Abstract

In contrast to the case of quasi-monochromatic waves, a focused optical pulse in the few-cycle limit may exhibit two independent curved wavefronts, associated with phase and group retardations, respectively. Focusing optical elements will generally affect these two wavefronts differently, thus leading to very different behavior of the pulse near focus. As limiting cases, we consider an ideal diffractive lens introducing only phase retardations and a perfect non-dispersive refractive lens (or a curved mirror) introducing equal phase and group retardations. We study the resulting diffraction effects on the pulse, finding both strong deformations of the pulse shape and shifts in the spectrum. We then show how important these effects can be in highly nonlinear optics, by studying their role in attosecond pulse generation. In particular, the focusing effects are found to affect substantially the generation of isolated attosecond pulses in gases from few-cycle fundamental optical fields.

© 2013 OSA

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    [CrossRef] [PubMed]

2012

2011

2009

V. Tosa, K. T. Kim, and C. H. Nam, “Macroscopic generation of attosecond-pulse trains in strongly ionized media,” Phys. Rev. A79(4), 043828 (2009).
[CrossRef]

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys.81(1), 163–234 (2009).
[CrossRef]

V. Tosa, K. Kovacs, C. Altucci, and R. Velotta, “Generating single attosecond pulse using multicycle lasers in a polarization gate,” Opt. Express17(20), 17700–17710 (2009).
[CrossRef] [PubMed]

2008

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,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

2006

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science314(5798), 443–446 (2006).
[CrossRef] [PubMed]

L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wavefront shaping in the visible domain: switchable helical modes generation,” Appl. Phys. Lett.88(22), 221102 (2006).
[CrossRef]

2005

P. Polesana, D. Faccio, P. Di Trapani, A. Dubietis, A. Piskarskas, A. Couairon, and M. A. Porras, “High localization, focal depth and contrast by means of nonlinear Bessel beams,” Opt. Express13(16), 6160–6167 (2005).
[CrossRef] [PubMed]

M. T. Tavassoly, M. Amiri, E. Karimi, and H. R. Khalesifard, “Spectral modification by line singularity in Fresnel diffraction from 1D phase step,” Opt. Commun.255(1-3), 23–34 (2005).
[CrossRef]

2003

M. A. Porras, I. Gonzalo, and A. Mondello, “Pulsed light beams in vacuum with superluminal and negative group velocities,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(6), 066604 (2003).
[CrossRef] [PubMed]

C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, E. Priori, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, V. Tosa, and K. Midorikawa, “Phase-matching analysis of high-order harmonics generated by truncated Bessel beams in the sub-10-fs regime,” Phys. Rev. A68(3), 033806 (2003).
[CrossRef]

2002

M. A. Porras, “Diffraction effects in few-cycle optical pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.65(2), 026606 (2002).
[CrossRef] [PubMed]

G. Popescu and A. Dogariu, “Spectral anomalies at wave-front dislocations,” Phys. Rev. Lett.88(18), 183902 (2002).
[CrossRef] [PubMed]

2001

G. Gbur, T. D. Visser, and E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett.88(1), 013901 (2001).
[CrossRef] [PubMed]

1998

M. A. Porras, “Ultrashort pulsed Gaussian beams,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics58(1), 1086–1093 (1998).
[CrossRef]

1995

1994

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A49(3), 2117–2132 (1994).
[CrossRef] [PubMed]

1993

M. Kempe and W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A48(6), 4721–4729 (1993).
[CrossRef] [PubMed]

1985

I. P. Christov, “Propagation of femtosecond light pulses,” Opt. Commun.53(6), 364–366 (1985).
[CrossRef]

Alahmed, Z. A.

A. Wirth, M. T. Hassan, I. Grguras, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science334(6053), 195–200 (2011).
[CrossRef] [PubMed]

Altucci, C.

V. Tosa, K. Kovacs, C. Altucci, and R. Velotta, “Generating single attosecond pulse using multicycle lasers in a polarization gate,” Opt. Express17(20), 17700–17710 (2009).
[CrossRef] [PubMed]

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science314(5798), 443–446 (2006).
[CrossRef] [PubMed]

C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, E. Priori, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, V. Tosa, and K. Midorikawa, “Phase-matching analysis of high-order harmonics generated by truncated Bessel beams in the sub-10-fs regime,” Phys. Rev. A68(3), 033806 (2003).
[CrossRef]

Amiri, M.

M. T. Tavassoly, M. Amiri, E. Karimi, and H. R. Khalesifard, “Spectral modification by line singularity in Fresnel diffraction from 1D phase step,” Opt. Commun.255(1-3), 23–34 (2005).
[CrossRef]

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,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

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,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

Avaldi, L.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science314(5798), 443–446 (2006).
[CrossRef] [PubMed]

Azzeer, A. M.

A. Wirth, M. T. Hassan, I. Grguras, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science334(6053), 195–200 (2011).
[CrossRef] [PubMed]

Balcou, P.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A49(3), 2117–2132 (1994).
[CrossRef] [PubMed]

Banakh, V. A.

Benedetti, E.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science314(5798), 443–446 (2006).
[CrossRef] [PubMed]

Bruzzese, R.

C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, E. Priori, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, V. Tosa, and K. Midorikawa, “Phase-matching analysis of high-order harmonics generated by truncated Bessel beams in the sub-10-fs regime,” Phys. Rev. A68(3), 033806 (2003).
[CrossRef]

Calegari, F.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science314(5798), 443–446 (2006).
[CrossRef] [PubMed]

Christov, I. P.

I. P. Christov, “Propagation of femtosecond light pulses,” Opt. Commun.53(6), 364–366 (1985).
[CrossRef]

Corkum, P. B.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A49(3), 2117–2132 (1994).
[CrossRef] [PubMed]

Couairon, A.

de Lisio, C.

C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, E. Priori, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, V. Tosa, and K. Midorikawa, “Phase-matching analysis of high-order harmonics generated by truncated Bessel beams in the sub-10-fs regime,” Phys. Rev. A68(3), 033806 (2003).
[CrossRef]

De Silvestri, S.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science314(5798), 443–446 (2006).
[CrossRef] [PubMed]

Di Trapani, P.

Dogariu, A.

G. Popescu and A. Dogariu, “Spectral anomalies at wave-front dislocations,” Phys. Rev. Lett.88(18), 183902 (2002).
[CrossRef] [PubMed]

Dubietis, A.

Faccio, D.

Flammini, R.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science314(5798), 443–446 (2006).
[CrossRef] [PubMed]

Gagnon, J.

A. Wirth, M. T. Hassan, I. Grguras, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science334(6053), 195–200 (2011).
[CrossRef] [PubMed]

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,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

Gbur, G.

G. Gbur, T. D. Visser, and E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett.88(1), 013901 (2001).
[CrossRef] [PubMed]

Gonzalo, I.

M. A. Porras, I. Gonzalo, and A. Mondello, “Pulsed light beams in vacuum with superluminal and negative group velocities,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(6), 066604 (2003).
[CrossRef] [PubMed]

Goulielmakis, E.

A. Wirth, M. T. Hassan, I. Grguras, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science334(6053), 195–200 (2011).
[CrossRef] [PubMed]

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,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

Grguras, I.

A. Wirth, M. T. Hassan, I. Grguras, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science334(6053), 195–200 (2011).
[CrossRef] [PubMed]

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,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

Hassan, M. T.

A. Wirth, M. T. Hassan, I. Grguras, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science334(6053), 195–200 (2011).
[CrossRef] [PubMed]

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,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

Horvath, Z. L.

Ibragimov, E.

Ivanov, M.

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys.81(1), 163–234 (2009).
[CrossRef]

Ivanov, M. Y.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A49(3), 2117–2132 (1994).
[CrossRef] [PubMed]

Karimi, E.

M. T. Tavassoly, M. Amiri, E. Karimi, and H. R. Khalesifard, “Spectral modification by line singularity in Fresnel diffraction from 1D phase step,” Opt. Commun.255(1-3), 23–34 (2005).
[CrossRef]

Kempe, M.

M. Kempe and W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A48(6), 4721–4729 (1993).
[CrossRef] [PubMed]

Khalesifard, H. R.

M. T. Tavassoly, M. Amiri, E. Karimi, and H. R. Khalesifard, “Spectral modification by line singularity in Fresnel diffraction from 1D phase step,” Opt. Commun.255(1-3), 23–34 (2005).
[CrossRef]

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,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

Kim, K. T.

V. Tosa, K. T. Kim, and C. H. Nam, “Macroscopic generation of attosecond-pulse trains in strongly ionized media,” Phys. Rev. A79(4), 043828 (2009).
[CrossRef]

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,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

Kovacs, K.

Krausz, F.

A. Wirth, M. T. Hassan, I. Grguras, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science334(6053), 195–200 (2011).
[CrossRef] [PubMed]

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys.81(1), 163–234 (2009).
[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,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

L’Huillier, A.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A49(3), 2117–2132 (1994).
[CrossRef] [PubMed]

Lewenstein, M.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A49(3), 2117–2132 (1994).
[CrossRef] [PubMed]

Lienau, C.

Luu, T. T.

A. Wirth, M. T. Hassan, I. Grguras, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science334(6053), 195–200 (2011).
[CrossRef] [PubMed]

Major, B.

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wavefront shaping in the visible domain: switchable helical modes generation,” Appl. Phys. Lett.88(22), 221102 (2006).
[CrossRef]

Marrucci, L.

L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wavefront shaping in the visible domain: switchable helical modes generation,” Appl. Phys. Lett.88(22), 221102 (2006).
[CrossRef]

Mascheck, M.

Midorikawa, K.

C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, E. Priori, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, V. Tosa, and K. Midorikawa, “Phase-matching analysis of high-order harmonics generated by truncated Bessel beams in the sub-10-fs regime,” Phys. Rev. A68(3), 033806 (2003).
[CrossRef]

Mondello, A.

M. A. Porras, I. Gonzalo, and A. Mondello, “Pulsed light beams in vacuum with superluminal and negative group velocities,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(6), 066604 (2003).
[CrossRef] [PubMed]

Moulet, A.

A. Wirth, M. T. Hassan, I. Grguras, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science334(6053), 195–200 (2011).
[CrossRef] [PubMed]

Nam, C. H.

V. Tosa, K. T. Kim, and C. H. Nam, “Macroscopic generation of attosecond-pulse trains in strongly ionized media,” Phys. Rev. A79(4), 043828 (2009).
[CrossRef]

Nisoli, M.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science314(5798), 443–446 (2006).
[CrossRef] [PubMed]

C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, E. Priori, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, V. Tosa, and K. Midorikawa, “Phase-matching analysis of high-order harmonics generated by truncated Bessel beams in the sub-10-fs regime,” Phys. Rev. A68(3), 033806 (2003).
[CrossRef]

Pabst, S.

A. Wirth, M. T. Hassan, I. Grguras, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science334(6053), 195–200 (2011).
[CrossRef] [PubMed]

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wavefront shaping in the visible domain: switchable helical modes generation,” Appl. Phys. Lett.88(22), 221102 (2006).
[CrossRef]

Pascolini, M.

C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, E. Priori, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, V. Tosa, and K. Midorikawa, “Phase-matching analysis of high-order harmonics generated by truncated Bessel beams in the sub-10-fs regime,” Phys. Rev. A68(3), 033806 (2003).
[CrossRef]

Pervak, V.

A. Wirth, M. T. Hassan, I. Grguras, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science334(6053), 195–200 (2011).
[CrossRef] [PubMed]

Piglosiewicz, B.

Piskarskas, A.

Polesana, P.

Poletto, L.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science314(5798), 443–446 (2006).
[CrossRef] [PubMed]

C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, E. Priori, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, V. Tosa, and K. Midorikawa, “Phase-matching analysis of high-order harmonics generated by truncated Bessel beams in the sub-10-fs regime,” Phys. Rev. A68(3), 033806 (2003).
[CrossRef]

Popescu, G.

G. Popescu and A. Dogariu, “Spectral anomalies at wave-front dislocations,” Phys. Rev. Lett.88(18), 183902 (2002).
[CrossRef] [PubMed]

Porras, M. A.

M. A. Porras, Z. L. Horvath, and B. Major, “On the use of lenses to focus few-cycle pulses with controlled carrier-envelope phase,” Appl. Phys. B108(3), 521–531 (2012).
[CrossRef]

M. A. Porras, B. Major, and Z. L. Horvath, “Carrier-envelope phase shift of few-cycle pulses along the focus of lenses and mirrors beyond the nonreshaping pulse approximation: the effect of pulse chirp,” J. Opt. Soc. Am. B29(12), 3271–3276 (2012).
[CrossRef]

P. Polesana, D. Faccio, P. Di Trapani, A. Dubietis, A. Piskarskas, A. Couairon, and M. A. Porras, “High localization, focal depth and contrast by means of nonlinear Bessel beams,” Opt. Express13(16), 6160–6167 (2005).
[CrossRef] [PubMed]

M. A. Porras, I. Gonzalo, and A. Mondello, “Pulsed light beams in vacuum with superluminal and negative group velocities,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(6), 066604 (2003).
[CrossRef] [PubMed]

M. A. Porras, “Diffraction effects in few-cycle optical pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.65(2), 026606 (2002).
[CrossRef] [PubMed]

M. A. Porras, “Ultrashort pulsed Gaussian beams,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics58(1), 1086–1093 (1998).
[CrossRef]

Priori, E.

C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, E. Priori, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, V. Tosa, and K. Midorikawa, “Phase-matching analysis of high-order harmonics generated by truncated Bessel beams in the sub-10-fs regime,” Phys. Rev. A68(3), 033806 (2003).
[CrossRef]

Rudolph, W.

M. Kempe and W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A48(6), 4721–4729 (1993).
[CrossRef] [PubMed]

Sadiq, D.

Sansone, G.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science314(5798), 443–446 (2006).
[CrossRef] [PubMed]

Santra, R.

A. Wirth, M. T. Hassan, I. Grguras, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science334(6053), 195–200 (2011).
[CrossRef] [PubMed]

Schmidt, S.

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,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

Silies, M.

Stagira, S.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science314(5798), 443–446 (2006).
[CrossRef] [PubMed]

C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, E. Priori, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, V. Tosa, and K. Midorikawa, “Phase-matching analysis of high-order harmonics generated by truncated Bessel beams in the sub-10-fs regime,” Phys. Rev. A68(3), 033806 (2003).
[CrossRef]

Tavassoly, M. T.

M. T. Tavassoly, M. Amiri, E. Karimi, and H. R. Khalesifard, “Spectral modification by line singularity in Fresnel diffraction from 1D phase step,” Opt. Commun.255(1-3), 23–34 (2005).
[CrossRef]

Tosa, V.

V. Tosa, K. T. Kim, and C. H. Nam, “Macroscopic generation of attosecond-pulse trains in strongly ionized media,” Phys. Rev. A79(4), 043828 (2009).
[CrossRef]

V. Tosa, K. Kovacs, C. Altucci, and R. Velotta, “Generating single attosecond pulse using multicycle lasers in a polarization gate,” Opt. Express17(20), 17700–17710 (2009).
[CrossRef] [PubMed]

C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, E. Priori, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, V. Tosa, and K. Midorikawa, “Phase-matching analysis of high-order harmonics generated by truncated Bessel beams in the sub-10-fs regime,” Phys. Rev. A68(3), 033806 (2003).
[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,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

Vasa, P.

Velotta, R.

V. Tosa, K. Kovacs, C. Altucci, and R. Velotta, “Generating single attosecond pulse using multicycle lasers in a polarization gate,” Opt. Express17(20), 17700–17710 (2009).
[CrossRef] [PubMed]

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science314(5798), 443–446 (2006).
[CrossRef] [PubMed]

Villoresi, P.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science314(5798), 443–446 (2006).
[CrossRef] [PubMed]

C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, E. Priori, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, V. Tosa, and K. Midorikawa, “Phase-matching analysis of high-order harmonics generated by truncated Bessel beams in the sub-10-fs regime,” Phys. Rev. A68(3), 033806 (2003).
[CrossRef]

Visser, T. D.

G. Gbur, T. D. Visser, and E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett.88(1), 013901 (2001).
[CrossRef] [PubMed]

Vozzi, C.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science314(5798), 443–446 (2006).
[CrossRef] [PubMed]

Wirth, A.

A. Wirth, M. T. Hassan, I. Grguras, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science334(6053), 195–200 (2011).
[CrossRef] [PubMed]

Wolf, E.

G. Gbur, T. D. Visser, and E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett.88(1), 013901 (2001).
[CrossRef] [PubMed]

Yakovlev, V. S.

A. Wirth, M. T. Hassan, I. Grguras, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science334(6053), 195–200 (2011).
[CrossRef] [PubMed]

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,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. B

M. A. Porras, Z. L. Horvath, and B. Major, “On the use of lenses to focus few-cycle pulses with controlled carrier-envelope phase,” Appl. Phys. B108(3), 521–531 (2012).
[CrossRef]

Appl. Phys. Lett.

L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wavefront shaping in the visible domain: switchable helical modes generation,” Appl. Phys. Lett.88(22), 221102 (2006).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

I. P. Christov, “Propagation of femtosecond light pulses,” Opt. Commun.53(6), 364–366 (1985).
[CrossRef]

M. T. Tavassoly, M. Amiri, E. Karimi, and H. R. Khalesifard, “Spectral modification by line singularity in Fresnel diffraction from 1D phase step,” Opt. Commun.255(1-3), 23–34 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, E. Priori, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, V. Tosa, and K. Midorikawa, “Phase-matching analysis of high-order harmonics generated by truncated Bessel beams in the sub-10-fs regime,” Phys. Rev. A68(3), 033806 (2003).
[CrossRef]

M. Kempe and W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A48(6), 4721–4729 (1993).
[CrossRef] [PubMed]

V. Tosa, K. T. Kim, and C. H. Nam, “Macroscopic generation of attosecond-pulse trains in strongly ionized media,” Phys. Rev. A79(4), 043828 (2009).
[CrossRef]

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A49(3), 2117–2132 (1994).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

M. A. Porras, I. Gonzalo, and A. Mondello, “Pulsed light beams in vacuum with superluminal and negative group velocities,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(6), 066604 (2003).
[CrossRef] [PubMed]

M. A. Porras, “Diffraction effects in few-cycle optical pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.65(2), 026606 (2002).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics

M. A. Porras, “Ultrashort pulsed Gaussian beams,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics58(1), 1086–1093 (1998).
[CrossRef]

Phys. Rev. Lett.

G. Gbur, T. D. Visser, and E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett.88(1), 013901 (2001).
[CrossRef] [PubMed]

G. Popescu and A. Dogariu, “Spectral anomalies at wave-front dislocations,” Phys. Rev. Lett.88(18), 183902 (2002).
[CrossRef] [PubMed]

Rev. Mod. Phys.

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys.81(1), 163–234 (2009).
[CrossRef]

Science

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science314(5798), 443–446 (2006).
[CrossRef] [PubMed]

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,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

A. Wirth, M. T. Hassan, I. Grguras, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science334(6053), 195–200 (2011).
[CrossRef] [PubMed]

Other

V. E. Zuev, V. A. Banakh, and V. V. Pokasov,Optics of the Turbolent Atmosphere (Gidrometeoizdat, 1988).

D. V. Apeksimov, S. N. Bagaev, Y. E. Geints, A. A. Zemlyanov, A. M. Kabanov, A. V. Kirpichnikov, Y. V. Kistenev, G. M. Krekov, M. M. Krekova, G. G. Matvienko, V. K. Oshlakov, E. K. Panina, V. V. Petrov, E. V. Pestryakov, Y. N. Ponomarev, A. Y. Suhanov, B. A. Tikhomirov, V. I. Trunvo, S. R. Uogintas, S. A. Frolov, and D. G. Hudorozhkov, Atmospheric Optics, S. N. Bagaev and G. G. Matvienko eds. (SB RAS Press, 2010).

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Figures (6)

Fig. 1
Fig. 1

Schematic description of the two distinct wavefronts characterizing, to first approximation, the effects of generalized focusing on a few-cycle optical pulse: the solid curve corresponds to the carrier-phase wavefront, following the location of the optical oscillation peak versus the transverse coordinates, while the dotted curve corresponds to the group (or pulse) wavefront, following the location of the pulse maximum. These two wavefront surfaces are characterized by the corresponding curvature radii Rp and Rg, respectively.

Fig. 2
Fig. 2

Left (blue) and right (red) side of each column show the pulse and spectrum shape of optical field amplitude (square root of the energy density) for (a) focusing by an ideal diffractive lens and (b) focusing by an ideal non-dispersive lens (or a curved mirror) on axis (ρ = 0) and at various distances ρ from the beam axis, relative to the beam waist a0 in the focal plane. See text for the choice of parameter values. �� = tz/c is the retarded time at the given z ..

Fig. 3
Fig. 3

Relative shift of the spectrum peak for a Gaussian pulse beam at the focus of an ideal non-dispersive lens (or focusing mirror) as a function of radius in units of the focal-plane beam waist a0.

Fig. 4
Fig. 4

(a) Spectra of single dipole response for the two 1.8 fs pulses, on-axis. The shaded grey area indicates the spectral region used to plot the radial dependence of dipole intensity shown in (b).

Fig. 5
Fig. 5

Power spectra of harmonics generated by the 1.8 fs pulses (a) and 4.5 fs pulses (b).

Fig. 6
Fig. 6

Single attosecond pulses obtained by filtering the cutoff of the spectra in Fig. 5. Vertical axis in arbitrary but same units in all panels.

Equations (4)

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

E(ρ,φ,0;t)= A 0 e ρ 2 w 0 2 i ω 0 (t+ ς p ρ 2 ) ( t+ ς g ρ 2 τ 0 ) 2 ,
E ˜ (ρ,φ,0;ω)= 1 2π E(ρ,φ,0;t) e iωt dt= A 0 τ 0 2 2 e ρ 2 w 0 2 i ω 0 ς ω ρ 2 τ 0 2 4 (ω ω 0 ) 2 ,
E ˜ (ρ,φ,z;ω)= A 0 τ 0 2 2 α(z,ω) e i ω c zα(z,ω)( 1+i ω 0 ζ ω w 0 2 ) ρ 2 w 0 2 i ω 0 ς ω ρ 2 τ 0 2 4 (ω ω 0 ) 2 ,
α(z,ω)= q(0) q(z) = ω w 0 2 ω w 0 2 +2cz(i ω 0 ζ ω w 0 2 ) .

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