Abstract

High order harmonic generation (HHG) has shown its impact on several applications in Attosecond Science and Atomic and Molecular Physics. Owing to the complexity of the experimental setup for the generation and characterization of harmonics, as well as to the large computational costs of numerical modelling, HHG is generally performed and modelled in collinear geometry. Recently, several experiments have been performed exploiting non-collinear geometry, such as HHG in a grating of excited molecules created by crossing beams. In such studies, harmonics were observed at propagation directions different from those of the driving pulses; moreover the scattered harmonics were angularly dispersed.

In this work we report on a new regime of HHG driven by multiple beams, where the harmonics are generated by three synchronized, intense laser pulses organized in a non-planar geometry. Although the configuration we explore is well within the strong-field regime, the scattered harmonics we observe are not angularly dispersed.

© 2014 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref]
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2014 (2)

C. M. Heyl, P. Rudawski, F. Brizuela, S. N. Bengtsson, J. Mauritsson, and A. L’Huillier, “Macroscopic effects in noncollinear high-order harmonic generation,” Phys. Rev. Lett. 112, 143902 (2014)
[Crossref] [PubMed]

C. M. Heyl, S. N. Bengtsson, S. Carlström, J. Mauritsson, C. L. Arnold, and A. L’Huillier, “Noncollinear optical gating,” New J. Phys. 16052001 (2014).
[Crossref]

2012 (3)

A. Rupenyan, J. B. Bertrand, D. M. Villeneuve, and H. J. Wörner, “All-optical measurement of high-harmonic amplitudes and phases in aligned molecules,” Phys. Rev. Lett. 108, 033903 (2012).
[Crossref] [PubMed]

F. Calegari, M. Lucchini, M. Negro, C. Vozzi, L. Poletto, O. Svelto, S. De Silvestri, G. Sansone, S. Stagira, and M. Nisoli, “Temporal gating methods for the generation of isolated attosecond pulses,” J. Phys. B Atom. Molec. Opt. Phys. 45, 074002 (2012)
[Crossref]

J. A. Wheeler, A. Borot, S. Monchoce, H. Vincenti, A. Ricci, A. Malvache, R. Lopez-Martens, and F. Quere, “Attosecond lighthouses from plasma mirrors,” Nature Phot. 6, 829–833 (2012).
[Crossref]

2011 (3)

C. Vozzi, M. Negro, F. Calegari, G. Sansone, M. Nisoli, S. De Silvestri, and S. Stagira, “Generalized molecular orbital tomography,” Nature Phys. 7, 822–826 (2011).
[Crossref]

J. B. Bertrand, H. J. Wörner, H.-C. Bandulet, É. Bisson, M. Spanner, J.-C. Kieffer, D. M. Villeneuve, and P. B. Corkum, “Ultrahigh-order wave mixing in noncollinear high harmonic generation,” Phys. Rev. Lett. 106, 023001 (2011).
[Crossref] [PubMed]

H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334, 208–212 (2011).
[Crossref]

2010 (1)

2009 (2)

D. Shafir, Y. Mairesse, D. M. Villeneuve, P. B. Corkum, and N. Dudovich, “Atomic wavefunctions probed through strong-field light-matter interaction,” Nature Phys. 5, 412–416 (2009).
[Crossref]

O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Y. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature 460, 972–977 (2009).
[Crossref] [PubMed]

2008 (2)

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

Y. Mairesse, D. Zeidler, N. Dudovich, M. Spanner, J. Levesque, D. M. Villeneuve, and P. B. Corkum, “High-order harmonic transient grating spectroscopy in a molecular jet,” Phys. Rev. Lett. 100, 143903 (2008).
[Crossref] [PubMed]

2007 (1)

2006 (1)

A. Fleischer and N. Moiseyev, “Attosecond laser pulse synthesis using bichromatic high-order harmonic generation,” Phys. Rev. A 74, 053806 (2006).
[Crossref]

2004 (2)

G. Sansone, C. Vozzi, S. Stagira, and M. Nisoli, “Nonadiabatic quantum path analysis of high-order harmonic generation: Role of the carrier-envelope phase on short and long paths,” Phys. Rev. A 70, 013411 (2004).
[Crossref]

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. Kieffer, P. Corkum, and D. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432, 867–871 (2004).
[Crossref] [PubMed]

2002 (1)

S. V. Fomichev, P. Breger, B. Carré, P. Agostini, and D. F. Zaretsky, “Non-collinear high-harmonic generation,” Laser Phys. 12, 383–388, (2002).

1996 (1)

A. V. Birulin, V. T. Platonenko, and V. V. Strelkov, “High-order harmonic generation in colliding beams,” Quantum Electron. 26, 377–378 (1996).
[Crossref]

Agostini, P.

S. V. Fomichev, P. Breger, B. Carré, P. Agostini, and D. F. Zaretsky, “Non-collinear high-harmonic generation,” Laser Phys. 12, 383–388, (2002).

Aquila, A. L.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

Arnold, C. L.

C. M. Heyl, S. N. Bengtsson, S. Carlström, J. Mauritsson, C. L. Arnold, and A. L’Huillier, “Noncollinear optical gating,” New J. Phys. 16052001 (2014).
[Crossref]

Attwood, D. T.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

Bandulet, H.-C.

J. B. Bertrand, H. J. Wörner, H.-C. Bandulet, É. Bisson, M. Spanner, J.-C. Kieffer, D. M. Villeneuve, and P. B. Corkum, “Ultrahigh-order wave mixing in noncollinear high harmonic generation,” Phys. Rev. Lett. 106, 023001 (2011).
[Crossref] [PubMed]

Bengtsson, S. N.

C. M. Heyl, S. N. Bengtsson, S. Carlström, J. Mauritsson, C. L. Arnold, and A. L’Huillier, “Noncollinear optical gating,” New J. Phys. 16052001 (2014).
[Crossref]

C. M. Heyl, P. Rudawski, F. Brizuela, S. N. Bengtsson, J. Mauritsson, and A. L’Huillier, “Macroscopic effects in noncollinear high-order harmonic generation,” Phys. Rev. Lett. 112, 143902 (2014)
[Crossref] [PubMed]

Bertrand, J. B.

A. Rupenyan, J. B. Bertrand, D. M. Villeneuve, and H. J. Wörner, “All-optical measurement of high-harmonic amplitudes and phases in aligned molecules,” Phys. Rev. Lett. 108, 033903 (2012).
[Crossref] [PubMed]

H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334, 208–212 (2011).
[Crossref]

J. B. Bertrand, H. J. Wörner, H.-C. Bandulet, É. Bisson, M. Spanner, J.-C. Kieffer, D. M. Villeneuve, and P. B. Corkum, “Ultrahigh-order wave mixing in noncollinear high harmonic generation,” Phys. Rev. Lett. 106, 023001 (2011).
[Crossref] [PubMed]

Birulin, A. V.

A. V. Birulin, V. T. Platonenko, and V. V. Strelkov, “High-order harmonic generation in colliding beams,” Quantum Electron. 26, 377–378 (1996).
[Crossref]

Bisson, É.

J. B. Bertrand, H. J. Wörner, H.-C. Bandulet, É. Bisson, M. Spanner, J.-C. Kieffer, D. M. Villeneuve, and P. B. Corkum, “Ultrahigh-order wave mixing in noncollinear high harmonic generation,” Phys. Rev. Lett. 106, 023001 (2011).
[Crossref] [PubMed]

Blanchet, V.

H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334, 208–212 (2011).
[Crossref]

Borot, A.

J. A. Wheeler, A. Borot, S. Monchoce, H. Vincenti, A. Ricci, A. Malvache, R. Lopez-Martens, and F. Quere, “Attosecond lighthouses from plasma mirrors,” Nature Phot. 6, 829–833 (2012).
[Crossref]

Breger, P.

S. V. Fomichev, P. Breger, B. Carré, P. Agostini, and D. F. Zaretsky, “Non-collinear high-harmonic generation,” Laser Phys. 12, 383–388, (2002).

Brizuela, F.

C. M. Heyl, P. Rudawski, F. Brizuela, S. N. Bengtsson, J. Mauritsson, and A. L’Huillier, “Macroscopic effects in noncollinear high-order harmonic generation,” Phys. Rev. Lett. 112, 143902 (2014)
[Crossref] [PubMed]

Bucksbaum, P. H.

Calegari, F.

F. Calegari, M. Lucchini, M. Negro, C. Vozzi, L. Poletto, O. Svelto, S. De Silvestri, G. Sansone, S. Stagira, and M. Nisoli, “Temporal gating methods for the generation of isolated attosecond pulses,” J. Phys. B Atom. Molec. Opt. Phys. 45, 074002 (2012)
[Crossref]

C. Vozzi, M. Negro, F. Calegari, G. Sansone, M. Nisoli, S. De Silvestri, and S. Stagira, “Generalized molecular orbital tomography,” Nature Phys. 7, 822–826 (2011).
[Crossref]

Carlström, S.

C. M. Heyl, S. N. Bengtsson, S. Carlström, J. Mauritsson, C. L. Arnold, and A. L’Huillier, “Noncollinear optical gating,” New J. Phys. 16052001 (2014).
[Crossref]

Carré, B.

S. V. Fomichev, P. Breger, B. Carré, P. Agostini, and D. F. Zaretsky, “Non-collinear high-harmonic generation,” Laser Phys. 12, 383–388, (2002).

Compton, R.

Constant, E.

H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334, 208–212 (2011).
[Crossref]

Corkum, P.

O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Y. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature 460, 972–977 (2009).
[Crossref] [PubMed]

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. Kieffer, P. Corkum, and D. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432, 867–871 (2004).
[Crossref] [PubMed]

Corkum, P. B.

H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334, 208–212 (2011).
[Crossref]

J. B. Bertrand, H. J. Wörner, H.-C. Bandulet, É. Bisson, M. Spanner, J.-C. Kieffer, D. M. Villeneuve, and P. B. Corkum, “Ultrahigh-order wave mixing in noncollinear high harmonic generation,” Phys. Rev. Lett. 106, 023001 (2011).
[Crossref] [PubMed]

D. Shafir, Y. Mairesse, D. M. Villeneuve, P. B. Corkum, and N. Dudovich, “Atomic wavefunctions probed through strong-field light-matter interaction,” Nature Phys. 5, 412–416 (2009).
[Crossref]

Y. Mairesse, D. Zeidler, N. Dudovich, M. Spanner, J. Levesque, D. M. Villeneuve, and P. B. Corkum, “High-order harmonic transient grating spectroscopy in a molecular jet,” Phys. Rev. Lett. 100, 143903 (2008).
[Crossref] [PubMed]

De Silvestri, S.

F. Calegari, M. Lucchini, M. Negro, C. Vozzi, L. Poletto, O. Svelto, S. De Silvestri, G. Sansone, S. Stagira, and M. Nisoli, “Temporal gating methods for the generation of isolated attosecond pulses,” J. Phys. B Atom. Molec. Opt. Phys. 45, 074002 (2012)
[Crossref]

C. Vozzi, M. Negro, F. Calegari, G. Sansone, M. Nisoli, S. De Silvestri, and S. Stagira, “Generalized molecular orbital tomography,” Nature Phys. 7, 822–826 (2011).
[Crossref]

Dubrouil, A.

H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334, 208–212 (2011).
[Crossref]

Dudovich, N.

D. Shafir, Y. Mairesse, D. M. Villeneuve, P. B. Corkum, and N. Dudovich, “Atomic wavefunctions probed through strong-field light-matter interaction,” Nature Phys. 5, 412–416 (2009).
[Crossref]

O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Y. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature 460, 972–977 (2009).
[Crossref] [PubMed]

Y. Mairesse, D. Zeidler, N. Dudovich, M. Spanner, J. Levesque, D. M. Villeneuve, and P. B. Corkum, “High-order harmonic transient grating spectroscopy in a molecular jet,” Phys. Rev. Lett. 100, 143903 (2008).
[Crossref] [PubMed]

Fabre, B.

H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334, 208–212 (2011).
[Crossref]

Farrell, J. P.

Filin, A.

Fleischer, A.

A. Fleischer and N. Moiseyev, “Attosecond laser pulse synthesis using bichromatic high-order harmonic generation,” Phys. Rev. A 74, 053806 (2006).
[Crossref]

Fomichev, S. V.

S. V. Fomichev, P. Breger, B. Carré, P. Agostini, and D. F. Zaretsky, “Non-collinear high-harmonic generation,” Laser Phys. 12, 383–388, (2002).

Gaarde, M. B.

Gagnon, J.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

Goulielmakis, E.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

Gühr, M.

Gullikson, E. M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

Heyl, C. M.

C. M. Heyl, S. N. Bengtsson, S. Carlström, J. Mauritsson, C. L. Arnold, and A. L’Huillier, “Noncollinear optical gating,” New J. Phys. 16052001 (2014).
[Crossref]

C. M. Heyl, P. Rudawski, F. Brizuela, S. N. Bengtsson, J. Mauritsson, and A. L’Huillier, “Macroscopic effects in noncollinear high-order harmonic generation,” Phys. Rev. Lett. 112, 143902 (2014)
[Crossref] [PubMed]

Higuet, J.

H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334, 208–212 (2011).
[Crossref]

Hofstetter, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

Itatani, J.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. Kieffer, P. Corkum, and D. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432, 867–871 (2004).
[Crossref] [PubMed]

Ivanov, M. Y.

O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Y. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature 460, 972–977 (2009).
[Crossref] [PubMed]

Kieffer, J.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. Kieffer, P. Corkum, and D. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432, 867–871 (2004).
[Crossref] [PubMed]

Kieffer, J.-C.

J. B. Bertrand, H. J. Wörner, H.-C. Bandulet, É. Bisson, M. Spanner, J.-C. Kieffer, D. M. Villeneuve, and P. B. Corkum, “Ultrahigh-order wave mixing in noncollinear high harmonic generation,” Phys. Rev. Lett. 106, 023001 (2011).
[Crossref] [PubMed]

Kienberger, R.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

Kleineberg, U.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

Krausz, F.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

L’Huillier, A.

C. M. Heyl, S. N. Bengtsson, S. Carlström, J. Mauritsson, C. L. Arnold, and A. L’Huillier, “Noncollinear optical gating,” New J. Phys. 16052001 (2014).
[Crossref]

C. M. Heyl, P. Rudawski, F. Brizuela, S. N. Bengtsson, J. Mauritsson, and A. L’Huillier, “Macroscopic effects in noncollinear high-order harmonic generation,” Phys. Rev. Lett. 112, 143902 (2014)
[Crossref] [PubMed]

Levesque, J.

Y. Mairesse, D. Zeidler, N. Dudovich, M. Spanner, J. Levesque, D. M. Villeneuve, and P. B. Corkum, “High-order harmonic transient grating spectroscopy in a molecular jet,” Phys. Rev. Lett. 100, 143903 (2008).
[Crossref] [PubMed]

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. Kieffer, P. Corkum, and D. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432, 867–871 (2004).
[Crossref] [PubMed]

Levis, R.

Lopez-Martens, R.

J. A. Wheeler, A. Borot, S. Monchoce, H. Vincenti, A. Ricci, A. Malvache, R. Lopez-Martens, and F. Quere, “Attosecond lighthouses from plasma mirrors,” Nature Phot. 6, 829–833 (2012).
[Crossref]

Lucchini, M.

F. Calegari, M. Lucchini, M. Negro, C. Vozzi, L. Poletto, O. Svelto, S. De Silvestri, G. Sansone, S. Stagira, and M. Nisoli, “Temporal gating methods for the generation of isolated attosecond pulses,” J. Phys. B Atom. Molec. Opt. Phys. 45, 074002 (2012)
[Crossref]

Mairesse, Y.

H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334, 208–212 (2011).
[Crossref]

O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Y. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature 460, 972–977 (2009).
[Crossref] [PubMed]

D. Shafir, Y. Mairesse, D. M. Villeneuve, P. B. Corkum, and N. Dudovich, “Atomic wavefunctions probed through strong-field light-matter interaction,” Nature Phys. 5, 412–416 (2009).
[Crossref]

Y. Mairesse, D. Zeidler, N. Dudovich, M. Spanner, J. Levesque, D. M. Villeneuve, and P. B. Corkum, “High-order harmonic transient grating spectroscopy in a molecular jet,” Phys. Rev. Lett. 100, 143903 (2008).
[Crossref] [PubMed]

Malvache, A.

J. A. Wheeler, A. Borot, S. Monchoce, H. Vincenti, A. Ricci, A. Malvache, R. Lopez-Martens, and F. Quere, “Attosecond lighthouses from plasma mirrors,” Nature Phot. 6, 829–833 (2012).
[Crossref]

Mauritsson, J.

C. M. Heyl, P. Rudawski, F. Brizuela, S. N. Bengtsson, J. Mauritsson, and A. L’Huillier, “Macroscopic effects in noncollinear high-order harmonic generation,” Phys. Rev. Lett. 112, 143902 (2014)
[Crossref] [PubMed]

C. M. Heyl, S. N. Bengtsson, S. Carlström, J. Mauritsson, C. L. Arnold, and A. L’Huillier, “Noncollinear optical gating,” New J. Phys. 16052001 (2014).
[Crossref]

McFarland, B. K.

Mével, E.

H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334, 208–212 (2011).
[Crossref]

Moiseyev, N.

A. Fleischer and N. Moiseyev, “Attosecond laser pulse synthesis using bichromatic high-order harmonic generation,” Phys. Rev. A 74, 053806 (2006).
[Crossref]

Monchoce, S.

J. A. Wheeler, A. Borot, S. Monchoce, H. Vincenti, A. Ricci, A. Malvache, R. Lopez-Martens, and F. Quere, “Attosecond lighthouses from plasma mirrors,” Nature Phot. 6, 829–833 (2012).
[Crossref]

Negro, M.

F. Calegari, M. Lucchini, M. Negro, C. Vozzi, L. Poletto, O. Svelto, S. De Silvestri, G. Sansone, S. Stagira, and M. Nisoli, “Temporal gating methods for the generation of isolated attosecond pulses,” J. Phys. B Atom. Molec. Opt. Phys. 45, 074002 (2012)
[Crossref]

C. Vozzi, M. Negro, F. Calegari, G. Sansone, M. Nisoli, S. De Silvestri, and S. Stagira, “Generalized molecular orbital tomography,” Nature Phys. 7, 822–826 (2011).
[Crossref]

Niikura, H.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. Kieffer, P. Corkum, and D. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432, 867–871 (2004).
[Crossref] [PubMed]

Nisoli, M.

F. Calegari, M. Lucchini, M. Negro, C. Vozzi, L. Poletto, O. Svelto, S. De Silvestri, G. Sansone, S. Stagira, and M. Nisoli, “Temporal gating methods for the generation of isolated attosecond pulses,” J. Phys. B Atom. Molec. Opt. Phys. 45, 074002 (2012)
[Crossref]

C. Vozzi, M. Negro, F. Calegari, G. Sansone, M. Nisoli, S. De Silvestri, and S. Stagira, “Generalized molecular orbital tomography,” Nature Phys. 7, 822–826 (2011).
[Crossref]

G. Sansone, C. Vozzi, S. Stagira, and M. Nisoli, “Nonadiabatic quantum path analysis of high-order harmonic generation: Role of the carrier-envelope phase on short and long paths,” Phys. Rev. A 70, 013411 (2004).
[Crossref]

Patchkovskii, S.

H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334, 208–212 (2011).
[Crossref]

O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Y. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature 460, 972–977 (2009).
[Crossref] [PubMed]

Pepin, H.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. Kieffer, P. Corkum, and D. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432, 867–871 (2004).
[Crossref] [PubMed]

Platonenko, V. T.

A. V. Birulin, V. T. Platonenko, and V. V. Strelkov, “High-order harmonic generation in colliding beams,” Quantum Electron. 26, 377–378 (1996).
[Crossref]

Poletto, L.

F. Calegari, M. Lucchini, M. Negro, C. Vozzi, L. Poletto, O. Svelto, S. De Silvestri, G. Sansone, S. Stagira, and M. Nisoli, “Temporal gating methods for the generation of isolated attosecond pulses,” J. Phys. B Atom. Molec. Opt. Phys. 45, 074002 (2012)
[Crossref]

Quere, F.

J. A. Wheeler, A. Borot, S. Monchoce, H. Vincenti, A. Ricci, A. Malvache, R. Lopez-Martens, and F. Quere, “Attosecond lighthouses from plasma mirrors,” Nature Phot. 6, 829–833 (2012).
[Crossref]

Ricci, A.

J. A. Wheeler, A. Borot, S. Monchoce, H. Vincenti, A. Ricci, A. Malvache, R. Lopez-Martens, and F. Quere, “Attosecond lighthouses from plasma mirrors,” Nature Phot. 6, 829–833 (2012).
[Crossref]

Romanov, D.

Rudawski, P.

C. M. Heyl, P. Rudawski, F. Brizuela, S. N. Bengtsson, J. Mauritsson, and A. L’Huillier, “Macroscopic effects in noncollinear high-order harmonic generation,” Phys. Rev. Lett. 112, 143902 (2014)
[Crossref] [PubMed]

Ruf, H.

H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334, 208–212 (2011).
[Crossref]

Rupenyan, A.

A. Rupenyan, J. B. Bertrand, D. M. Villeneuve, and H. J. Wörner, “All-optical measurement of high-harmonic amplitudes and phases in aligned molecules,” Phys. Rev. Lett. 108, 033903 (2012).
[Crossref] [PubMed]

Sansone, G.

F. Calegari, M. Lucchini, M. Negro, C. Vozzi, L. Poletto, O. Svelto, S. De Silvestri, G. Sansone, S. Stagira, and M. Nisoli, “Temporal gating methods for the generation of isolated attosecond pulses,” J. Phys. B Atom. Molec. Opt. Phys. 45, 074002 (2012)
[Crossref]

C. Vozzi, M. Negro, F. Calegari, G. Sansone, M. Nisoli, S. De Silvestri, and S. Stagira, “Generalized molecular orbital tomography,” Nature Phys. 7, 822–826 (2011).
[Crossref]

G. Sansone, C. Vozzi, S. Stagira, and M. Nisoli, “Nonadiabatic quantum path analysis of high-order harmonic generation: Role of the carrier-envelope phase on short and long paths,” Phys. Rev. A 70, 013411 (2004).
[Crossref]

Schultze, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

Shafir, D.

D. Shafir, Y. Mairesse, D. M. Villeneuve, P. B. Corkum, and N. Dudovich, “Atomic wavefunctions probed through strong-field light-matter interaction,” Nature Phys. 5, 412–416 (2009).
[Crossref]

Smirnova, O.

O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Y. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature 460, 972–977 (2009).
[Crossref] [PubMed]

Spanner, M.

H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334, 208–212 (2011).
[Crossref]

J. B. Bertrand, H. J. Wörner, H.-C. Bandulet, É. Bisson, M. Spanner, J.-C. Kieffer, D. M. Villeneuve, and P. B. Corkum, “Ultrahigh-order wave mixing in noncollinear high harmonic generation,” Phys. Rev. Lett. 106, 023001 (2011).
[Crossref] [PubMed]

Y. Mairesse, D. Zeidler, N. Dudovich, M. Spanner, J. Levesque, D. M. Villeneuve, and P. B. Corkum, “High-order harmonic transient grating spectroscopy in a molecular jet,” Phys. Rev. Lett. 100, 143903 (2008).
[Crossref] [PubMed]

Spector, L. S.

Stagira, S.

F. Calegari, M. Lucchini, M. Negro, C. Vozzi, L. Poletto, O. Svelto, S. De Silvestri, G. Sansone, S. Stagira, and M. Nisoli, “Temporal gating methods for the generation of isolated attosecond pulses,” J. Phys. B Atom. Molec. Opt. Phys. 45, 074002 (2012)
[Crossref]

C. Vozzi, M. Negro, F. Calegari, G. Sansone, M. Nisoli, S. De Silvestri, and S. Stagira, “Generalized molecular orbital tomography,” Nature Phys. 7, 822–826 (2011).
[Crossref]

G. Sansone, C. Vozzi, S. Stagira, and M. Nisoli, “Nonadiabatic quantum path analysis of high-order harmonic generation: Role of the carrier-envelope phase on short and long paths,” Phys. Rev. A 70, 013411 (2004).
[Crossref]

Strelkov, V. V.

A. V. Birulin, V. T. Platonenko, and V. V. Strelkov, “High-order harmonic generation in colliding beams,” Quantum Electron. 26, 377–378 (1996).
[Crossref]

Svelto, O.

F. Calegari, M. Lucchini, M. Negro, C. Vozzi, L. Poletto, O. Svelto, S. De Silvestri, G. Sansone, S. Stagira, and M. Nisoli, “Temporal gating methods for the generation of isolated attosecond pulses,” J. Phys. B Atom. Molec. Opt. Phys. 45, 074002 (2012)
[Crossref]

Uiberacker, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

Villeneuve, D.

O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Y. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature 460, 972–977 (2009).
[Crossref] [PubMed]

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. Kieffer, P. Corkum, and D. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432, 867–871 (2004).
[Crossref] [PubMed]

Villeneuve, D. M.

A. Rupenyan, J. B. Bertrand, D. M. Villeneuve, and H. J. Wörner, “All-optical measurement of high-harmonic amplitudes and phases in aligned molecules,” Phys. Rev. Lett. 108, 033903 (2012).
[Crossref] [PubMed]

H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334, 208–212 (2011).
[Crossref]

J. B. Bertrand, H. J. Wörner, H.-C. Bandulet, É. Bisson, M. Spanner, J.-C. Kieffer, D. M. Villeneuve, and P. B. Corkum, “Ultrahigh-order wave mixing in noncollinear high harmonic generation,” Phys. Rev. Lett. 106, 023001 (2011).
[Crossref] [PubMed]

D. Shafir, Y. Mairesse, D. M. Villeneuve, P. B. Corkum, and N. Dudovich, “Atomic wavefunctions probed through strong-field light-matter interaction,” Nature Phys. 5, 412–416 (2009).
[Crossref]

Y. Mairesse, D. Zeidler, N. Dudovich, M. Spanner, J. Levesque, D. M. Villeneuve, and P. B. Corkum, “High-order harmonic transient grating spectroscopy in a molecular jet,” Phys. Rev. Lett. 100, 143903 (2008).
[Crossref] [PubMed]

Vincenti, H.

J. A. Wheeler, A. Borot, S. Monchoce, H. Vincenti, A. Ricci, A. Malvache, R. Lopez-Martens, and F. Quere, “Attosecond lighthouses from plasma mirrors,” Nature Phot. 6, 829–833 (2012).
[Crossref]

Vozzi, C.

F. Calegari, M. Lucchini, M. Negro, C. Vozzi, L. Poletto, O. Svelto, S. De Silvestri, G. Sansone, S. Stagira, and M. Nisoli, “Temporal gating methods for the generation of isolated attosecond pulses,” J. Phys. B Atom. Molec. Opt. Phys. 45, 074002 (2012)
[Crossref]

C. Vozzi, M. Negro, F. Calegari, G. Sansone, M. Nisoli, S. De Silvestri, and S. Stagira, “Generalized molecular orbital tomography,” Nature Phys. 7, 822–826 (2011).
[Crossref]

G. Sansone, C. Vozzi, S. Stagira, and M. Nisoli, “Nonadiabatic quantum path analysis of high-order harmonic generation: Role of the carrier-envelope phase on short and long paths,” Phys. Rev. A 70, 013411 (2004).
[Crossref]

Wheeler, J. A.

J. A. Wheeler, A. Borot, S. Monchoce, H. Vincenti, A. Ricci, A. Malvache, R. Lopez-Martens, and F. Quere, “Attosecond lighthouses from plasma mirrors,” Nature Phot. 6, 829–833 (2012).
[Crossref]

Wörner, H. J.

A. Rupenyan, J. B. Bertrand, D. M. Villeneuve, and H. J. Wörner, “All-optical measurement of high-harmonic amplitudes and phases in aligned molecules,” Phys. Rev. Lett. 108, 033903 (2012).
[Crossref] [PubMed]

H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334, 208–212 (2011).
[Crossref]

J. B. Bertrand, H. J. Wörner, H.-C. Bandulet, É. Bisson, M. Spanner, J.-C. Kieffer, D. M. Villeneuve, and P. B. Corkum, “Ultrahigh-order wave mixing in noncollinear high harmonic generation,” Phys. Rev. Lett. 106, 023001 (2011).
[Crossref] [PubMed]

Yakovlev, V. S.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

Zaretsky, D. F.

S. V. Fomichev, P. Breger, B. Carré, P. Agostini, and D. F. Zaretsky, “Non-collinear high-harmonic generation,” Laser Phys. 12, 383–388, (2002).

Zeidler, D.

Y. Mairesse, D. Zeidler, N. Dudovich, M. Spanner, J. Levesque, D. M. Villeneuve, and P. B. Corkum, “High-order harmonic transient grating spectroscopy in a molecular jet,” Phys. Rev. Lett. 100, 143903 (2008).
[Crossref] [PubMed]

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. Kieffer, P. Corkum, and D. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432, 867–871 (2004).
[Crossref] [PubMed]

J. Phys. B Atom. Molec. Opt. Phys. (1)

F. Calegari, M. Lucchini, M. Negro, C. Vozzi, L. Poletto, O. Svelto, S. De Silvestri, G. Sansone, S. Stagira, and M. Nisoli, “Temporal gating methods for the generation of isolated attosecond pulses,” J. Phys. B Atom. Molec. Opt. Phys. 45, 074002 (2012)
[Crossref]

Laser Phys. (1)

S. V. Fomichev, P. Breger, B. Carré, P. Agostini, and D. F. Zaretsky, “Non-collinear high-harmonic generation,” Laser Phys. 12, 383–388, (2002).

Nature (2)

O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Y. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature 460, 972–977 (2009).
[Crossref] [PubMed]

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. Kieffer, P. Corkum, and D. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432, 867–871 (2004).
[Crossref] [PubMed]

Nature Phot. (1)

J. A. Wheeler, A. Borot, S. Monchoce, H. Vincenti, A. Ricci, A. Malvache, R. Lopez-Martens, and F. Quere, “Attosecond lighthouses from plasma mirrors,” Nature Phot. 6, 829–833 (2012).
[Crossref]

Nature Phys. (2)

C. Vozzi, M. Negro, F. Calegari, G. Sansone, M. Nisoli, S. De Silvestri, and S. Stagira, “Generalized molecular orbital tomography,” Nature Phys. 7, 822–826 (2011).
[Crossref]

D. Shafir, Y. Mairesse, D. M. Villeneuve, P. B. Corkum, and N. Dudovich, “Atomic wavefunctions probed through strong-field light-matter interaction,” Nature Phys. 5, 412–416 (2009).
[Crossref]

New J. Phys. (1)

C. M. Heyl, S. N. Bengtsson, S. Carlström, J. Mauritsson, C. L. Arnold, and A. L’Huillier, “Noncollinear optical gating,” New J. Phys. 16052001 (2014).
[Crossref]

Opt. Lett. (2)

Phys. Rev. A (2)

A. Fleischer and N. Moiseyev, “Attosecond laser pulse synthesis using bichromatic high-order harmonic generation,” Phys. Rev. A 74, 053806 (2006).
[Crossref]

G. Sansone, C. Vozzi, S. Stagira, and M. Nisoli, “Nonadiabatic quantum path analysis of high-order harmonic generation: Role of the carrier-envelope phase on short and long paths,” Phys. Rev. A 70, 013411 (2004).
[Crossref]

Phys. Rev. Lett. (4)

A. Rupenyan, J. B. Bertrand, D. M. Villeneuve, and H. J. Wörner, “All-optical measurement of high-harmonic amplitudes and phases in aligned molecules,” Phys. Rev. Lett. 108, 033903 (2012).
[Crossref] [PubMed]

J. B. Bertrand, H. J. Wörner, H.-C. Bandulet, É. Bisson, M. Spanner, J.-C. Kieffer, D. M. Villeneuve, and P. B. Corkum, “Ultrahigh-order wave mixing in noncollinear high harmonic generation,” Phys. Rev. Lett. 106, 023001 (2011).
[Crossref] [PubMed]

C. M. Heyl, P. Rudawski, F. Brizuela, S. N. Bengtsson, J. Mauritsson, and A. L’Huillier, “Macroscopic effects in noncollinear high-order harmonic generation,” Phys. Rev. Lett. 112, 143902 (2014)
[Crossref] [PubMed]

Y. Mairesse, D. Zeidler, N. Dudovich, M. Spanner, J. Levesque, D. M. Villeneuve, and P. B. Corkum, “High-order harmonic transient grating spectroscopy in a molecular jet,” Phys. Rev. Lett. 100, 143903 (2008).
[Crossref] [PubMed]

Quantum Electron. (1)

A. V. Birulin, V. T. Platonenko, and V. V. Strelkov, “High-order harmonic generation in colliding beams,” Quantum Electron. 26, 377–378 (1996).
[Crossref]

Science (2)

H. J. Wörner, J. B. Bertrand, B. Fabre, J. Higuet, H. Ruf, A. Dubrouil, S. Patchkovskii, M. Spanner, Y. Mairesse, V. Blanchet, E. Mével, E. Constant, P. B. Corkum, and D. M. Villeneuve, “Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy,” Science 334, 208–212 (2011).
[Crossref]

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1 Experimental setup: three laser beams are focused in the gas jet in the BoxCARS configuration; high harmonic radiation emerges from the interaction region along a fourth (reference) direction aligned to the XUV spectrometer.
Fig. 2
Fig. 2 Scan of the scattered harmonics spectra acquired in krypton as a function of the delay of one of the laser pulses with respect to the other two, which are kept synchronized.
Fig. 3
Fig. 3 a) Harmonic spectra generated in the reference direction in xenon (blue solid line) and krypton (red dashed line) at synchronization of the three beams. b) Harmonic spectrum generated in the reference direction in argon (green solid line) at synchronization of the three beams.
Fig. 4
Fig. 4 Predicted emission directions of harmonics generated by three laser beams (shown as empty circles) positioned at the three vertices of a square, for orders ranging from 7th to 25th. Harmonics are not angularly dispersed only in the three driving directions (not shown) and in the reference direction (indicated by an arrow). Θx and Θy are the angles formed with x and y axes; θ0 is the angle formed by the driving beams with the same axes.
Fig. 5
Fig. 5 Numerical simulation reporting the far-field profile of the 11th harmonic emission corresponding to short (left panel) and long (right panel) electron quantum paths. Simulations consider propagation in a 1-mm thick medium and neglect neutral and plasma contribution to the phase matching.

Tables (1)

Tables Icon

Table 1 Nonlinear wave mixing processes corresponding to generation of harmonic 13th driven by three foundamental laser pulses with identical frequency.

Equations (9)

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{ ω X = i n i ω i k X = i n i k i i n i = 2 m + 1 = q , n i , m
{ ω X = q ω 0 k X = q k 0 z u z + k 0 [ ( n 3 n 2 n 1 ) u x + ( n 1 n 2 n 3 ) u y ]
{ 2 n 1 2 + 2 n 1 n 2 + n 2 2 2 n 1 + n 2 = q n 3 = q n 1 n 2
n 1 = ( q n 2 ) ± q 2 n 2 2 2 .
E = A { exp [ i ( k 1 r ) ] + exp [ i ( k 2 r ) ] + exp [ i ( k 3 r ) ] } exp [ i ω 0 t ]
E = A ρ ( x , y ) exp [ i ϕ ( x , y ) ] exp [ i ( k 0 z z ω 0 t ) ]
{ ρ 2 ( x , y ) = 4 cos 2 [ k 0 ( x y ) ] + 4 cos [ k 0 ( x + y ) ] cos [ k 0 ( x y ) ] + 1 ϕ ( x , y ) = arctan [ sin [ k 0 ( x + y ) ] 2 cos [ k 0 ( x y ) ] + cos [ k 0 ( x + y ) ] ]
d s / l ( q ) ( x , y ) = SP s / l { A ρ ( x , y ) } exp [ i q ϕ ( x , y ) ] exp [ i q k 0 z z ]
I s / l ( κ x , κ y ) l 2 | F s / l ( κ x , κ y ) | 2 sinc 2 ( Δ k l 2 )

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