.J. Russell, “Vacuum UV to IR supercontinuum generation by impulsive Raman self-scattering in hydrogen-filled PCF,” in CLEO: 2014, OSA Technical Digest (online) (Optical Society of America, 2014), p. paper FW1D.1.

Christodoulides, D. N.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
[Crossref] [PubMed]

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O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
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G. Korn, O. Dühr, and A. Nazarkin, “Observation of raman self-conversion of fs-pulse frequency due to impulsive excitation of molecular vibrations,” Phys. Rev. Lett. 81, 1215–1218 (1998).
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T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752 (1999).
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A. Nazarkin, G. Korn, M. Wittmann, and T. Elsaesser, “Generation of multiple phase-locked stokes and anti-stokes components in an impulsively excited raman medium,” Phys. Rev. Lett. 83, 2560–2563 (1999).
[Crossref]

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K. Ihara, C. Eshima, S. Zaitsu, S. Kamitomo, K. Shinzen, Y. Hirakawa, and T. Imasaka, “Molecular-optic modulator,” Appl. Phys. Lett. 88, 074101 (2006).
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M. Ghulinyan, C. J. Oton, Z. Gaburro, L. Pavesi, C. Toninelli, and D. S. Wiersma, “Zener tunneling of light waves in an optical superlattice,” Phys. Rev. Lett. 94, 127401 (2005).
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O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
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V. P. Kalosha and J. Herrmann, “Phase relations, quasicontinuous spectra and subfemtosecond pulses in high-order stimulated raman scattering with short-pulse excitation,” Phys. Rev. Lett. 85, 1226–1229 (2000).
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K. Ihara, C. Eshima, S. Zaitsu, S. Kamitomo, K. Shinzen, Y. Hirakawa, and T. Imasaka, “Molecular-optic modulator,” Appl. Phys. Lett. 88, 074101 (2006).
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H. Kawano, Y. Hirakawa, and T. Imasaka, “Generation of high-order rotational lines in hydrogen by four-wave raman mixing in the femtosecond regime,” IEEE. J. Quantum Electron. 34, 260–268 (1998).
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O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
[Crossref]

Hölzer, P.

P. St.J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278–286 (2014).
[Crossref]

W. Chang, P. Hölzer, J. C. Travers, and P. St.J. Russell, “Combined soliton pulse compression and plasma-related frequency upconversion in gas-filled photonic crystal fiber,” Opt. Lett 38, 2984–2987 (2013).
[Crossref] [PubMed]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Soliton self-frequency blue-shift in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[Crossref]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[Crossref] [PubMed]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source in ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
[Crossref]

W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018–21027 (2011).
[Crossref] [PubMed]

Iafrate, G. J.

G. J. Iafrate, J. P. Reynolds, J. He, and J. B. Krieger, “Bloch electron dynamics in spatially homogeneous electric fields,” Int. J. of High Speed Electr. 9, 223 (1998).
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K. Ihara, C. Eshima, S. Zaitsu, S. Kamitomo, K. Shinzen, Y. Hirakawa, and T. Imasaka, “Molecular-optic modulator,” Appl. Phys. Lett. 88, 074101 (2006).
[Crossref]

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K. Ihara, C. Eshima, S. Zaitsu, S. Kamitomo, K. Shinzen, Y. Hirakawa, and T. Imasaka, “Molecular-optic modulator,” Appl. Phys. Lett. 88, 074101 (2006).
[Crossref]

H. Kawano, Y. Hirakawa, and T. Imasaka, “Generation of high-order rotational lines in hydrogen by four-wave raman mixing in the femtosecond regime,” IEEE. J. Quantum Electron. 34, 260–268 (1998).
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P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[Crossref] [PubMed]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Soliton self-frequency blue-shift in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[Crossref]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source in ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
[Crossref]

W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018–21027 (2011).
[Crossref] [PubMed]

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B 28, A11–A26 (2011).
[Crossref]

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V. P. Kalosha and J. Herrmann, “Phase relations, quasicontinuous spectra and subfemtosecond pulses in high-order stimulated raman scattering with short-pulse excitation,” Phys. Rev. Lett. 85, 1226–1229 (2000).
[Crossref] [PubMed]

Kamitomo, S.

K. Ihara, C. Eshima, S. Zaitsu, S. Kamitomo, K. Shinzen, Y. Hirakawa, and T. Imasaka, “Molecular-optic modulator,” Appl. Phys. Lett. 88, 074101 (2006).
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R. A. Bartels, S. Backus, M. Murnane, and H. Kapteyn, “Impulsive stimulated raman scattering excitation of molecular vibrations via nonlinear pulse shaping,” Chem. Phys. Lett. 374, 326–333 (2003).
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Kawano, H.

H. Kawano, Y. Hirakawa, and T. Imasaka, “Generation of high-order rotational lines in hydrogen by four-wave raman mixing in the femtosecond regime,” IEEE. J. Quantum Electron. 34, 260–268 (1998).
[Crossref]

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O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
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V. S. Butylkin, A. E. Kaplan, Y. G. Khronopulo, and E. I. Yakubovich, Resonant Nonlinear Interaction of Light with Matter (Springer-Verlag, 1989), 1st ed.
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F. Benabid, J. C. Knight, G. Antonopoulos, and P. St.J. Russell, “Stimulated raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
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Korn, G.

M. Wittmann, A. Nazarkin, and G. Korn, “fs-pulse synthesis using phase modulation by impulsively excited molecular vibrations,” Phys. Rev. Lett. 84, 5508–5511 (2000).
[Crossref] [PubMed]

A. Nazarkin, G. Korn, M. Wittmann, and T. Elsaesser, “Generation of multiple phase-locked stokes and anti-stokes components in an impulsively excited raman medium,” Phys. Rev. Lett. 83, 2560–2563 (1999).
[Crossref]

G. Korn, O. Dühr, and A. Nazarkin, “Observation of raman self-conversion of fs-pulse frequency due to impulsive excitation of molecular vibrations,” Phys. Rev. Lett. 81, 1215–1218 (1998).
[Crossref]

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O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
[Crossref]

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G. J. Iafrate, J. P. Reynolds, J. He, and J. B. Krieger, “Bloch electron dynamics in spatially homogeneous electric fields,” Int. J. of High Speed Electr. 9, 223 (1998).
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T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752 (1999).
[Crossref]

Light, P.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
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[Crossref]

Marini, A.

M. F. Saleh, A. Marini, and F. Biancalana, “Shock-induced 𝒫𝒯 -symmetric potentials in gas-filled photonic crystal fibers,” Phys. Rev. A 89, 023801 (2014).
[Crossref]

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A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
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R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756 (1999).
[Crossref]

Murnane, M.

R. A. Bartels, S. Backus, M. Murnane, and H. Kapteyn, “Impulsive stimulated raman scattering excitation of molecular vibrations via nonlinear pulse shaping,” Chem. Phys. Lett. 374, 326–333 (2003).
[Crossref]

Nazarkin, A.

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source in ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
[Crossref]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[Crossref] [PubMed]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Soliton self-frequency blue-shift in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[Crossref]

W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018–21027 (2011).
[Crossref] [PubMed]

M. Wittmann, A. Nazarkin, and G. Korn, “fs-pulse synthesis using phase modulation by impulsively excited molecular vibrations,” Phys. Rev. Lett. 84, 5508–5511 (2000).
[Crossref] [PubMed]

A. Nazarkin, G. Korn, M. Wittmann, and T. Elsaesser, “Generation of multiple phase-locked stokes and anti-stokes components in an impulsively excited raman medium,” Phys. Rev. Lett. 83, 2560–2563 (1999).
[Crossref]

G. Korn, O. Dühr, and A. Nazarkin, “Observation of raman self-conversion of fs-pulse frequency due to impulsive excitation of molecular vibrations,” Phys. Rev. Lett. 81, 1215–1218 (1998).
[Crossref]

Nold, J.

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[Crossref] [PubMed]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source in ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
[Crossref]

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B 28, A11–A26 (2011).
[Crossref]

W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018–21027 (2011).
[Crossref] [PubMed]

Onishchukov, G.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
[Crossref] [PubMed]

Oton, C. J.

M. Ghulinyan, C. J. Oton, Z. Gaburro, L. Pavesi, C. Toninelli, and D. S. Wiersma, “Zener tunneling of light waves in an optical superlattice,” Phys. Rev. Lett. 94, 127401 (2005).
[Crossref] [PubMed]

Pavesi, L.

M. Ghulinyan, C. J. Oton, Z. Gaburro, L. Pavesi, C. Toninelli, and D. S. Wiersma, “Zener tunneling of light waves in an optical superlattice,” Phys. Rev. Lett. 94, 127401 (2005).
[Crossref] [PubMed]

Pertsch, T.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752 (1999).
[Crossref]

Peschel, U.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
[Crossref] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756 (1999).
[Crossref]

Regensburger, A.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
[Crossref] [PubMed]

Reynolds, J. P.

G. J. Iafrate, J. P. Reynolds, J. He, and J. B. Krieger, “Bloch electron dynamics in spatially homogeneous electric fields,” Int. J. of High Speed Electr. 9, 223 (1998).
[Crossref]

Robinson, J. S.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
[Crossref]

Russell, P. St.J.

F. Belli, A. Abdolvand, W. Chang, J. C. Travers, and P. St.J. Russell, “Vacuum-ultraviolet to infrared supercontinuum in hydrogen-filled photonic crystal fiber,” Optica 2, 292–300 (2015).
[Crossref]

P. St.J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278–286 (2014).
[Crossref]

W. Chang, P. Hölzer, J. C. Travers, and P. St.J. Russell, “Combined soliton pulse compression and plasma-related frequency upconversion in gas-filled photonic crystal fiber,” Opt. Lett 38, 2984–2987 (2013).
[Crossref] [PubMed]

M. F. Saleh, W. Chang, J. C. Travers, P. St.J. Russell, and F. Biancalana, “Plasma-induced asymmetric self-phase modulation and modulational instability in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 109, 113902 (2012).
[Crossref] [PubMed]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Soliton self-frequency blue-shift in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[Crossref]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[Crossref] [PubMed]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source in ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
[Crossref]

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B 28, A11–A26 (2011).
[Crossref]

W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018–21027 (2011).
[Crossref] [PubMed]

P. St.J. Russell, “Photonic-crystal fibers,” J. Light. Technol. 24, 4729–4749 (2006).
[Crossref]

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

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St.J. Russell, “Stimulated raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[Crossref] [PubMed]

F. Belli, A. Abdolvand, W. Chang, J. C. Travers, and P. St.J. Russell, “Vacuum UV to IR supercontinuum generation by impulsive Raman self-scattering in hydrogen-filled PCF,” in CLEO: 2014, OSA Technical Digest (online) (Optical Society of America, 2014), p. paper FW1D.1.

Saleh, M. F.

M. F. Saleh, A. Marini, and F. Biancalana, “Shock-induced 𝒫𝒯 -symmetric potentials in gas-filled photonic crystal fibers,” Phys. Rev. A 89, 023801 (2014).
[Crossref]

M. F. Saleh, W. Chang, J. C. Travers, P. St.J. Russell, and F. Biancalana, “Plasma-induced asymmetric self-phase modulation and modulational instability in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 109, 113902 (2012).
[Crossref] [PubMed]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Soliton self-frequency blue-shift in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[Crossref]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
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O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
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K. Ihara, C. Eshima, S. Zaitsu, S. Kamitomo, K. Shinzen, Y. Hirakawa, and T. Imasaka, “Molecular-optic modulator,” Appl. Phys. Lett. 88, 074101 (2006).
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R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756 (1999).
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O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
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O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
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M. Ghulinyan, C. J. Oton, Z. Gaburro, L. Pavesi, C. Toninelli, and D. S. Wiersma, “Zener tunneling of light waves in an optical superlattice,” Phys. Rev. Lett. 94, 127401 (2005).
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Travers, J. C.

F. Belli, A. Abdolvand, W. Chang, J. C. Travers, and P. St.J. Russell, “Vacuum-ultraviolet to infrared supercontinuum in hydrogen-filled photonic crystal fiber,” Optica 2, 292–300 (2015).
[Crossref]

P. St.J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278–286 (2014).
[Crossref]

W. Chang, P. Hölzer, J. C. Travers, and P. St.J. Russell, “Combined soliton pulse compression and plasma-related frequency upconversion in gas-filled photonic crystal fiber,” Opt. Lett 38, 2984–2987 (2013).
[Crossref] [PubMed]

M. F. Saleh, W. Chang, J. C. Travers, P. St.J. Russell, and F. Biancalana, “Plasma-induced asymmetric self-phase modulation and modulational instability in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 109, 113902 (2012).
[Crossref] [PubMed]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Soliton self-frequency blue-shift in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[Crossref]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[Crossref] [PubMed]

W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018–21027 (2011).
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J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B 28, A11–A26 (2011).
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F. Belli, A. Abdolvand, W. Chang, J. C. Travers, and P. St.J. Russell, “Vacuum UV to IR supercontinuum generation by impulsive Raman self-scattering in hydrogen-filled PCF,” in CLEO: 2014, OSA Technical Digest (online) (Optical Society of America, 2014), p. paper FW1D.1.

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G. H. Wannier, “Wave functions and effective Hamiltonian for Bloch electrons in an electric field,” Phys. Rev. 117, 432 (1960).
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M. J. Weber, CRC Handbook of Laser Science and Technology Supplement 2: Optical Materials (CRC press, 1994), 1st ed.

Wiersma, D. S.

M. Ghulinyan, C. J. Oton, Z. Gaburro, L. Pavesi, C. Toninelli, and D. S. Wiersma, “Zener tunneling of light waves in an optical superlattice,” Phys. Rev. Lett. 94, 127401 (2005).
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Wittmann, M.

M. Wittmann, A. Nazarkin, and G. Korn, “fs-pulse synthesis using phase modulation by impulsively excited molecular vibrations,” Phys. Rev. Lett. 84, 5508–5511 (2000).
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A. Nazarkin, G. Korn, M. Wittmann, and T. Elsaesser, “Generation of multiple phase-locked stokes and anti-stokes components in an impulsively excited raman medium,” Phys. Rev. Lett. 83, 2560–2563 (1999).
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Wong, G. K. L.

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source in ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
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Yakubovich, E. I.

V. S. Butylkin, A. E. Kaplan, Y. G. Khronopulo, and E. I. Yakubovich, Resonant Nonlinear Interaction of Light with Matter (Springer-Verlag, 1989), 1st ed.
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S. Yoshikawa and T. Imasaka, “A new approach for the generation of ultrashort optical pulses,” Opt. Comm. 96, 94–98 (1993).
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K. Ihara, C. Eshima, S. Zaitsu, S. Kamitomo, K. Shinzen, Y. Hirakawa, and T. Imasaka, “Molecular-optic modulator,” Appl. Phys. Lett. 88, 074101 (2006).
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Zener, C.

C. Zener, “A theory of electrical breakdown of solid dielectrics,” R. Soc. Lond. A 145, 523 (1934).
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Appl. Phys. B (1)

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369 (2009).
[Crossref]

Appl. Phys. Lett. (1)

K. Ihara, C. Eshima, S. Zaitsu, S. Kamitomo, K. Shinzen, Y. Hirakawa, and T. Imasaka, “Molecular-optic modulator,” Appl. Phys. Lett. 88, 074101 (2006).
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Chem. Phys. Lett. (1)

R. A. Bartels, S. Backus, M. Murnane, and H. Kapteyn, “Impulsive stimulated raman scattering excitation of molecular vibrations via nonlinear pulse shaping,” Chem. Phys. Lett. 374, 326–333 (2003).
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P. St.J. Russell, “Photonic-crystal fibers,” J. Light. Technol. 24, 4729–4749 (2006).
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J. Opt. Soc. Am. B (1)

Nat. Photon. (1)

P. St.J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278–286 (2014).
[Crossref]

Nature (1)

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
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Opt. Comm. (1)

S. Yoshikawa and T. Imasaka, “A new approach for the generation of ultrashort optical pulses,” Opt. Comm. 96, 94–98 (1993).
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Opt. Express (1)

Opt. Lett (2)

W. Chang, P. Hölzer, J. C. Travers, and P. St.J. Russell, “Combined soliton pulse compression and plasma-related frequency upconversion in gas-filled photonic crystal fiber,” Opt. Lett 38, 2984–2987 (2013).
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Optica (1)

Phys. Rev. (1)

G. H. Wannier, “Wave functions and effective Hamiltonian for Bloch electrons in an electric field,” Phys. Rev. 117, 432 (1960).
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Phys. Rev. A (4)

P. Kinsler, “Optical pulse propagation with minimal approximations,” Phys. Rev. A 81, 013819 (2010).
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M. F. Saleh, A. Marini, and F. Biancalana, “Shock-induced 𝒫𝒯 -symmetric potentials in gas-filled photonic crystal fibers,” Phys. Rev. A 89, 023801 (2014).
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V. Mizrahi and D. P. Shelton, “Nonlinear susceptibility of h2 and d2 accurately measured over a wide range of wavelengths,” Phys. Rev. A 32, 3454–3460 (1985).
[Crossref] [PubMed]

W. K. Bischel and M. J. Dyer, “Temperature dependence of the raman linewidth and line shift for the q(1) and q(0) transitions in normal and para-H2,” Phys. Rev. A 33, 3113–3123 (1986).
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Phys. Rev. Lett. (12)

M. F. Saleh, W. Chang, J. C. Travers, P. St.J. Russell, and F. Biancalana, “Plasma-induced asymmetric self-phase modulation and modulational instability in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 109, 113902 (2012).
[Crossref] [PubMed]

A. Nazarkin, G. Korn, M. Wittmann, and T. Elsaesser, “Generation of multiple phase-locked stokes and anti-stokes components in an impulsively excited raman medium,” Phys. Rev. Lett. 83, 2560–2563 (1999).
[Crossref]

V. P. Kalosha and J. Herrmann, “Phase relations, quasicontinuous spectra and subfemtosecond pulses in high-order stimulated raman scattering with short-pulse excitation,” Phys. Rev. Lett. 85, 1226–1229 (2000).
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G. Korn, O. Dühr, and A. Nazarkin, “Observation of raman self-conversion of fs-pulse frequency due to impulsive excitation of molecular vibrations,” Phys. Rev. Lett. 81, 1215–1218 (1998).
[Crossref]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[Crossref] [PubMed]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Soliton self-frequency blue-shift in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[Crossref]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source in ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
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T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752 (1999).
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R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756 (1999).
[Crossref]

M. Ghulinyan, C. J. Oton, Z. Gaburro, L. Pavesi, C. Toninelli, and D. S. Wiersma, “Zener tunneling of light waves in an optical superlattice,” Phys. Rev. Lett. 94, 127401 (2005).
[Crossref] [PubMed]

A. E. Kaplan, “Subfemtosecond pulses in mode-locked 2π solitons of the cascade stimulated raman scattering,” Phys. Rev. Lett. 73, 1243–1246 (1994).
[Crossref] [PubMed]

M. Wittmann, A. Nazarkin, and G. Korn, “fs-pulse synthesis using phase modulation by impulsively excited molecular vibrations,” Phys. Rev. Lett. 84, 5508–5511 (2000).
[Crossref] [PubMed]

R. Soc. Lond. A (1)

C. Zener, “A theory of electrical breakdown of solid dielectrics,” R. Soc. Lond. A 145, 523 (1934).
[Crossref]

Science (2)

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St.J. Russell, “Stimulated raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
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P. St.J. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
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Z. Phys. (1)

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V. S. Butylkin, A. E. Kaplan, Y. G. Khronopulo, and E. I. Yakubovich, Resonant Nonlinear Interaction of Light with Matter (Springer-Verlag, 1989), 1st ed.
[Crossref]

F. Belli, A. Abdolvand, W. Chang, J. C. Travers, and P. St.J. Russell, “Vacuum UV to IR supercontinuum generation by impulsive Raman self-scattering in hydrogen-filled PCF,” in CLEO: 2014, OSA Technical Digest (online) (Optical Society of America, 2014), p. paper FW1D.1.

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

M. J. Weber, CRC Handbook of Laser Science and Technology Supplement 2: Optical Materials (CRC press, 1994), 1st ed.

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Figures (3)

Fig. 1
Fig. 1 Temporal evolution of an accelerated oscillating Raman polarization with period Λ = 56.7 fs induced by a propagating fundamental soliton with an amplitude V1 = 1.33, a central wavelength 1064 nm, and a FWHM 15 fs in a H2-filled HC-PCF with a Kagomelattice cross section, a flat-to-flat core diameter 18 μm, a zero dispersion wavelength 413 nm, a gas pressure 7 bar, and a rotational Raman frequency ωR = 17.6 THz. The dashed yellow line represents the temporal evolution of the soliton that excites the coherence wave. The simulation parameters are γ = 7.07 × 10−6 W−1m−1, β2 = −3425.5 fs2/m, Aeff = 134μm2, α12 = 0.8 × 10−41 C m2/V [14, 34], and t0 = 11.34 fs. The parameter γ is calculated using the nonlinear susceptibility of H2 [35]. For these parameters, we have found that higher-order dispersion and self steepening effects have a weak influence on the soliton dynamics. All subsequent calculations in this paper are based on these values.
Fig. 2
Fig. 2 A portion of the absolute eigenstates of a Raman-induced temporal periodic crystals with a lattice constant Λ = 56.7 fs in the presence of a force with magnitude g1 = 0.1408 in the positive-delay direction. The vertical axis represents the corresponding eigenvalues −q. The dotted-dashed line is the potential under the applied force.
Fig. 3
Fig. 3 (a) Bandstructure of the temporal crystal induced by the leading ultrashort soliton propagating in the H2-filled Kagome-lattice HC-PCF with m = 1 in the absence of the applied force. (b) Temporal evolution of a weak probe in the accelerated periodic temporal crystal. The probe initial temporal profile is a Gaussian pulse with FWHM 133.6 fs superimposed on the first Bloch mode of the periodic crystal in the absence of the applied force. The contour plot is given in a logarithmic scale and truncated at −60 dB.

Equations (5)

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t w + w + 1 T 1 = i α 12 h ¯ ( ρ 12 ρ 12 * ) E 2 , [ t + 1 T 2 i ω R ] ρ 12 = i 2 h ¯ [ α 12 w + ( α 11 α 22 ) ρ 12 ] E 2 ,
[ i ξ + D ^ ( i τ ) + | ψ | 2 + η Re ( ρ 12 ) ] ψ = 0 , τ w + ( w + 1 ) t 0 T 1 = 4 μ w Im ( ρ 12 ) | ψ | 2 , [ τ + t 0 T 2 i δ ] ρ 12 = i μ w | ψ | 2 ,
i ξ ψ + i β 1 z 0 t 0 τ ψ + 1 2 τ 2 ψ + | ψ | 2 ψ + R ( τ ) ψ = 0 ,
i ξ ψ 2 + i u 2 τ ψ 2 + 1 2 m τ 2 ψ 2 + 2 κ V 1 sin ( δ τ ˜ ) ψ 2 = 0 ,
i ξ ϕ = 1 2 m τ ˜ 2 ϕ + [ 2 κ V 1 sin ( δ τ ˜ ) + g 1 τ ˜ ] ϕ .

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