Abstract

We report on a procedure to focalize few-cycle laser pulses in dispersive media with controlled waveform. Stationarity of the carrier-envelope phase for extended depth of focus is attained by shaping the spatial dispersion of the ultrashort beam. An adjustable group velocity is locally tuned in order to match a prescribed phase velocity at focus. A hybrid diffractive-refractive lens system is proposed to drive the wavefield to an immersion microscope objective under convenient broadband modulation. Numerical simulations demonstrate robustness over positioning of this dispersive beam expander.

©2008 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  27. J. M. Bendickson, E. N. Glytsis, and T. K. Gaylord, “Metallic surface-relief on-axis and off-axis focusing diffractive cylindrical mirrors,” J. Opt. Soc. Am. A 16, 113–130 (1999).
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2008 (4)

2007 (5)

2006 (1)

S. E. Irvine, P. Dombi, G. Farkas, and A. Elezzabi, “Influence of the carrier-envelope phase of few-cycle pulses on ponderomotive surface-plasmon electron acceleration,” Phys. Rev. Lett. 97, 146,801 (2006).
[Crossref]

2005 (1)

2004 (2)

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[Crossref] [PubMed]

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113,001 (2004).
[Crossref]

2003 (1)

M. A. Porras, G. Valiulis, and P. D. Trapani, “Unified description of Bessel X waves with cone dispersion and tilted pulses,” Phys. Rev. E 68, 016,613 (2003).
[Crossref]

2002 (1)

M. A. Porras, “Diffraction effects in few-cycle optical pulses,” Phys. Rev. E 65, 026,606 (2002).
[Crossref]

2001 (1)

1999 (3)

Z. L. Horváth and Z. Bor, “Reshaping of femtosecond pulses by the Gouy phase shift,” Phys. Rev. E 60, 2337–2346 (1999).
[Crossref]

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle Terahertz pulses,” Phys. Rev. Lett.  83, 3410–3413 (1999).
[Crossref]

J. M. Bendickson, E. N. Glytsis, and T. K. Gaylord, “Metallic surface-relief on-axis and off-axis focusing diffractive cylindrical mirrors,” J. Opt. Soc. Am. A 16, 113–130 (1999).
[Crossref]

1998 (1)

1997 (1)

V. Moreno, J. F. Román, and J. R. Salgueiro, “High efficiency diffractive lenses: Deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[Crossref]

1995 (1)

1992 (1)

1986 (1)

A. E. Siegman, Lasers (University Science Books, Mill Valley, 1986).

1981 (1)

1980 (1)

1938 (1)

1890 (1)

L. G. Gouy, “Sur une propriété nouvelle des ondes lumineuses,” Compt. Rendue Acad. Sci. (Paris) 110, 1251–1253 (1890).

Andrés, P.

Baltuska, A.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[Crossref] [PubMed]

Baltuška, A.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113,001 (2004).
[Crossref]

Bendickson, J. M.

Bor, Z.

Z. L. Horváth and Z. Bor, “Reshaping of femtosecond pulses by the Gouy phase shift,” Phys. Rev. E 60, 2337–2346 (1999).
[Crossref]

Boyd, R. W.

Caballero, M. T.

Caraquitena, J.

Climent, V.

Dombi, P.

P. Dombi and P. Rácz, “Ultrafast monoenergetic electron source by optical waveform control of surface plasmons,” Opt. Express 16, 2887–2893 (2008).
[Crossref] [PubMed]

S. E. Irvine, P. Dombi, G. Farkas, and A. Elezzabi, “Influence of the carrier-envelope phase of few-cycle pulses on ponderomotive surface-plasmon electron acceleration,” Phys. Rev. Lett. 97, 146,801 (2006).
[Crossref]

Drescher, M.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[Crossref] [PubMed]

Elezzabi, A.

S. E. Irvine, P. Dombi, G. Farkas, and A. Elezzabi, “Influence of the carrier-envelope phase of few-cycle pulses on ponderomotive surface-plasmon electron acceleration,” Phys. Rev. Lett. 97, 146,801 (2006).
[Crossref]

Escuti, M. J.

Farkas, G.

S. E. Irvine, P. Dombi, G. Farkas, and A. Elezzabi, “Influence of the carrier-envelope phase of few-cycle pulses on ponderomotive surface-plasmon electron acceleration,” Phys. Rev. Lett. 97, 146,801 (2006).
[Crossref]

Feng, S.

Fernández-Alonso, M.

Gaylord, T. K.

Glytsis, E. N.

Gonzalo, I.

Goulielmakis, E.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113,001 (2004).
[Crossref]

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[Crossref] [PubMed]

Gouy, L. G.

L. G. Gouy, “Sur une propriété nouvelle des ondes lumineuses,” Compt. Rendue Acad. Sci. (Paris) 110, 1251–1253 (1890).

Heinzmann, U.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[Crossref] [PubMed]

Hellwarth, R. W.

Hof, K. D.

Horváth, Z. L.

Z. L. Horváth and Z. Bor, “Reshaping of femtosecond pulses by the Gouy phase shift,” Phys. Rev. E 60, 2337–2346 (1999).
[Crossref]

Ibragimov, E.

Irvine, S. E.

S. E. Irvine, P. Dombi, G. Farkas, and A. Elezzabi, “Influence of the carrier-envelope phase of few-cycle pulses on ponderomotive surface-plasmon electron acceleration,” Phys. Rev. Lett. 97, 146,801 (2006).
[Crossref]

Kienberger, R.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[Crossref] [PubMed]

Klein, M. W.

Kleineberg, U.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[Crossref] [PubMed]

Krausz, F.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[Crossref] [PubMed]

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113,001 (2004).
[Crossref]

Lancis, J.

Lezius, M.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113,001 (2004).
[Crossref]

Lindner, F.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113,001 (2004).
[Crossref]

Mínguez-Vega, G.

Miret, J. J.

Moreno, V.

V. Moreno, J. F. Román, and J. R. Salgueiro, “High efficiency diffractive lenses: Deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[Crossref]

Morris, G. M.

Oh, C.

Paulus, G. G.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113,001 (2004).
[Crossref]

Porras, M. A.

M. A. Porras, C. J. Zapata-Rodríguez, and I. Gonzalo, “Gouy wave modes: undistorted pulse focalization in a dispersive medium,” Opt. Lett. 32, 3287–3289 (2007).
[Crossref] [PubMed]

M. A. Porras, G. Valiulis, and P. D. Trapani, “Unified description of Bessel X waves with cone dispersion and tilted pulses,” Phys. Rev. E 68, 016,613 (2003).
[Crossref]

M. A. Porras, “Diffraction effects in few-cycle optical pulses,” Phys. Rev. E 65, 026,606 (2002).
[Crossref]

Rácz, P.

Román, J. F.

V. Moreno, J. F. Román, and J. R. Salgueiro, “High efficiency diffractive lenses: Deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[Crossref]

Rubinowicz, A.

Rudd, J. V.

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle Terahertz pulses,” Phys. Rev. Lett.  83, 3410–3413 (1999).
[Crossref]

Ruffin, A. B.

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle Terahertz pulses,” Phys. Rev. Lett.  83, 3410–3413 (1999).
[Crossref]

Salgueiro, J. R.

V. Moreno, J. F. Román, and J. R. Salgueiro, “High efficiency diffractive lenses: Deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[Crossref]

Scrinzi, A.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[Crossref] [PubMed]

Sharp, T. E.

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, Mill Valley, 1986).

Tajahuerce, E.

Trapani, P. D.

M. A. Porras, G. Valiulis, and P. D. Trapani, “Unified description of Bessel X waves with cone dispersion and tilted pulses,” Phys. Rev. E 68, 016,613 (2003).
[Crossref]

Tritschler, T.

Uiberacker, M.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[Crossref] [PubMed]

Valiulis, G.

M. A. Porras, G. Valiulis, and P. D. Trapani, “Unified description of Bessel X waves with cone dispersion and tilted pulses,” Phys. Rev. E 68, 016,613 (2003).
[Crossref]

Walther, H.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113,001 (2004).
[Crossref]

Wegener, M.

Westerwalbesloh, T.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[Crossref] [PubMed]

Whitaker, J. F.

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle Terahertz pulses,” Phys. Rev. Lett.  83, 3410–3413 (1999).
[Crossref]

Winful, H. G.

Wisoff, P. J.

Yakovlev, V.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[Crossref] [PubMed]

Zapata-Rodríguez, C. J.

Am. J. Phys. (1)

V. Moreno, J. F. Román, and J. R. Salgueiro, “High efficiency diffractive lenses: Deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[Crossref]

Appl. Opt. (3)

Compt. Rendue Acad. Sci. (Paris) (1)

L. G. Gouy, “Sur une propriété nouvelle des ondes lumineuses,” Compt. Rendue Acad. Sci. (Paris) 110, 1251–1253 (1890).

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

C. J. Zapata-Rodríguez, “Focal waveforms with tunable carrier frequency using dispersive aperturing,” Opt. Commun. 281, 4840–4843 (2008).
[Crossref]

Opt. Express (3)

Opt. Lett. (7)

Phys. Rev. E (3)

Z. L. Horváth and Z. Bor, “Reshaping of femtosecond pulses by the Gouy phase shift,” Phys. Rev. E 60, 2337–2346 (1999).
[Crossref]

M. A. Porras, “Diffraction effects in few-cycle optical pulses,” Phys. Rev. E 65, 026,606 (2002).
[Crossref]

M. A. Porras, G. Valiulis, and P. D. Trapani, “Unified description of Bessel X waves with cone dispersion and tilted pulses,” Phys. Rev. E 68, 016,613 (2003).
[Crossref]

Phys. Rev. Lett. (3)

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle Terahertz pulses,” Phys. Rev. Lett.  83, 3410–3413 (1999).
[Crossref]

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113,001 (2004).
[Crossref]

S. E. Irvine, P. Dombi, G. Farkas, and A. Elezzabi, “Influence of the carrier-envelope phase of few-cycle pulses on ponderomotive surface-plasmon electron acceleration,” Phys. Rev. Lett. 97, 146,801 (2006).
[Crossref]

Science (1)

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[Crossref] [PubMed]

Other (1)

A. E. Siegman, Lasers (University Science Books, Mill Valley, 1986).

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Figures (3)

Fig. 1.
Fig. 1. Phase velocity (dashed line) and group velocity (solid lines) represented in (a) for pulsed Gaussian beams of different 0( 0=34) propagating in fused silica at ω 0=3.14 fs-1. In (b) we also show the CEP evolution along the optical axis.
Fig. 2.
Fig. 2. Schematic diagram of the focusing setup: L 1 and L 2 are components of the diffractive doublet; L 3 is the refractive lens and MO is the microscope objective.
Fig. 3.
Fig. 3. Evolution of the wavefield and envelope at different on-axis points ζ of the focal volume. Negative values of ζ are drawn in dashed lines and positive values in solid lines. Subfigures (a)–(b) correspond to isodiffracting Gaussian beams focused onto bulk fused silica. Time domain is given in terms of the local time t′. In (c)–(d) we employ a CEP-stationarity procedure.

Equations (18)

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

E ( t , z ) = E 0 ( t ' ) cos ( ω 0 t ' ϕ 0 ) ,
z ϕ 0 = ω 0 ( 1 v p 1 v g ) ,
ε ( ω , z ) = z R exp ( i k z ) i q ε ( ω , 0 ) ,
k z = k z R z 2 + z R 2 ,
v p = c [ n p 0 1 0 ( 1 + ζ 2 ) ] 1 ,
v g = c [ n g 0 + 0 ( 1 - ζ 2 ) 0 ( 1 + ζ 2 ) 2 ] 1 ,
0 = ( 1 + 0 Δ n 0 ) ,
ϕ 0 ( ζ ) = arctan ( ζ ) 0 Δ n 0 ζ 0 ζ ζ 2 + 1 ,
s = 2 f k s i n ,
in 0 = 1 + Δ n 0 n p 0 ( ω 0 2 f 2 c 2 in 0 1 ) .
in 0 = ˜ in 0 + 2 ω 0 A ˙ 0 A 0 .
η ( ω ) = sin⁡ c 2 ( ω ω 0 1 ) ,
d 3 = [ d 1 d 2 ( d 1 + d 2 ) f 2 ] f 3 d 1 ( d 2 f 2 f 3 ) + f 2 ( f 3 d 2 )
q in = A q ˜ in + B C q ˜ in + D ,
f 3 = d 2 + ( d 1 f 10 ) 2 d 1 ,
f 20 = ( d 1 f 10 ) 2 f 10 .
f 10 = d 1 ( 1 + 2 Δ in 0 )
η ̅ = 1 1 s 2 η d Ω 1 1 s 2 d Ω ,

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