Abstract

We study the nonlinear propagation of space-time pulsed beams, also known as time-diffracting beams, a recently introduced class of diffraction-free spatiotemporal wave packets whose temporal-transversal structure is that of diffraction in time. We report on the spontaneous formation of propagation-invariant, spatiotemporally compressed pulsed beams carrying finite power from exciting time-diffracting Gaussian beams in media with cubic Kerr nonlinearity at powers below the critical power for collapse, and also with other collapse-arresting nonlinearities above the critical power. Their attraction property makes the experimental observation of the self-trapped pulsed beams in cubic Kerr media feasible. The structure in the temporal and transversal dimensions of the self-trapped wave packets is shown to be the same as the structure in the axial and transversal dimensions of the self-focusing and (arrested) collapse of monochromatic Gaussian beams.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  2. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
  3. T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 70, 1401 (1993).
  4. A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear airy beams,” Phys. Rev. A 84, 021807 (2011).
  5. C. Xie, V. Jukna, C. Milián, R. Giust, I. Ouadghiri-Idrissi, T. Itina, J. M. Dudley, A. Couairon, and F. Courvoisier, “Tubular filamentation for laser material processing,” Sci. Rep. 5, 8914 (2015).
  6. P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
  7. H. E. Kondakci and A. F. Abouraddy, “Diffraction-free pulsed optical beams via space-time correlations,” Opt. Express 24, 28659–28668 (2016).
  8. K. J. Parker and M. A. Alonso, “Longitudinal iso-phase condition and needle pulses,” Opt. Express 24, 28669–28677 (2016).
  9. H. E. Kondakci and A. F. Abouraddy, “Diffraction-free space-time light sheets,” Nature Photon. 11, 733–740 (2017).
  10. H. E. Kondakci and A. F. Abouraddy, “Airy wavepackets accelerating in space-time,” Phys. Rev. Lett. 120, 163901 (2018).
  11. H. E. Kondakci, M. Yessenov, M. Meem, D. Reyes, D. Thul, S. R. Farichild, M. Richardson, R. Menon, and A. F. Abouraddy, “Synthesizing broadband propagation-invariant space-time wave packets using transmissive phase plates,” Opt. Express 26, 13628–13638 (2018).
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  13. P. Saari and K. Reivelt, “Generation and classification of localized waves by Lorentz transformations in Fourier space,” Phys. Rev. E 69, 036612 (2004).
  14. M. A. Porras and P. Di Trapani, “Localized and stationary light wave modes in dispersive media,” Phys. Rev. E 69, 066606 (2004).
  15. M. A. Porras, “Diffraction-free and dispersion-free pulsed beam propagation in dispersive media,” Opt. Lett. 26, 1364-1366 (2001).
  16. M. A. Porras, “Gaussian beams diffracting in time,” Opt. Lett. 42, 4679–4682 (2017).
  17. M. A. Porras, “Nature, diffraction-free propagation via space-time correlations, and nonlinear generation of time-diffracting light beams,” Phys. Rev. A 97, 063803 (2018).
  18. C. Sulem and P. L. Sulem, The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse, (Springer, 2004).
  19. I. G. Koprinkov, A. Suda, P. Q. Wang, and K. Midorikawa, “Self-Compression of high-intensity femtosecond optical pulses and spatiotemporal soliton generation,” Phys. Rev. Lett. 84, 3847 (2000).
  20. G. Fibich and B. Ilan, “Optical light bullets in a pure Kerr medium,” Opt. Lett. 29, 887–889 (2004).
  21. N. N. Akhmediev, “Spatial solitons in Kerr and Kerr-like media,” Opt. Quant. Electron. 30, 535–569 (1998).
  22. M. Segev, “Optical spatial solitons,” Opt. Quant. Electron. 30, 503–533 (1998).
  23. G. Fibich, The Nonlinear Schrödinger Equation: Singular Solutions and Optical Collapse (Springer, 2015).
  24. C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, “Nonlinear electromagnetic X waves,” Phys. Rev. Lett. 90, 170406 (2003).
  25. 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).
  26. 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).
  27. G. Fibich and A. L. Gaeta, “Critical power for self-focusing in bulk media and in hollow waveguides,” Opt. Lett. 25, 335–337 (2000).
  28. L. J. Wong and I. Kaminer, “Abruptly focusing and defocusing needles of light and closed-form electromagnetic wavepackets,” ACS Photon. 4, 1131–1137 (2017).
  29. G. Fibich, “Some modern aspects of self-focusing theory,” R. W. Boyd, S. G. Lukishova, and Y. Shen, eds. Self-focusing: Past and Present (Springer, 2009).

2018 (3)

H. E. Kondakci and A. F. Abouraddy, “Airy wavepackets accelerating in space-time,” Phys. Rev. Lett. 120, 163901 (2018).

H. E. Kondakci, M. Yessenov, M. Meem, D. Reyes, D. Thul, S. R. Farichild, M. Richardson, R. Menon, and A. F. Abouraddy, “Synthesizing broadband propagation-invariant space-time wave packets using transmissive phase plates,” Opt. Express 26, 13628–13638 (2018).

M. A. Porras, “Nature, diffraction-free propagation via space-time correlations, and nonlinear generation of time-diffracting light beams,” Phys. Rev. A 97, 063803 (2018).

2017 (3)

H. E. Kondakci and A. F. Abouraddy, “Diffraction-free space-time light sheets,” Nature Photon. 11, 733–740 (2017).

M. A. Porras, “Gaussian beams diffracting in time,” Opt. Lett. 42, 4679–4682 (2017).

L. J. Wong and I. Kaminer, “Abruptly focusing and defocusing needles of light and closed-form electromagnetic wavepackets,” ACS Photon. 4, 1131–1137 (2017).

2016 (2)

2015 (1)

C. Xie, V. Jukna, C. Milián, R. Giust, I. Ouadghiri-Idrissi, T. Itina, J. M. Dudley, A. Couairon, and F. Courvoisier, “Tubular filamentation for laser material processing,” Sci. Rep. 5, 8914 (2015).

2011 (1)

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear airy beams,” Phys. Rev. A 84, 021807 (2011).

2009 (1)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).

2007 (1)

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).

2006 (1)

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).

2004 (3)

G. Fibich and B. Ilan, “Optical light bullets in a pure Kerr medium,” Opt. Lett. 29, 887–889 (2004).

P. Saari and K. Reivelt, “Generation and classification of localized waves by Lorentz transformations in Fourier space,” Phys. Rev. E 69, 036612 (2004).

M. A. Porras and P. Di Trapani, “Localized and stationary light wave modes in dispersive media,” Phys. Rev. E 69, 066606 (2004).

2003 (2)

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, “Nonlinear electromagnetic X waves,” Phys. Rev. Lett. 90, 170406 (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).

2001 (1)

2000 (2)

I. G. Koprinkov, A. Suda, P. Q. Wang, and K. Midorikawa, “Self-Compression of high-intensity femtosecond optical pulses and spatiotemporal soliton generation,” Phys. Rev. Lett. 84, 3847 (2000).

G. Fibich and A. L. Gaeta, “Critical power for self-focusing in bulk media and in hollow waveguides,” Opt. Lett. 25, 335–337 (2000).

1998 (2)

N. N. Akhmediev, “Spatial solitons in Kerr and Kerr-like media,” Opt. Quant. Electron. 30, 535–569 (1998).

M. Segev, “Optical spatial solitons,” Opt. Quant. Electron. 30, 503–533 (1998).

1993 (1)

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 70, 1401 (1993).

1987 (1)

Abdollahpour, D.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear airy beams,” Phys. Rev. A 84, 021807 (2011).

Abouraddy, A. F.

Akhmediev, N. N.

N. N. Akhmediev, “Spatial solitons in Kerr and Kerr-like media,” Opt. Quant. Electron. 30, 535–569 (1998).

Alonso, M. A.

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).

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).

Christodoulides, D. N.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).

Conti, C.

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).

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, “Nonlinear electromagnetic X waves,” Phys. Rev. Lett. 90, 170406 (2003).

Couairon, A.

C. Xie, V. Jukna, C. Milián, R. Giust, I. Ouadghiri-Idrissi, T. Itina, J. M. Dudley, A. Couairon, and F. Courvoisier, “Tubular filamentation for laser material processing,” Sci. Rep. 5, 8914 (2015).

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear airy beams,” Phys. Rev. A 84, 021807 (2011).

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).

Courvoisier, F.

C. Xie, V. Jukna, C. Milián, R. Giust, I. Ouadghiri-Idrissi, T. Itina, J. M. Dudley, A. Couairon, and F. Courvoisier, “Tubular filamentation for laser material processing,” Sci. Rep. 5, 8914 (2015).

Di Trapani, P.

M. A. Porras and P. Di Trapani, “Localized and stationary light wave modes in dispersive media,” Phys. Rev. E 69, 066606 (2004).

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).

Dubietis, A.

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).

Dudley, J. M.

C. Xie, V. Jukna, C. Milián, R. Giust, I. Ouadghiri-Idrissi, T. Itina, J. M. Dudley, A. Couairon, and F. Courvoisier, “Tubular filamentation for laser material processing,” Sci. Rep. 5, 8914 (2015).

Durnin, J.

Faccio, D.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear airy beams,” Phys. Rev. A 84, 021807 (2011).

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).

Farichild, S. R.

Fibich, G.

G. Fibich and B. Ilan, “Optical light bullets in a pure Kerr medium,” Opt. Lett. 29, 887–889 (2004).

G. Fibich and A. L. Gaeta, “Critical power for self-focusing in bulk media and in hollow waveguides,” Opt. Lett. 25, 335–337 (2000).

G. Fibich, “Some modern aspects of self-focusing theory,” R. W. Boyd, S. G. Lukishova, and Y. Shen, eds. Self-focusing: Past and Present (Springer, 2009).

G. Fibich, The Nonlinear Schrödinger Equation: Singular Solutions and Optical Collapse (Springer, 2015).

Gaeta, A. L.

Giust, R.

C. Xie, V. Jukna, C. Milián, R. Giust, I. Ouadghiri-Idrissi, T. Itina, J. M. Dudley, A. Couairon, and F. Courvoisier, “Tubular filamentation for laser material processing,” Sci. Rep. 5, 8914 (2015).

Herminghaus, S.

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 70, 1401 (1993).

Hernández-Figueroa, H. E.

H. E. Hernández-Figueroa, M. Zamboni-Rached, and E. Recami, Localized Waves, (Wiley, 2008).

Ilan, B.

Itina, T.

C. Xie, V. Jukna, C. Milián, R. Giust, I. Ouadghiri-Idrissi, T. Itina, J. M. Dudley, A. Couairon, and F. Courvoisier, “Tubular filamentation for laser material processing,” Sci. Rep. 5, 8914 (2015).

Jedrkiewicz, O.

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, “Nonlinear electromagnetic X waves,” Phys. Rev. Lett. 90, 170406 (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).

Jukna, V.

C. Xie, V. Jukna, C. Milián, R. Giust, I. Ouadghiri-Idrissi, T. Itina, J. M. Dudley, A. Couairon, and F. Courvoisier, “Tubular filamentation for laser material processing,” Sci. Rep. 5, 8914 (2015).

Kaminer, I.

L. J. Wong and I. Kaminer, “Abruptly focusing and defocusing needles of light and closed-form electromagnetic wavepackets,” ACS Photon. 4, 1131–1137 (2017).

Kolesik, M.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).

Kondakci, H. E.

Koprinkov, I. G.

I. G. Koprinkov, A. Suda, P. Q. Wang, and K. Midorikawa, “Self-Compression of high-intensity femtosecond optical pulses and spatiotemporal soliton generation,” Phys. Rev. Lett. 84, 3847 (2000).

Lotti, A.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear airy beams,” Phys. Rev. A 84, 021807 (2011).

Meem, M.

Menon, R.

Midorikawa, K.

I. G. Koprinkov, A. Suda, P. Q. Wang, and K. Midorikawa, “Self-Compression of high-intensity femtosecond optical pulses and spatiotemporal soliton generation,” Phys. Rev. Lett. 84, 3847 (2000).

Milián, C.

C. Xie, V. Jukna, C. Milián, R. Giust, I. Ouadghiri-Idrissi, T. Itina, J. M. Dudley, A. Couairon, and F. Courvoisier, “Tubular filamentation for laser material processing,” Sci. Rep. 5, 8914 (2015).

Moloney, J. V.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).

Ouadghiri-Idrissi, I.

C. Xie, V. Jukna, C. Milián, R. Giust, I. Ouadghiri-Idrissi, T. Itina, J. M. Dudley, A. Couairon, and F. Courvoisier, “Tubular filamentation for laser material processing,” Sci. Rep. 5, 8914 (2015).

Panagiotopoulos, P.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear airy beams,” Phys. Rev. A 84, 021807 (2011).

Papazoglou, D. G.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear airy beams,” Phys. Rev. A 84, 021807 (2011).

Parker, K. J.

Piskarskas, A.

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).

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, “Nonlinear electromagnetic X waves,” Phys. Rev. Lett. 90, 170406 (2003).

Polynkin, P.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).

Porras, M. A.

M. A. Porras, “Nature, diffraction-free propagation via space-time correlations, and nonlinear generation of time-diffracting light beams,” Phys. Rev. A 97, 063803 (2018).

M. A. Porras, “Gaussian beams diffracting in time,” Opt. Lett. 42, 4679–4682 (2017).

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).

M. A. Porras and P. Di Trapani, “Localized and stationary light wave modes in dispersive media,” Phys. Rev. E 69, 066606 (2004).

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

Recami, E.

H. E. Hernández-Figueroa, M. Zamboni-Rached, and E. Recami, Localized Waves, (Wiley, 2008).

Reivelt, K.

P. Saari and K. Reivelt, “Generation and classification of localized waves by Lorentz transformations in Fourier space,” Phys. Rev. E 69, 036612 (2004).

Reyes, D.

Richardson, M.

Saari, P.

P. Saari and K. Reivelt, “Generation and classification of localized waves by Lorentz transformations in Fourier space,” Phys. Rev. E 69, 036612 (2004).

Segev, M.

M. Segev, “Optical spatial solitons,” Opt. Quant. Electron. 30, 503–533 (1998).

Siviloglou, G. A.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).

Suda, A.

I. G. Koprinkov, A. Suda, P. Q. Wang, and K. Midorikawa, “Self-Compression of high-intensity femtosecond optical pulses and spatiotemporal soliton generation,” Phys. Rev. Lett. 84, 3847 (2000).

Sulem, C.

C. Sulem and P. L. Sulem, The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse, (Springer, 2004).

Sulem, P. L.

C. Sulem and P. L. Sulem, The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse, (Springer, 2004).

Thul, D.

Trapani, P. Di

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).

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, “Nonlinear electromagnetic X waves,” Phys. Rev. Lett. 90, 170406 (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).

Trillo, S.

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, “Nonlinear electromagnetic X waves,” Phys. Rev. Lett. 90, 170406 (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).

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).

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, “Nonlinear electromagnetic X waves,” Phys. Rev. Lett. 90, 170406 (2003).

Tzortzakis, S.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear airy beams,” Phys. Rev. A 84, 021807 (2011).

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).

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, “Nonlinear electromagnetic X waves,” Phys. Rev. Lett. 90, 170406 (2003).

Wang, P. Q.

I. G. Koprinkov, A. Suda, P. Q. Wang, and K. Midorikawa, “Self-Compression of high-intensity femtosecond optical pulses and spatiotemporal soliton generation,” Phys. Rev. Lett. 84, 3847 (2000).

Wong, L. J.

L. J. Wong and I. Kaminer, “Abruptly focusing and defocusing needles of light and closed-form electromagnetic wavepackets,” ACS Photon. 4, 1131–1137 (2017).

Wulle, T.

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 70, 1401 (1993).

Xie, C.

C. Xie, V. Jukna, C. Milián, R. Giust, I. Ouadghiri-Idrissi, T. Itina, J. M. Dudley, A. Couairon, and F. Courvoisier, “Tubular filamentation for laser material processing,” Sci. Rep. 5, 8914 (2015).

Yessenov, M.

Zamboni-Rached, M.

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L. J. Wong and I. Kaminer, “Abruptly focusing and defocusing needles of light and closed-form electromagnetic wavepackets,” ACS Photon. 4, 1131–1137 (2017).

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H. E. Kondakci and A. F. Abouraddy, “Diffraction-free space-time light sheets,” Nature Photon. 11, 733–740 (2017).

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Figures (3)

Fig. 1
Fig. 1 (a) ST distribution (y = 0 section) of amplitude of a superluminal (α > 0) TDGB of power P = 0:791Pc at the entrance plane z = 0 of the nonlinear medium and as it propagates in medium. (b,c) On-axis amplitude (r = 0) and transversal amplitude at pulse center (τ = t′ + αz = 0) of the input TDGB (dashed curves) and of the propagation-invariant pulsed beam (solid curves). Red dashed curves: On-axis amplitude and transversal amplitude at τ = 0 for the nonlinear focusing in τ/α obtained as the solution of Eq. (6) with initial condition in Eq. (8) at τ/α = −20 with the same zR and power. (d) Fluence of the input TDGB in free space (z < 0) and in the nonlinear medium (z > 0). The fluence is normalized to the peak fluence of the input TDGB. (e) Peak fluence and peak intensity at each propagation distance, normalized to their values for the input TDGB. (f) Diffracting transversal amplitude of the luminal pulse at t′ = 0 at increasing propagation distances. (g) Instantaneous linear and nonlinear Hamiltonian of the input TDGB.
Fig. 2
Fig. 2 (a, b) Peak intensity and fluence as functions of propagation distance for input TDGBs of the indicated powers, normalized to their values for the input TDGB. (c,d) On-axis amplitudes (r = 0) and transversal amplitudes at pulse center (τ = t′ + αz = 0) of input TDGBs (dashed curves) and of the propagation-invariant pulsed beams (solid curves). Red dashed curves: On-axis amplitudes and transversal amplitudes at τ = 0 for the nonlinear focusing in τ/α obtained as the solution of Eq. (6) with initial condition in Eq. (8) at τ/α = −20 with the same zR and powers.
Fig. 3
Fig. 3 (a) For input super and subluminal TDGBs of power P = 1.5Pc in a medium with self-focusing cubic and self-defocusing quintic nonlinearities (n = n0 + n2I + n4I2) such that | n 4 I 0 2 / n 2 I 0 | = 0.2, spatiotemporal distribution of amplitude (y = 0 section) at z = 0 and at sufficiently long distance (z = 10zR). (b) and (c) On-axis amplitude of the input TDGB (dashed curves) and of the propagation-invariant pulsed beam (solid curves) as functions of the local time τ in the respective cases of super and subluminal input TDGB. Red dashed curves: On-axis amplitude for nonlinear focusing along the length τ/α of the initial condition in Eq. (8) at τ/α = −20 with the same zR and power in the same cubic-quintic medium. (d) Peak fluence and peak intensity at each propagation distance, normalized to their values for the input TDGB. (e) Transversal amplitude profile of the luminal spatial soliton formed about t′ = 0.

Equations (8)

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z A = i 2 k 0 Δ A + i k 0 n 2 n 0 | A | 2 A ,
A ( r , t ' , z ) = I 0 i z R ( t + α z ) / α i z R exp [ i k 0 r 2 2 [ ( t + α z ) / α i z R ] ] ,
τ = t + α z = t z / v g ,
H( t )= | A | 2 dxdy k 0 2 n 2 n 0 | A | 4 dxdy,
H ( t ' ) = H L [ 1 0.948 P P c 1 1 + ( t / t 0 ) 2 ] ,
τ A α = i 2 k 0 α Δ A α + i k 0 n 2 n 0 α | A α | 2 A α ,
H= | A α | 2 dxdy k 0 2 n 2 n 0 | A α | 4 dxdy,
A α ( r , τ ) τ / α I 0 i z R τ / α i z R exp [ i k 0 r 2 2 [ τ / α i z R ] ] ,

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