Abstract

The conical diffraction mounting in which the direction of incident light belongs to a plane parallel to the direction of the grooves has the unique property of maintaining high diffraction efficiency, even in the extreme-ultraviolet (EUV) region. This property is useful for designing high-throughput time-delay-compensated monochromators for the spectral selection of ultrashort EUV pulses as the high-order harmonics generated by the interaction between an ultrashort laser pulse and a gas jet. The time compensation allows one to exploit the femtosecond scale duration of the harmonics both to have high intensity and to reach an unprecedented temporal resolution for pump and probe experiments. Because two gratings have to be used for time compensation, the high diffraction efficiency becomes an essential requirement, which can be fulfilled by the conical diffraction mounting. Measurements recently accomplished at the Bending Magnet for Emission Absorption and Reflectivity (BEAR) beam line (ELETTRA Synchrotron, Trieste, Italy) for three gratings in the 1090  nm region are reported here that show a peak efficiency of as much as 0.7 in the first order. A model computing the electromagnetic propagation and the grating efficiency, implemented and tested with the experimental data, permits the study and design of rather complex systems operating in the conical mounting. Basic physical principles and mathematical aspects of the model are discussed here.

© 2006 Optical Society of America

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    [CrossRef]
  2. A. Rundquist, C. G. Durfee, Z.-G Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, "Phase-matched generation of coherent soft x-rays," Science 280, 1412-1415 (1998).
    [CrossRef] [PubMed]
  3. M. Bellini, C. Lynga, A. Tozzi, M. B. Gaarde, T. W. Hänsch, A. L'Huillier, and C. G. Walstrom, "Temporal coherence of ultrashort high-order harmonic pulses," Phys. Rev. Lett. 81, 297-300 (1998).
    [CrossRef]
  4. M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, "High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime," Phys. Rev. Lett. 88, 033902 (2002).
    [CrossRef] [PubMed]
  5. M. Protopapas, C. H. Keitel, and P. L. Knight, "Atomic physics with super-high intensity lasers," Rep. Prog. Phys. 60, 389-486 (1997).
    [CrossRef]
  6. M. Lewenstein, P. Salieres, A. L'Huillier, and P. Antoine, "Study of the spatial and temporal coherence of high order harmonics," in Advances in Atomic, Molecular and Optical Physics, B. Bederson and H. Walther, eds. (Academic, London, 1998), Vol. 41.
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    [CrossRef]
  10. L. Poletto and G. Tondello, "Time-compensated EUV and soft x-ray monochromator for ultrashort high-order harmonic pulses," Pure Appl. Opt. 3, 374-379 (2001).
    [CrossRef]
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    [CrossRef]
  13. P. Villoresi, S. Bonora, M. Pascolini, L. Poletto, G. Tondello, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, and S. De Silvestri, "Optimization of high-order harmonic generation by adaptive control of sub-10 fs pulse wavefront," Opt. Lett. 29, 207-209 (2004).
    [CrossRef] [PubMed]
  14. W. Cash and R. Kohnert, "Very high x-ray efficiency from a blazed grating," Appl. Opt. 21, 17-18 (1982).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  16. R. McEntaffer, S. Osterman, W. Cash, J. Gilchrist, J. Flamand, B. Touzet, F. Bonnemason, and C. Brach, "X-ray performance of gratings in the extreme off-plane mount," in Optics for EUV, X-Ray, and Gamma-Ray Astronomy, O. Citterio and S. L. O'Dell, eds., Proc. SPIE 5168, 492-498 (2004).
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    [CrossRef]
  19. C. Altucci, R. Bruzzese, C. de Lisio, V. Tosa, P. Barbiero, L. Poletto, G. Tondello, P. Villoresi, M. Nisoli, S. Stagira, G. Cerullo, S. De Silvestri, and O. Svelto, "Beam divergence of high-order harmonics generated in the few-optical cycle regime," J. Phys. IV 11, 351-354 (2001).
    [CrossRef]
  20. L. Poletto, G. Tondello, and P. Villoresi, "High-order laser harmonics detection in the EUV and soft x-ray spectral regions," Rev. Sci. Instrum. 72, 2868-2874 (2001).
    [CrossRef]
  21. See the detailed description of the BEAR beam line at the ELETTRA Synchrotron in Trieste, Italy, available at http://www.elettra.trieste.it/experiments/beamlines/bear/index.html.
  22. M. Nevière, in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, 1980).
  23. B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50-30000 eV, Z = 1-92," At. Data Nucl. Data Tables 54, 181-342 (1993).
    [CrossRef]
  24. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972).

2004 (3)

L. Poletto, S. Bonora, M. Pascolini, and P. Villoresi, "Time-frequency analysis of single-shot high-order harmonic spectra," Rev. Sci. Instrum. 75, 4413-4418 (2004).
[CrossRef]

L. Poletto, "Time-compensated grazing-incidence monochromator for extreme-ultraviolet and soft x-ray high-order harmonics," Appl. Phys. B 78, 1013-1016 (2004).
[CrossRef]

P. Villoresi, S. Bonora, M. Pascolini, L. Poletto, G. Tondello, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, and S. De Silvestri, "Optimization of high-order harmonic generation by adaptive control of sub-10 fs pulse wavefront," Opt. Lett. 29, 207-209 (2004).
[CrossRef] [PubMed]

2002 (2)

M. Wieland, R. Frueke, T. Wilhein, C. Spielmann, M. Pohl, and U. Kleineberg, "Submicron extreme ultraviolet imaging using high-harmonic radiation," Appl. Phys. Lett. 81, 2520-2522 (2002).
[CrossRef]

M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, "High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime," Phys. Rev. Lett. 88, 033902 (2002).
[CrossRef] [PubMed]

2001 (3)

C. Altucci, R. Bruzzese, C. de Lisio, V. Tosa, P. Barbiero, L. Poletto, G. Tondello, P. Villoresi, M. Nisoli, S. Stagira, G. Cerullo, S. De Silvestri, and O. Svelto, "Beam divergence of high-order harmonics generated in the few-optical cycle regime," J. Phys. IV 11, 351-354 (2001).
[CrossRef]

L. Poletto, G. Tondello, and P. Villoresi, "High-order laser harmonics detection in the EUV and soft x-ray spectral regions," Rev. Sci. Instrum. 72, 2868-2874 (2001).
[CrossRef]

L. Poletto and G. Tondello, "Time-compensated EUV and soft x-ray monochromator for ultrashort high-order harmonic pulses," Pure Appl. Opt. 3, 374-379 (2001).
[CrossRef]

2000 (1)

T. Brabec and F. Krausz, "Intense few-cycle laser fields: frontiers of nonlinear optics," Rev. Mod. Phys. 72, 545-591 (2000).
[CrossRef]

1999 (1)

1998 (2)

A. Rundquist, C. G. Durfee, Z.-G Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, "Phase-matched generation of coherent soft x-rays," Science 280, 1412-1415 (1998).
[CrossRef] [PubMed]

M. Bellini, C. Lynga, A. Tozzi, M. B. Gaarde, T. W. Hänsch, A. L'Huillier, and C. G. Walstrom, "Temporal coherence of ultrashort high-order harmonic pulses," Phys. Rev. Lett. 81, 297-300 (1998).
[CrossRef]

1997 (1)

M. Protopapas, C. H. Keitel, and P. L. Knight, "Atomic physics with super-high intensity lasers," Rep. Prog. Phys. 60, 389-486 (1997).
[CrossRef]

1993 (1)

B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50-30000 eV, Z = 1-92," At. Data Nucl. Data Tables 54, 181-342 (1993).
[CrossRef]

1982 (2)

1981 (1)

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972).

Altucci, C.

M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, "High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime," Phys. Rev. Lett. 88, 033902 (2002).
[CrossRef] [PubMed]

C. Altucci, R. Bruzzese, C. de Lisio, V. Tosa, P. Barbiero, L. Poletto, G. Tondello, P. Villoresi, M. Nisoli, S. Stagira, G. Cerullo, S. De Silvestri, and O. Svelto, "Beam divergence of high-order harmonics generated in the few-optical cycle regime," J. Phys. IV 11, 351-354 (2001).
[CrossRef]

Antoine, P.

M. Lewenstein, P. Salieres, A. L'Huillier, and P. Antoine, "Study of the spatial and temporal coherence of high order harmonics," in Advances in Atomic, Molecular and Optical Physics, B. Bederson and H. Walther, eds. (Academic, London, 1998), Vol. 41.

Backus, S.

A. Rundquist, C. G. Durfee, Z.-G Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, "Phase-matched generation of coherent soft x-rays," Science 280, 1412-1415 (1998).
[CrossRef] [PubMed]

Barbiero, P.

C. Altucci, R. Bruzzese, C. de Lisio, V. Tosa, P. Barbiero, L. Poletto, G. Tondello, P. Villoresi, M. Nisoli, S. Stagira, G. Cerullo, S. De Silvestri, and O. Svelto, "Beam divergence of high-order harmonics generated in the few-optical cycle regime," J. Phys. IV 11, 351-354 (2001).
[CrossRef]

Bellini, M.

M. Bellini, C. Lynga, A. Tozzi, M. B. Gaarde, T. W. Hänsch, A. L'Huillier, and C. G. Walstrom, "Temporal coherence of ultrashort high-order harmonic pulses," Phys. Rev. Lett. 81, 297-300 (1998).
[CrossRef]

Bonnemason, F.

R. McEntaffer, S. Osterman, W. Cash, J. Gilchrist, J. Flamand, B. Touzet, F. Bonnemason, and C. Brach, "X-ray performance of gratings in the extreme off-plane mount," in Optics for EUV, X-Ray, and Gamma-Ray Astronomy, O. Citterio and S. L. O'Dell, eds., Proc. SPIE 5168, 492-498 (2004).

Bonora, S.

Brabec, T.

T. Brabec and F. Krausz, "Intense few-cycle laser fields: frontiers of nonlinear optics," Rev. Mod. Phys. 72, 545-591 (2000).
[CrossRef]

Brach, C.

R. McEntaffer, S. Osterman, W. Cash, J. Gilchrist, J. Flamand, B. Touzet, F. Bonnemason, and C. Brach, "X-ray performance of gratings in the extreme off-plane mount," in Optics for EUV, X-Ray, and Gamma-Ray Astronomy, O. Citterio and S. L. O'Dell, eds., Proc. SPIE 5168, 492-498 (2004).

Bruzzese, R.

M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, "High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime," Phys. Rev. Lett. 88, 033902 (2002).
[CrossRef] [PubMed]

C. Altucci, R. Bruzzese, C. de Lisio, V. Tosa, P. Barbiero, L. Poletto, G. Tondello, P. Villoresi, M. Nisoli, S. Stagira, G. Cerullo, S. De Silvestri, and O. Svelto, "Beam divergence of high-order harmonics generated in the few-optical cycle regime," J. Phys. IV 11, 351-354 (2001).
[CrossRef]

Cash, W.

W. Cash, "Echelle spectrographs at grazing incidence," Appl. Opt. 21, 710-717 (1982).
[CrossRef] [PubMed]

W. Cash and R. Kohnert, "Very high x-ray efficiency from a blazed grating," Appl. Opt. 21, 17-18 (1982).
[CrossRef] [PubMed]

R. McEntaffer, S. Osterman, W. Cash, J. Gilchrist, J. Flamand, B. Touzet, F. Bonnemason, and C. Brach, "X-ray performance of gratings in the extreme off-plane mount," in Optics for EUV, X-Ray, and Gamma-Ray Astronomy, O. Citterio and S. L. O'Dell, eds., Proc. SPIE 5168, 492-498 (2004).

Cerullo, G.

M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, "High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime," Phys. Rev. Lett. 88, 033902 (2002).
[CrossRef] [PubMed]

C. Altucci, R. Bruzzese, C. de Lisio, V. Tosa, P. Barbiero, L. Poletto, G. Tondello, P. Villoresi, M. Nisoli, S. Stagira, G. Cerullo, S. De Silvestri, and O. Svelto, "Beam divergence of high-order harmonics generated in the few-optical cycle regime," J. Phys. IV 11, 351-354 (2001).
[CrossRef]

Chang, Z.-G

A. Rundquist, C. G. Durfee, Z.-G Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, "Phase-matched generation of coherent soft x-rays," Science 280, 1412-1415 (1998).
[CrossRef] [PubMed]

Davis, J. C.

B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50-30000 eV, Z = 1-92," At. Data Nucl. Data Tables 54, 181-342 (1993).
[CrossRef]

de Lisio, C.

M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, "High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime," Phys. Rev. Lett. 88, 033902 (2002).
[CrossRef] [PubMed]

C. Altucci, R. Bruzzese, C. de Lisio, V. Tosa, P. Barbiero, L. Poletto, G. Tondello, P. Villoresi, M. Nisoli, S. Stagira, G. Cerullo, S. De Silvestri, and O. Svelto, "Beam divergence of high-order harmonics generated in the few-optical cycle regime," J. Phys. IV 11, 351-354 (2001).
[CrossRef]

De Silvestri, S.

P. Villoresi, S. Bonora, M. Pascolini, L. Poletto, G. Tondello, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, and S. De Silvestri, "Optimization of high-order harmonic generation by adaptive control of sub-10 fs pulse wavefront," Opt. Lett. 29, 207-209 (2004).
[CrossRef] [PubMed]

M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, "High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime," Phys. Rev. Lett. 88, 033902 (2002).
[CrossRef] [PubMed]

C. Altucci, R. Bruzzese, C. de Lisio, V. Tosa, P. Barbiero, L. Poletto, G. Tondello, P. Villoresi, M. Nisoli, S. Stagira, G. Cerullo, S. De Silvestri, and O. Svelto, "Beam divergence of high-order harmonics generated in the few-optical cycle regime," J. Phys. IV 11, 351-354 (2001).
[CrossRef]

Durfee, C. G.

A. Rundquist, C. G. Durfee, Z.-G Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, "Phase-matched generation of coherent soft x-rays," Science 280, 1412-1415 (1998).
[CrossRef] [PubMed]

Ederer, D. L.

J. A. R. Samson and D. L. Ederer, Vacuum Ultraviolet Spectroscopy II (Academic, 1998).

Flamand, J.

R. McEntaffer, S. Osterman, W. Cash, J. Gilchrist, J. Flamand, B. Touzet, F. Bonnemason, and C. Brach, "X-ray performance of gratings in the extreme off-plane mount," in Optics for EUV, X-Ray, and Gamma-Ray Astronomy, O. Citterio and S. L. O'Dell, eds., Proc. SPIE 5168, 492-498 (2004).

Frueke, R.

M. Wieland, R. Frueke, T. Wilhein, C. Spielmann, M. Pohl, and U. Kleineberg, "Submicron extreme ultraviolet imaging using high-harmonic radiation," Appl. Phys. Lett. 81, 2520-2522 (2002).
[CrossRef]

Gaarde, M. B.

M. Bellini, C. Lynga, A. Tozzi, M. B. Gaarde, T. W. Hänsch, A. L'Huillier, and C. G. Walstrom, "Temporal coherence of ultrashort high-order harmonic pulses," Phys. Rev. Lett. 81, 297-300 (1998).
[CrossRef]

Gilchrist, J.

R. McEntaffer, S. Osterman, W. Cash, J. Gilchrist, J. Flamand, B. Touzet, F. Bonnemason, and C. Brach, "X-ray performance of gratings in the extreme off-plane mount," in Optics for EUV, X-Ray, and Gamma-Ray Astronomy, O. Citterio and S. L. O'Dell, eds., Proc. SPIE 5168, 492-498 (2004).

Gullikson, E. M.

B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50-30000 eV, Z = 1-92," At. Data Nucl. Data Tables 54, 181-342 (1993).
[CrossRef]

Hänsch, T. W.

M. Bellini, C. Lynga, A. Tozzi, M. B. Gaarde, T. W. Hänsch, A. L'Huillier, and C. G. Walstrom, "Temporal coherence of ultrashort high-order harmonic pulses," Phys. Rev. Lett. 81, 297-300 (1998).
[CrossRef]

Henke, B. L.

B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50-30000 eV, Z = 1-92," At. Data Nucl. Data Tables 54, 181-342 (1993).
[CrossRef]

Herne, C.

A. Rundquist, C. G. Durfee, Z.-G Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, "Phase-matched generation of coherent soft x-rays," Science 280, 1412-1415 (1998).
[CrossRef] [PubMed]

Kapteyn, H. C.

A. Rundquist, C. G. Durfee, Z.-G Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, "Phase-matched generation of coherent soft x-rays," Science 280, 1412-1415 (1998).
[CrossRef] [PubMed]

Keitel, C. H.

M. Protopapas, C. H. Keitel, and P. L. Knight, "Atomic physics with super-high intensity lasers," Rep. Prog. Phys. 60, 389-486 (1997).
[CrossRef]

Kleineberg, U.

M. Wieland, R. Frueke, T. Wilhein, C. Spielmann, M. Pohl, and U. Kleineberg, "Submicron extreme ultraviolet imaging using high-harmonic radiation," Appl. Phys. Lett. 81, 2520-2522 (2002).
[CrossRef]

Knight, P. L.

M. Protopapas, C. H. Keitel, and P. L. Knight, "Atomic physics with super-high intensity lasers," Rep. Prog. Phys. 60, 389-486 (1997).
[CrossRef]

Kohnert, R.

Krausz, F.

T. Brabec and F. Krausz, "Intense few-cycle laser fields: frontiers of nonlinear optics," Rev. Mod. Phys. 72, 545-591 (2000).
[CrossRef]

Lewenstein, M.

M. Lewenstein, P. Salieres, A. L'Huillier, and P. Antoine, "Study of the spatial and temporal coherence of high order harmonics," in Advances in Atomic, Molecular and Optical Physics, B. Bederson and H. Walther, eds. (Academic, London, 1998), Vol. 41.

L'Huillier, A.

M. Bellini, C. Lynga, A. Tozzi, M. B. Gaarde, T. W. Hänsch, A. L'Huillier, and C. G. Walstrom, "Temporal coherence of ultrashort high-order harmonic pulses," Phys. Rev. Lett. 81, 297-300 (1998).
[CrossRef]

M. Lewenstein, P. Salieres, A. L'Huillier, and P. Antoine, "Study of the spatial and temporal coherence of high order harmonics," in Advances in Atomic, Molecular and Optical Physics, B. Bederson and H. Walther, eds. (Academic, London, 1998), Vol. 41.

Lynga, C.

M. Bellini, C. Lynga, A. Tozzi, M. B. Gaarde, T. W. Hänsch, A. L'Huillier, and C. G. Walstrom, "Temporal coherence of ultrashort high-order harmonic pulses," Phys. Rev. Lett. 81, 297-300 (1998).
[CrossRef]

McEntaffer, R.

R. McEntaffer, S. Osterman, W. Cash, J. Gilchrist, J. Flamand, B. Touzet, F. Bonnemason, and C. Brach, "X-ray performance of gratings in the extreme off-plane mount," in Optics for EUV, X-Ray, and Gamma-Ray Astronomy, O. Citterio and S. L. O'Dell, eds., Proc. SPIE 5168, 492-498 (2004).

Murnane, M. M.

A. Rundquist, C. G. Durfee, Z.-G Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, "Phase-matched generation of coherent soft x-rays," Science 280, 1412-1415 (1998).
[CrossRef] [PubMed]

Nevière, M.

M. Nevière, in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, 1980).

Nisoli, M.

P. Villoresi, S. Bonora, M. Pascolini, L. Poletto, G. Tondello, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, and S. De Silvestri, "Optimization of high-order harmonic generation by adaptive control of sub-10 fs pulse wavefront," Opt. Lett. 29, 207-209 (2004).
[CrossRef] [PubMed]

M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, "High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime," Phys. Rev. Lett. 88, 033902 (2002).
[CrossRef] [PubMed]

C. Altucci, R. Bruzzese, C. de Lisio, V. Tosa, P. Barbiero, L. Poletto, G. Tondello, P. Villoresi, M. Nisoli, S. Stagira, G. Cerullo, S. De Silvestri, and O. Svelto, "Beam divergence of high-order harmonics generated in the few-optical cycle regime," J. Phys. IV 11, 351-354 (2001).
[CrossRef]

Osterman, S.

R. McEntaffer, S. Osterman, W. Cash, J. Gilchrist, J. Flamand, B. Touzet, F. Bonnemason, and C. Brach, "X-ray performance of gratings in the extreme off-plane mount," in Optics for EUV, X-Ray, and Gamma-Ray Astronomy, O. Citterio and S. L. O'Dell, eds., Proc. SPIE 5168, 492-498 (2004).

Pascolini, M.

P. Villoresi, S. Bonora, M. Pascolini, L. Poletto, G. Tondello, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, and S. De Silvestri, "Optimization of high-order harmonic generation by adaptive control of sub-10 fs pulse wavefront," Opt. Lett. 29, 207-209 (2004).
[CrossRef] [PubMed]

L. Poletto, S. Bonora, M. Pascolini, and P. Villoresi, "Time-frequency analysis of single-shot high-order harmonic spectra," Rev. Sci. Instrum. 75, 4413-4418 (2004).
[CrossRef]

M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, "High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime," Phys. Rev. Lett. 88, 033902 (2002).
[CrossRef] [PubMed]

Pohl, M.

M. Wieland, R. Frueke, T. Wilhein, C. Spielmann, M. Pohl, and U. Kleineberg, "Submicron extreme ultraviolet imaging using high-harmonic radiation," Appl. Phys. Lett. 81, 2520-2522 (2002).
[CrossRef]

Poletto, L.

P. Villoresi, S. Bonora, M. Pascolini, L. Poletto, G. Tondello, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, and S. De Silvestri, "Optimization of high-order harmonic generation by adaptive control of sub-10 fs pulse wavefront," Opt. Lett. 29, 207-209 (2004).
[CrossRef] [PubMed]

L. Poletto, S. Bonora, M. Pascolini, and P. Villoresi, "Time-frequency analysis of single-shot high-order harmonic spectra," Rev. Sci. Instrum. 75, 4413-4418 (2004).
[CrossRef]

L. Poletto, "Time-compensated grazing-incidence monochromator for extreme-ultraviolet and soft x-ray high-order harmonics," Appl. Phys. B 78, 1013-1016 (2004).
[CrossRef]

M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, "High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime," Phys. Rev. Lett. 88, 033902 (2002).
[CrossRef] [PubMed]

C. Altucci, R. Bruzzese, C. de Lisio, V. Tosa, P. Barbiero, L. Poletto, G. Tondello, P. Villoresi, M. Nisoli, S. Stagira, G. Cerullo, S. De Silvestri, and O. Svelto, "Beam divergence of high-order harmonics generated in the few-optical cycle regime," J. Phys. IV 11, 351-354 (2001).
[CrossRef]

L. Poletto, G. Tondello, and P. Villoresi, "High-order laser harmonics detection in the EUV and soft x-ray spectral regions," Rev. Sci. Instrum. 72, 2868-2874 (2001).
[CrossRef]

L. Poletto and G. Tondello, "Time-compensated EUV and soft x-ray monochromator for ultrashort high-order harmonic pulses," Pure Appl. Opt. 3, 374-379 (2001).
[CrossRef]

Priori, E.

M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, "High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime," Phys. Rev. Lett. 88, 033902 (2002).
[CrossRef] [PubMed]

Protopapas, M.

M. Protopapas, C. H. Keitel, and P. L. Knight, "Atomic physics with super-high intensity lasers," Rep. Prog. Phys. 60, 389-486 (1997).
[CrossRef]

Rundquist, A.

A. Rundquist, C. G. Durfee, Z.-G Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, "Phase-matched generation of coherent soft x-rays," Science 280, 1412-1415 (1998).
[CrossRef] [PubMed]

Salieres, P.

M. Lewenstein, P. Salieres, A. L'Huillier, and P. Antoine, "Study of the spatial and temporal coherence of high order harmonics," in Advances in Atomic, Molecular and Optical Physics, B. Bederson and H. Walther, eds. (Academic, London, 1998), Vol. 41.

Samson, J. A. R.

J. A. R. Samson and D. L. Ederer, Vacuum Ultraviolet Spectroscopy II (Academic, 1998).

Sansone, G.

P. Villoresi, S. Bonora, M. Pascolini, L. Poletto, G. Tondello, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, and S. De Silvestri, "Optimization of high-order harmonic generation by adaptive control of sub-10 fs pulse wavefront," Opt. Lett. 29, 207-209 (2004).
[CrossRef] [PubMed]

M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, "High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime," Phys. Rev. Lett. 88, 033902 (2002).
[CrossRef] [PubMed]

Spielmann, C.

M. Wieland, R. Frueke, T. Wilhein, C. Spielmann, M. Pohl, and U. Kleineberg, "Submicron extreme ultraviolet imaging using high-harmonic radiation," Appl. Phys. Lett. 81, 2520-2522 (2002).
[CrossRef]

Spiller, E.

E. Spiller, Soft X-Ray Optics (SPIE Press, 1994).
[CrossRef]

Stagira, S.

P. Villoresi, S. Bonora, M. Pascolini, L. Poletto, G. Tondello, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, and S. De Silvestri, "Optimization of high-order harmonic generation by adaptive control of sub-10 fs pulse wavefront," Opt. Lett. 29, 207-209 (2004).
[CrossRef] [PubMed]

M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, "High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime," Phys. Rev. Lett. 88, 033902 (2002).
[CrossRef] [PubMed]

C. Altucci, R. Bruzzese, C. de Lisio, V. Tosa, P. Barbiero, L. Poletto, G. Tondello, P. Villoresi, M. Nisoli, S. Stagira, G. Cerullo, S. De Silvestri, and O. Svelto, "Beam divergence of high-order harmonics generated in the few-optical cycle regime," J. Phys. IV 11, 351-354 (2001).
[CrossRef]

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972).

Svelto, O.

C. Altucci, R. Bruzzese, C. de Lisio, V. Tosa, P. Barbiero, L. Poletto, G. Tondello, P. Villoresi, M. Nisoli, S. Stagira, G. Cerullo, S. De Silvestri, and O. Svelto, "Beam divergence of high-order harmonics generated in the few-optical cycle regime," J. Phys. IV 11, 351-354 (2001).
[CrossRef]

Tondello, G.

P. Villoresi, S. Bonora, M. Pascolini, L. Poletto, G. Tondello, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, and S. De Silvestri, "Optimization of high-order harmonic generation by adaptive control of sub-10 fs pulse wavefront," Opt. Lett. 29, 207-209 (2004).
[CrossRef] [PubMed]

M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, "High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime," Phys. Rev. Lett. 88, 033902 (2002).
[CrossRef] [PubMed]

C. Altucci, R. Bruzzese, C. de Lisio, V. Tosa, P. Barbiero, L. Poletto, G. Tondello, P. Villoresi, M. Nisoli, S. Stagira, G. Cerullo, S. De Silvestri, and O. Svelto, "Beam divergence of high-order harmonics generated in the few-optical cycle regime," J. Phys. IV 11, 351-354 (2001).
[CrossRef]

L. Poletto, G. Tondello, and P. Villoresi, "High-order laser harmonics detection in the EUV and soft x-ray spectral regions," Rev. Sci. Instrum. 72, 2868-2874 (2001).
[CrossRef]

L. Poletto and G. Tondello, "Time-compensated EUV and soft x-ray monochromator for ultrashort high-order harmonic pulses," Pure Appl. Opt. 3, 374-379 (2001).
[CrossRef]

Tosa, V.

C. Altucci, R. Bruzzese, C. de Lisio, V. Tosa, P. Barbiero, L. Poletto, G. Tondello, P. Villoresi, M. Nisoli, S. Stagira, G. Cerullo, S. De Silvestri, and O. Svelto, "Beam divergence of high-order harmonics generated in the few-optical cycle regime," J. Phys. IV 11, 351-354 (2001).
[CrossRef]

Touzet, B.

R. McEntaffer, S. Osterman, W. Cash, J. Gilchrist, J. Flamand, B. Touzet, F. Bonnemason, and C. Brach, "X-ray performance of gratings in the extreme off-plane mount," in Optics for EUV, X-Ray, and Gamma-Ray Astronomy, O. Citterio and S. L. O'Dell, eds., Proc. SPIE 5168, 492-498 (2004).

Tozzi, A.

M. Bellini, C. Lynga, A. Tozzi, M. B. Gaarde, T. W. Hänsch, A. L'Huillier, and C. G. Walstrom, "Temporal coherence of ultrashort high-order harmonic pulses," Phys. Rev. Lett. 81, 297-300 (1998).
[CrossRef]

Villoresi, P.

L. Poletto, S. Bonora, M. Pascolini, and P. Villoresi, "Time-frequency analysis of single-shot high-order harmonic spectra," Rev. Sci. Instrum. 75, 4413-4418 (2004).
[CrossRef]

P. Villoresi, S. Bonora, M. Pascolini, L. Poletto, G. Tondello, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, and S. De Silvestri, "Optimization of high-order harmonic generation by adaptive control of sub-10 fs pulse wavefront," Opt. Lett. 29, 207-209 (2004).
[CrossRef] [PubMed]

M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, "High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime," Phys. Rev. Lett. 88, 033902 (2002).
[CrossRef] [PubMed]

C. Altucci, R. Bruzzese, C. de Lisio, V. Tosa, P. Barbiero, L. Poletto, G. Tondello, P. Villoresi, M. Nisoli, S. Stagira, G. Cerullo, S. De Silvestri, and O. Svelto, "Beam divergence of high-order harmonics generated in the few-optical cycle regime," J. Phys. IV 11, 351-354 (2001).
[CrossRef]

L. Poletto, G. Tondello, and P. Villoresi, "High-order laser harmonics detection in the EUV and soft x-ray spectral regions," Rev. Sci. Instrum. 72, 2868-2874 (2001).
[CrossRef]

P. Villoresi, "Compensation of optical path lengths in extreme-ultraviolet and soft-x-ray monochromators for ultrafast pulses," Appl. Opt. 38, 6040-6049 (1999).
[CrossRef]

Visser, H.

Vozzi, C.

Walstrom, C. G.

M. Bellini, C. Lynga, A. Tozzi, M. B. Gaarde, T. W. Hänsch, A. L'Huillier, and C. G. Walstrom, "Temporal coherence of ultrashort high-order harmonic pulses," Phys. Rev. Lett. 81, 297-300 (1998).
[CrossRef]

Werner, W.

Wieland, M.

M. Wieland, R. Frueke, T. Wilhein, C. Spielmann, M. Pohl, and U. Kleineberg, "Submicron extreme ultraviolet imaging using high-harmonic radiation," Appl. Phys. Lett. 81, 2520-2522 (2002).
[CrossRef]

Wilhein, T.

M. Wieland, R. Frueke, T. Wilhein, C. Spielmann, M. Pohl, and U. Kleineberg, "Submicron extreme ultraviolet imaging using high-harmonic radiation," Appl. Phys. Lett. 81, 2520-2522 (2002).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. B (1)

L. Poletto, "Time-compensated grazing-incidence monochromator for extreme-ultraviolet and soft x-ray high-order harmonics," Appl. Phys. B 78, 1013-1016 (2004).
[CrossRef]

Appl. Phys. Lett. (1)

M. Wieland, R. Frueke, T. Wilhein, C. Spielmann, M. Pohl, and U. Kleineberg, "Submicron extreme ultraviolet imaging using high-harmonic radiation," Appl. Phys. Lett. 81, 2520-2522 (2002).
[CrossRef]

At. Data Nucl. Data Tables (1)

B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50-30000 eV, Z = 1-92," At. Data Nucl. Data Tables 54, 181-342 (1993).
[CrossRef]

J. Phys. IV (1)

C. Altucci, R. Bruzzese, C. de Lisio, V. Tosa, P. Barbiero, L. Poletto, G. Tondello, P. Villoresi, M. Nisoli, S. Stagira, G. Cerullo, S. De Silvestri, and O. Svelto, "Beam divergence of high-order harmonics generated in the few-optical cycle regime," J. Phys. IV 11, 351-354 (2001).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (2)

M. Bellini, C. Lynga, A. Tozzi, M. B. Gaarde, T. W. Hänsch, A. L'Huillier, and C. G. Walstrom, "Temporal coherence of ultrashort high-order harmonic pulses," Phys. Rev. Lett. 81, 297-300 (1998).
[CrossRef]

M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, "High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime," Phys. Rev. Lett. 88, 033902 (2002).
[CrossRef] [PubMed]

Pure Appl. Opt. (1)

L. Poletto and G. Tondello, "Time-compensated EUV and soft x-ray monochromator for ultrashort high-order harmonic pulses," Pure Appl. Opt. 3, 374-379 (2001).
[CrossRef]

Rep. Prog. Phys. (1)

M. Protopapas, C. H. Keitel, and P. L. Knight, "Atomic physics with super-high intensity lasers," Rep. Prog. Phys. 60, 389-486 (1997).
[CrossRef]

Rev. Mod. Phys. (1)

T. Brabec and F. Krausz, "Intense few-cycle laser fields: frontiers of nonlinear optics," Rev. Mod. Phys. 72, 545-591 (2000).
[CrossRef]

Rev. Sci. Instrum. (2)

L. Poletto, G. Tondello, and P. Villoresi, "High-order laser harmonics detection in the EUV and soft x-ray spectral regions," Rev. Sci. Instrum. 72, 2868-2874 (2001).
[CrossRef]

L. Poletto, S. Bonora, M. Pascolini, and P. Villoresi, "Time-frequency analysis of single-shot high-order harmonic spectra," Rev. Sci. Instrum. 75, 4413-4418 (2004).
[CrossRef]

Science (1)

A. Rundquist, C. G. Durfee, Z.-G Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, "Phase-matched generation of coherent soft x-rays," Science 280, 1412-1415 (1998).
[CrossRef] [PubMed]

Other (7)

J. A. R. Samson and D. L. Ederer, Vacuum Ultraviolet Spectroscopy II (Academic, 1998).

M. Lewenstein, P. Salieres, A. L'Huillier, and P. Antoine, "Study of the spatial and temporal coherence of high order harmonics," in Advances in Atomic, Molecular and Optical Physics, B. Bederson and H. Walther, eds. (Academic, London, 1998), Vol. 41.

E. Spiller, Soft X-Ray Optics (SPIE Press, 1994).
[CrossRef]

R. McEntaffer, S. Osterman, W. Cash, J. Gilchrist, J. Flamand, B. Touzet, F. Bonnemason, and C. Brach, "X-ray performance of gratings in the extreme off-plane mount," in Optics for EUV, X-Ray, and Gamma-Ray Astronomy, O. Citterio and S. L. O'Dell, eds., Proc. SPIE 5168, 492-498 (2004).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972).

See the detailed description of the BEAR beam line at the ELETTRA Synchrotron in Trieste, Italy, available at http://www.elettra.trieste.it/experiments/beamlines/bear/index.html.

M. Nevière, in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, 1980).

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Figures (7)

Fig. 1
Fig. 1

Geometry of the conical diffraction.

Fig. 2
Fig. 2

Monochromator with a plane grating in conical diffraction illuminated in parallel light. (a) Grating on blaze at each wavelength: We perform the wavelength scanning by changing the altitude and keeping the azimuth constant. (b) Grating on blaze at one wavelength: We perform the wavelength scanning by changing the azimuth and keeping the altitude constant.

Fig. 3
Fig. 3

Schematic of the time-delay-compensated monochromator for HHs with two toroidal gratings in conical diffraction.

Fig. 4
Fig. 4

Schematic of the time-delay-compensated monochromator for HHs with four toroidal mirrors and two plane gratings in conical diffraction. Ti:Sa, Ti:sapphire.

Fig. 5
Fig. 5

Efficiency of the three tested gratings in conical diffraction mounting.

Fig. 6
Fig. 6

Efficiency of grating 2 in the classic diffraction mounting (α + β = 165°).

Fig. 7
Fig. 7

Conical diffraction in the plane of the groove profile.

Tables (3)

Tables Icon

Table 1 Characteristics of the Time-Delay-Compensated Monochromator

Tables Icon

Table 2 Optical Performance and Analysis of the Compensation of Optical Path Lengths for the Time-Delay-Compensated Monochromator a

Tables Icon

Table 3 Gratings Tested at the BEAR

Equations (37)

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

α = k i sin θ sin φ ,
β = k i cos θ sin φ ,
γ = k i cos φ .
k x m = α m = α + m K ,
k y m = β m = [ ( k i     2 k z     2 ) k x m 2 ] 1 / 2 ,
k z m = γ m γ .
sin φ ( sin θ + sin θ m ) = m λ σ .
θ + θ m = 2 δ .
θ = θ m = δ ,
2 sin φ sin δ = m λ σ .
2 sin φ sin θ m = m λ σ ,
e m = sin θ m sin θ ε 0 | E z m | 2 + μ 0 | H z m | 2 ε 0 | E z     i | 2 + μ 0 | H z     i | 2 ,
e m = e m , TE cos 2 ζ + e m , TM sin 2 ζ .
U i , j = E z j = { 1 j = i , i n 0 otherwise ,
U i , j = H z j = { 1 j = i N , i > n 0 otherwise .
ψ ¯ = ψ 1 U ¯ 1 + + ψ N U ¯ N .
ψ ¯ t ( 0 ) = ( M A ) 1 ψ ¯ i ( a ) ,
ψ ¯ d ( a ) = M B ψ ¯ t ( 0 ) = M B ( M A ) 1 ψ ¯ i ( a ) .
ε ( x , y ) = n = + ε n ( y ) exp ( i n K x ) ,
u d ( x , y ) = n = + R ( n ) exp ( j α n x + j β n 1 y ) , y > a , u t ( x , y ) = n = + T ( n ) exp ( j α n x j β n 2 y ) , y < 0 ,
sin θ n 1 = sin θ + n λ / d .
E y n ( y ) = 1 ω m [ ε 1 ( y ) ] n m [ γ H x m ( y ) α m H z m ( y ) ] ,
H y n ( y ) = 1 ω μ 0 [ α n E z n ( y ) γ E x n ( y ) ] ,
E z n y ( y ) = m A n m ( y ) H z m ( y ) + B n m ( y ) H x m ( y ) ,
E x n y ( y ) = m C n m ( y ) H z m ( y ) + D n m ( y ) H x m ( y ) ,
H z n y ( y ) = m E n m ( y ) E z m ( y ) + F n m ( y ) E x m ( y ) ,
H x n y ( y ) = m G n m ( y ) E z m ( y ) + H n m ( y ) E x m ( y ) ,
A n m ( y ) = j ω [ 1 ε ( y ) ] n m γ α m ,
B n m ( y ) = j ω [ 1 ε ( y ) ] n m γ 2 j ω μ 0 δ n m ,
C n m ( y ) = j ω [ 1 ε ( y ) ] n m α n α m j ω μ 0 δ n m ,
D n m ( y ) = j ω [ 1 ε ( y ) ] n m γ α n ,
E n m ( y ) = j ω μ 0 γ α n δ n m ,
F n m ( y ) = j ω [ ε ( y ) ] n m j ω μ 0 γ 2 δ n m ,
G n m ( y ) = j ω [ ε ( y ) ] n m + j ω μ 0 α n     2 δ n m ,
H n m ( y ) = j ω μ 0 γ α n δ n m .
ψ ¯ y ( y ) = V ( y ) ψ ¯ ( y ) ,
V ( y ) = [ 0 0 A n m B n m 0 0 C n m D n m E n m F n m 0 0 G n m H n m 0 0 ] ,     n , m = 1 : N .

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