Abstract

In this paper we illustrate how the localization of the stationary two-dimensional solution of the propagation equation strongly depends on the features of its spatio-temporal spectral bandwidth. We especially investigate the role of the ultra-broad temporal support and of the spatial bandwidth of the spectrum on the high localization in one spatial dimension of ”Bessel-like” or ”blade-like” beams, quasi-stationarily propagating in normally dispersive materials, and potentially interesting for microfabrication applications.

© 2013 OSA

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    [CrossRef] [PubMed]
  2. H. Sonajalg, M. Ratsep, and P. Saari, “Demonstration of the Bessel-X pulse propagating with strong lateral and longitudinal localization in a dispersive medium,” Opt. Lett.22, 310–312 (1997).
    [CrossRef] [PubMed]
  3. M. A. Porras, “Diffraction-free and dispersion-free pulsed beam propagation in dispersive media,” Opt. Lett.26, 1364–1366 (2001).
    [CrossRef]
  4. M. A. Porras, R. Borghi, and M. Santarsiero, “Suppression of dispersive broadening of light pulses with Bessel-Gauss beams,” Opt. Commun.206, 235–241 (2002).
    [CrossRef]
  5. S. Orlov, A. Piskarskas, and A. Stabinis, “Localized optical subcycle pulses in dispersive media,” Opt. Lett.27, 2167–2169 (2002); 27, 2103–2105 (2002).
    [CrossRef]
  6. M. A. Porras, S. Trillo, and C. Conti, “Paraxial envelope X waves,” Opt. Lett.28, 1090–1092 (2003).
    [CrossRef] [PubMed]
  7. M. A. Porras, G. Valiulis, and P. Di Trapani, “Unified description of Bessel X waves with cone dispersion and tilted pulses,” Phys. Rev. Lett. E68, 016613 (2003).
  8. P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously Generated X-Shaped Light Bullets,” Phys. Rev. Lett.91, 093904 (2003).
    [CrossRef] [PubMed]
  9. M. Kolesik, E. M. Wright, and J. V. Moloney, “Dynamic Nonlinear X Waves for Femtosecond Pulse Propagation in Water,” Phys. Rev. Lett.92, 253901 (2004).
    [CrossRef] [PubMed]
  10. D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, “Conical Emission, Pulse Splitting, and X-Wave Parametric Amplification in Nonlinear Dynamics of Ultrashort Light Pulses,” Phys. Rev. Lett.96, 193901 (2006).
    [CrossRef] [PubMed]
  11. P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of Conical Waves in Focusing, Dispersive, and Dissipative Kerr Media,” Phys. Rev. Lett.99, 223902 (2007).
    [CrossRef]
  12. O. Jedrkiewicz, M. Clerici, E. Rubino, and P. Di Trapani, “Generation and control of phase-locked conical wave packets in type-I seeded optical parametric amplification,” Phys. Rev. A80, 033813 (2009).
    [CrossRef]
  13. A. Couairon, E. Gaiauskas, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear X-wave formation by femtosecond filamentation in Kerr media,” Phys. Rev. E73, 016608 (2006).
    [CrossRef]
  14. M. A. Porras and P. Di Trapani, “Localized and stationary light wave modes in dispersive media,” Phys. Rev. E69, 066606 (2004).
    [CrossRef]
  15. D. N. Christodoulides, N. K. Efremidis, P. Di Trapani, and B. A. Malomed, “Bessel X waves in two- and three-dimensional bidispersive optical systems,” Opt. Lett.29, 1446–1448 (2004).
  16. C.R. Phipps, Laser ablation and its Applications (Springer, 2007).
    [CrossRef]
  17. M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett.97, 081102 (2010).
    [CrossRef]
  18. M.K. Bhuyan, F. Courvoisier, H.S. Phing, O. Jedrkiewicz, S. Recchia, P. Di Trapani, and J.M. Dudley, “Laser micro- and nanostructuring using femtosecond Bessel beams,” Eur. Phys. J. Special Topics199, 101–110 (2011); and see references therein.
    [CrossRef]
  19. A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett.101, 071110 (2012).
    [CrossRef]
  20. G. Valiulis, O. Jedrkiewicz, Y.-D. Wang, and P. Di Trapani, in preparation.
  21. M. Dallaire, N. McCarthy, and M. Piché, “Spatiotemporal bessel beams: theory and experiments,” Opt. Express17, 18148–18164 (2009).
    [CrossRef] [PubMed]

2012

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett.101, 071110 (2012).
[CrossRef]

2011

M.K. Bhuyan, F. Courvoisier, H.S. Phing, O. Jedrkiewicz, S. Recchia, P. Di Trapani, and J.M. Dudley, “Laser micro- and nanostructuring using femtosecond Bessel beams,” Eur. Phys. J. Special Topics199, 101–110 (2011); and see references therein.
[CrossRef]

2010

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett.97, 081102 (2010).
[CrossRef]

2009

O. Jedrkiewicz, M. Clerici, E. Rubino, and P. Di Trapani, “Generation and control of phase-locked conical wave packets in type-I seeded optical parametric amplification,” Phys. Rev. A80, 033813 (2009).
[CrossRef]

M. Dallaire, N. McCarthy, and M. Piché, “Spatiotemporal bessel beams: theory and experiments,” Opt. Express17, 18148–18164 (2009).
[CrossRef] [PubMed]

2007

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of Conical Waves in Focusing, Dispersive, and Dissipative Kerr Media,” Phys. Rev. Lett.99, 223902 (2007).
[CrossRef]

2006

A. Couairon, E. Gaiauskas, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear X-wave formation by femtosecond filamentation in Kerr media,” Phys. Rev. E73, 016608 (2006).
[CrossRef]

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, “Conical Emission, Pulse Splitting, and X-Wave Parametric Amplification in Nonlinear Dynamics of Ultrashort Light Pulses,” Phys. Rev. Lett.96, 193901 (2006).
[CrossRef] [PubMed]

2004

M. Kolesik, E. M. Wright, and J. V. Moloney, “Dynamic Nonlinear X Waves for Femtosecond Pulse Propagation in Water,” Phys. Rev. Lett.92, 253901 (2004).
[CrossRef] [PubMed]

M. A. Porras and P. Di Trapani, “Localized and stationary light wave modes in dispersive media,” Phys. Rev. E69, 066606 (2004).
[CrossRef]

D. N. Christodoulides, N. K. Efremidis, P. Di Trapani, and B. A. Malomed, “Bessel X waves in two- and three-dimensional bidispersive optical systems,” Opt. Lett.29, 1446–1448 (2004).

2003

M. A. Porras, G. Valiulis, and P. Di Trapani, “Unified description of Bessel X waves with cone dispersion and tilted pulses,” Phys. Rev. Lett. E68, 016613 (2003).

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously Generated X-Shaped Light Bullets,” Phys. Rev. Lett.91, 093904 (2003).
[CrossRef] [PubMed]

M. A. Porras, S. Trillo, and C. Conti, “Paraxial envelope X waves,” Opt. Lett.28, 1090–1092 (2003).
[CrossRef] [PubMed]

2002

S. Orlov, A. Piskarskas, and A. Stabinis, “Localized optical subcycle pulses in dispersive media,” Opt. Lett.27, 2167–2169 (2002); 27, 2103–2105 (2002).
[CrossRef]

M. A. Porras, R. Borghi, and M. Santarsiero, “Suppression of dispersive broadening of light pulses with Bessel-Gauss beams,” Opt. Commun.206, 235–241 (2002).
[CrossRef]

2001

1997

1996

Bhuyan, M. K.

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett.97, 081102 (2010).
[CrossRef]

Bhuyan, M.K.

M.K. Bhuyan, F. Courvoisier, H.S. Phing, O. Jedrkiewicz, S. Recchia, P. Di Trapani, and J.M. Dudley, “Laser micro- and nanostructuring using femtosecond Bessel beams,” Eur. Phys. J. Special Topics199, 101–110 (2011); and see references therein.
[CrossRef]

Borghi, R.

M. A. Porras, R. Borghi, and M. Santarsiero, “Suppression of dispersive broadening of light pulses with Bessel-Gauss beams,” Opt. Commun.206, 235–241 (2002).
[CrossRef]

Bragheri, F.

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, “Conical Emission, Pulse Splitting, and X-Wave Parametric Amplification in Nonlinear Dynamics of Ultrashort Light Pulses,” Phys. Rev. Lett.96, 193901 (2006).
[CrossRef] [PubMed]

Christodoulides, D. N.

D. N. Christodoulides, N. K. Efremidis, P. Di Trapani, and B. A. Malomed, “Bessel X waves in two- and three-dimensional bidispersive optical systems,” Opt. Lett.29, 1446–1448 (2004).

Clerici, M.

O. Jedrkiewicz, M. Clerici, E. Rubino, and P. Di Trapani, “Generation and control of phase-locked conical wave packets in type-I seeded optical parametric amplification,” Phys. Rev. A80, 033813 (2009).
[CrossRef]

Conti, C.

M. A. Porras, S. Trillo, and C. Conti, “Paraxial envelope X waves,” Opt. Lett.28, 1090–1092 (2003).
[CrossRef] [PubMed]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously Generated X-Shaped Light Bullets,” Phys. Rev. Lett.91, 093904 (2003).
[CrossRef] [PubMed]

Couairon, A.

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of Conical Waves in Focusing, Dispersive, and Dissipative Kerr Media,” Phys. Rev. Lett.99, 223902 (2007).
[CrossRef]

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, “Conical Emission, Pulse Splitting, and X-Wave Parametric Amplification in Nonlinear Dynamics of Ultrashort Light Pulses,” Phys. Rev. Lett.96, 193901 (2006).
[CrossRef] [PubMed]

A. Couairon, E. Gaiauskas, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear X-wave formation by femtosecond filamentation in Kerr media,” Phys. Rev. E73, 016608 (2006).
[CrossRef]

Courvoisier, F.

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett.101, 071110 (2012).
[CrossRef]

M.K. Bhuyan, F. Courvoisier, H.S. Phing, O. Jedrkiewicz, S. Recchia, P. Di Trapani, and J.M. Dudley, “Laser micro- and nanostructuring using femtosecond Bessel beams,” Eur. Phys. J. Special Topics199, 101–110 (2011); and see references therein.
[CrossRef]

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett.97, 081102 (2010).
[CrossRef]

Dallaire, M.

Di Trapani, P.

M.K. Bhuyan, F. Courvoisier, H.S. Phing, O. Jedrkiewicz, S. Recchia, P. Di Trapani, and J.M. Dudley, “Laser micro- and nanostructuring using femtosecond Bessel beams,” Eur. Phys. J. Special Topics199, 101–110 (2011); and see references therein.
[CrossRef]

O. Jedrkiewicz, M. Clerici, E. Rubino, and P. Di Trapani, “Generation and control of phase-locked conical wave packets in type-I seeded optical parametric amplification,” Phys. Rev. A80, 033813 (2009).
[CrossRef]

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of Conical Waves in Focusing, Dispersive, and Dissipative Kerr Media,” Phys. Rev. Lett.99, 223902 (2007).
[CrossRef]

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, “Conical Emission, Pulse Splitting, and X-Wave Parametric Amplification in Nonlinear Dynamics of Ultrashort Light Pulses,” Phys. Rev. Lett.96, 193901 (2006).
[CrossRef] [PubMed]

A. Couairon, E. Gaiauskas, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear X-wave formation by femtosecond filamentation in Kerr media,” Phys. Rev. E73, 016608 (2006).
[CrossRef]

D. N. Christodoulides, N. K. Efremidis, P. Di Trapani, and B. A. Malomed, “Bessel X waves in two- and three-dimensional bidispersive optical systems,” Opt. Lett.29, 1446–1448 (2004).

M. A. Porras and P. Di Trapani, “Localized and stationary light wave modes in dispersive media,” Phys. Rev. E69, 066606 (2004).
[CrossRef]

M. A. Porras, G. Valiulis, and P. Di Trapani, “Unified description of Bessel X waves with cone dispersion and tilted pulses,” Phys. Rev. Lett. E68, 016613 (2003).

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously Generated X-Shaped Light Bullets,” Phys. Rev. Lett.91, 093904 (2003).
[CrossRef] [PubMed]

G. Valiulis, O. Jedrkiewicz, Y.-D. Wang, and P. Di Trapani, in preparation.

Dubietis, A.

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of Conical Waves in Focusing, Dispersive, and Dissipative Kerr Media,” Phys. Rev. Lett.99, 223902 (2007).
[CrossRef]

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, “Conical Emission, Pulse Splitting, and X-Wave Parametric Amplification in Nonlinear Dynamics of Ultrashort Light Pulses,” Phys. Rev. Lett.96, 193901 (2006).
[CrossRef] [PubMed]

A. Couairon, E. Gaiauskas, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear X-wave formation by femtosecond filamentation in Kerr media,” Phys. Rev. E73, 016608 (2006).
[CrossRef]

Dudley, J. M.

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett.101, 071110 (2012).
[CrossRef]

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett.97, 081102 (2010).
[CrossRef]

Dudley, J.M.

M.K. Bhuyan, F. Courvoisier, H.S. Phing, O. Jedrkiewicz, S. Recchia, P. Di Trapani, and J.M. Dudley, “Laser micro- and nanostructuring using femtosecond Bessel beams,” Eur. Phys. J. Special Topics199, 101–110 (2011); and see references therein.
[CrossRef]

Efremidis, N. K.

D. N. Christodoulides, N. K. Efremidis, P. Di Trapani, and B. A. Malomed, “Bessel X waves in two- and three-dimensional bidispersive optical systems,” Opt. Lett.29, 1446–1448 (2004).

Faccio, D.

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of Conical Waves in Focusing, Dispersive, and Dissipative Kerr Media,” Phys. Rev. Lett.99, 223902 (2007).
[CrossRef]

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, “Conical Emission, Pulse Splitting, and X-Wave Parametric Amplification in Nonlinear Dynamics of Ultrashort Light Pulses,” Phys. Rev. Lett.96, 193901 (2006).
[CrossRef] [PubMed]

A. Couairon, E. Gaiauskas, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear X-wave formation by femtosecond filamentation in Kerr media,” Phys. Rev. E73, 016608 (2006).
[CrossRef]

Froehly, L.

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett.101, 071110 (2012).
[CrossRef]

Furfaro, L.

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett.101, 071110 (2012).
[CrossRef]

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett.97, 081102 (2010).
[CrossRef]

Gaiauskas, E.

A. Couairon, E. Gaiauskas, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear X-wave formation by femtosecond filamentation in Kerr media,” Phys. Rev. E73, 016608 (2006).
[CrossRef]

Jacquot, M.

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett.101, 071110 (2012).
[CrossRef]

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett.97, 081102 (2010).
[CrossRef]

Jedrkiewicz, O.

M.K. Bhuyan, F. Courvoisier, H.S. Phing, O. Jedrkiewicz, S. Recchia, P. Di Trapani, and J.M. Dudley, “Laser micro- and nanostructuring using femtosecond Bessel beams,” Eur. Phys. J. Special Topics199, 101–110 (2011); and see references therein.
[CrossRef]

O. Jedrkiewicz, M. Clerici, E. Rubino, and P. Di Trapani, “Generation and control of phase-locked conical wave packets in type-I seeded optical parametric amplification,” Phys. Rev. A80, 033813 (2009).
[CrossRef]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously Generated X-Shaped Light Bullets,” Phys. Rev. Lett.91, 093904 (2003).
[CrossRef] [PubMed]

G. Valiulis, O. Jedrkiewicz, Y.-D. Wang, and P. Di Trapani, in preparation.

Kolesik, M.

M. Kolesik, E. M. Wright, and J. V. Moloney, “Dynamic Nonlinear X Waves for Femtosecond Pulse Propagation in Water,” Phys. Rev. Lett.92, 253901 (2004).
[CrossRef] [PubMed]

Lacourt, P. A.

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett.101, 071110 (2012).
[CrossRef]

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett.97, 081102 (2010).
[CrossRef]

Malomed, B. A.

D. N. Christodoulides, N. K. Efremidis, P. Di Trapani, and B. A. Malomed, “Bessel X waves in two- and three-dimensional bidispersive optical systems,” Opt. Lett.29, 1446–1448 (2004).

Mathis, A.

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett.101, 071110 (2012).
[CrossRef]

McCarthy, N.

Moloney, J. V.

M. Kolesik, E. M. Wright, and J. V. Moloney, “Dynamic Nonlinear X Waves for Femtosecond Pulse Propagation in Water,” Phys. Rev. Lett.92, 253901 (2004).
[CrossRef] [PubMed]

Orlov, S.

Parola, A.

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of Conical Waves in Focusing, Dispersive, and Dissipative Kerr Media,” Phys. Rev. Lett.99, 223902 (2007).
[CrossRef]

Phing, H.S.

M.K. Bhuyan, F. Courvoisier, H.S. Phing, O. Jedrkiewicz, S. Recchia, P. Di Trapani, and J.M. Dudley, “Laser micro- and nanostructuring using femtosecond Bessel beams,” Eur. Phys. J. Special Topics199, 101–110 (2011); and see references therein.
[CrossRef]

Phipps, C.R.

C.R. Phipps, Laser ablation and its Applications (Springer, 2007).
[CrossRef]

Piché, M.

Piskarskas, A.

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of Conical Waves in Focusing, Dispersive, and Dissipative Kerr Media,” Phys. Rev. Lett.99, 223902 (2007).
[CrossRef]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously Generated X-Shaped Light Bullets,” Phys. Rev. Lett.91, 093904 (2003).
[CrossRef] [PubMed]

S. Orlov, A. Piskarskas, and A. Stabinis, “Localized optical subcycle pulses in dispersive media,” Opt. Lett.27, 2167–2169 (2002); 27, 2103–2105 (2002).
[CrossRef]

Polesana, P.

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of Conical Waves in Focusing, Dispersive, and Dissipative Kerr Media,” Phys. Rev. Lett.99, 223902 (2007).
[CrossRef]

Porras, M. A.

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of Conical Waves in Focusing, Dispersive, and Dissipative Kerr Media,” Phys. Rev. Lett.99, 223902 (2007).
[CrossRef]

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, “Conical Emission, Pulse Splitting, and X-Wave Parametric Amplification in Nonlinear Dynamics of Ultrashort Light Pulses,” Phys. Rev. Lett.96, 193901 (2006).
[CrossRef] [PubMed]

M. A. Porras and P. Di Trapani, “Localized and stationary light wave modes in dispersive media,” Phys. Rev. E69, 066606 (2004).
[CrossRef]

M. A. Porras, G. Valiulis, and P. Di Trapani, “Unified description of Bessel X waves with cone dispersion and tilted pulses,” Phys. Rev. Lett. E68, 016613 (2003).

M. A. Porras, S. Trillo, and C. Conti, “Paraxial envelope X waves,” Opt. Lett.28, 1090–1092 (2003).
[CrossRef] [PubMed]

M. A. Porras, R. Borghi, and M. Santarsiero, “Suppression of dispersive broadening of light pulses with Bessel-Gauss beams,” Opt. Commun.206, 235–241 (2002).
[CrossRef]

M. A. Porras, “Diffraction-free and dispersion-free pulsed beam propagation in dispersive media,” Opt. Lett.26, 1364–1366 (2001).
[CrossRef]

Ratsep, M.

Recchia, S.

M.K. Bhuyan, F. Courvoisier, H.S. Phing, O. Jedrkiewicz, S. Recchia, P. Di Trapani, and J.M. Dudley, “Laser micro- and nanostructuring using femtosecond Bessel beams,” Eur. Phys. J. Special Topics199, 101–110 (2011); and see references therein.
[CrossRef]

Rubino, E.

O. Jedrkiewicz, M. Clerici, E. Rubino, and P. Di Trapani, “Generation and control of phase-locked conical wave packets in type-I seeded optical parametric amplification,” Phys. Rev. A80, 033813 (2009).
[CrossRef]

Saari, P.

Salut, R.

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett.97, 081102 (2010).
[CrossRef]

Santarsiero, M.

M. A. Porras, R. Borghi, and M. Santarsiero, “Suppression of dispersive broadening of light pulses with Bessel-Gauss beams,” Opt. Commun.206, 235–241 (2002).
[CrossRef]

Sonajalg, H.

Stabinis, A.

Trillo, S.

M. A. Porras, S. Trillo, and C. Conti, “Paraxial envelope X waves,” Opt. Lett.28, 1090–1092 (2003).
[CrossRef] [PubMed]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously Generated X-Shaped Light Bullets,” Phys. Rev. Lett.91, 093904 (2003).
[CrossRef] [PubMed]

Trull, J.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously Generated X-Shaped Light Bullets,” Phys. Rev. Lett.91, 093904 (2003).
[CrossRef] [PubMed]

Valiulis, G.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously Generated X-Shaped Light Bullets,” Phys. Rev. Lett.91, 093904 (2003).
[CrossRef] [PubMed]

M. A. Porras, G. Valiulis, and P. Di Trapani, “Unified description of Bessel X waves with cone dispersion and tilted pulses,” Phys. Rev. Lett. E68, 016613 (2003).

G. Valiulis, O. Jedrkiewicz, Y.-D. Wang, and P. Di Trapani, in preparation.

Wang, Y.-D.

G. Valiulis, O. Jedrkiewicz, Y.-D. Wang, and P. Di Trapani, in preparation.

Wright, E. M.

M. Kolesik, E. M. Wright, and J. V. Moloney, “Dynamic Nonlinear X Waves for Femtosecond Pulse Propagation in Water,” Phys. Rev. Lett.92, 253901 (2004).
[CrossRef] [PubMed]

Appl. Phys. Lett.

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett.97, 081102 (2010).
[CrossRef]

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett.101, 071110 (2012).
[CrossRef]

Eur. Phys. J. Special Topics

M.K. Bhuyan, F. Courvoisier, H.S. Phing, O. Jedrkiewicz, S. Recchia, P. Di Trapani, and J.M. Dudley, “Laser micro- and nanostructuring using femtosecond Bessel beams,” Eur. Phys. J. Special Topics199, 101–110 (2011); and see references therein.
[CrossRef]

Opt. Commun.

M. A. Porras, R. Borghi, and M. Santarsiero, “Suppression of dispersive broadening of light pulses with Bessel-Gauss beams,” Opt. Commun.206, 235–241 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

O. Jedrkiewicz, M. Clerici, E. Rubino, and P. Di Trapani, “Generation and control of phase-locked conical wave packets in type-I seeded optical parametric amplification,” Phys. Rev. A80, 033813 (2009).
[CrossRef]

Phys. Rev. E

A. Couairon, E. Gaiauskas, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear X-wave formation by femtosecond filamentation in Kerr media,” Phys. Rev. E73, 016608 (2006).
[CrossRef]

M. A. Porras and P. Di Trapani, “Localized and stationary light wave modes in dispersive media,” Phys. Rev. E69, 066606 (2004).
[CrossRef]

Phys. Rev. Lett.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously Generated X-Shaped Light Bullets,” Phys. Rev. Lett.91, 093904 (2003).
[CrossRef] [PubMed]

M. Kolesik, E. M. Wright, and J. V. Moloney, “Dynamic Nonlinear X Waves for Femtosecond Pulse Propagation in Water,” Phys. Rev. Lett.92, 253901 (2004).
[CrossRef] [PubMed]

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, “Conical Emission, Pulse Splitting, and X-Wave Parametric Amplification in Nonlinear Dynamics of Ultrashort Light Pulses,” Phys. Rev. Lett.96, 193901 (2006).
[CrossRef] [PubMed]

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of Conical Waves in Focusing, Dispersive, and Dissipative Kerr Media,” Phys. Rev. Lett.99, 223902 (2007).
[CrossRef]

Phys. Rev. Lett. E

M. A. Porras, G. Valiulis, and P. Di Trapani, “Unified description of Bessel X waves with cone dispersion and tilted pulses,” Phys. Rev. Lett. E68, 016613 (2003).

Other

C.R. Phipps, Laser ablation and its Applications (Springer, 2007).
[CrossRef]

G. Valiulis, O. Jedrkiewicz, Y.-D. Wang, and P. Di Trapani, in preparation.

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Figures (5)

Fig. 1
Fig. 1

Intensity profiles of the 2D stationary solution of the wave equation (with relative time integrated curves), featured by different normal dispersion spectral supports (kx = Δ(Ω)) shown in the top right corner insets.

Fig. 2
Fig. 2

Sketch of the experimental setup based on a pulse shaper with a folded diffraction grating as in [21]. The reflective mask now constituted by hyperbolic branches selects the optical frequencies that are recombined on the diffraction grating. The second cylindrical lens produces the spatial Fourier transform of the mask.

Fig. 3
Fig. 3

Time integrated spatial images (a,b,c) and corresponding central transverse intensity profiles (d,e,f) of the beam generated after the linear beam shaper. The mask spectrum (right) had an angular gap of 0.01 rad (case a,d), 0,02 rad (case b,e), and 0,04 rad (case c,f) respectively. The real branches thickness was 1mm (mask placed in the Fourier plane of the lens after the grating.)

Fig. 4
Fig. 4

Time integrated spatial images, recorded in air for different z propagation positions, of the 1D spatial WP generated by means of a mask (in a)) with a gap between the branches of 0,008 rad and branches thickness 2.5 mm. In b) a neat transverse intensity profile recorded at z=0 (10mm before the exact Fourier Plane of the second cylindrical lens).

Fig. 5
Fig. 5

Images and transverse profiles (right column) of the beams generated by using different portions of the spatio-temporal spectral support (left column).

Equations (5)

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A ( η , x , z ) = 1 ( 2 π ) 2 S 0 ( Ω , k x ) × exp ( i ( Ω η k x x G ( Ω , k x ) z ) ) d Ω d k x ,
G ( Ω , k x ) = k 2 ( ω 0 + Ω ) k x 2 ( k 0 + Ω u 0 ) ,
k 2 ( ω 0 + Ω ) k x 2 = k 0 + γ + Ω ( γ 1 + u 0 1 ) + γ 2 k x .
A = e i β z S 0 ( Ω ) cos ( Δ ( Ω ) x ) e i Ω [ t z / u g r ] d Ω 2 π .
A ( ξ , 0 ) = S 00 μ π ξ σ 2 × [ ( μ + a ) sin ( 1 2 ξ ( a u ) ) + ( μ a ) sin ( 1 2 ξ ( a + μ ) ) ]

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