Abstract

We show an experimental and computational comparison between the resolution power, the contrast and the focal depth of a nonlin-early propagated diffraction-free beam and of other beams (a linear and a nonlinearly propagated Gaussian pulse): launching a nondiffractive Bessel pulse in a solution of Coumarine 120 in methanol creates a high contrast, 40 mm long, 10 μm width fluorescence channel excited by 3-photon absorption process. This fluorescence channel exhibits the same contrast and resolution of a tightly focused Gaussian pulse, but reaches a focal depth that outclasses by orders of magnitude that reached by an equivalent Gaussian pulse.

© 2005 Optical Society of America

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  1. J. Durnin, J.J. Micheli, and J.H. Heberly: “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499–1501 (1987)
    [Crossref] [PubMed]
  2. H. Sõnajalg, M. Rätsep, and P. Saari: “Demonstration of the Bessel-X pulse propagating with strong lateral and longitudinal localization in dispersive medium,” Opt. Lett. 22, 310–312 (1996)
    [Crossref]
  3. D. McGloin and K. Dholakia: “Bessel beams: diffraction in a new light,” Contemporary Physics 46, 15–28 (2005)
    [Crossref]
  4. S. Orlov, A. Piskarskas, and A. Stabinis: “Localized optical subcycle pulses in dispersive media,” Opt. Lett. 27, 2167–2169 (2002)
    [Crossref]
  5. R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piche, G. Rousseau, and M. Fortin: “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67, 063820 (2003).
    [Crossref]
  6. T. Wulle and S. Herminghaus: “Nonlinear Optics of Bessel Beams,” Phys. Rev. Lett. 70, 1401–1403 (1993)
    [Crossref] [PubMed]
  7. R. Gadonas, A. Marcinkevicius, A. Piskarskas, V. Smilgevicius, and A. Stabinis: “Traveling wave optical parametric generator pumped by a conical beam,” Opt. Commun. 146, 253–256 (1998)
    [Crossref]
  8. M.A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani: “Nonlinear Unbalanced Bessel beams: stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004)
    [Crossref] [PubMed]
  9. H. Schroeder and S.L. Chin: “Visualization of the evolution of multiple filaments in methanol,” Opt. Commun. 234399–406 (2004)
    [Crossref]
  10. T. Brabec and F. Krausz: “Nonlinear Optical Pulse Propagation in the Single-Cycle Regime,” Phys. Rev. Lett. 78, 3282–3285 (1997)
    [Crossref]
  11. A. M. Perelomov, V. S. Popov, and M. V. Terent’ev: “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966)
  12. A. Dubietis, E. Gaižauskas, G. Tamošauskas, and P. Di Trapani: “Light filaments without self channeling,” Phys. Rev. Lett. 92, 253903 (2004)
    [Crossref] [PubMed]
  13. W. Liu, S.L. Chin, O. Kosareva, I.S. Golubtsov, and V.P. Kandidov: “Multiple refocusing of a femtosecond laser pulse in a dispersive liquid (methanol),” Opt. Commun. 225, 193–209 (2003)
    [Crossref]
  14. M. Erdelyi, Z. L. Horvath, G. Szabo, Zs. Bor, F.K. Tittel, J.R. Cavallaro, and M.C. Smayling: “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15, 287–292 (1997)
    [Crossref]
  15. J. Amako, D. Sawaki, and E. Fujii: “Microstructuring transparent materials by use of nondiffracting ultrashort pulse beams generated by diffractive optics,” J. Opt. Soc. Am. B 20, 2562–2568 (2003)
    [Crossref]

2005 (1)

D. McGloin and K. Dholakia: “Bessel beams: diffraction in a new light,” Contemporary Physics 46, 15–28 (2005)
[Crossref]

2004 (3)

M.A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani: “Nonlinear Unbalanced Bessel beams: stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004)
[Crossref] [PubMed]

H. Schroeder and S.L. Chin: “Visualization of the evolution of multiple filaments in methanol,” Opt. Commun. 234399–406 (2004)
[Crossref]

A. Dubietis, E. Gaižauskas, G. Tamošauskas, and P. Di Trapani: “Light filaments without self channeling,” Phys. Rev. Lett. 92, 253903 (2004)
[Crossref] [PubMed]

2003 (3)

W. Liu, S.L. Chin, O. Kosareva, I.S. Golubtsov, and V.P. Kandidov: “Multiple refocusing of a femtosecond laser pulse in a dispersive liquid (methanol),” Opt. Commun. 225, 193–209 (2003)
[Crossref]

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piche, G. Rousseau, and M. Fortin: “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67, 063820 (2003).
[Crossref]

J. Amako, D. Sawaki, and E. Fujii: “Microstructuring transparent materials by use of nondiffracting ultrashort pulse beams generated by diffractive optics,” J. Opt. Soc. Am. B 20, 2562–2568 (2003)
[Crossref]

2002 (1)

1998 (1)

R. Gadonas, A. Marcinkevicius, A. Piskarskas, V. Smilgevicius, and A. Stabinis: “Traveling wave optical parametric generator pumped by a conical beam,” Opt. Commun. 146, 253–256 (1998)
[Crossref]

1997 (2)

M. Erdelyi, Z. L. Horvath, G. Szabo, Zs. Bor, F.K. Tittel, J.R. Cavallaro, and M.C. Smayling: “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15, 287–292 (1997)
[Crossref]

T. Brabec and F. Krausz: “Nonlinear Optical Pulse Propagation in the Single-Cycle Regime,” Phys. Rev. Lett. 78, 3282–3285 (1997)
[Crossref]

1996 (1)

1993 (1)

T. Wulle and S. Herminghaus: “Nonlinear Optics of Bessel Beams,” Phys. Rev. Lett. 70, 1401–1403 (1993)
[Crossref] [PubMed]

1987 (1)

J. Durnin, J.J. Micheli, and J.H. Heberly: “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499–1501 (1987)
[Crossref] [PubMed]

1966 (1)

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev: “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966)

Amako, J.

Bor, Zs.

M. Erdelyi, Z. L. Horvath, G. Szabo, Zs. Bor, F.K. Tittel, J.R. Cavallaro, and M.C. Smayling: “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15, 287–292 (1997)
[Crossref]

Brabec, T.

T. Brabec and F. Krausz: “Nonlinear Optical Pulse Propagation in the Single-Cycle Regime,” Phys. Rev. Lett. 78, 3282–3285 (1997)
[Crossref]

Cavallaro, J.R.

M. Erdelyi, Z. L. Horvath, G. Szabo, Zs. Bor, F.K. Tittel, J.R. Cavallaro, and M.C. Smayling: “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15, 287–292 (1997)
[Crossref]

Chin, S.L.

H. Schroeder and S.L. Chin: “Visualization of the evolution of multiple filaments in methanol,” Opt. Commun. 234399–406 (2004)
[Crossref]

W. Liu, S.L. Chin, O. Kosareva, I.S. Golubtsov, and V.P. Kandidov: “Multiple refocusing of a femtosecond laser pulse in a dispersive liquid (methanol),” Opt. Commun. 225, 193–209 (2003)
[Crossref]

Dholakia, K.

D. McGloin and K. Dholakia: “Bessel beams: diffraction in a new light,” Contemporary Physics 46, 15–28 (2005)
[Crossref]

Dubietis, A.

A. Dubietis, E. Gaižauskas, G. Tamošauskas, and P. Di Trapani: “Light filaments without self channeling,” Phys. Rev. Lett. 92, 253903 (2004)
[Crossref] [PubMed]

M.A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani: “Nonlinear Unbalanced Bessel beams: stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004)
[Crossref] [PubMed]

Durnin, J.

J. Durnin, J.J. Micheli, and J.H. Heberly: “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499–1501 (1987)
[Crossref] [PubMed]

Erdelyi, M.

M. Erdelyi, Z. L. Horvath, G. Szabo, Zs. Bor, F.K. Tittel, J.R. Cavallaro, and M.C. Smayling: “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15, 287–292 (1997)
[Crossref]

Faccio, D.

M.A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani: “Nonlinear Unbalanced Bessel beams: stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004)
[Crossref] [PubMed]

Fortin, M.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piche, G. Rousseau, and M. Fortin: “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67, 063820 (2003).
[Crossref]

Fujii, E.

Gadonas, R.

R. Gadonas, A. Marcinkevicius, A. Piskarskas, V. Smilgevicius, and A. Stabinis: “Traveling wave optical parametric generator pumped by a conical beam,” Opt. Commun. 146, 253–256 (1998)
[Crossref]

Gaižauskas, E.

A. Dubietis, E. Gaižauskas, G. Tamošauskas, and P. Di Trapani: “Light filaments without self channeling,” Phys. Rev. Lett. 92, 253903 (2004)
[Crossref] [PubMed]

Golubtsov, I.S.

W. Liu, S.L. Chin, O. Kosareva, I.S. Golubtsov, and V.P. Kandidov: “Multiple refocusing of a femtosecond laser pulse in a dispersive liquid (methanol),” Opt. Commun. 225, 193–209 (2003)
[Crossref]

Griebner, U.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piche, G. Rousseau, and M. Fortin: “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67, 063820 (2003).
[Crossref]

Grunwald, R.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piche, G. Rousseau, and M. Fortin: “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67, 063820 (2003).
[Crossref]

Heberly, J.H.

J. Durnin, J.J. Micheli, and J.H. Heberly: “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499–1501 (1987)
[Crossref] [PubMed]

Herminghaus, S.

T. Wulle and S. Herminghaus: “Nonlinear Optics of Bessel Beams,” Phys. Rev. Lett. 70, 1401–1403 (1993)
[Crossref] [PubMed]

Horvath, Z. L.

M. Erdelyi, Z. L. Horvath, G. Szabo, Zs. Bor, F.K. Tittel, J.R. Cavallaro, and M.C. Smayling: “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15, 287–292 (1997)
[Crossref]

Kandidov, V.P.

W. Liu, S.L. Chin, O. Kosareva, I.S. Golubtsov, and V.P. Kandidov: “Multiple refocusing of a femtosecond laser pulse in a dispersive liquid (methanol),” Opt. Commun. 225, 193–209 (2003)
[Crossref]

Kebbel, V.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piche, G. Rousseau, and M. Fortin: “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67, 063820 (2003).
[Crossref]

Kosareva, O.

W. Liu, S.L. Chin, O. Kosareva, I.S. Golubtsov, and V.P. Kandidov: “Multiple refocusing of a femtosecond laser pulse in a dispersive liquid (methanol),” Opt. Commun. 225, 193–209 (2003)
[Crossref]

Krausz, F.

T. Brabec and F. Krausz: “Nonlinear Optical Pulse Propagation in the Single-Cycle Regime,” Phys. Rev. Lett. 78, 3282–3285 (1997)
[Crossref]

Kummrow, A.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piche, G. Rousseau, and M. Fortin: “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67, 063820 (2003).
[Crossref]

Liu, W.

W. Liu, S.L. Chin, O. Kosareva, I.S. Golubtsov, and V.P. Kandidov: “Multiple refocusing of a femtosecond laser pulse in a dispersive liquid (methanol),” Opt. Commun. 225, 193–209 (2003)
[Crossref]

Marcinkevicius, A.

R. Gadonas, A. Marcinkevicius, A. Piskarskas, V. Smilgevicius, and A. Stabinis: “Traveling wave optical parametric generator pumped by a conical beam,” Opt. Commun. 146, 253–256 (1998)
[Crossref]

McGloin, D.

D. McGloin and K. Dholakia: “Bessel beams: diffraction in a new light,” Contemporary Physics 46, 15–28 (2005)
[Crossref]

Micheli, J.J.

J. Durnin, J.J. Micheli, and J.H. Heberly: “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499–1501 (1987)
[Crossref] [PubMed]

Neumann, U.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piche, G. Rousseau, and M. Fortin: “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67, 063820 (2003).
[Crossref]

Nibbering, E. T. J.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piche, G. Rousseau, and M. Fortin: “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67, 063820 (2003).
[Crossref]

Orlov, S.

Parola, A.

M.A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani: “Nonlinear Unbalanced Bessel beams: stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004)
[Crossref] [PubMed]

Perelomov, A. M.

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev: “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966)

Piche, M.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piche, G. Rousseau, and M. Fortin: “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67, 063820 (2003).
[Crossref]

Piskarskas, A.

S. Orlov, A. Piskarskas, and A. Stabinis: “Localized optical subcycle pulses in dispersive media,” Opt. Lett. 27, 2167–2169 (2002)
[Crossref]

R. Gadonas, A. Marcinkevicius, A. Piskarskas, V. Smilgevicius, and A. Stabinis: “Traveling wave optical parametric generator pumped by a conical beam,” Opt. Commun. 146, 253–256 (1998)
[Crossref]

Popov, V. S.

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev: “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966)

Porras, M.A.

M.A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani: “Nonlinear Unbalanced Bessel beams: stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004)
[Crossref] [PubMed]

Rätsep, M.

Rini, M.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piche, G. Rousseau, and M. Fortin: “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67, 063820 (2003).
[Crossref]

Rousseau, G.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piche, G. Rousseau, and M. Fortin: “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67, 063820 (2003).
[Crossref]

Saari, P.

Sawaki, D.

Schroeder, H.

H. Schroeder and S.L. Chin: “Visualization of the evolution of multiple filaments in methanol,” Opt. Commun. 234399–406 (2004)
[Crossref]

Smayling, M.C.

M. Erdelyi, Z. L. Horvath, G. Szabo, Zs. Bor, F.K. Tittel, J.R. Cavallaro, and M.C. Smayling: “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15, 287–292 (1997)
[Crossref]

Smilgevicius, V.

R. Gadonas, A. Marcinkevicius, A. Piskarskas, V. Smilgevicius, and A. Stabinis: “Traveling wave optical parametric generator pumped by a conical beam,” Opt. Commun. 146, 253–256 (1998)
[Crossref]

Sõnajalg, H.

Stabinis, A.

S. Orlov, A. Piskarskas, and A. Stabinis: “Localized optical subcycle pulses in dispersive media,” Opt. Lett. 27, 2167–2169 (2002)
[Crossref]

R. Gadonas, A. Marcinkevicius, A. Piskarskas, V. Smilgevicius, and A. Stabinis: “Traveling wave optical parametric generator pumped by a conical beam,” Opt. Commun. 146, 253–256 (1998)
[Crossref]

Szabo, G.

M. Erdelyi, Z. L. Horvath, G. Szabo, Zs. Bor, F.K. Tittel, J.R. Cavallaro, and M.C. Smayling: “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15, 287–292 (1997)
[Crossref]

Tamošauskas, G.

A. Dubietis, E. Gaižauskas, G. Tamošauskas, and P. Di Trapani: “Light filaments without self channeling,” Phys. Rev. Lett. 92, 253903 (2004)
[Crossref] [PubMed]

Terent’ev, M. V.

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev: “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966)

Tittel, F.K.

M. Erdelyi, Z. L. Horvath, G. Szabo, Zs. Bor, F.K. Tittel, J.R. Cavallaro, and M.C. Smayling: “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15, 287–292 (1997)
[Crossref]

Trapani, P. Di

M.A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani: “Nonlinear Unbalanced Bessel beams: stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004)
[Crossref] [PubMed]

A. Dubietis, E. Gaižauskas, G. Tamošauskas, and P. Di Trapani: “Light filaments without self channeling,” Phys. Rev. Lett. 92, 253903 (2004)
[Crossref] [PubMed]

Wulle, T.

T. Wulle and S. Herminghaus: “Nonlinear Optics of Bessel Beams,” Phys. Rev. Lett. 70, 1401–1403 (1993)
[Crossref] [PubMed]

Contemporary Physics (1)

D. McGloin and K. Dholakia: “Bessel beams: diffraction in a new light,” Contemporary Physics 46, 15–28 (2005)
[Crossref]

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

J. Vac. Sci. Technol. B (1)

M. Erdelyi, Z. L. Horvath, G. Szabo, Zs. Bor, F.K. Tittel, J.R. Cavallaro, and M.C. Smayling: “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15, 287–292 (1997)
[Crossref]

Opt. Commun. (3)

H. Schroeder and S.L. Chin: “Visualization of the evolution of multiple filaments in methanol,” Opt. Commun. 234399–406 (2004)
[Crossref]

W. Liu, S.L. Chin, O. Kosareva, I.S. Golubtsov, and V.P. Kandidov: “Multiple refocusing of a femtosecond laser pulse in a dispersive liquid (methanol),” Opt. Commun. 225, 193–209 (2003)
[Crossref]

R. Gadonas, A. Marcinkevicius, A. Piskarskas, V. Smilgevicius, and A. Stabinis: “Traveling wave optical parametric generator pumped by a conical beam,” Opt. Commun. 146, 253–256 (1998)
[Crossref]

Opt. Lett. (2)

Phys. Rev. A (1)

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piche, G. Rousseau, and M. Fortin: “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67, 063820 (2003).
[Crossref]

Phys. Rev. Lett. (5)

T. Wulle and S. Herminghaus: “Nonlinear Optics of Bessel Beams,” Phys. Rev. Lett. 70, 1401–1403 (1993)
[Crossref] [PubMed]

J. Durnin, J.J. Micheli, and J.H. Heberly: “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499–1501 (1987)
[Crossref] [PubMed]

M.A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani: “Nonlinear Unbalanced Bessel beams: stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004)
[Crossref] [PubMed]

A. Dubietis, E. Gaižauskas, G. Tamošauskas, and P. Di Trapani: “Light filaments without self channeling,” Phys. Rev. Lett. 92, 253903 (2004)
[Crossref] [PubMed]

T. Brabec and F. Krausz: “Nonlinear Optical Pulse Propagation in the Single-Cycle Regime,” Phys. Rev. Lett. 78, 3282–3285 (1997)
[Crossref]

Sov. Phys. JETP (1)

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev: “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966)

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Figures (6)

Fig. 1.
Fig. 1.

Experimental setup. A linearly polarized Gaussian 1055 nm wavelength, 1 ps pulse is converted into a Bessel pulse using an axicon with 2.3 degrees base angle. The Bessel pulse (which remains focused on a 10 cm distance) passes through a 4 cm cell filled with a light Coumarine 120 methanol solution. 3-photon fluorescence is recorded by CCD side imaging.

Fig. 2.
Fig. 2.

(a): Fluorescence channel generated by a Bessel beam; total energy: 1000 μJ; central-peak energy: 15 μJ; beam length: 1 ps; Bessel’s FWHM: 20 μm; axicon illuminated by a 4 mm FWHM Gaussian beam. (b): Fluorescence channel generated by a pulsed Gaussian beam of the same FWHM diameter; input energy: 70 μJ; (c-d): Numerical results relative to the two cases of above (see text for details)

Fig. 3.
Fig. 3.

(a): Comparison between linear scattering of a linear Bessel beam (527 nm wavelength and 10 μm FWHM) and (b) the trace left by the 3-photon fluorescence lit by a Bessel pulse of 20 μm of FWHM when intensity is high (1 mJ at 1 ps with 1055 nm wavelength).

Fig. 4.
Fig. 4.

(a): fluence profile of a pulsed Bessel beam (1 ps, 20 μm FWHM, 1 mJ 1055nm wavelength pulse) launched in a Coumarine 120 methanol 10% molar solution. The dye has an absorption peak at 350 nm corresponding to a 3-photon absorption. (b): a great difference in behavior is observed for a Gaussian beam of the same FWHM diameter with energy equal to the energy contained within the first zero of the Bessel beam (15 μJ). Note the different z scale with respect to (a)

Fig. 5.
Fig. 5.

(a) Energy nonlinear loss profile (function L(r, z)) computed on the Bessel (1 ps, 20 μm FWHM, 1 mJ 1055nm wavelength pulse) propagation. Comparison is made with the same computation on the propagation of a Gaussian beam (1 ps, 20 μm FWHM, 15 μJ 1055nm wavelength pulse) (b) of the same energy and FWHM as Bessel’s pulse central spot.

Fig. 6.
Fig. 6.

(a): beam profile at half maximum of the same Bessel pulse as in Fig. 4 launched in the same Coumarine methanol solution (solid line). Dashed line corresponds to the linear propagation of the same pulse. (b): beam profile at half maximum of the same Gaussian as in Fig. 4 Gaussian beam launched in the Coumarine methanol solution (solid line), compared to its linear propagation (dashed line).

Equations (8)

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

U ̂ ̂ z = i [ 2 2 k + k 2 ( n 2 ω 2 k 2 c 2 U ̂ 2 ) ] ̂ + TF { N ( ) } ,
N ( ) = SF [ ( t ) ] + NLL [ ( t ) ]
SF [ ( t ) ] = i k 0 n 2 T 2 ( t ) 2 ( t )
NLL [ ( t ) ] = T β K 2 ρ 2 K 2
I ( r , z , t ) z = D ( r , z , t ) ( r , z , t )
with D ( r , z , t ) = ( i 2 k ) ( * Δ 2 Δ 2 * ) ik ( * 2 t 2 2 * t 2 )
and ( r , z , t ) = β I K ( r , z , t )
L ( z , r ) = t ( r , z , t ) dt

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