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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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2007 (2)

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

G. Genty, P. Kinsler, B. Kibler, and 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 (3)

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, and 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]

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

2005 (8)

A. Efimov and 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]

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

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

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 and A. Savchenko, “Glass micro-fibers for efficient third harmonic generation,” Opt. Express 13, 6798–6806 (2005).
[CrossRef] [PubMed]

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

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

2004 (1)

V. L. Kalashnikov, E. Sorokin, S. Naumov, I. T. Sorokina, V. V. Ravi Kanth Kumar, and 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 (6)

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]

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]

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

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, and 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]

T. Schreiber, J. Limpert, H. Zellmer, A. Tünnermann, and K. P. Hansen, “High average power supercontinuum generation in photonic crystal fibers,” Opt. Commun. 228, 71–78 (2003).
[CrossRef]

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

2002 (5)

2001 (3)

2000 (1)

1999 (1)

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

1998 (1)

1997 (2)

1976 (1)

1975 (1)

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

Agrawal, G.P.

G.P. Agrawal : Nonlinear fiber optics3rd ed., (Academic Press, New York, 2001), p 263.

Akimov, D. A.

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, and 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]

Alfimov, M. V.

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, and 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]

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, and 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]

Arriaga, J.

Backus, S.

Bagayev, S. N.

A. B. Fedotov, Ping Zhou, Yu. N. Kondrat’ev, S. N. Bagayev, V. S. Shevandin, K. V. Dukel’skiî, 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]

Baggett, J. C.

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

Baumberg, J. J.

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

Belardi, W.

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

Beloglazov, V. I.

Berkovsky, A.N.

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

Birks, T. A.

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]

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, and 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]

Buryak, A. V.

Chorvat, D.

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]

Coen, S.

Coyle, S.

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

Dudley, J. M.

Dudley, J.M.

Dukel’skiî, K. V.

A. B. Fedotov, Ping Zhou, Yu. N. Kondrat’ev, S. N. Bagayev, V. S. Shevandin, K. V. Dukel’skiî, 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]

Durfee III, C. G.

Efimov, A.

Eggleton, B. J.

Fedotov, A. B.

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, and 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]

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]

A. N. Naumov, A. B. Fedotov, A. M. Zheltikov, V. V. Yakovlev, L. A. Mel’nikov, V. I. Beloglazov, N. B. Skibina, and 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]

A. B. Fedotov, Ping Zhou, Yu. N. Kondrat’ev, S. N. Bagayev, V. S. Shevandin, K. V. Dukel’skiî, 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. 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]

Furusawa, K.

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

Gaeta, A. L.

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

Genty, G.

George, A. K.

V. L. Kalashnikov, E. Sorokin, S. Naumov, I. T. Sorokina, V. V. Ravi Kanth Kumar, and 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]

Giammanco, F.

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]

Grossard, N.

Grubsky, V.

Hansen, K. P.

T. Schreiber, J. Limpert, H. Zellmer, A. Tünnermann, and K. P. Hansen, “High average power supercontinuum generation in photonic crystal fibers,” Opt. Commun. 228, 71–78 (2003).
[CrossRef]

Homoelle, D.

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

Ivanov, A. A.

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]

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, and 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]

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, and 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]

Joly, N. Y.

Kalashnikov, V. L.

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

V. L. Kalashnikov, E. Sorokin, S. Naumov, I. T. Sorokina, V. V. Ravi Kanth Kumar, and 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]

Kapteyn, H. C.

Kibler, B.

Kinsler, P.

Kivshar, Y. S.

Knight, J. C.

Kolevatova, O. A.

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, and 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]

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]

Kondrat’ev, Yu. N.

A. B. Fedotov, Ping Zhou, Yu. N. Kondrat’ev, S. N. Bagayev, V. S. Shevandin, K. V. Dukel’skiî, 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]

Konorov, S. O.

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]

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]

Koroteev, N. I.

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

Kozlov, S.A.

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

Leibolt, W. H.

Limpert, J.

T. Schreiber, J. Limpert, H. Zellmer, A. Tünnermann, and K. P. Hansen, “High average power supercontinuum generation in photonic crystal fibers,” Opt. Commun. 228, 71–78 (2003).
[CrossRef]

Lorenc, D.

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]

Mailotte, H.

Marsili, P.

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]

Mel’nikov, L. A.

Moll, K. D.

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

Monro, T. M.

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

Moores, M. D.

Murnane, M. M.

Naumov, A. N.

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, and 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]

A. N. Naumov and A. M. Zheltikov, “Asymmetric spectral broadening and temporal evolution of cross-phase-modulated third-harmonic pulses,” Opt. Express 10, 122–127 (2002).
[PubMed]

A. N. Naumov, A. B. Fedotov, A. M. Zheltikov, V. V. Yakovlev, L. A. Mel’nikov, V. I. Beloglazov, N. B. Skibina, and 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]

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]

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

Naumov, S.

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

V. L. Kalashnikov, E. Sorokin, S. Naumov, I. T. Sorokina, V. V. Ravi Kanth Kumar, and 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]

Netti, C.

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

Omenetto, F. G.

Paschotta, R.

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

Podshivalov, A. A.

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, and 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]

Price, J. H. V.

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

Provino, L.

Ranka, J. K.

Ravi Kanth Kumar, V. V.

V. L. Kalashnikov, E. Sorokin, S. Naumov, I. T. Sorokina, V. V. Ravi Kanth Kumar, and 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]

Richardson, D. J.

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

Ruffini, A.

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]

Russell, P. S. Jt.

Russell, P. St. J.

Sammut, R. A.

Savchenko, A.

Schreiber, T.

T. Schreiber, J. Limpert, H. Zellmer, A. Tünnermann, and K. P. Hansen, “High average power supercontinuum generation in photonic crystal fibers,” Opt. Commun. 228, 71–78 (2003).
[CrossRef]

Serebrynnikov, E. E.

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]

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, and 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]

Shcherbakov, A. V.

Shevandin, V. S.

A. B. Fedotov, Ping Zhou, Yu. N. Kondrat’ev, S. N. Bagayev, V. S. Shevandin, K. V. Dukel’skiî, 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]

Shpolyanskiy, Yu.A.

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

Sidorov-Biryukov, D. A.

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]

Skibina, N. B.

Skryabin, D. V.

Smirnov, V. B.

A. B. Fedotov, Ping Zhou, Yu. N. Kondrat’ev, S. N. Bagayev, V. S. Shevandin, K. V. Dukel’skiî, 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]

Sorokin, E.

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

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

V. L. Kalashnikov, E. Sorokin, S. Naumov, I. T. Sorokina, V. V. Ravi Kanth Kumar, and 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]

Sorokina, I. T.

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

V. L. Kalashnikov, E. Sorokin, S. Naumov, I. T. Sorokina, V. V. Ravi Kanth Kumar, and 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]

Sorokina, I.T.

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

Stentz, A. J.

Stolen, R. H.

R. H. Stolen and W. H. Leibolt, “Optical fiber modes using stimulated four photon mixing,” Appl. Opt. 11, 239–243 (1976).
[CrossRef]

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

Tarasevitch, A. P.

A. B. Fedotov, Ping Zhou, Yu. N. Kondrat’ev, S. N. Bagayev, V. S. Shevandin, K. V. Dukel’skiî, 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]

Taylor, A. J.

Taylor, J.

Tünnermann, A.

T. Schreiber, J. Limpert, H. Zellmer, A. Tünnermann, and K. P. Hansen, “High average power supercontinuum generation in photonic crystal fibers,” Opt. Commun. 228, 71–78 (2003).
[CrossRef]

Uherek, F.

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]

von der Linde, D.

A. B. Fedotov, Ping Zhou, Yu. N. Kondrat’ev, S. N. Bagayev, V. S. Shevandin, K. V. Dukel’skiî, 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]

Wadsworth, W. J.

Windeler, R. S.

Xie, P.

P. Xie and 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]

Yakovlev, V. V.

Yulin, A.

Yulin, A. V.

Zellmer, H.

T. Schreiber, J. Limpert, H. Zellmer, A. Tünnermann, and K. P. Hansen, “High average power supercontinuum generation in photonic crystal fibers,” Opt. Commun. 228, 71–78 (2003).
[CrossRef]

Zhang, Zh.-Q.

P. Xie and 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]

Zheltikov, A.

Zheltikov, A. M.

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, and 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]

A. M. Zheltikov, “Third-harmonic generation with no signal at 3ω,” Phys. Rev. A 72, 043812 (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, and 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]

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]

A. N. Naumov, A. B. Fedotov, A. M. Zheltikov, V. V. Yakovlev, L. A. Mel’nikov, V. I. Beloglazov, N. B. Skibina, and 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]

A. N. Naumov and A. M. Zheltikov, “Asymmetric spectral broadening and temporal evolution of cross-phase-modulated third-harmonic pulses,” Opt. Express 10, 122–127 (2002).
[PubMed]

A. B. Fedotov, Ping Zhou, Yu. N. Kondrat’ev, S. N. Bagayev, V. S. Shevandin, K. V. Dukel’skiî, 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, and A. N. Naumov, “Self- and cross-phase modulation accompanyning third-harmonic generation in a hollow waveguide,” J. Exp. Theor. Phys. 88, 857–867 (1999).
[CrossRef]

Zheltikov, A.M.

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]

Zhou, Ping

A. B. Fedotov, Ping Zhou, Yu. N. Kondrat’ev, S. N. Bagayev, V. S. Shevandin, K. V. Dukel’skiî, 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]

Appl. Opt. (1)

Appl. Phys. B (4)

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

A. Efimov and 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, and 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, and 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. (1)

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

IEEE J. Quantum Electron. (1)

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. (1)

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

J. Exp. Theor. Phys. (3)

A. B. Fedotov, Ping Zhou, Yu. N. Kondrat’ev, S. N. Bagayev, V. S. Shevandin, K. V. Dukel’skiî, 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, and A. N. Naumov, “Self- and cross-phase modulation accompanyning third-harmonic 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 (5)

Opt. Commun. (1)

T. Schreiber, J. Limpert, H. Zellmer, A. Tünnermann, and K. P. Hansen, “High average power supercontinuum generation in photonic crystal fibers,” Opt. Commun. 228, 71–78 (2003).
[CrossRef]

Opt. Express (5)

Opt. Lett. (7)

Phys. Rev. A (2)

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

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

Phys. Rev. E (2)

P. Xie and 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. (1)

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. (1)

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

Other (1)

G.P. Agrawal : Nonlinear fiber optics3rd 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)

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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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