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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References

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Contemporary Physics

D. McGloin and K. Dholakia, �??Bessel beams: diffraction in a new light,�?? Contemporary Physics 46, 15-28 (2005).
[CrossRef]

J. Opt. Soc. Am. B

J. Vac. Sci. Technol. B

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.

R. Gadonas, A. Marcinkevicius, A. Piskarskas, V. Smilgevicius, A. Stabinis, �??Traveling wave optical parametric generator pumped by a conical beam,�?? Opt. Commun. 146, 253-256 (1998).
[CrossRef]

H. Schroeder and S.L. Chin, �??Visualization of the evolution of multiple filaments in methanol,�?? Opt. Commun. 234 399-406 (2004).
[CrossRef]

W. Liu, S.L. Chin, O. Kosareva, I.S. Golubtsov, V.P. Kandidov, �??Multiple refocusing of a femtosecond laser pulse in a dispersive liquid (methanol),�?? Opt. Commun. 225, 193-209 (2003).
[CrossRef]

Opt. Lett.

Phys. Rev. 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]

Phys. Rev. Lett.

T. Wulle and S. Herminghaus, �??Nonlinear Optics of Bessel Beams,�?? Phys. Rev. Lett. 70, 1401-1403 (1993).
[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]

J. Durnin, J.J. Micheli and J.H. Heberly, �??Diffraction-Free Beams,�?? Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

Sov. Phys. JETP

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)

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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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