Abstract

We theoretically investigate the formation of filament and plasma channel in Ar gas by intense femtosecond pulses in the Bessel, truncated Bessel, and combination of two Gaussian modes. Through the numerical results obtained by solving the generalized nonlinear Schrödinger equation coupled with the electron density evolution equation, we find that there is a radial energy flow during the propagation, which implies that the outer part of the Bessel beam serves as an energy reservoir for the filament formed around the central peak. The results we obtain for the Bessel and truncated Bessel incident beams are consistent in that we can obtain a longer filament and plasma channel if more energy is reserved in the outer part of the Bessel incident beam. More interestingly we show that the combined use of two Gaussian beams with different beam diameters increases the energy stored in the outer part of the beam, and as a result the lengths of the filament and plasma channel become remarkably longer. This can be a practical choice to improve the propagation properties.

©2010 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2009 (3)

2008 (3)

2006 (3)

P. Polesana, A. Dubietis, M. A. Porras, E. Kučinskas, D. Faccio, A. Couairon, and P. Di Trapani, “Near-field dynamics of ultrashort pulsed Bessel beams in media with Kerr nonlinearity,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(5), 056612 (2006).
[Crossref] [PubMed]

E. Gaižauskas, E. Vanagas, V. Jarutis, S. Juodkazis, V. Mizeikis, and H. Misawa, “Discrete damage traces from filamentation of Gauss-Bessel pulses,” Opt. Lett. 31(1), 80–82 (2006).
[Crossref] [PubMed]

Y. Matsuoka, Y. Kizuka, and T. Inoue, “The characteristics of laser micro drilling using a Bessel beam,” Appl. Phys., A Mater. Sci. Process. 84(4), 423–430 (2006).
[Crossref]

2005 (3)

2004 (2)

S. Skupin, L. Bergé, U. Peschel, and F. Lederer, “Interaction of femtosecond light filaments with obscurants in aerosols,” Phys. Rev. Lett. 93(2), 023901 (2004).
[Crossref] [PubMed]

T. Kondo, K. Yamasaki, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Three-dimensional microfabrication by femtosecond pulses in dielectrics,” Thin Solid Films 453–454, 550–556 (2004).
[Crossref]

2002 (1)

C. Altucci, R. Bruzzese, C. de Lisio, A. Porzio, S. Solimeno, and V. Tosa, “Diffractionless beams and their use for harmonic generation,” Opt. Lasers Eng. 37(5), 565–575 (2002).
[Crossref]

2001 (3)

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197(4-6), 239–245 (2001).
[Crossref]

A. Marcinkevičius, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Application of Bessel Beams for Microfabrication of Dielectrics by Femtosecond Laser,” Jpn. J. Appl. Phys. 40, L1197–L1199 (2001).
[Crossref]

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287–290 (2001).

2000 (1)

S. Chávez-Cerda and G. H. C. New, “Evolution of focused Hankel waves and Bessel beams,” Opt. Commun. 181(4-6), 369–377 (2000).
[Crossref]

1999 (1)

1998 (3)

1997 (3)

M. Erdélyi, Z. L. Horváth, G. Szabó, 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(2), 287–292 (1997).
[Crossref]

V. E. Peet and R. V. Tsubin, “Third-harmonic generation and multiphoton ionization in Bessel beams,” Phys. Rev. A 56(2), 1613–1620 (1997).
[Crossref]

K. Shinozaki, C. Xu, H. Sasaki, and T. Kamijoh, “A comparison of optical second-harmonic generation efficiency using Bessel and Gaussian beams in bulk crystals,” Opt. Commun. 133(1-6), 300–304 (1997).
[Crossref]

1996 (2)

S. P. Tewari, H. Huang, and R. W. Boyd, “Theory of third-harmonic generation using Bessel beams, and self-phase-matching,” Phys. Rev. A 54(3), 2314–2325 (1996).
[Crossref] [PubMed]

B. Lü, W. Huang, B. Zhang, F. Kong, and Q. Zhai, “Focusing properties of Bessel beams,” Opt. Commun. 131(4-6), 223–228 (1996).
[Crossref]

1988 (1)

1987 (2)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4(4), 651–654 (1987).
[Crossref]

1986 (1)

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).

1966 (1)

A. M. Perelemov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–933 (1966).

1965 (1)

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).

Abdollahpour, D.

Aközbek, N.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287–290 (2001).

Altucci, C.

C. Altucci, R. Bruzzese, C. de Lisio, A. Porzio, S. Solimeno, and V. Tosa, “Diffractionless beams and their use for harmonic generation,” Opt. Lasers Eng. 37(5), 565–575 (2002).
[Crossref]

Ammosov, M. V.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).

Arévalo, E.

Arlt, J.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197(4-6), 239–245 (2001).
[Crossref]

Becker, A.

W. Liu, F. Théberge, E. Arévalo, J.-F. Gravel, A. Becker, and S. L. Chin, “Experiment and simulations on the energy reservoir effect in femtosecond light filaments,” Opt. Lett. 30(19), 2602–2604 (2005).
[Crossref] [PubMed]

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287–290 (2001).

Bergé, L.

S. Skupin, L. Bergé, U. Peschel, and F. Lederer, “Interaction of femtosecond light filaments with obscurants in aerosols,” Phys. Rev. Lett. 93(2), 023901 (2004).
[Crossref] [PubMed]

Bor, Zs.

M. Erdélyi, Z. L. Horváth, G. Szabó, 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(2), 287–292 (1997).
[Crossref]

Bowden, C. M.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287–290 (2001).

Boyd, R. W.

S. P. Tewari, H. Huang, and R. W. Boyd, “Theory of third-harmonic generation using Bessel beams, and self-phase-matching,” Phys. Rev. A 54(3), 2314–2325 (1996).
[Crossref] [PubMed]

Bruzzese, R.

C. Altucci, R. Bruzzese, C. de Lisio, A. Porzio, S. Solimeno, and V. Tosa, “Diffractionless beams and their use for harmonic generation,” Opt. Lasers Eng. 37(5), 565–575 (2002).
[Crossref]

Caron, C. F. R.

Cavallaro, J. R.

M. Erdélyi, Z. L. Horváth, G. Szabó, 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(2), 287–292 (1997).
[Crossref]

Chávez-Cerda, S.

S. Chávez-Cerda and G. H. C. New, “Evolution of focused Hankel waves and Bessel beams,” Opt. Commun. 181(4-6), 369–377 (2000).
[Crossref]

Chin, S. L.

W. Liu, F. Théberge, E. Arévalo, J.-F. Gravel, A. Becker, and S. L. Chin, “Experiment and simulations on the energy reservoir effect in femtosecond light filaments,” Opt. Lett. 30(19), 2602–2604 (2005).
[Crossref] [PubMed]

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287–290 (2001).

Couairon, A.

D. Abdollahpour, P. Panagiotopoulos, M. Turconi, O. Jedrkiewicz, D. Faccio, P. Di Trapani, A. Couairon, D. G. Papazoglou, and S. Tzortzakis, “Long spatio-temporally stationary filaments in air using short pulse UV laser Bessel beams,” Opt. Express 17(7), 5052–5057 (2009).
[Crossref] [PubMed]

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, “Filamentation in Kerr media from pulsed Bessel beams,” Phys. Rev. A 77(4), 043814 (2008).
[Crossref]

P. Polesana, A. Dubietis, M. A. Porras, E. Kučinskas, D. Faccio, A. Couairon, and P. Di Trapani, “Near-field dynamics of ultrashort pulsed Bessel beams in media with Kerr nonlinearity,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(5), 056612 (2006).
[Crossref] [PubMed]

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. Express 13(16), 6160–6167 (2005).
[Crossref] [PubMed]

de Lisio, C.

C. Altucci, R. Bruzzese, C. de Lisio, A. Porzio, S. Solimeno, and V. Tosa, “Diffractionless beams and their use for harmonic generation,” Opt. Lasers Eng. 37(5), 565–575 (2002).
[Crossref]

Delone, N. B.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).

Dholakia, K.

D. Mcgloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005).
[Crossref]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197(4-6), 239–245 (2001).
[Crossref]

Di Trapani, P.

Dubietis, A.

P. Polesana, A. Dubietis, M. A. Porras, E. Kučinskas, D. Faccio, A. Couairon, and P. Di Trapani, “Near-field dynamics of ultrashort pulsed Bessel beams in media with Kerr nonlinearity,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(5), 056612 (2006).
[Crossref] [PubMed]

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. Express 13(16), 6160–6167 (2005).
[Crossref] [PubMed]

Durnin, J.

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Comparison of Bessel and Gaussian beams,” Opt. Lett. 13(2), 79–80 (1988).
[Crossref] [PubMed]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Erdélyi, M.

M. Erdélyi, Z. L. Horváth, G. Szabó, 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(2), 287–292 (1997).
[Crossref]

Faccio, D.

Franco, M.

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, “Filamentation in Kerr media from pulsed Bessel beams,” Phys. Rev. A 77(4), 043814 (2008).
[Crossref]

Gaeta, A. L.

Gaižauskas, E.

Garces-Chavez, V.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197(4-6), 239–245 (2001).
[Crossref]

Gravel, J.-F.

Hauri, C. P.

Horváth, Z. L.

M. Erdélyi, Z. L. Horváth, G. Szabó, 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(2), 287–292 (1997).
[Crossref]

Huang, H.

S. P. Tewari, H. Huang, and R. W. Boyd, “Theory of third-harmonic generation using Bessel beams, and self-phase-matching,” Phys. Rev. A 54(3), 2314–2325 (1996).
[Crossref] [PubMed]

Huang, W.

B. Lü, W. Huang, B. Zhang, F. Kong, and Q. Zhai, “Focusing properties of Bessel beams,” Opt. Commun. 131(4-6), 223–228 (1996).
[Crossref]

Inoue, T.

Y. Matsuoka, Y. Kizuka, and T. Inoue, “The characteristics of laser micro drilling using a Bessel beam,” Appl. Phys., A Mater. Sci. Process. 84(4), 423–430 (2006).
[Crossref]

Jarutis, V.

Jedrkiewicz, O.

Juodkazis, S.

E. Gaižauskas, E. Vanagas, V. Jarutis, S. Juodkazis, V. Mizeikis, and H. Misawa, “Discrete damage traces from filamentation of Gauss-Bessel pulses,” Opt. Lett. 31(1), 80–82 (2006).
[Crossref] [PubMed]

T. Kondo, K. Yamasaki, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Three-dimensional microfabrication by femtosecond pulses in dielectrics,” Thin Solid Films 453–454, 550–556 (2004).
[Crossref]

A. Marcinkevičius, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Application of Bessel Beams for Microfabrication of Dielectrics by Femtosecond Laser,” Jpn. J. Appl. Phys. 40, L1197–L1199 (2001).
[Crossref]

Kamijoh, T.

K. Shinozaki, C. Xu, H. Sasaki, and T. Kamijoh, “A comparison of optical second-harmonic generation efficiency using Bessel and Gaussian beams in bulk crystals,” Opt. Commun. 133(1-6), 300–304 (1997).
[Crossref]

Keldysh, L. V.

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).

Kizuka, Y.

Y. Matsuoka, Y. Kizuka, and T. Inoue, “The characteristics of laser micro drilling using a Bessel beam,” Appl. Phys., A Mater. Sci. Process. 84(4), 423–430 (2006).
[Crossref]

Kolesik, M.

Kondo, T.

T. Kondo, K. Yamasaki, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Three-dimensional microfabrication by femtosecond pulses in dielectrics,” Thin Solid Films 453–454, 550–556 (2004).
[Crossref]

Kong, F.

B. Lü, W. Huang, B. Zhang, F. Kong, and Q. Zhai, “Focusing properties of Bessel beams,” Opt. Commun. 131(4-6), 223–228 (1996).
[Crossref]

Krainov, V. P.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).

Kucinskas, E.

P. Polesana, A. Dubietis, M. A. Porras, E. Kučinskas, D. Faccio, A. Couairon, and P. Di Trapani, “Near-field dynamics of ultrashort pulsed Bessel beams in media with Kerr nonlinearity,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(5), 056612 (2006).
[Crossref] [PubMed]

Lederer, F.

S. Skupin, L. Bergé, U. Peschel, and F. Lederer, “Interaction of femtosecond light filaments with obscurants in aerosols,” Phys. Rev. Lett. 93(2), 023901 (2004).
[Crossref] [PubMed]

Liu, W.

Lopez-Martens, R. B.

Lü, B.

B. Lü, W. Huang, B. Zhang, F. Kong, and Q. Zhai, “Focusing properties of Bessel beams,” Opt. Commun. 131(4-6), 223–228 (1996).
[Crossref]

Marcinkevicius, A.

A. Marcinkevičius, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Application of Bessel Beams for Microfabrication of Dielectrics by Femtosecond Laser,” Jpn. J. Appl. Phys. 40, L1197–L1199 (2001).
[Crossref]

Matsuo, S.

T. Kondo, K. Yamasaki, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Three-dimensional microfabrication by femtosecond pulses in dielectrics,” Thin Solid Films 453–454, 550–556 (2004).
[Crossref]

A. Marcinkevičius, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Application of Bessel Beams for Microfabrication of Dielectrics by Femtosecond Laser,” Jpn. J. Appl. Phys. 40, L1197–L1199 (2001).
[Crossref]

Matsuoka, Y.

Y. Matsuoka, Y. Kizuka, and T. Inoue, “The characteristics of laser micro drilling using a Bessel beam,” Appl. Phys., A Mater. Sci. Process. 84(4), 423–430 (2006).
[Crossref]

Mcgloin, D.

D. Mcgloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005).
[Crossref]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Comparison of Bessel and Gaussian beams,” Opt. Lett. 13(2), 79–80 (1988).
[Crossref] [PubMed]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Misawa, H.

E. Gaižauskas, E. Vanagas, V. Jarutis, S. Juodkazis, V. Mizeikis, and H. Misawa, “Discrete damage traces from filamentation of Gauss-Bessel pulses,” Opt. Lett. 31(1), 80–82 (2006).
[Crossref] [PubMed]

T. Kondo, K. Yamasaki, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Three-dimensional microfabrication by femtosecond pulses in dielectrics,” Thin Solid Films 453–454, 550–556 (2004).
[Crossref]

A. Marcinkevičius, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Application of Bessel Beams for Microfabrication of Dielectrics by Femtosecond Laser,” Jpn. J. Appl. Phys. 40, L1197–L1199 (2001).
[Crossref]

Mizeikis, V.

E. Gaižauskas, E. Vanagas, V. Jarutis, S. Juodkazis, V. Mizeikis, and H. Misawa, “Discrete damage traces from filamentation of Gauss-Bessel pulses,” Opt. Lett. 31(1), 80–82 (2006).
[Crossref] [PubMed]

T. Kondo, K. Yamasaki, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Three-dimensional microfabrication by femtosecond pulses in dielectrics,” Thin Solid Films 453–454, 550–556 (2004).
[Crossref]

A. Marcinkevičius, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Application of Bessel Beams for Microfabrication of Dielectrics by Femtosecond Laser,” Jpn. J. Appl. Phys. 40, L1197–L1199 (2001).
[Crossref]

Mlejnek, M.

M. Mlejnek, E. M. Wright, and J. V. Moloney, “Femtosecond pulse propagation in argon: A pressure dependence study,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(4), 4903–4910 (1998).
[Crossref]

M. Mlejnek, E. M. Wright, and J. V. Moloney, “Dynamic spatial replenishment of femtosecond pulses propagating in air,” Opt. Lett. 23(5), 382–384 (1998).
[Crossref]

Moloney, J.

Moloney, J. V.

M. Mlejnek, E. M. Wright, and J. V. Moloney, “Dynamic spatial replenishment of femtosecond pulses propagating in air,” Opt. Lett. 23(5), 382–384 (1998).
[Crossref]

M. Mlejnek, E. M. Wright, and J. V. Moloney, “Femtosecond pulse propagation in argon: A pressure dependence study,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(4), 4903–4910 (1998).
[Crossref]

Nakajima, T.

New, G. H. C.

S. Chávez-Cerda and G. H. C. New, “Evolution of focused Hankel waves and Bessel beams,” Opt. Commun. 181(4-6), 369–377 (2000).
[Crossref]

Oral, E.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287–290 (2001).

Panagiotopoulos, P.

Papazoglou, D. G.

Peet, V. E.

V. E. Peet and R. V. Tsubin, “Third-harmonic generation and multiphoton ionization in Bessel beams,” Phys. Rev. A 56(2), 1613–1620 (1997).
[Crossref]

Perelemov, A. M.

A. M. Perelemov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–933 (1966).

Peschel, U.

S. Skupin, L. Bergé, U. Peschel, and F. Lederer, “Interaction of femtosecond light filaments with obscurants in aerosols,” Phys. Rev. Lett. 93(2), 023901 (2004).
[Crossref] [PubMed]

Piskarskas, A.

Polesana, P.

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, “Filamentation in Kerr media from pulsed Bessel beams,” Phys. Rev. A 77(4), 043814 (2008).
[Crossref]

P. Polesana, A. Dubietis, M. A. Porras, E. Kučinskas, D. Faccio, A. Couairon, and P. Di Trapani, “Near-field dynamics of ultrashort pulsed Bessel beams in media with Kerr nonlinearity,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(5), 056612 (2006).
[Crossref] [PubMed]

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. Express 13(16), 6160–6167 (2005).
[Crossref] [PubMed]

Polynkin, P.

Popov, V. S.

A. M. Perelemov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–933 (1966).

Porras, M. A.

P. Polesana, A. Dubietis, M. A. Porras, E. Kučinskas, D. Faccio, A. Couairon, and P. Di Trapani, “Near-field dynamics of ultrashort pulsed Bessel beams in media with Kerr nonlinearity,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(5), 056612 (2006).
[Crossref] [PubMed]

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. Express 13(16), 6160–6167 (2005).
[Crossref] [PubMed]

Porzio, A.

C. Altucci, R. Bruzzese, C. de Lisio, A. Porzio, S. Solimeno, and V. Tosa, “Diffractionless beams and their use for harmonic generation,” Opt. Lasers Eng. 37(5), 565–575 (2002).
[Crossref]

Potvliege, R. M.

Roberts, A.

Sasaki, H.

K. Shinozaki, C. Xu, H. Sasaki, and T. Kamijoh, “A comparison of optical second-harmonic generation efficiency using Bessel and Gaussian beams in bulk crystals,” Opt. Commun. 133(1-6), 300–304 (1997).
[Crossref]

Shinozaki, K.

K. Shinozaki, C. Xu, H. Sasaki, and T. Kamijoh, “A comparison of optical second-harmonic generation efficiency using Bessel and Gaussian beams in bulk crystals,” Opt. Commun. 133(1-6), 300–304 (1997).
[Crossref]

Sibbett, W.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197(4-6), 239–245 (2001).
[Crossref]

Skupin, S.

S. Skupin, L. Bergé, U. Peschel, and F. Lederer, “Interaction of femtosecond light filaments with obscurants in aerosols,” Phys. Rev. Lett. 93(2), 023901 (2004).
[Crossref] [PubMed]

Smayling, M. C.

M. Erdélyi, Z. L. Horváth, G. Szabó, 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(2), 287–292 (1997).
[Crossref]

Solimeno, S.

C. Altucci, R. Bruzzese, C. de Lisio, A. Porzio, S. Solimeno, and V. Tosa, “Diffractionless beams and their use for harmonic generation,” Opt. Lasers Eng. 37(5), 565–575 (2002).
[Crossref]

Song, Z.

Szabó, G.

M. Erdélyi, Z. L. Horváth, G. Szabó, 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(2), 287–292 (1997).
[Crossref]

Terent’ev, M. V.

A. M. Perelemov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–933 (1966).

Tewari, S. P.

S. P. Tewari, H. Huang, and R. W. Boyd, “Theory of third-harmonic generation using Bessel beams, and self-phase-matching,” Phys. Rev. A 54(3), 2314–2325 (1996).
[Crossref] [PubMed]

Théberge, F.

Tittel, F. K.

M. Erdélyi, Z. L. Horváth, G. Szabó, 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(2), 287–292 (1997).
[Crossref]

Tosa, V.

C. Altucci, R. Bruzzese, C. de Lisio, A. Porzio, S. Solimeno, and V. Tosa, “Diffractionless beams and their use for harmonic generation,” Opt. Lasers Eng. 37(5), 565–575 (2002).
[Crossref]

Tsubin, R. V.

V. E. Peet and R. V. Tsubin, “Third-harmonic generation and multiphoton ionization in Bessel beams,” Phys. Rev. A 56(2), 1613–1620 (1997).
[Crossref]

Turconi, M.

Tzortzakis, S.

Vanagas, E.

Vijayalakshmi, K.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287–290 (2001).

Vuong, L. T.

Wright, E. M.

M. Mlejnek, E. M. Wright, and J. V. Moloney, “Dynamic spatial replenishment of femtosecond pulses propagating in air,” Opt. Lett. 23(5), 382–384 (1998).
[Crossref]

M. Mlejnek, E. M. Wright, and J. V. Moloney, “Femtosecond pulse propagation in argon: A pressure dependence study,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(4), 4903–4910 (1998).
[Crossref]

Xu, C.

K. Shinozaki, C. Xu, H. Sasaki, and T. Kamijoh, “A comparison of optical second-harmonic generation efficiency using Bessel and Gaussian beams in bulk crystals,” Opt. Commun. 133(1-6), 300–304 (1997).
[Crossref]

Yamasaki, K.

T. Kondo, K. Yamasaki, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Three-dimensional microfabrication by femtosecond pulses in dielectrics,” Thin Solid Films 453–454, 550–556 (2004).
[Crossref]

Zhai, Q.

B. Lü, W. Huang, B. Zhang, F. Kong, and Q. Zhai, “Focusing properties of Bessel beams,” Opt. Commun. 131(4-6), 223–228 (1996).
[Crossref]

Zhang, B.

B. Lü, W. Huang, B. Zhang, F. Kong, and Q. Zhai, “Focusing properties of Bessel beams,” Opt. Commun. 131(4-6), 223–228 (1996).
[Crossref]

Zhang, Z.

Appl. Phys. B (1)

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287–290 (2001).

Appl. Phys., A Mater. Sci. Process. (1)

Y. Matsuoka, Y. Kizuka, and T. Inoue, “The characteristics of laser micro drilling using a Bessel beam,” Appl. Phys., A Mater. Sci. Process. 84(4), 423–430 (2006).
[Crossref]

Contemp. Phys. (1)

D. Mcgloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005).
[Crossref]

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

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

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

M. Erdélyi, Z. L. Horváth, G. Szabó, 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(2), 287–292 (1997).
[Crossref]

Jpn. J. Appl. Phys. (1)

A. Marcinkevičius, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Application of Bessel Beams for Microfabrication of Dielectrics by Femtosecond Laser,” Jpn. J. Appl. Phys. 40, L1197–L1199 (2001).
[Crossref]

Opt. Commun. (4)

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197(4-6), 239–245 (2001).
[Crossref]

B. Lü, W. Huang, B. Zhang, F. Kong, and Q. Zhai, “Focusing properties of Bessel beams,” Opt. Commun. 131(4-6), 223–228 (1996).
[Crossref]

S. Chávez-Cerda and G. H. C. New, “Evolution of focused Hankel waves and Bessel beams,” Opt. Commun. 181(4-6), 369–377 (2000).
[Crossref]

K. Shinozaki, C. Xu, H. Sasaki, and T. Kamijoh, “A comparison of optical second-harmonic generation efficiency using Bessel and Gaussian beams in bulk crystals,” Opt. Commun. 133(1-6), 300–304 (1997).
[Crossref]

Opt. Express (6)

Opt. Lasers Eng. (1)

C. Altucci, R. Bruzzese, C. de Lisio, A. Porzio, S. Solimeno, and V. Tosa, “Diffractionless beams and their use for harmonic generation,” Opt. Lasers Eng. 37(5), 565–575 (2002).
[Crossref]

Opt. Lett. (4)

Phys. Rev. A (3)

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, “Filamentation in Kerr media from pulsed Bessel beams,” Phys. Rev. A 77(4), 043814 (2008).
[Crossref]

V. E. Peet and R. V. Tsubin, “Third-harmonic generation and multiphoton ionization in Bessel beams,” Phys. Rev. A 56(2), 1613–1620 (1997).
[Crossref]

S. P. Tewari, H. Huang, and R. W. Boyd, “Theory of third-harmonic generation using Bessel beams, and self-phase-matching,” Phys. Rev. A 54(3), 2314–2325 (1996).
[Crossref] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

P. Polesana, A. Dubietis, M. A. Porras, E. Kučinskas, D. Faccio, A. Couairon, and P. Di Trapani, “Near-field dynamics of ultrashort pulsed Bessel beams in media with Kerr nonlinearity,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(5), 056612 (2006).
[Crossref] [PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

M. Mlejnek, E. M. Wright, and J. V. Moloney, “Femtosecond pulse propagation in argon: A pressure dependence study,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(4), 4903–4910 (1998).
[Crossref]

Phys. Rev. Lett. (2)

S. Skupin, L. Bergé, U. Peschel, and F. Lederer, “Interaction of femtosecond light filaments with obscurants in aerosols,” Phys. Rev. Lett. 93(2), 023901 (2004).
[Crossref] [PubMed]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Sov. Phys. JETP (3)

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).

A. M. Perelemov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–933 (1966).

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).

Thin Solid Films (1)

T. Kondo, K. Yamasaki, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Three-dimensional microfabrication by femtosecond pulses in dielectrics,” Thin Solid Films 453–454, 550–556 (2004).
[Crossref]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, 1995).

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Figures (18)

Fig. 1
Fig. 1 The transverse profiles of a 100 µm diameter (FWHM as shown by the red arrows) Bessel beam as a function of (a) x and y (b) r.
Fig. 2
Fig. 2 Evolution of the partial powers integrated over the different beam radii within (a) 100 µm, (b) 200 µm, (c) 500 µm, and (d) rmax as a function of time t and propagation distance z.
Fig. 3
Fig. 3 Evolution of the spectral profiles integrated over the beam radius within (a) 100 µm, (b) 200 µm, (c) 500 µm, and (d) rmax as a function of propagation distance.
Fig. 4
Fig. 4 Evolution of the temporal profiles at the (a) central peak and (b)-(i) first eight lobes as a function of propagation distance.
Fig. 5
Fig. 5 Evolution of the spectral profiles at the (a) central peak and (b)-(i) first eight lobes as a function of propagation distance.
Fig. 6
Fig. 6 Change of the percentage of pulse energy contained in the different beam radii as a function of propagation distance.
Fig. 7
Fig. 7 Change of the maximum and minimum values of the field current, i.e., max{j(r,t,z)} and min{j(r,t,z)} for a given z, for the Bessel and Gaussian incident beams during the propagation. Positive (negative) field current stands for the outflow (inflow) of the energy.
Fig. 8
Fig. 8 Normalized field current integrated over time as a function of radius at (a) z = 1 cm, (b) 3 cm, (c) 25 cm, and (d) 50 cm for the Bessel and Gaussian incident beams.
Fig. 9
Fig. 9 Normalized field current as functions of time and radius at (a) z = 1 cm, (b) 3 cm, (c) 15 cm, and (d) 50 cm for the Bessel incident beam.
Fig. 10
Fig. 10 Same with Fig. 9 but for the Gaussian incident beam.
Fig. 11
Fig. 11 Variation of the beam diameter of the truncated Bessel beam with (a) 100 µm and (b) 150 µm incident beam diameters as a function of propagation distance. Incident beams are truncated at the radii of 250 µm and 500 µm for both (a) and (b).
Fig. 12
Fig. 12 Transverse profiles of the pulse as functions of propagation distance and beam radius for the 100 µm incident beam diameter truncated at the radii of (a) 250 µm and (b) 500 µm. Similar results are shown for the 150 µm incident beam diameter truncated at the radii of (c) 250 µm and (d) 500 µm.
Fig. 13
Fig. 13 Variation of the ionization probability at r = 0 for the truncated Bessel beam with (a) 100 and (b) 150 µm incident diameter (FWHM) as a function of propagation distance. In both cases the beam is truncated at the radius of 250 and 500 µm.
Fig. 14
Fig. 14 Ionization probability as functions of propagation distance and beam radius for the 100 µm incident beam diameter truncated at the radii of (a) 250 µm and (b) 500 µm. Similar results for the 150 µm incident beam diameter are shown for the truncation radii of (c) 250 µm and (d) 500 µm.
Fig. 15
Fig. 15 Spatial profiles of the combined two Gaussian beams for case A, C, and D.
Fig. 16
Fig. 16 Variation of beam diameter as a function of propagation distance for (a) Group 1 (case A, B, C, and D), (b) Group 2 (case C, D, E, and F), and (c) Group 3 (case C, D, G, and H).
Fig. 17
Fig. 17 Variation of ionization probability at r = 0 as a function of propagation distance for (a) Group 1 (case A, B, C, and D), (b) Group 2 (case C, D, E, and F), and (c) Group 3 (case C, D, G, and H).
Fig. 18
Fig. 18 Variation of the (a) beam diameter and (b) ionization probability at r = 0 for the 50 fs Bessel and Gaussian beam as a function of propagation distance.

Tables (1)

Tables Icon

Table 1 Comparison of Total energy, Beam Diameter, and Peak Intensity for Cases A–H Where Values are Normalized with Respect to Those for Case A

Equations (6)

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

ε b ( r , t , 0 ) = ε 0 J 0 ( k r r ) exp ( t 2 / t 0 2 ) ,
k = k z 2 + k r 2 = 2 π / λ .
ε / z = i ( 2 ε / r 2 + ε / r / r ) / 2 k 0 n 0 i k ' ' ( 2 ε / t 2 ) / 2 + i k 0 n 2 | ε | 2 ε i k 0 ρ ε / 2 n 0 ρ c σ ρ ε / 2 U i W ( I ) ( ρ n t ρ ) ε / 2 I ,
ρ / t = W ( I ) ( ρ n t ρ ) + σ ρ | ε | 2 / U i .
j ( r , t , z ) = 1 2 i ( ε * ( r , t , z ) ε r ε ( r , t , z ) ε * r ) .
ε g 0 ( r , t , 0 ) = ε 0 exp ( r 2 / w 0 2 t 2 / t 0 2 ) ,

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