Abstract

We numerically study chirped four-wave mixing for VUV pulse generation in hollow waveguides filled with a noble gas. Taking into account ionization effects we predict the generation of signal pulses at 160 nm with shortest durations up to 6.5 fs, highest pulse energy up to the mJ level and maximum energy efficiency of about 30% by broadband chirped idler pulses at 800 nm and narrow-band pump pulses at 270 nm. Using cascaded processes sub-10-fs pulses in the spectral range from 90 to 140 nm can also be generated.

© 2008 Optical Society of America

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References

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  1. P. Baum, S. Lochbrunner, and E. Riedle, "Tunable sub-10-fs ultraviolet pulses generated by achromatic frequency doubling," Opt. Lett. 29, 1686-1688 (2004).
    [CrossRef] [PubMed]
  2. M. Wittmann, M. T. Wick, O. Steinkellner, P. Farmanara, V. Stert, W. Radlo, G. Korn, and I. V. Hertel, "Generation of femtosecond VUV pulses and their application to time resolved spectroscopy in the gas phase," Opt. Commun. 173, 323-331 (2000).
    [CrossRef]
  3. T. Sekikawa, T. Ohno, T. Yamazaki, Y. Nabekawa, and S. Watanabe "Pulse Compression of a High-Order Harmonic by Compensating the Atomic Dipole Phase," Phys. Rev. Lett. 83, 2564-2567 (1999).
    [CrossRef]
  4. K. Kosma, S. A. Trushin, W. E. Schmid and W. Fuß "Vacuum ultraviolet pulses of 11 fs from fifth-harmonic generation of a Ti:sapphire laser," Opt. Lett. 33, 723-725 (2008).
    [CrossRef] [PubMed]
  5. C. G. DurfeeIII, S. Backus, H. C. Kaptayn, and M. M. Murnane, "Intense 8-fs pulse generation in the deep ultraviolet," Opt. Lett. 24, 697-699 (1999).
    [CrossRef]
  6. P. Tzankov, O. Steinkellner, J. Zheng, M. Mero,W. Freyer, A. Husakou, I. Babushkin, J. Herrmann, and F. Noack, "High-power fifth-harmonic generation of femtosecond pulses in the vacuum ultraviolet using a Ti:sapphire laser," Opt. Express 15, 6389-6395 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-10-6389.
    [CrossRef] [PubMed]
  7. I. V. Babushkin, F. Noack, and J. Herrmann, "Generation of sub-5 fs pulses in vacuum ultraviolet using four-wave frequency mixing in hollow waveguides," Opt. Lett.  33, 938-940 (2008).
    [CrossRef] [PubMed]
  8. A. V. Husakou, and J. Herrmann, "Supercontinuum Generation of Higher-Order Solitons by Fission in Photonic Crystal Fibers," Phys. Rev. Lett. 87, 203901-203901-4 (2001).
    [CrossRef] [PubMed]
  9. D.-S. Guo and G. W. F. Drake, "Stationary solutions for an electron in an intense laser field. II Multimode case," J. Phys. A 25, 5377-5394 (1992).
    [CrossRef]
  10. H. R. Reis, "Effect of an intense electromagnetic field on a weakly bound system," Phys. Rev. A 221786-1813 (1980).
    [CrossRef]
  11. I. Babushkin, A. Husakou, and J. Herrmann, "Fifth Harmonic Generation in Hollow Waveguides In Vacuum Ultraviolet," (to be published)
  12. P. J. Leonard, "Refractive Indices, Verdet Constants, Polarizabilities of Inert Gases," At. Data Nucl. Data. Tabels 14, 21-37 (1974).
    [CrossRef]
  13. E. A. J. Marcatili and R. A. Schmelzer, "Hollow Metallic and Dielectric Waveguides for Long Distance Optical Transmissions and Lasers," Bell Syst. Tech. J. 43, 1783-1809 (1964).

2008 (2)

2007 (1)

2004 (1)

2000 (1)

M. Wittmann, M. T. Wick, O. Steinkellner, P. Farmanara, V. Stert, W. Radlo, G. Korn, and I. V. Hertel, "Generation of femtosecond VUV pulses and their application to time resolved spectroscopy in the gas phase," Opt. Commun. 173, 323-331 (2000).
[CrossRef]

1999 (2)

T. Sekikawa, T. Ohno, T. Yamazaki, Y. Nabekawa, and S. Watanabe "Pulse Compression of a High-Order Harmonic by Compensating the Atomic Dipole Phase," Phys. Rev. Lett. 83, 2564-2567 (1999).
[CrossRef]

C. G. DurfeeIII, S. Backus, H. C. Kaptayn, and M. M. Murnane, "Intense 8-fs pulse generation in the deep ultraviolet," Opt. Lett. 24, 697-699 (1999).
[CrossRef]

1992 (1)

D.-S. Guo and G. W. F. Drake, "Stationary solutions for an electron in an intense laser field. II Multimode case," J. Phys. A 25, 5377-5394 (1992).
[CrossRef]

1980 (1)

H. R. Reis, "Effect of an intense electromagnetic field on a weakly bound system," Phys. Rev. A 221786-1813 (1980).
[CrossRef]

1974 (1)

P. J. Leonard, "Refractive Indices, Verdet Constants, Polarizabilities of Inert Gases," At. Data Nucl. Data. Tabels 14, 21-37 (1974).
[CrossRef]

1964 (1)

E. A. J. Marcatili and R. A. Schmelzer, "Hollow Metallic and Dielectric Waveguides for Long Distance Optical Transmissions and Lasers," Bell Syst. Tech. J. 43, 1783-1809 (1964).

Babushkin, I.

Babushkin, I. V.

Backus, S.

Baum, P.

Drake, G. W. F.

D.-S. Guo and G. W. F. Drake, "Stationary solutions for an electron in an intense laser field. II Multimode case," J. Phys. A 25, 5377-5394 (1992).
[CrossRef]

Durfee, C. G.

Farmanara, P.

M. Wittmann, M. T. Wick, O. Steinkellner, P. Farmanara, V. Stert, W. Radlo, G. Korn, and I. V. Hertel, "Generation of femtosecond VUV pulses and their application to time resolved spectroscopy in the gas phase," Opt. Commun. 173, 323-331 (2000).
[CrossRef]

Freyer, W.

Fuß, W.

Guo, D.-S.

D.-S. Guo and G. W. F. Drake, "Stationary solutions for an electron in an intense laser field. II Multimode case," J. Phys. A 25, 5377-5394 (1992).
[CrossRef]

Herrmann, J.

Husakou, A.

Husakou, A. V.

A. V. Husakou, and J. Herrmann, "Supercontinuum Generation of Higher-Order Solitons by Fission in Photonic Crystal Fibers," Phys. Rev. Lett. 87, 203901-203901-4 (2001).
[CrossRef] [PubMed]

Kaptayn, H. C.

Kosma, K.

Leonard, P. J.

P. J. Leonard, "Refractive Indices, Verdet Constants, Polarizabilities of Inert Gases," At. Data Nucl. Data. Tabels 14, 21-37 (1974).
[CrossRef]

Lochbrunner, S.

Marcatili, E. A. J.

E. A. J. Marcatili and R. A. Schmelzer, "Hollow Metallic and Dielectric Waveguides for Long Distance Optical Transmissions and Lasers," Bell Syst. Tech. J. 43, 1783-1809 (1964).

Mero, M.

Murnane, M. M.

Nabekawa, Y.

T. Sekikawa, T. Ohno, T. Yamazaki, Y. Nabekawa, and S. Watanabe "Pulse Compression of a High-Order Harmonic by Compensating the Atomic Dipole Phase," Phys. Rev. Lett. 83, 2564-2567 (1999).
[CrossRef]

Noack, F.

Ohno, T.

T. Sekikawa, T. Ohno, T. Yamazaki, Y. Nabekawa, and S. Watanabe "Pulse Compression of a High-Order Harmonic by Compensating the Atomic Dipole Phase," Phys. Rev. Lett. 83, 2564-2567 (1999).
[CrossRef]

Reis, H. R.

H. R. Reis, "Effect of an intense electromagnetic field on a weakly bound system," Phys. Rev. A 221786-1813 (1980).
[CrossRef]

Riedle, E.

Schmelzer, R. A.

E. A. J. Marcatili and R. A. Schmelzer, "Hollow Metallic and Dielectric Waveguides for Long Distance Optical Transmissions and Lasers," Bell Syst. Tech. J. 43, 1783-1809 (1964).

Schmid, W. E.

Sekikawa, T.

T. Sekikawa, T. Ohno, T. Yamazaki, Y. Nabekawa, and S. Watanabe "Pulse Compression of a High-Order Harmonic by Compensating the Atomic Dipole Phase," Phys. Rev. Lett. 83, 2564-2567 (1999).
[CrossRef]

Steinkellner, O.

P. Tzankov, O. Steinkellner, J. Zheng, M. Mero,W. Freyer, A. Husakou, I. Babushkin, J. Herrmann, and F. Noack, "High-power fifth-harmonic generation of femtosecond pulses in the vacuum ultraviolet using a Ti:sapphire laser," Opt. Express 15, 6389-6395 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-10-6389.
[CrossRef] [PubMed]

M. Wittmann, M. T. Wick, O. Steinkellner, P. Farmanara, V. Stert, W. Radlo, G. Korn, and I. V. Hertel, "Generation of femtosecond VUV pulses and their application to time resolved spectroscopy in the gas phase," Opt. Commun. 173, 323-331 (2000).
[CrossRef]

Stert, V.

M. Wittmann, M. T. Wick, O. Steinkellner, P. Farmanara, V. Stert, W. Radlo, G. Korn, and I. V. Hertel, "Generation of femtosecond VUV pulses and their application to time resolved spectroscopy in the gas phase," Opt. Commun. 173, 323-331 (2000).
[CrossRef]

Trushin, S. A.

Tzankov, P.

Watanabe, S.

T. Sekikawa, T. Ohno, T. Yamazaki, Y. Nabekawa, and S. Watanabe "Pulse Compression of a High-Order Harmonic by Compensating the Atomic Dipole Phase," Phys. Rev. Lett. 83, 2564-2567 (1999).
[CrossRef]

Wick, M. T.

M. Wittmann, M. T. Wick, O. Steinkellner, P. Farmanara, V. Stert, W. Radlo, G. Korn, and I. V. Hertel, "Generation of femtosecond VUV pulses and their application to time resolved spectroscopy in the gas phase," Opt. Commun. 173, 323-331 (2000).
[CrossRef]

Wittmann, M.

M. Wittmann, M. T. Wick, O. Steinkellner, P. Farmanara, V. Stert, W. Radlo, G. Korn, and I. V. Hertel, "Generation of femtosecond VUV pulses and their application to time resolved spectroscopy in the gas phase," Opt. Commun. 173, 323-331 (2000).
[CrossRef]

Yamazaki, T.

T. Sekikawa, T. Ohno, T. Yamazaki, Y. Nabekawa, and S. Watanabe "Pulse Compression of a High-Order Harmonic by Compensating the Atomic Dipole Phase," Phys. Rev. Lett. 83, 2564-2567 (1999).
[CrossRef]

Zheng, J.

Bell Syst. Tech. J. (1)

E. A. J. Marcatili and R. A. Schmelzer, "Hollow Metallic and Dielectric Waveguides for Long Distance Optical Transmissions and Lasers," Bell Syst. Tech. J. 43, 1783-1809 (1964).

Data Nucl. Data. Tabels (1)

P. J. Leonard, "Refractive Indices, Verdet Constants, Polarizabilities of Inert Gases," At. Data Nucl. Data. Tabels 14, 21-37 (1974).
[CrossRef]

Fifth Harmonic Generation in Hollow Waveguides In Vacuum Ultraviolet (1)

I. Babushkin, A. Husakou, and J. Herrmann, "Fifth Harmonic Generation in Hollow Waveguides In Vacuum Ultraviolet," (to be published)

J. Phys. A (1)

D.-S. Guo and G. W. F. Drake, "Stationary solutions for an electron in an intense laser field. II Multimode case," J. Phys. A 25, 5377-5394 (1992).
[CrossRef]

Opt. Commun. (1)

M. Wittmann, M. T. Wick, O. Steinkellner, P. Farmanara, V. Stert, W. Radlo, G. Korn, and I. V. Hertel, "Generation of femtosecond VUV pulses and their application to time resolved spectroscopy in the gas phase," Opt. Commun. 173, 323-331 (2000).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. A (1)

H. R. Reis, "Effect of an intense electromagnetic field on a weakly bound system," Phys. Rev. A 221786-1813 (1980).
[CrossRef]

Phys. Rev. Lett. (1)

T. Sekikawa, T. Ohno, T. Yamazaki, Y. Nabekawa, and S. Watanabe "Pulse Compression of a High-Order Harmonic by Compensating the Atomic Dipole Phase," Phys. Rev. Lett. 83, 2564-2567 (1999).
[CrossRef]

Other (1)

A. V. Husakou, and J. Herrmann, "Supercontinuum Generation of Higher-Order Solitons by Fission in Photonic Crystal Fibers," Phys. Rev. Lett. 87, 203901-203901-4 (2001).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1.
Fig. 1.

Dispersion characteristics and losses for different waveguide diameters. In (a) the dependence of the GVD on the wavelength, in (b) the wave vector mismatch δk versus pressure and in (c) the loss α versus wavelength are shown for waveguides with the diameters d=100 µm, d=200 µm, d=300 µm (red, blue and magenta curves correspondingly).

Fig. 2.
Fig. 2.

Spectrum (a,c,e) and compressed VUV pulse shapes (b,d,f) after 20 cm propagation in a waveguide with a diameter d=100 µm and a pressure p=30 Torr. In (a,b) the input energy is J I =J P =0:65 mJ and the pulse duration is 300 fs, in (c,d) the input energy is J I =J P =2:6 mJ and the pulse duration is 1.2 ps and in (e,f) the input energy is J I =J P =20 mJ and the pulse duration is 10 ps. In (a,c,e) the spectral intensity is shown by red and the phase by green lines. In (b,d,f), the insets show the ideally compressed pulse shapes. The chirp of the idler is obtained by its propagation through MgF2 glass with a length of 2 cm, 8 cm and 67 cm for [(a),(b)], [(c),(d)] and [(e),(f)] correspondingly.

Fig. 3.
Fig. 3.

Energy of the VUV pulse and pulse duration after compression versus input energy (a,b) and input duration (c,d) for J I =J P . In (a),(b) the input pump and idler pulses have 300 fs duration. The black, red and green lines correspond to the diameters d=100, 200 and 300 µm and phase matching pressures 28, 7, and 3 Torrs. In (c,d) d=100 µm is assumed. In (d) the black curve shows the optimized compression by a MgF2 layer, the blue one shows the ideal compression and the red curve represents the prediction of the analytical solution.

Fig. 4.
Fig. 4.

Spectrum (a) and shapes (b,c) of the signal pulses in the spectral interval below 150 nm for the input wavelengthes λ I =570 nm and λ P =267 nm. In (a) the spectral intensity and phase versus wavelength is shown by red and green lines. In (b,c) the signal obtained by selecting the spectral interval from 117 to 135 nm (b) and from 90 to 104 nm (c) and compresed by propagation in a Ar-filled waveguide is shown. The insets show ideally compresed pulse shapes.

Equations (1)

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E z = i { β ( ω ) ω v } E + i μ 0 ω 2 2 β ( ω ) P nl ( z , ω ) .

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