Abstract

We demonstrate that quasi-phase-matching of the third-harmonic generation process can be obtained for a pulse pump in the photonic crystal fiber with a refractive-index grating. Conversion efficiency is calculated numerically using a system of coupled generalized nonlinear Schrödinger equations. We propose a special design of the microstructured fiber for the third-harmonic generation and analyze different phenomena limiting the maximum efficiency for short (femtosecond) and long (picosecond) pump pulses. Moreover, we show that a certain level of a group-velocity mismatch between the pump and the third harmonic can increase the maximum efficiency in the long pulse regime.

© 2011 Optical Society of America

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    [CrossRef]
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2011 (1)

K. Tarnowski, B. Kibler, C. Finot, and W. Urbanczyk, “Quasi-phase-matched third harmonic generation in optical fibers using refractive-index gratings,” IEEE J. Quantum Electron. 47, 622–629 (2011).
[CrossRef]

2010 (2)

2008 (4)

T. Mizunami, Y. Sadakane, and Y. Tatsumoto, “Second-harmonic generation from thermally-poled twin-hole silica-glass optical fiber and enhancement by quasi phase matching,” Thin Solid Films 516, 5890–5893 (2008).
[CrossRef]

G. Genty, B. Kibler, P. Kinsler, and J. M. Dudley, “Harmonic extended supercontinuum generation and carrier envelope phase dependent spectral broadening in silica nanowires,” Opt. Express 16, 10886–10893 (2008).
[CrossRef] [PubMed]

B. Kibler, R. Fischer, G. Genty, D. N. Neshev, and J. M. Dudley, “Simultaneous femtosecond pulse spectral broadening and third harmonic generation in highly nonlinear fiber: experiments and numerical simulations,” Appl. Phys. B 91, 349–352(2008).
[CrossRef]

A. Bétourné, Y. Quiquempois, G. Bouwmans, and M. Douay, “Design of a photonic crystal fiber for phase matched frequency doubling or tripling,” Opt. Express 16, 14255–14262 (2008).
[CrossRef] [PubMed]

2007 (2)

2006 (1)

2005 (3)

S. A. Vasil’ev, O. I. Medvedkov, I. G. Korolev, A. S. Bozhkov, A. S. Kurkov, and E. M. Dianov, “Fibre gratings and their applications,” Quantum Electron. 35, 1085–1103 (2005).
[CrossRef]

A. M. Zheltikov, “Third-harmonic generation with no signal at 3ω0,” Phys. Rev. A 72, 043812 (2005).
[CrossRef]

S. Konorov, A. Ivanov, D. Ivanov, M. Alfimov, and A. Zheltikov, “Ultrafast photonic-crystal fiber light flash for streak-camera fluorescence measurements,” Opt. Express 13, 5682–5688(2005).
[CrossRef] [PubMed]

2003 (2)

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 fsCr:forsterite laser pulses in a tapered fiber,” Appl. Phys. B 76, 515–519 (2003).
[CrossRef]

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 microstrutured fibers,” Opt. Express 11, 2567–2576 (2003).
[CrossRef] [PubMed]

2002 (2)

A. N. Naumov and A. M. Zheltikov, “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]

T. Schneider and J. Reif, “Influence of an ultrafast transient refractive-index grating on nonlinear optical phenomena,” Phys. Rev. A 65, 023801 (2002).
[CrossRef]

2001 (2)

Th. Schneider, R. P. Schmid, and J. Reif, “Efficient self phase matched third harmonic generation of ultrashort pulses in a material with positive dispersion,” Appl. Phys. B 72, 563–565(2001).
[CrossRef]

F. G. Omenetto, A. J. Taylor, M. D. Moores, J. Arriaga, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Simultaneous generation of spectrally distinct third harmonics in a photonic crystal fiber,” Opt. Lett. 26, 1158–1160 (2001).
[CrossRef]

2000 (2)

1999 (1)

1994 (1)

J. Thøgersen and J. Mark, “Third harmonic generation in standard and erbium-doped fibers,” Opt. Commun. 110, 435–444(1994).
[CrossRef]

1993 (3)

D. L. Nicácio, E. A. Gouveia, N. M. Borges, and A. S. Gouveia-Neto, “Third-harmonic generation in GeO2-doped silica single-mode optical fibers,” Appl. Phys. Lett. 62, 2179–2181 (1993).
[CrossRef]

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435–436 (1993).
[CrossRef]

P. J. Lemaire, R. M. Atkins, V. Mizrahi, and W. A. Reed, “High pressure H2 loading asa technique for achieving ultrahigh UV photosensitivity and thermal sensitivity in GeO2 doped optical fibers,” Electron. Lett. 29, 1191–1193 (1993).
[CrossRef]

1992 (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654(1992).
[CrossRef]

1990 (1)

T. Suhara and H. Nishihara, “Theoretical analysis of waveguide second-harmonic generation phase matched with uniform and chirped gratings,” IEEE J. Quantum Electron. 26, 1265–1276(1990).
[CrossRef]

1983 (1)

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Agrawal, G. P.

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

Aitchison, J. S.

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 fsCr:forsterite laser pulses in a tapered fiber,” Appl. Phys. B 76, 515–519 (2003).
[CrossRef]

Alfimov, M.

Alfimov, M. V.

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 fsCr:forsterite laser pulses in a tapered fiber,” Appl. Phys. B 76, 515–519 (2003).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Arnold, J. M.

Arriaga, J.

Atkins, R. M.

P. J. Lemaire, R. M. Atkins, V. Mizrahi, and W. A. Reed, “High pressure H2 loading asa technique for achieving ultrahigh UV photosensitivity and thermal sensitivity in GeO2 doped optical fibers,” Electron. Lett. 29, 1191–1193 (1993).
[CrossRef]

Bétourné, A.

Birks, T. 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 fsCr:forsterite laser pulses in a tapered fiber,” Appl. Phys. B 76, 515–519 (2003).
[CrossRef]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Borges, N. M.

D. L. Nicácio, E. A. Gouveia, N. M. Borges, and A. S. Gouveia-Neto, “Third-harmonic generation in GeO2-doped silica single-mode optical fibers,” Appl. Phys. Lett. 62, 2179–2181 (1993).
[CrossRef]

Bouwmans, G.

Bozhkov, A. S.

S. A. Vasil’ev, O. I. Medvedkov, I. G. Korolev, A. S. Bozhkov, A. S. Kurkov, and E. M. Dianov, “Fibre gratings and their applications,” Quantum Electron. 35, 1085–1103 (2005).
[CrossRef]

Brown, C. T. A.

Bryce, A. C.

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654(1992).
[CrossRef]

Chaudhari, C.

Dianov, E. M.

S. A. Vasil’ev, O. I. Medvedkov, I. G. Korolev, A. S. Bozhkov, A. S. Kurkov, and E. M. Dianov, “Fibre gratings and their applications,” Quantum Electron. 35, 1085–1103 (2005).
[CrossRef]

Douay, M.

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Dudley, J. M.

B. Kibler, R. Fischer, G. Genty, D. N. Neshev, and J. M. Dudley, “Simultaneous femtosecond pulse spectral broadening and third harmonic generation in highly nonlinear fiber: experiments and numerical simulations,” Appl. Phys. B 91, 349–352(2008).
[CrossRef]

G. Genty, B. Kibler, P. Kinsler, and J. M. Dudley, “Harmonic extended supercontinuum generation and carrier envelope phase dependent spectral broadening in silica nanowires,” Opt. Express 16, 10886–10893 (2008).
[CrossRef] [PubMed]

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

J. M. Dudley and J. R. Taylor, Supercontinuum Generation in Optical Fibres (Cambridge University, 2010).
[CrossRef]

Dyott, R. B.

R. B. Dyott, Elliptical Fiber Waveguides (Artech, 1995).

Ebrahimzadeh, M.

Efimov, A.

Fejer, M. M.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654(1992).
[CrossRef]

Finot, C.

K. Tarnowski, B. Kibler, C. Finot, and W. Urbanczyk, “Quasi-phase-matched third harmonic generation in optical fibers using refractive-index gratings,” IEEE J. Quantum Electron. 47, 622–629 (2011).
[CrossRef]

Fischer, R.

B. Kibler, R. Fischer, G. Genty, D. N. Neshev, and J. M. Dudley, “Simultaneous femtosecond pulse spectral broadening and third harmonic generation in highly nonlinear fiber: experiments and numerical simulations,” Appl. Phys. B 91, 349–352(2008).
[CrossRef]

Gabriagues, J. M.

Genty, G.

Gouveia, E. A.

D. L. Nicácio, E. A. Gouveia, N. M. Borges, and A. S. Gouveia-Neto, “Third-harmonic generation in GeO2-doped silica single-mode optical fibers,” Appl. Phys. Lett. 62, 2179–2181 (1993).
[CrossRef]

Gouveia-Neto, A. S.

D. L. Nicácio, E. A. Gouveia, N. M. Borges, and A. S. Gouveia-Neto, “Third-harmonic generation in GeO2-doped silica single-mode optical fibers,” Appl. Phys. Lett. 62, 2179–2181 (1993).
[CrossRef]

Helmy, A. S.

Hutchings, D. C.

Ivanov, A.

Ivanov, 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 fsCr:forsterite laser pulses in a tapered fiber,” Appl. Phys. B 76, 515–519 (2003).
[CrossRef]

Ivanov, D.

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654(1992).
[CrossRef]

Kibler, B.

K. Tarnowski, B. Kibler, C. Finot, and W. Urbanczyk, “Quasi-phase-matched third harmonic generation in optical fibers using refractive-index gratings,” IEEE J. Quantum Electron. 47, 622–629 (2011).
[CrossRef]

G. Genty, B. Kibler, P. Kinsler, and J. M. Dudley, “Harmonic extended supercontinuum generation and carrier envelope phase dependent spectral broadening in silica nanowires,” Opt. Express 16, 10886–10893 (2008).
[CrossRef] [PubMed]

B. Kibler, R. Fischer, G. Genty, D. N. Neshev, and J. M. Dudley, “Simultaneous femtosecond pulse spectral broadening and third harmonic generation in highly nonlinear fiber: experiments and numerical simulations,” Appl. Phys. B 91, 349–352(2008).
[CrossRef]

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

Kinsler, P.

Kito, C.

Kleckner, T. C.

Klein, M. E.

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 fsCr:forsterite laser pulses in a tapered fiber,” Appl. Phys. B 76, 515–519 (2003).
[CrossRef]

Konorov, S.

Korolev, I. G.

S. A. Vasil’ev, O. I. Medvedkov, I. G. Korolev, A. S. Bozhkov, A. S. Kurkov, and E. M. Dianov, “Fibre gratings and their applications,” Quantum Electron. 35, 1085–1103 (2005).
[CrossRef]

Kurkov, A. S.

S. A. Vasil’ev, O. I. Medvedkov, I. G. Korolev, A. S. Bozhkov, A. S. Kurkov, and E. M. Dianov, “Fibre gratings and their applications,” Quantum Electron. 35, 1085–1103 (2005).
[CrossRef]

Lægsgaard, J.

Lemaire, P. J.

P. J. Lemaire, R. M. Atkins, V. Mizrahi, and W. A. Reed, “High pressure H2 loading asa technique for achieving ultrahigh UV photosensitivity and thermal sensitivity in GeO2 doped optical fibers,” Electron. Lett. 29, 1191–1193 (1993).
[CrossRef]

Liao, M.

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654(1992).
[CrossRef]

Mark, J.

J. Thøgersen and J. Mark, “Third harmonic generation in standard and erbium-doped fibers,” Opt. Commun. 110, 435–444(1994).
[CrossRef]

Marsh, J. H.

Medvedkov, O. I.

S. A. Vasil’ev, O. I. Medvedkov, I. G. Korolev, A. S. Bozhkov, A. S. Kurkov, and E. M. Dianov, “Fibre gratings and their applications,” Quantum Electron. 35, 1085–1103 (2005).
[CrossRef]

Meyn, J.-P.

Mizrahi, V.

P. J. Lemaire, R. M. Atkins, V. Mizrahi, and W. A. Reed, “High pressure H2 loading asa technique for achieving ultrahigh UV photosensitivity and thermal sensitivity in GeO2 doped optical fibers,” Electron. Lett. 29, 1191–1193 (1993).
[CrossRef]

Mizunami, T.

T. Mizunami, Y. Sadakane, and Y. Tatsumoto, “Second-harmonic generation from thermally-poled twin-hole silica-glass optical fiber and enhancement by quasi phase matching,” Thin Solid Films 516, 5890–5893 (2008).
[CrossRef]

Moores, M. D.

Moutzouris, K.

Nada, N.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435–436 (1993).
[CrossRef]

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 fsCr:forsterite laser pulses in a tapered fiber,” Appl. Phys. B 76, 515–519 (2003).
[CrossRef]

A. N. Naumov and A. M. Zheltikov, “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]

Neshev, D. N.

B. Kibler, R. Fischer, G. Genty, D. N. Neshev, and J. M. Dudley, “Simultaneous femtosecond pulse spectral broadening and third harmonic generation in highly nonlinear fiber: experiments and numerical simulations,” Appl. Phys. B 91, 349–352(2008).
[CrossRef]

Nicácio, D. L.

D. L. Nicácio, E. A. Gouveia, N. M. Borges, and A. S. Gouveia-Neto, “Third-harmonic generation in GeO2-doped silica single-mode optical fibers,” Appl. Phys. Lett. 62, 2179–2181 (1993).
[CrossRef]

Nishihara, H.

T. Suhara and H. Nishihara, “Theoretical analysis of waveguide second-harmonic generation phase matched with uniform and chirped gratings,” IEEE J. Quantum Electron. 26, 1265–1276(1990).
[CrossRef]

Ohishi, Y.

Omenetto, F. G.

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Podshivalov, A. A.

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P. J. Lemaire, R. M. Atkins, V. Mizrahi, and W. A. Reed, “High pressure H2 loading asa technique for achieving ultrahigh UV photosensitivity and thermal sensitivity in GeO2 doped optical fibers,” Electron. Lett. 29, 1191–1193 (1993).
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T. Schneider and J. Reif, “Influence of an ultrafast transient refractive-index grating on nonlinear optical phenomena,” Phys. Rev. A 65, 023801 (2002).
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Russell, P. St. J.

Sadakane, Y.

T. Mizunami, Y. Sadakane, and Y. Tatsumoto, “Second-harmonic generation from thermally-poled twin-hole silica-glass optical fiber and enhancement by quasi phase matching,” Thin Solid Films 516, 5890–5893 (2008).
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M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435–436 (1993).
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T. Schneider and J. Reif, “Influence of an ultrafast transient refractive-index grating on nonlinear optical phenomena,” Phys. Rev. A 65, 023801 (2002).
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Th. Schneider, R. P. Schmid, and J. Reif, “Efficient self phase matched third harmonic generation of ultrashort pulses in a material with positive dispersion,” Appl. Phys. B 72, 563–565(2001).
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K. Tarnowski, B. Kibler, C. Finot, and W. Urbanczyk, “Quasi-phase-matched third harmonic generation in optical fibers using refractive-index gratings,” IEEE J. Quantum Electron. 47, 622–629 (2011).
[CrossRef]

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T. Mizunami, Y. Sadakane, and Y. Tatsumoto, “Second-harmonic generation from thermally-poled twin-hole silica-glass optical fiber and enhancement by quasi phase matching,” Thin Solid Films 516, 5890–5893 (2008).
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J. Thøgersen and J. Mark, “Third harmonic generation in standard and erbium-doped fibers,” Opt. Commun. 110, 435–444(1994).
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K. Tarnowski, B. Kibler, C. Finot, and W. Urbanczyk, “Quasi-phase-matched third harmonic generation in optical fibers using refractive-index gratings,” IEEE J. Quantum Electron. 47, 622–629 (2011).
[CrossRef]

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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 microstrutured fibers,” Opt. Express 11, 2567–2576 (2003).
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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 fsCr:forsterite laser pulses in a tapered fiber,” Appl. Phys. B 76, 515–519 (2003).
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F. G. Omenetto, A. J. Taylor, M. D. Moores, J. Arriaga, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Simultaneous generation of spectrally distinct third harmonics in a photonic crystal fiber,” Opt. Lett. 26, 1158–1160 (2001).
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M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435–436 (1993).
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A. M. Zheltikov, “Third-harmonic generation with no signal at 3ω0,” Phys. Rev. A 72, 043812 (2005).
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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 fsCr:forsterite laser pulses in a tapered fiber,” Appl. Phys. B 76, 515–519 (2003).
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A. N. Naumov and A. M. Zheltikov, “Enhanced χ(3) interactions of unamplified femtosecond Cr:forsterite laser pulses in photonic-crystal fibers,” J. Opt. Soc. Am. B 19, 2183–2190 (2002).
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Appl. Phys. B (3)

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 fsCr:forsterite laser pulses in a tapered fiber,” Appl. Phys. B 76, 515–519 (2003).
[CrossRef]

B. Kibler, R. Fischer, G. Genty, D. N. Neshev, and J. M. Dudley, “Simultaneous femtosecond pulse spectral broadening and third harmonic generation in highly nonlinear fiber: experiments and numerical simulations,” Appl. Phys. B 91, 349–352(2008).
[CrossRef]

Th. Schneider, R. P. Schmid, and J. Reif, “Efficient self phase matched third harmonic generation of ultrashort pulses in a material with positive dispersion,” Appl. Phys. B 72, 563–565(2001).
[CrossRef]

Appl. Phys. Lett. (2)

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435–436 (1993).
[CrossRef]

D. L. Nicácio, E. A. Gouveia, N. M. Borges, and A. S. Gouveia-Neto, “Third-harmonic generation in GeO2-doped silica single-mode optical fibers,” Appl. Phys. Lett. 62, 2179–2181 (1993).
[CrossRef]

Electron. Lett. (1)

P. J. Lemaire, R. M. Atkins, V. Mizrahi, and W. A. Reed, “High pressure H2 loading asa technique for achieving ultrahigh UV photosensitivity and thermal sensitivity in GeO2 doped optical fibers,” Electron. Lett. 29, 1191–1193 (1993).
[CrossRef]

IEEE J. Quantum Electron. (3)

T. Suhara and H. Nishihara, “Theoretical analysis of waveguide second-harmonic generation phase matched with uniform and chirped gratings,” IEEE J. Quantum Electron. 26, 1265–1276(1990).
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[CrossRef]

K. Tarnowski, B. Kibler, C. Finot, and W. Urbanczyk, “Quasi-phase-matched third harmonic generation in optical fibers using refractive-index gratings,” IEEE J. Quantum Electron. 47, 622–629 (2011).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

J. Thøgersen and J. Mark, “Third harmonic generation in standard and erbium-doped fibers,” Opt. Commun. 110, 435–444(1994).
[CrossRef]

Opt. Express (6)

Opt. Lett. (6)

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Phys. Rev. A (2)

A. M. Zheltikov, “Third-harmonic generation with no signal at 3ω0,” Phys. Rev. A 72, 043812 (2005).
[CrossRef]

T. Schneider and J. Reif, “Influence of an ultrafast transient refractive-index grating on nonlinear optical phenomena,” Phys. Rev. A 65, 023801 (2002).
[CrossRef]

Quantum Electron. (1)

S. A. Vasil’ev, O. I. Medvedkov, I. G. Korolev, A. S. Bozhkov, A. S. Kurkov, and E. M. Dianov, “Fibre gratings and their applications,” Quantum Electron. 35, 1085–1103 (2005).
[CrossRef]

Thin Solid Films (1)

T. Mizunami, Y. Sadakane, and Y. Tatsumoto, “Second-harmonic generation from thermally-poled twin-hole silica-glass optical fiber and enhancement by quasi phase matching,” Thin Solid Films 516, 5890–5893 (2008).
[CrossRef]

Other (4)

R. B. Dyott, Elliptical Fiber Waveguides (Artech, 1995).

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

J. M. Dudley and J. R. Taylor, Supercontinuum Generation in Optical Fibres (Cambridge University, 2010).
[CrossRef]

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

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Figures (8)

Fig. 1
Fig. 1

Design of the optimized PCF for TH generation: (a) cross section of the fiber showing germanium-doped inclusion in the core (black), silica glass (dark gray), and air holes (light gray), (b) material refractive index in the core region, black line shows the refractive index of pure silica glass and germanium-doped glass before grating inscription, gray line shows the maximum material refractive index in the grating.

Fig. 2
Fig. 2

Spectral characteristics of the optimized PCF: (a) effective refractive index calculated for minimum and maximum values of the refractive index in the grating, (b) group velocity for the average refractive index in the grating, circles indicate the pump at 1.56 μm and TH at 0.52 μm with group velocity matched at 0.662 c , (c) group-velocity dispersion and nonlinear parameter γ ( 1 / W / km ) for average refractive index in the grating.

Fig. 3
Fig. 3

(a) Conversion efficiency as a function of propagation distance for different pulse durations. (b) Maximum efficiency as a function of pulse duration. (c) Propagation distance corresponding to maximum efficiency. Colors denote three conversion regimes: short pump pulse < 4 ps , intermediate pump pulse, and long pump pulse > 7 ps , respectively.

Fig. 4
Fig. 4

THG for the 100 fs pump pulse as a function of the propagation distance. From left to right: (a) efficiency η (line thickness represents oscillations characteristic for the QPM process), (b) normalized spectral intensity evolution represented in false colors and a logarithmic scale for the TH and pump windows, and (c) temporal intensity profiles shown at specific distances for the pump (red line) and TH (blue line) signals. TH signal is magnified by a factor of 2000 for better comparison.

Fig. 5
Fig. 5

THG for the 10 ps pump pulse as a function of propagation distance. From left to right: (a) efficiency η, (b) normalized spectral intensity evolution represented in false colors and a logarithmic scale for the TH and pump windows, and (c) temporal intensity profiles shown at specific distances for the pump (red line) and TH (blue line) signals. TH signal is magnified by a factor of 30 for better comparison.

Fig. 6
Fig. 6

THG for the 4 ps pump pulse as a function of the propagation distance. From left to right: (a) efficiency η, (b) normalized spectral intensity evolution represented in false colors and a logarithmic scale for the TH and pump windows, and (c) temporal intensity profiles shown at specific distances for the pump (red line) and TH (blue line) signals. TH signal is magnified by a factor of 10 for better comparison.

Fig. 7
Fig. 7

(a) Maximum conversion efficiency as a function of the pump wavelength for the 10 ps initial pulse with a peak power of 10 kW . (b) Difference between the group velocities of pump and its TH as a function of the pump wavelength in the designed PCF with group-velocity matching for the pump at 1.56 μm .

Fig. 8
Fig. 8

THG for the 10 ps pump pulse at 1.65 μm as a function of the propagation distance. From left to right: (a) efficiency η, (b) normalized spectral intensity evolution represented in false colors and a logarithmic scale for the TH and pump windows, and (c) temporal intensity profiles shown at specific distances for the pump (red line) and TH (blue line) signals. TH signal is magnified by a factor of 15 for better comparison.

Equations (5)

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

U p z = i β p U p + i n 2 ω c A eff 1 / 4 F { U ¯ p ( | U ¯ p | 2 + 2 | U ¯ TH | 2 ) + U ¯ p 2 U ¯ TH * } ,
U TH z = i β TH U TH + i n 2 ω c A eff 1 / 4 F { U ¯ TH ( | U ¯ TH | 2 + 2 | U ¯ p | 2 ) + 1 3 U ¯ p 3 } ,
K = β 3 ω 3 β ω + n 2 3 ω c ( 2 f XPM f SPM ω ) P ω ,
L = 2 π K .
K = β 3 ω 3 β ω + n 2 3 ω c ( 2 f XPM f SPM ω ) P ω + ζ ,

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