Abstract

We analyze the third harmonic generation by the supercontinuum at 1.5 µm in nonlinear-glass microstructured fibers. The numerical model includes the real field dynamics and allows analyzing the spectral as well as the temporal structure of the generated field. The calculated third harmonic and supercontinuum spectra are compared with the experiment in the SF6 glass PCF pumped by a femtosecond Cr4+:YAG oscillator. The spectral structure of the third harmonic is composed of the 10–20 high-order modes excited at the phase matching points around 500–550 nm. The individual third harmonic modes have spectral widths of 2–4 nm. In the time domain, the third harmonic signal is a ~10-ps pulse with ps-scale slow modulation, containing subpicosecond ripples at its trailing edge.

© 2007 Optical Society of America

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  1. J. M. Dudley, G. Genty, S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78,1135-1184 (2006).
    [CrossRef]
  2. V. L. Kalashnikov, E. Sorokin, I. T. Sorokina, "Raman effects in the infrared supercontinuum generation in softglass PCFs," Appl. Phys. B. 87, 37-44 (2007)
    [CrossRef] [PubMed]
  3. R. H. Stolen, "Phase-matched-stimulated four-wave mixing in silica-fiber waveguides," IEEE J. Quantum Electron. QE-11,100-103 (1975).
    [CrossRef]
  4. R. H. Stolen and W. H. Leibolt, "Optical fiber modes using stimulated four photon mixing," Appl. Opt. 11,239-243 (1976).
    [CrossRef]
  5. J. M. Dudley, L. Provino, N. Grossard, H. Mailotte, R. S. Windeler, B. J. Eggleton, S. Coen, "Supercontinuum generation in air-silica microstructured fibers with nanosecond and femtosecond pulse pumping," J. Opt. Soc. Am. B 19,765-771 (2002).
    [CrossRef]
  6. J. H. V. Price, T. M. Monro, K. Furusawa, W. Belardi, J. C. Baggett, S. Coyle, C. Netti, J. J. Baumberg, R. Paschotta, D. J. Richardson, "UV generation in a pure-silica holey fiber," Appl. Phys. B 77,291-298 (2003).
    [CrossRef]
  7. C. G. DurfeeIII, S. Backus, M. M. Murnane, and H. C. Kapteyn, "Ultrabroadband phase-matched optical parametric generation in the ultraviolet by use of guided waves," Opt. Lett. 22,1565-1567 (1997).
    [CrossRef]
  8. A. M. Zheltikov, N. I. Koroteev, A. N. Naumov, "Self- and cross-phase modulation accompanyning thirdharmonic generation in a hollow waveguide," J. Exp. Theor. Phys. 88,857-867 (1999).
    [CrossRef]
  9. J. K. Ranka, R. S. Windeler, A. J. Stentz, "Optical properties of high-delta air-silica microstructure optical fibers," Opt. Lett. 25,796-798 (2000).
    [CrossRef]
  10. A. N. Naumov, D. A. Sidorov-Biryukov, F. Giammanco, A. B. Fedotov, P. Marsili, A. Ruffini, O. A. Kolevatova, and A.M. Zheltikov, "Four-wave mixing of picosecond pulses in hollow fibers: phase matching and the influence of high-order waveguide modes," J. Exp. Theor. Phys. 93,247-255 (2001).
    [CrossRef]
  11. S. O. Konorov, A. B. Fedotov, and A. M. Zheltikov, "Enhanced four-wave mixing in a hollow-core photonic crystal fiber," Opt. Lett. 28,1448-1450 (2003).
    [CrossRef] [PubMed]
  12. K. D. Moll, D. Homoelle, and A. L. Gaeta, "Conical harmonic generation in isotropic matherials," Phys. Rev. Lett. 88,153901 (2002).
    [CrossRef] [PubMed]
  13. T. Schreiber, J. Limpert, H. Zellmer, A. T¨unnermann, K. P. Hansen, "High average power supercontinuum generation in photonic crystal fibers," Opt. Commun. 228,71-78 (2003).
    [CrossRef]
  14. A. N. Naumov, A. B. Fedotov, A. M. Zheltikov, V. V. Yakovlev, L. A. Mel’nikov, V. I. Beloglazov, N. B. Skibina, A. V. Shcherbakov, "Enhanced χ(3) interactions of unamplified femtosecond Cr:forsterite laser pulses in photonic-crystal fibers," J. Opt. Soc. Am. B 19,2183-2190 (2002).
    [CrossRef]
  15. F. G. Omenetto, A. J. Taylor, M. D. Moores, J. Arriaga, J. C. Knight, W. J. Wadsworth, P. S. Jt. Russell, "Simultaneous generation of spectrally distinct third harmonics in a photonic crystal fiber," Opt. Lett. 26,1158-1160 (2001).
    [CrossRef]
  16. N. Y. Joly, T. A. Birks, A. Yulin, J. C. Knight, and P. St. J. Russell, "Linear and nonlinear guidance in an ultralow loss planar glass membrane," Opt. Lett. 30,2469-2471 (2005).
    [CrossRef] [PubMed]
  17. A. Efimov, A. J. Taylor, F. G. Omenetto, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, "Phase-matched third harmonic generation in microstructured fibers," Opt. Express 11,2567-2576 (2003).
    [CrossRef] [PubMed]
  18. A. A. Ivanov, D. Lorenc, F. Uherek, E. E. Serebrynnikov, S. O. Konorov, M. V. Alfimov, D. Chorvat, and A. M. Zheltikov, "Multimode anharmonic third-order harmonic generation in a photonic-crystal fiber," Phys. Rev. E 73,016610 (2006).
    [CrossRef]
  19. A. B. Fedotov, Ping Zhou, Yu. N. Kondrat’ev, S. N. Bagayev, V. S. Shevandin, K. V. Dukel’skiˆı, V. B. Smirnov, A. P. Tarasevitch, D. von der Linde, and A. M. Zheltikov, "The mode structure and spectral properties of supercontinuum emission from microstructured fibers," J. Exp. Theor. Phys. 95,851-860 (2002).
    [CrossRef]
  20. V. Grubsky, A. Savchenko, "Glass micro-fibers for efficient third harmonic generation," Opt. Express 13, 6798- 6806 (2005).
    [CrossRef] [PubMed]
  21. R. A. Sammut, A. V. Buryak, Y. S. Kivshar, "Modification of solitary waves by third-harmonic generation," Opt. Lett. 22, 1385-1387 (1997).
    [CrossRef]
  22. R. A. Sammut, A. V. Buryak, Y. S. Kivshar, "Bright and dark solitary waves in the presence of third-harmonic generation," J. Opt. Soc. Am. B 15, 1488-1496 (1998).
    [CrossRef]
  23. F. G. Omenetto, A. J. Taylor, M. D. Moores, J. Arriaga, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Simulataneous generation of spectrally distinct third harmonics in a photonic fiber," Opt. Lett. 26,1158-1160 (2001).
    [CrossRef]
  24. F. G. Omenetto, A. Efimov, J. Taylor, J. C. Knight,W. J. Wadsworth, and P. St. J. Russell, "Polarization dependent harmonic generation in microstructured fibers," Opt. Express 11,61-67 (2003).
    [CrossRef] [PubMed]
  25. A. Efimov, A. J. Taylor, "Spectral-temporal dynamics of ultrashort Raman solitons and their role in third-order harmonic generation in photonic crystal fibers," Appl. Phys. B 80,721-725 (2005).
    [CrossRef]
  26. E. E. Serebrynnikov, A. B. Fedotov, A. M. Zheltikov, A. A. Ivanov, M. V. Alfimov, V. I. Beloglazov, N. B. Skibina, D. V. Skryabin, A. V. Yulin, J. C. Knight, "Third-harmonic generation by Raman-shifted solitons in a photonic-crystal fiber," J. Opt. Soc. Am. B 23,1975-1980 (2006).
    [CrossRef]
  27. A. N. Naumov, and A. M. Zheltikov, "Asymmetric spectral broadening and temporal evolution of cross-phasemodulated third-harmonic pulses," Opt. Express 10,122-127 (2002).
    [PubMed]
  28. D. A. Akimov, A. A. Ivanov, A. N. Naumov, O. A. Kolevatova, M. V. Alfimov, T. A. Birks, W. J. Wadsworth, P. St. J. Russell, A. A. Podshivalov, A. M. Zheltikov, "Generation of a spectrally asymmetric third harmonic with unamplified 30-fs Cr:forsterite laser pulses in a tapered fiber," Appl. Phys. B 76,515-519 (2003).
    [CrossRef]
  29. A. Zheltikov, "Multimode guided non-3ω third-harmonic generation by ultrashort laser pulses," J. Opt. Soc. Am. B 22,2263-2269 (2005).
    [CrossRef]
  30. A. M. Zheltikov, "Third-harmonic generation with no signal at 3ω," Phys. Rev. A 72,043812 (2005).
    [CrossRef]
  31. G. Genty, P. Kinsler, B. Kibler, J.M. Dudley, "Non linear envelope equation modeling of sub-cycle dynamics and harmonic generation in nonlinear waveguides," Opt. Express 15, 5382-5387 (2007).
    [CrossRef] [PubMed]
  32. A.N. Berkovsky, S.A. Kozlov, Yu.A. Shpolyanskiy, "Self-focusing of few-cycle light pulses in dielectric media," Phys. Rev. A 72, 043821 (2005).
    [CrossRef]
  33. V. L. Kalashnikov, E. Sorokin, S. Naumov, I. T. Sorokina, V. V. Ravi Kanth Kumar, A. K. George, "Low-threshold supercontinuum generation from an extruded SF6 PCF using a compact Cr4+:YAG laser," Appl. Phys. B 79, 591- 596 (2004).
    [CrossRef]
  34. E. Sorokin, S. Naumov, I.T. Sorokina, "Ultrabroadband infrared solid-state lasers," IEEE J. Sel. Top. Quantum Electron. 11, 690-712 (2005).
    [CrossRef]
  35. P. Xie, Zh.-Q. Zhang, "Large enhancement of third-harmonic generation induced by coupled gap solitons in χ(3) nonlinear photonic crystals," Phys. Rev. E 71, 026610 (2005).
    [CrossRef]
  36. G.P. Agrawal: Nonlinear fiber optics 3rd ed., (Academic Press, New York, 2001), p 263.

2007

V. L. Kalashnikov, E. Sorokin, I. T. Sorokina, "Raman effects in the infrared supercontinuum generation in softglass PCFs," Appl. Phys. B. 87, 37-44 (2007)
[CrossRef] [PubMed]

G. Genty, P. Kinsler, B. Kibler, J.M. Dudley, "Non linear envelope equation modeling of sub-cycle dynamics and harmonic generation in nonlinear waveguides," Opt. Express 15, 5382-5387 (2007).
[CrossRef] [PubMed]

2006

E. E. Serebrynnikov, A. B. Fedotov, A. M. Zheltikov, A. A. Ivanov, M. V. Alfimov, V. I. Beloglazov, N. B. Skibina, D. V. Skryabin, A. V. Yulin, J. C. Knight, "Third-harmonic generation by Raman-shifted solitons in a photonic-crystal fiber," J. Opt. Soc. Am. B 23,1975-1980 (2006).
[CrossRef]

A. A. Ivanov, D. Lorenc, F. Uherek, E. E. Serebrynnikov, S. O. Konorov, M. V. Alfimov, D. Chorvat, and A. M. Zheltikov, "Multimode anharmonic third-order harmonic generation in a photonic-crystal fiber," Phys. Rev. E 73,016610 (2006).
[CrossRef]

J. M. Dudley, G. Genty, S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78,1135-1184 (2006).
[CrossRef]

2005

N. Y. Joly, T. A. Birks, A. Yulin, J. C. Knight, and P. St. J. Russell, "Linear and nonlinear guidance in an ultralow loss planar glass membrane," Opt. Lett. 30,2469-2471 (2005).
[CrossRef] [PubMed]

V. Grubsky, A. Savchenko, "Glass micro-fibers for efficient third harmonic generation," Opt. Express 13, 6798- 6806 (2005).
[CrossRef] [PubMed]

A. Efimov, A. J. Taylor, "Spectral-temporal dynamics of ultrashort Raman solitons and their role in third-order harmonic generation in photonic crystal fibers," Appl. Phys. B 80,721-725 (2005).
[CrossRef]

A. Zheltikov, "Multimode guided non-3ω third-harmonic generation by ultrashort laser pulses," J. Opt. Soc. Am. B 22,2263-2269 (2005).
[CrossRef]

A. M. Zheltikov, "Third-harmonic generation with no signal at 3ω," Phys. Rev. A 72,043812 (2005).
[CrossRef]

A.N. Berkovsky, S.A. Kozlov, Yu.A. Shpolyanskiy, "Self-focusing of few-cycle light pulses in dielectric media," Phys. Rev. A 72, 043821 (2005).
[CrossRef]

E. Sorokin, S. Naumov, I.T. Sorokina, "Ultrabroadband infrared solid-state lasers," IEEE J. Sel. Top. Quantum Electron. 11, 690-712 (2005).
[CrossRef]

P. Xie, Zh.-Q. Zhang, "Large enhancement of third-harmonic generation induced by coupled gap solitons in χ(3) nonlinear photonic crystals," Phys. Rev. E 71, 026610 (2005).
[CrossRef]

2004

V. L. Kalashnikov, E. Sorokin, S. Naumov, I. T. Sorokina, V. V. Ravi Kanth Kumar, A. K. George, "Low-threshold supercontinuum generation from an extruded SF6 PCF using a compact Cr4+:YAG laser," Appl. Phys. B 79, 591- 596 (2004).
[CrossRef]

2003

F. G. Omenetto, A. Efimov, J. Taylor, J. C. Knight,W. J. Wadsworth, and P. St. J. Russell, "Polarization dependent harmonic generation in microstructured fibers," Opt. Express 11,61-67 (2003).
[CrossRef] [PubMed]

A. Efimov, A. J. Taylor, F. G. Omenetto, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, "Phase-matched third harmonic generation in microstructured fibers," Opt. Express 11,2567-2576 (2003).
[CrossRef] [PubMed]

T. Schreiber, J. Limpert, H. Zellmer, A. T¨unnermann, K. P. Hansen, "High average power supercontinuum generation in photonic crystal fibers," Opt. Commun. 228,71-78 (2003).
[CrossRef]

S. O. Konorov, A. B. Fedotov, and A. M. Zheltikov, "Enhanced four-wave mixing in a hollow-core photonic crystal fiber," Opt. Lett. 28,1448-1450 (2003).
[CrossRef] [PubMed]

J. H. V. Price, T. M. Monro, K. Furusawa, W. Belardi, J. C. Baggett, S. Coyle, C. Netti, J. J. Baumberg, R. Paschotta, D. J. Richardson, "UV generation in a pure-silica holey fiber," Appl. Phys. B 77,291-298 (2003).
[CrossRef]

D. A. Akimov, A. A. Ivanov, A. N. Naumov, O. A. Kolevatova, M. V. Alfimov, T. A. Birks, W. J. Wadsworth, P. St. J. Russell, A. A. Podshivalov, A. M. Zheltikov, "Generation of a spectrally asymmetric third harmonic with unamplified 30-fs Cr:forsterite laser pulses in a tapered fiber," Appl. Phys. B 76,515-519 (2003).
[CrossRef]

2002

2001

2000

1999

A. M. Zheltikov, N. I. Koroteev, A. N. Naumov, "Self- and cross-phase modulation accompanyning thirdharmonic generation in a hollow waveguide," J. Exp. Theor. Phys. 88,857-867 (1999).
[CrossRef]

1998

1997

1976

1975

R. H. Stolen, "Phase-matched-stimulated four-wave mixing in silica-fiber waveguides," IEEE J. Quantum Electron. QE-11,100-103 (1975).
[CrossRef]

Appl. Opt.

Appl. Phys. B

J. H. V. Price, T. M. Monro, K. Furusawa, W. Belardi, J. C. Baggett, S. Coyle, C. Netti, J. J. Baumberg, R. Paschotta, D. J. Richardson, "UV generation in a pure-silica holey fiber," Appl. Phys. B 77,291-298 (2003).
[CrossRef]

A. Efimov, A. J. Taylor, "Spectral-temporal dynamics of ultrashort Raman solitons and their role in third-order harmonic generation in photonic crystal fibers," Appl. Phys. B 80,721-725 (2005).
[CrossRef]

D. A. Akimov, A. A. Ivanov, A. N. Naumov, O. A. Kolevatova, M. V. Alfimov, T. A. Birks, W. J. Wadsworth, P. St. J. Russell, A. A. Podshivalov, A. M. Zheltikov, "Generation of a spectrally asymmetric third harmonic with unamplified 30-fs Cr:forsterite laser pulses in a tapered fiber," Appl. Phys. B 76,515-519 (2003).
[CrossRef]

V. L. Kalashnikov, E. Sorokin, S. Naumov, I. T. Sorokina, V. V. Ravi Kanth Kumar, A. K. George, "Low-threshold supercontinuum generation from an extruded SF6 PCF using a compact Cr4+:YAG laser," Appl. Phys. B 79, 591- 596 (2004).
[CrossRef]

Appl. Phys. B.

V. L. Kalashnikov, E. Sorokin, I. T. Sorokina, "Raman effects in the infrared supercontinuum generation in softglass PCFs," Appl. Phys. B. 87, 37-44 (2007)
[CrossRef] [PubMed]

IEEE J. Quantum Electron.

R. H. Stolen, "Phase-matched-stimulated four-wave mixing in silica-fiber waveguides," IEEE J. Quantum Electron. QE-11,100-103 (1975).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

E. Sorokin, S. Naumov, I.T. Sorokina, "Ultrabroadband infrared solid-state lasers," IEEE J. Sel. Top. Quantum Electron. 11, 690-712 (2005).
[CrossRef]

J. Exp. Theor. Phys.

A. B. Fedotov, Ping Zhou, Yu. N. Kondrat’ev, S. N. Bagayev, V. S. Shevandin, K. V. Dukel’skiˆı, V. B. Smirnov, A. P. Tarasevitch, D. von der Linde, and A. M. Zheltikov, "The mode structure and spectral properties of supercontinuum emission from microstructured fibers," J. Exp. Theor. Phys. 95,851-860 (2002).
[CrossRef]

A. M. Zheltikov, N. I. Koroteev, A. N. Naumov, "Self- and cross-phase modulation accompanyning thirdharmonic generation in a hollow waveguide," J. Exp. Theor. Phys. 88,857-867 (1999).
[CrossRef]

A. N. Naumov, D. A. Sidorov-Biryukov, F. Giammanco, A. B. Fedotov, P. Marsili, A. Ruffini, O. A. Kolevatova, and A.M. Zheltikov, "Four-wave mixing of picosecond pulses in hollow fibers: phase matching and the influence of high-order waveguide modes," J. Exp. Theor. Phys. 93,247-255 (2001).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

T. Schreiber, J. Limpert, H. Zellmer, A. T¨unnermann, K. P. Hansen, "High average power supercontinuum generation in photonic crystal fibers," Opt. Commun. 228,71-78 (2003).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

A. M. Zheltikov, "Third-harmonic generation with no signal at 3ω," Phys. Rev. A 72,043812 (2005).
[CrossRef]

A.N. Berkovsky, S.A. Kozlov, Yu.A. Shpolyanskiy, "Self-focusing of few-cycle light pulses in dielectric media," Phys. Rev. A 72, 043821 (2005).
[CrossRef]

Phys. Rev. E

P. Xie, Zh.-Q. Zhang, "Large enhancement of third-harmonic generation induced by coupled gap solitons in χ(3) nonlinear photonic crystals," Phys. Rev. E 71, 026610 (2005).
[CrossRef]

A. A. Ivanov, D. Lorenc, F. Uherek, E. E. Serebrynnikov, S. O. Konorov, M. V. Alfimov, D. Chorvat, and A. M. Zheltikov, "Multimode anharmonic third-order harmonic generation in a photonic-crystal fiber," Phys. Rev. E 73,016610 (2006).
[CrossRef]

Phys. Rev. Lett.

K. D. Moll, D. Homoelle, and A. L. Gaeta, "Conical harmonic generation in isotropic matherials," Phys. Rev. Lett. 88,153901 (2002).
[CrossRef] [PubMed]

Rev. Mod. Phys.

J. M. Dudley, G. Genty, S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78,1135-1184 (2006).
[CrossRef]

Other

G.P. Agrawal: Nonlinear fiber optics 3rd ed., (Academic Press, New York, 2001), p 263.

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Figures (11)

Fig. 1.
Fig. 1.

Cross section of the SF6 PCF (upper graph) and field intensity distributions for the two lowest infrared modes and one visible mode (lower graph, see text for mode designations).

Fig. 2.
Fig. 2.

Effective index of refraction n eff,M at the fundamental wavelength (≈λ0, M=1, 2) and at the third harmonic (≈λ0/3, M=69-80). Red circles show the phase matching points. SF6 PCF with 2.5 µm core.

Fig. 3.
Fig. 3.

Experimental SC spectrum (red) from the SF6 PCF with a 2.5 µm core. Blue curve shows the spectrum of the input pulse. The spectrometer resolution was 1.4 nm.

Fig. 4.
Fig. 4.

Experimental TH spectrum from the SF6 PCF with a 2.5 µm core and its mode decomposition according to from Fig. 2. The spectrometer resolution was 0.5 nm

Fig. 5.
Fig. 5.

Effective index of refraction neff, M for modes at fundamental wavelength: (a) M=1 (solid black), M=2 (dashed black); (b) M=3 (solid black), M=4 (dashed black). Colored lines show the effective indices of refraction for the third harmonic modes (≈λ0/3, modes are not enumerated). SF6 PCF with 4.5 µm core.

Fig. 6.
Fig. 6.

Experimental spectra of the SC (red) and TH (black) from SF6 PCF with 4.5 µm core. Blue curve shows the input pulse spectrum. All three spectra are normalized separately for better visibility.

Fig. 7.
Fig. 7.

Intensity profile of the TH radiation from the 4.5 µm core of SF6 PCF, taken at approximately 3 cm free propagation distance after the fiber end. The individual mode patterns can not be resolved.

Fig. 8.
Fig. 8.

Spatial profiles of the three TH modes in the cylindrical 5.2 µm core of the SF6 PCF.

Fig. 9.
Fig. 9.

Calculated: the SC (a) and the TH (b) spectra for the modes of Fig. 8.

Fig. 10.
Fig. 10.

Calculated: SC (fundamental) and TH temporal profiles for the modes of Fig. 6 at 4 cm propagation length. (a) Full time window of the TH signal (log scale). (b) Trailing edge of the TH pulse, corresponding to the beginning of the TH generation (linear scale).

Fig. 11.
Fig. 11.

Calculated evolution of the total TH energy fraction for the modes of Fig. 8.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

a F z = i 2 β 2 ( ω ω F ) 2 a F t 2 + i γ F ( 1 + i ω F ) { [ a F 2 + 2 ξ a TH 2 ] a F + ξ a F * 2 a TH exp ( i z Δ k ) } ,
a TH z = i 2 β 2 ( ω ω TH ) 2 a TH t 2 δ a TH t + i γ TH ( 1 + i ω TH ) ×
{ [ a TH 2 + 2 ξ a F 2 ] a TH + ξ a F 3 exp ( i z Δ k ) } .

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