Abstract

The extraction of the spectrum corresponding to a single extreme-ultraviolet ultrashort pulse embedded in an extended spectrum may alter the duration of the pulse itself. This is due to the spectral filtering of optics and the differences in the optical path of the rays caused by ordinary diffraction when a grating is used. The basic mechanism that leads to the latter effect is the difference of one wavelength of the path length of two rays diffracted at the first order by nearby grating grooves. A study of these effects and some possible solutions obtained from using a pair of diffraction gratings is presented. The aim of this study is the selection without dispersion of one or more high-order laser harmonics produced by a pulse lasting a few femtoseconds and interacting with a gas jet.

© 1999 Optical Society of America

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References

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  1. S. A. Akhmanov, V. A. Vysloukh, A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, New York, 1992).
  2. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).
  3. J. A. R. Samson, Techniques of Vacuum Ultraviolet Spectroscopy (Wiley, New York, 1967).
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  5. O. Svelto, Principle of Lasers, 4th ed. (Plenum, New York, 1998).
    [CrossRef]
  6. O. E. Martinez, “Pulse distortion in tilted pulsed schemes for ultrashort pulses,” Opt. Commun. 59, 229–232 (1986).
    [CrossRef]
  7. O. E. Martinez, “Grating and prism compressor in the case of finite beam size,” J. Opt. Soc. Am. B 3, 929–934 (1986).
    [CrossRef]
  8. K. J. Schafer, K. C. Kulander, J. A. Squier, C. P. Barty, “Proposed generation of subfemtosecond VUV pulses from high order harmonics,” in Generation Amplification and Measurement of Ultrashort Laser Pulses III, W. E. White, D. H. Reitze, eds., Proc. SPIE2701, 248–257 (1996).
    [CrossRef]
  9. P. B. Corkum, “Plasma perspective on strong-field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
    [CrossRef] [PubMed]
  10. M. Protopapas, C. H. Keitel, P. L. Knight, “Atomic physics with superhigh intensity laser,” Rep. Prog. Phys. 60, 389–486 (1997).
    [CrossRef]
  11. M. D. Perry, J. K. Crane, “High order harmonics with mixed fields,” Phys. Rev. A 48, R4051–R4054 (1993).
    [CrossRef]
  12. F. Giammanco, P. Ceccherini, C. Tagliavini, M. Malvezzi, P. Villoresi, G. Tondello, “Coherent VUV radiation by harmonic conversion of mixed fields in gases,” Laser Phys. 7, 22–31 (1997).
  13. M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, R. Szipöcs, K. Ferencz, Ch. Spielmann, S. Sartania, F. Krausz, “Compression of high-energy laser pulses below 5 fs,” Opt. Lett. 22, 522–524 (1997).
    [CrossRef] [PubMed]
  14. M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, G. Tampea, Ch. Spielmann, F. Krausz, “Toward a terawatt-scale sub-10-fs laser technology,” IEEE J. Sel. Top. Quantum Electron. 4, 414–420 (1998).
    [CrossRef]
  15. P. Salières, A. L’Huillier, P. Antoine, M. Lewenstein, “Study of the spatial and temporal coherence of high order harmonics,” in Advances in Atomic, Molecular and Optical Physics, B. Bederson, H. Walther, eds. (Institute of Physics, London, 1998).
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    [CrossRef]
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    [CrossRef]
  23. G. Bonfante, “Light path simulation—ray-tracing code,” Master’s thesis (Università degli Studi di Padova, Italy, 1989).
  24. P. Salières, T. Ditmire, M. D. Perry, A. L’Hullier, M. Lewenstein, “Angular distribution of high order harmonics generated by a femtosecond laser,” J. Phys. B 29, 4771–4786 (1996).
    [CrossRef]
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1999 (1)

1998 (2)

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, G. Tampea, Ch. Spielmann, F. Krausz, “Toward a terawatt-scale sub-10-fs laser technology,” IEEE J. Sel. Top. Quantum Electron. 4, 414–420 (1998).
[CrossRef]

I. P. Christov, M. M. Murname, H. C. Kapteyn, “Generation and propagation of attosecond x-ray pulses in gaseous media,” Phys. Rev. A 57, R2285–R2288 (1998).
[CrossRef]

1997 (4)

K. J. Schafer, K. C. Kulander, “High harmonic generation from ultrafast pump laser,” Phys. Rev. Lett. 78, 638–641 (1997).
[CrossRef]

M. Protopapas, C. H. Keitel, P. L. Knight, “Atomic physics with superhigh intensity laser,” Rep. Prog. Phys. 60, 389–486 (1997).
[CrossRef]

F. Giammanco, P. Ceccherini, C. Tagliavini, M. Malvezzi, P. Villoresi, G. Tondello, “Coherent VUV radiation by harmonic conversion of mixed fields in gases,” Laser Phys. 7, 22–31 (1997).

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, R. Szipöcs, K. Ferencz, Ch. Spielmann, S. Sartania, F. Krausz, “Compression of high-energy laser pulses below 5 fs,” Opt. Lett. 22, 522–524 (1997).
[CrossRef] [PubMed]

1996 (2)

P. Salières, T. Ditmire, M. D. Perry, A. L’Hullier, M. Lewenstein, “Angular distribution of high order harmonics generated by a femtosecond laser,” J. Phys. B 29, 4771–4786 (1996).
[CrossRef]

P. Antoine, A. L’Huillier, M. Lewenstein, “Attosecond pulse trains using high-order harmonics,” Phys. Rev. Lett. 77, 1234–1237 (1996).
[CrossRef] [PubMed]

1993 (2)

P. B. Corkum, “Plasma perspective on strong-field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
[CrossRef] [PubMed]

M. D. Perry, J. K. Crane, “High order harmonics with mixed fields,” Phys. Rev. A 48, R4051–R4054 (1993).
[CrossRef]

1986 (2)

O. E. Martinez, “Pulse distortion in tilted pulsed schemes for ultrashort pulses,” Opt. Commun. 59, 229–232 (1986).
[CrossRef]

O. E. Martinez, “Grating and prism compressor in the case of finite beam size,” J. Opt. Soc. Am. B 3, 929–934 (1986).
[CrossRef]

1985 (1)

I. P. Christov, “Propagation of femtosecond light pulses,” Opt. Commun. 53, 364–366 (1985).
[CrossRef]

1962 (1)

1950 (1)

1945 (1)

Akhmanov, S. A.

S. A. Akhmanov, V. A. Vysloukh, A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, New York, 1992).

Antoine, P.

P. Antoine, A. L’Huillier, M. Lewenstein, “Attosecond pulse trains using high-order harmonics,” Phys. Rev. Lett. 77, 1234–1237 (1996).
[CrossRef] [PubMed]

P. Salières, A. L’Huillier, P. Antoine, M. Lewenstein, “Study of the spatial and temporal coherence of high order harmonics,” in Advances in Atomic, Molecular and Optical Physics, B. Bederson, H. Walther, eds. (Institute of Physics, London, 1998).

Barty, C. P.

K. J. Schafer, K. C. Kulander, J. A. Squier, C. P. Barty, “Proposed generation of subfemtosecond VUV pulses from high order harmonics,” in Generation Amplification and Measurement of Ultrashort Laser Pulses III, W. E. White, D. H. Reitze, eds., Proc. SPIE2701, 248–257 (1996).
[CrossRef]

Beutler, H. G.

Bonfante, G.

G. Bonfante, “Light path simulation—ray-tracing code,” Master’s thesis (Università degli Studi di Padova, Italy, 1989).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Ceccherini, P.

P. Ceccherini, M.-G. Pelizzo, P. Villoresi, S. De Silvestri, M. Nisoli, S. Stagira, “Surface damage of extreme ultraviolet gratings exposed to high-energy laser pulses,” Appl. Opt. 38, 4720–4724 (1999).
[CrossRef]

F. Giammanco, P. Ceccherini, C. Tagliavini, M. Malvezzi, P. Villoresi, G. Tondello, “Coherent VUV radiation by harmonic conversion of mixed fields in gases,” Laser Phys. 7, 22–31 (1997).

Cheng, Z.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, G. Tampea, Ch. Spielmann, F. Krausz, “Toward a terawatt-scale sub-10-fs laser technology,” IEEE J. Sel. Top. Quantum Electron. 4, 414–420 (1998).
[CrossRef]

Chirkin, A. S.

S. A. Akhmanov, V. A. Vysloukh, A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, New York, 1992).

Christov, I. P.

I. P. Christov, M. M. Murname, H. C. Kapteyn, “Generation and propagation of attosecond x-ray pulses in gaseous media,” Phys. Rev. A 57, R2285–R2288 (1998).
[CrossRef]

I. P. Christov, “Propagation of femtosecond light pulses,” Opt. Commun. 53, 364–366 (1985).
[CrossRef]

Corkum, P. B.

P. B. Corkum, “Plasma perspective on strong-field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
[CrossRef] [PubMed]

Crane, J. K.

M. D. Perry, J. K. Crane, “High order harmonics with mixed fields,” Phys. Rev. A 48, R4051–R4054 (1993).
[CrossRef]

De Silvestri, S.

Ditmire, T.

P. Salières, T. Ditmire, M. D. Perry, A. L’Hullier, M. Lewenstein, “Angular distribution of high order harmonics generated by a femtosecond laser,” J. Phys. B 29, 4771–4786 (1996).
[CrossRef]

Ferencz, K.

Giammanco, F.

F. Giammanco, P. Ceccherini, C. Tagliavini, M. Malvezzi, P. Villoresi, G. Tondello, “Coherent VUV radiation by harmonic conversion of mixed fields in gases,” Laser Phys. 7, 22–31 (1997).

Haber, H.

Hutley, M. C.

M. C. Hutley, Diffraction Gratings (Academic, London, 1982).

Kapteyn, H. C.

I. P. Christov, M. M. Murname, H. C. Kapteyn, “Generation and propagation of attosecond x-ray pulses in gaseous media,” Phys. Rev. A 57, R2285–R2288 (1998).
[CrossRef]

Keitel, C. H.

M. Protopapas, C. H. Keitel, P. L. Knight, “Atomic physics with superhigh intensity laser,” Rep. Prog. Phys. 60, 389–486 (1997).
[CrossRef]

Knight, P. L.

M. Protopapas, C. H. Keitel, P. L. Knight, “Atomic physics with superhigh intensity laser,” Rep. Prog. Phys. 60, 389–486 (1997).
[CrossRef]

Krausz, F.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, G. Tampea, Ch. Spielmann, F. Krausz, “Toward a terawatt-scale sub-10-fs laser technology,” IEEE J. Sel. Top. Quantum Electron. 4, 414–420 (1998).
[CrossRef]

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, R. Szipöcs, K. Ferencz, Ch. Spielmann, S. Sartania, F. Krausz, “Compression of high-energy laser pulses below 5 fs,” Opt. Lett. 22, 522–524 (1997).
[CrossRef] [PubMed]

Kulander, K. C.

K. J. Schafer, K. C. Kulander, “High harmonic generation from ultrafast pump laser,” Phys. Rev. Lett. 78, 638–641 (1997).
[CrossRef]

K. J. Schafer, K. C. Kulander, J. A. Squier, C. P. Barty, “Proposed generation of subfemtosecond VUV pulses from high order harmonics,” in Generation Amplification and Measurement of Ultrashort Laser Pulses III, W. E. White, D. H. Reitze, eds., Proc. SPIE2701, 248–257 (1996).
[CrossRef]

L’Huillier, A.

P. Antoine, A. L’Huillier, M. Lewenstein, “Attosecond pulse trains using high-order harmonics,” Phys. Rev. Lett. 77, 1234–1237 (1996).
[CrossRef] [PubMed]

P. Salières, A. L’Huillier, P. Antoine, M. Lewenstein, “Study of the spatial and temporal coherence of high order harmonics,” in Advances in Atomic, Molecular and Optical Physics, B. Bederson, H. Walther, eds. (Institute of Physics, London, 1998).

L’Hullier, A.

P. Salières, T. Ditmire, M. D. Perry, A. L’Hullier, M. Lewenstein, “Angular distribution of high order harmonics generated by a femtosecond laser,” J. Phys. B 29, 4771–4786 (1996).
[CrossRef]

Lewenstein, M.

P. Salières, T. Ditmire, M. D. Perry, A. L’Hullier, M. Lewenstein, “Angular distribution of high order harmonics generated by a femtosecond laser,” J. Phys. B 29, 4771–4786 (1996).
[CrossRef]

P. Antoine, A. L’Huillier, M. Lewenstein, “Attosecond pulse trains using high-order harmonics,” Phys. Rev. Lett. 77, 1234–1237 (1996).
[CrossRef] [PubMed]

P. Salières, A. L’Huillier, P. Antoine, M. Lewenstein, “Study of the spatial and temporal coherence of high order harmonics,” in Advances in Atomic, Molecular and Optical Physics, B. Bederson, H. Walther, eds. (Institute of Physics, London, 1998).

Malvezzi, M.

F. Giammanco, P. Ceccherini, C. Tagliavini, M. Malvezzi, P. Villoresi, G. Tondello, “Coherent VUV radiation by harmonic conversion of mixed fields in gases,” Laser Phys. 7, 22–31 (1997).

Martinez, O. E.

O. E. Martinez, “Pulse distortion in tilted pulsed schemes for ultrashort pulses,” Opt. Commun. 59, 229–232 (1986).
[CrossRef]

O. E. Martinez, “Grating and prism compressor in the case of finite beam size,” J. Opt. Soc. Am. B 3, 929–934 (1986).
[CrossRef]

Murname, M. M.

I. P. Christov, M. M. Murname, H. C. Kapteyn, “Generation and propagation of attosecond x-ray pulses in gaseous media,” Phys. Rev. A 57, R2285–R2288 (1998).
[CrossRef]

Murty, M. V. R. K.

Nisoli, M.

Pelizzo, M.-G.

Perry, M. D.

P. Salières, T. Ditmire, M. D. Perry, A. L’Hullier, M. Lewenstein, “Angular distribution of high order harmonics generated by a femtosecond laser,” J. Phys. B 29, 4771–4786 (1996).
[CrossRef]

M. D. Perry, J. K. Crane, “High order harmonics with mixed fields,” Phys. Rev. A 48, R4051–R4054 (1993).
[CrossRef]

Protopapas, M.

M. Protopapas, C. H. Keitel, P. L. Knight, “Atomic physics with superhigh intensity laser,” Rep. Prog. Phys. 60, 389–486 (1997).
[CrossRef]

Salières, P.

P. Salières, T. Ditmire, M. D. Perry, A. L’Hullier, M. Lewenstein, “Angular distribution of high order harmonics generated by a femtosecond laser,” J. Phys. B 29, 4771–4786 (1996).
[CrossRef]

P. Salières, A. L’Huillier, P. Antoine, M. Lewenstein, “Study of the spatial and temporal coherence of high order harmonics,” in Advances in Atomic, Molecular and Optical Physics, B. Bederson, H. Walther, eds. (Institute of Physics, London, 1998).

Samson, J. A. R.

J. A. R. Samson, Techniques of Vacuum Ultraviolet Spectroscopy (Wiley, New York, 1967).

Sartania, S.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, G. Tampea, Ch. Spielmann, F. Krausz, “Toward a terawatt-scale sub-10-fs laser technology,” IEEE J. Sel. Top. Quantum Electron. 4, 414–420 (1998).
[CrossRef]

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, R. Szipöcs, K. Ferencz, Ch. Spielmann, S. Sartania, F. Krausz, “Compression of high-energy laser pulses below 5 fs,” Opt. Lett. 22, 522–524 (1997).
[CrossRef] [PubMed]

Schafer, K. J.

K. J. Schafer, K. C. Kulander, “High harmonic generation from ultrafast pump laser,” Phys. Rev. Lett. 78, 638–641 (1997).
[CrossRef]

K. J. Schafer, K. C. Kulander, J. A. Squier, C. P. Barty, “Proposed generation of subfemtosecond VUV pulses from high order harmonics,” in Generation Amplification and Measurement of Ultrashort Laser Pulses III, W. E. White, D. H. Reitze, eds., Proc. SPIE2701, 248–257 (1996).
[CrossRef]

Spencer, G. H.

Spielmann, Ch.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, G. Tampea, Ch. Spielmann, F. Krausz, “Toward a terawatt-scale sub-10-fs laser technology,” IEEE J. Sel. Top. Quantum Electron. 4, 414–420 (1998).
[CrossRef]

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, R. Szipöcs, K. Ferencz, Ch. Spielmann, S. Sartania, F. Krausz, “Compression of high-energy laser pulses below 5 fs,” Opt. Lett. 22, 522–524 (1997).
[CrossRef] [PubMed]

Squier, J. A.

K. J. Schafer, K. C. Kulander, J. A. Squier, C. P. Barty, “Proposed generation of subfemtosecond VUV pulses from high order harmonics,” in Generation Amplification and Measurement of Ultrashort Laser Pulses III, W. E. White, D. H. Reitze, eds., Proc. SPIE2701, 248–257 (1996).
[CrossRef]

Stagira, S.

Svelto, O.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, G. Tampea, Ch. Spielmann, F. Krausz, “Toward a terawatt-scale sub-10-fs laser technology,” IEEE J. Sel. Top. Quantum Electron. 4, 414–420 (1998).
[CrossRef]

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, R. Szipöcs, K. Ferencz, Ch. Spielmann, S. Sartania, F. Krausz, “Compression of high-energy laser pulses below 5 fs,” Opt. Lett. 22, 522–524 (1997).
[CrossRef] [PubMed]

O. Svelto, Principle of Lasers, 4th ed. (Plenum, New York, 1998).
[CrossRef]

Szipöcs, R.

Tagliavini, C.

F. Giammanco, P. Ceccherini, C. Tagliavini, M. Malvezzi, P. Villoresi, G. Tondello, “Coherent VUV radiation by harmonic conversion of mixed fields in gases,” Laser Phys. 7, 22–31 (1997).

Tampea, G.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, G. Tampea, Ch. Spielmann, F. Krausz, “Toward a terawatt-scale sub-10-fs laser technology,” IEEE J. Sel. Top. Quantum Electron. 4, 414–420 (1998).
[CrossRef]

Tondello, G.

F. Giammanco, P. Ceccherini, C. Tagliavini, M. Malvezzi, P. Villoresi, G. Tondello, “Coherent VUV radiation by harmonic conversion of mixed fields in gases,” Laser Phys. 7, 22–31 (1997).

Villoresi, P.

P. Ceccherini, M.-G. Pelizzo, P. Villoresi, S. De Silvestri, M. Nisoli, S. Stagira, “Surface damage of extreme ultraviolet gratings exposed to high-energy laser pulses,” Appl. Opt. 38, 4720–4724 (1999).
[CrossRef]

F. Giammanco, P. Ceccherini, C. Tagliavini, M. Malvezzi, P. Villoresi, G. Tondello, “Coherent VUV radiation by harmonic conversion of mixed fields in gases,” Laser Phys. 7, 22–31 (1997).

Vysloukh, V. A.

S. A. Akhmanov, V. A. Vysloukh, A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, New York, 1992).

Welford, W. T.

W. T. Welford, Aberrations of Optical Systems (Hilger, Bristol, 1991).

W. T. Welford, “Aberration theory of gratings and grating mountings,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1965), Vol. 4, 243–280.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Appl. Opt. (1)

IEEE J. Sel. Top. Quantum Electron. (1)

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, G. Tampea, Ch. Spielmann, F. Krausz, “Toward a terawatt-scale sub-10-fs laser technology,” IEEE J. Sel. Top. Quantum Electron. 4, 414–420 (1998).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. B (1)

J. Phys. B (1)

P. Salières, T. Ditmire, M. D. Perry, A. L’Hullier, M. Lewenstein, “Angular distribution of high order harmonics generated by a femtosecond laser,” J. Phys. B 29, 4771–4786 (1996).
[CrossRef]

Laser Phys. (1)

F. Giammanco, P. Ceccherini, C. Tagliavini, M. Malvezzi, P. Villoresi, G. Tondello, “Coherent VUV radiation by harmonic conversion of mixed fields in gases,” Laser Phys. 7, 22–31 (1997).

Opt. Commun. (2)

O. E. Martinez, “Pulse distortion in tilted pulsed schemes for ultrashort pulses,” Opt. Commun. 59, 229–232 (1986).
[CrossRef]

I. P. Christov, “Propagation of femtosecond light pulses,” Opt. Commun. 53, 364–366 (1985).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (2)

M. D. Perry, J. K. Crane, “High order harmonics with mixed fields,” Phys. Rev. A 48, R4051–R4054 (1993).
[CrossRef]

I. P. Christov, M. M. Murname, H. C. Kapteyn, “Generation and propagation of attosecond x-ray pulses in gaseous media,” Phys. Rev. A 57, R2285–R2288 (1998).
[CrossRef]

Phys. Rev. Lett. (3)

P. Antoine, A. L’Huillier, M. Lewenstein, “Attosecond pulse trains using high-order harmonics,” Phys. Rev. Lett. 77, 1234–1237 (1996).
[CrossRef] [PubMed]

K. J. Schafer, K. C. Kulander, “High harmonic generation from ultrafast pump laser,” Phys. Rev. Lett. 78, 638–641 (1997).
[CrossRef]

P. B. Corkum, “Plasma perspective on strong-field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

M. Protopapas, C. H. Keitel, P. L. Knight, “Atomic physics with superhigh intensity laser,” Rep. Prog. Phys. 60, 389–486 (1997).
[CrossRef]

Other (10)

K. J. Schafer, K. C. Kulander, J. A. Squier, C. P. Barty, “Proposed generation of subfemtosecond VUV pulses from high order harmonics,” in Generation Amplification and Measurement of Ultrashort Laser Pulses III, W. E. White, D. H. Reitze, eds., Proc. SPIE2701, 248–257 (1996).
[CrossRef]

S. A. Akhmanov, V. A. Vysloukh, A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, New York, 1992).

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

J. A. R. Samson, Techniques of Vacuum Ultraviolet Spectroscopy (Wiley, New York, 1967).

M. C. Hutley, Diffraction Gratings (Academic, London, 1982).

O. Svelto, Principle of Lasers, 4th ed. (Plenum, New York, 1998).
[CrossRef]

P. Salières, A. L’Huillier, P. Antoine, M. Lewenstein, “Study of the spatial and temporal coherence of high order harmonics,” in Advances in Atomic, Molecular and Optical Physics, B. Bederson, H. Walther, eds. (Institute of Physics, London, 1998).

G. Bonfante, “Light path simulation—ray-tracing code,” Master’s thesis (Università degli Studi di Padova, Italy, 1989).

W. T. Welford, “Aberration theory of gratings and grating mountings,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1965), Vol. 4, 243–280.

W. T. Welford, Aberrations of Optical Systems (Hilger, Bristol, 1991).

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Figures (6)

Fig. 1
Fig. 1

Comparison of the lengths of the ray paths during diffraction in a Rowland mounting.

Fig. 2
Fig. 2

Grating configurations that provide path-length compensations: (a) NEIE; (b) EII.

Fig. 3
Fig. 3

Ray tracing of the normal-incidence-compensated monochromator for two wavelengths of H15, λ1 = 53.3 nm and λ2 = 53.6 nm, and for α = 35.81°. The coordinate origin is in the vertex of the first grating, the z axis is along the grating normal, and the x is axis in the tangential direction. The units are millimeters.

Fig. 4
Fig. 4

Ray tracing of the grazing-incidence-compensated monochromator (H125: λ1 = 6.4 nm and λ2 = 6.2 nm, α = 86.79°). The axis orientation is as in Fig. 3. The units are millimeters.

Fig. 5
Fig. 5

Ray plot at the focal plane for H125 of a Ti:S laser, λ = 6.4 nm, with two toroidal gratings, 150 grooves/mm, R = 4 m, ρ = 19.3 mm. The η axis in the dispersion plane is normal to the chief ray at the focal point, which belongs to the xz plane.

Fig. 6
Fig. 6

Scheme of a four-grating compensated monochromator for the grazing-incidence region.

Tables (2)

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Table 1 Analysis of the Compensation of Optical Path Lengths for Various Harmonics at Normal Incidence

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Table 2 Prediction for the Compensation of Optical Path Lengths in the Grazing-Incidence Region

Equations (28)

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Δω1/2Δτ1/2=4 log 2=2.77,
ΔOP=Ndsin α-sin β=Nmλ,
pen=R cos α=324 mm,
ρ=R cos α cos β=267 mm.
s=cτ1/2d cos βmλ.
f/#inst=Rmλcτ1/2d.
ΔOP=ttransitΔvg.
dvgdω=1ttransitdOPdω-λ22πOPdOPdλ,
k2=-1vg2vgω,
OP=SP+PI+mλd x,
OPx=0,  OPy=0,
dˆ=rˆ+mλdgˆ.
z=R-R-ρ+p2-y21/22-x21/2,
rˆ=L, M, N=ξ-xAP, η-yAP, ζ-zAP,
dˆ=L, M, N=ξ-xAP, η-yAP, ζ-zAP,
L+L+N+Nzx-mλd=0,
M+M+N+Nzy=0,
zx=xR-ρ+ρ2-y21/22-x21/2,
zy=R-ρ+ρ2-y21/2yR-ρ+ρ2-y21/221/2-x2ρ2-y21/2,
L2+M2+N2=1.
N=-A2A1+1A1A22-A1A31/2,
A1=zx2+zy2+1,
A2=B1zx+B2zy,
A3=B12+B22-1,
B1=-mλd-L-N zx,
B2=-M-N zy.
L=B1-N zx,
M=B2-N zy.

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