Abstract

Strong self-focusing and defocusing of optical radiation with Gaussian spatial and temporal distribution due to cascading second harmonic generation without a significant change in the beam profile and the pulse shape for the fundamental wave under the condition of group velocity matching in the axial-symmetric case for a bulk medium is considered, and the maximum intensity of an optical beam increases in 70 times (or more) in comparison with the intensity of incident optical radiation. This result is obtained for pulse duration, which belongs to a time interval from microseconds to picoseconds, for which the dispersion of group velocity is negligible. Self-focusing of laser radiation allows the realization of the mode that is similar to Kerr-lens mode locking, but for laser systems generating the optical radiation with a duration from microseconds to picoseconds.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  30. Y. Pang, V. Yanovsky, F. Wise, and B. I. Minkov, “Self-mode-locked Cr:forsterite laser,” Opt. Lett. 18, 1168–1170 (1993).
    [CrossRef]
  31. V. A. Trofimov and T. M. Lysak, “Highly efficient SHG of a sequence of laser pulses with a random peak intensity and duration,” Opt. Spectrosc. 107, 399–406 (2009).
    [CrossRef]
  32. V. A. Trofimov and T. M. Lysak, “Catastrophic self-focusing of axially symmetric laser beams due to cascading SHG,” in Technical Program of 14th International Conference on Laser Optics (LO-2010) (IOP, 2010), p. 27.
  33. V. A. Trofimov and T. M. Lysak, “Catastrophic self-focusing of axially symmetric laser beams due to cascading SHG,” Proc. SPIE 7822, 78220E (2011).
  34. T. M. Lysak and V. A. Trofimov, “Achieving high-efficiency second harmonic generation in a sequence of laser pulses with random peak intensity. Part I. Efficient generation in optical fibers,” Comput. Math. Model. 19, 333–342 (2008).
    [CrossRef]
  35. T. M. Lysak and V. A. Trofimov, “Achieving high-efficiency second harmonic generation in a sequence of laser pulses with random peak intensity. Part II. Suppression of intensity fluctuations in a quadratic-nonlinearity medium,” Computat. Math. Model. 20, 1–25 (2009).
    [CrossRef]
  36. T. M. Lysak and V. A. Trofimov, “Achieving high-efficiency second harmonic generation in a sequence of laser pulses with random peak intensity. Part III. Propagation of pulses in a bulk medium,” Comput. Math. Model. 20, 101–112 (2009).
    [CrossRef]
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    [CrossRef]

2011 (1)

V. A. Trofimov and T. M. Lysak, “Catastrophic self-focusing of axially symmetric laser beams due to cascading SHG,” Proc. SPIE 7822, 78220E (2011).

2009 (3)

T. M. Lysak and V. A. Trofimov, “Achieving high-efficiency second harmonic generation in a sequence of laser pulses with random peak intensity. Part II. Suppression of intensity fluctuations in a quadratic-nonlinearity medium,” Computat. Math. Model. 20, 1–25 (2009).
[CrossRef]

T. M. Lysak and V. A. Trofimov, “Achieving high-efficiency second harmonic generation in a sequence of laser pulses with random peak intensity. Part III. Propagation of pulses in a bulk medium,” Comput. Math. Model. 20, 101–112 (2009).
[CrossRef]

V. A. Trofimov and T. M. Lysak, “Highly efficient SHG of a sequence of laser pulses with a random peak intensity and duration,” Opt. Spectrosc. 107, 399–406 (2009).
[CrossRef]

2008 (1)

T. M. Lysak and V. A. Trofimov, “Achieving high-efficiency second harmonic generation in a sequence of laser pulses with random peak intensity. Part I. Efficient generation in optical fibers,” Comput. Math. Model. 19, 333–342 (2008).
[CrossRef]

2007 (4)

V. A. Trofimov and V. V. Trofimov, “High effective SHG of femtosecond pulse with ring profile of beam in bulk medium with cubic nonlinear response,” Proc. SPIE 6610, 66100R (2007).
[CrossRef]

X. Zeng, S. Ashihara, T. Shimura, and K. Kuroda, “Adiabatic femtosecond pulse compression and control by using quadratic cascading nonlinearity,” Proc. SPIE 6839, 68390B (2007).
[CrossRef]

G. Xie, D. Zhang, L. Qian, H. Zhu, and D. Tang, “Multi-stage pulse compression by use of cascaded quadratic nonlinearity,” Opt. Commun. 273, 207–213 (2007).
[CrossRef]

M. Bache, O. Bang, J. Moses, and F. W. Wise, “Nonlocal explanation of stationary and nonstationary regimes in cascaded soliton pulse compression,” Opt. Lett. 32, 2490–2492 (2007).
[CrossRef]

2006 (2)

X. Zeng, S. Ashihara, N. Fujioka, T. Shimura, and K. Kuroda, “Adiabatic compression of quadratic temporal solitons in aperiodic quasi-phase-matching gratings,” Opt. Express 14, 9358–9370 (2006).
[CrossRef]

V. A. Trofimov and V. V. Trofimov, “On compression of femtosecond pulses with basic and doubled frequencies,” Proc. SPIE 6165, 616502 (2006).
[CrossRef]

2003 (2)

S. Minardi, J. Yu, G. Blasi, A. Varanavičius, G. Valiulis, A. Beržanskis, A. Piskarskas, and P. Di Trapani, “Red solitons: evidence of spatiotemporal instability in χ(2) spatial soliton dynamics,” Phys. Rev. Lett. 91, 123901 (2003).
[CrossRef]

G. I. Stegeman, R. Schiek, H. Fang, R. Malendevich, L. Jankovic, L. Torner, W. Sohle, and G. Schreiber, “Beam evolution in quadratically nonlinear one-dimensional media: LiNbO3 slab waveguides,” Laser Phys. 13, 137–147 (2003).

2002 (3)

2001 (2)

K. Beckitt, F. Wise, L. Qian, L. A. Walker, and E. Canto-Said, “Compensation for self-focusing by use of cascade quadratic nonlinearity,” Opt. Lett. 26, 1696–1698 (2001).
[CrossRef]

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities in self-trapping due to parametric frequency conversion,” Phys. Rev. Lett. 87, 183902 (2001).
[CrossRef]

1999 (4)

1998 (2)

A. M. Weiner, A. M. Kan’an, and D. E. Leaird, “High-efficiency blue generation by frequency doubling of femtosecond pulses in a thick nonlinear crystal,” Opt. Lett. 23, 1441–1443 (1998).
[CrossRef]

K. Mori, Y. Tamaki, M. Obara, and K. Midorikawa, “Second-harmonic generation of femtosecond high-intensity Ti:sapphire laser pulses,” J. Appl. Phys. 83, 2915–2919 (1998).
[CrossRef]

1997 (1)

L. Bergé, O. Bang, J. Juul Rasmussen, and V. K. Mezentsev, “Self-focusing and soliton-like structures in material with competing quadratic and cubic nonlinearity,” Phys. Rev. E 55, 3555–3570 (1997).
[CrossRef]

1996 (1)

G. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

1995 (1)

L. Berge, V. K. Mezentsev, J. Juul Rasmussen, and J. Wyller, “Formation of stable solitons in quadratic nonlinear media,” Phys. Rev. A 52, R28–R31 (1995).
[CrossRef]

1994 (1)

1993 (3)

Y. Pang, V. Yanovsky, F. Wise, and B. I. Minkov, “Self-mode-locked Cr:forsterite laser,” Opt. Lett. 18, 1168–1170 (1993).
[CrossRef]

V. Yanovsky, Y. Pang, F. Wise, and B. I. Minkov, “Generation of 25 fs pulses from a self-mode-locked Cr:forsterite laser with optimized group delay dispersion,” Opt. Lett. 18, 1541–1543 (1993).
[CrossRef]

M. V. Komissarova, A. P. Sukhorukov, and V. A. Trofimov, “Self-compression of the fundamental and second-harmonic pulses in media with quadratic and cubic nonlinearities,” Bull. Russ. Acad. Sci. Phys. Suppl. Phys. Vibrat. 57, 189–192 (1993).

1992 (3)

1991 (1)

Ashihara, S.

Bache, M.

Bang, O.

M. Bache, O. Bang, J. Moses, and F. W. Wise, “Nonlocal explanation of stationary and nonstationary regimes in cascaded soliton pulse compression,” Opt. Lett. 32, 2490–2492 (2007).
[CrossRef]

L. Bergé, O. Bang, J. Juul Rasmussen, and V. K. Mezentsev, “Self-focusing and soliton-like structures in material with competing quadratic and cubic nonlinearity,” Phys. Rev. E 55, 3555–3570 (1997).
[CrossRef]

Beckitt, K.

Berge, L.

L. Berge, V. K. Mezentsev, J. Juul Rasmussen, and J. Wyller, “Formation of stable solitons in quadratic nonlinear media,” Phys. Rev. A 52, R28–R31 (1995).
[CrossRef]

Bergé, L.

L. Bergé, O. Bang, J. Juul Rasmussen, and V. K. Mezentsev, “Self-focusing and soliton-like structures in material with competing quadratic and cubic nonlinearity,” Phys. Rev. E 55, 3555–3570 (1997).
[CrossRef]

Beržanskis, A.

S. Minardi, J. Yu, G. Blasi, A. Varanavičius, G. Valiulis, A. Beržanskis, A. Piskarskas, and P. Di Trapani, “Red solitons: evidence of spatiotemporal instability in χ(2) spatial soliton dynamics,” Phys. Rev. Lett. 91, 123901 (2003).
[CrossRef]

Blasi, G.

S. Minardi, J. Yu, G. Blasi, A. Varanavičius, G. Valiulis, A. Beržanskis, A. Piskarskas, and P. Di Trapani, “Red solitons: evidence of spatiotemporal instability in χ(2) spatial soliton dynamics,” Phys. Rev. Lett. 91, 123901 (2003).
[CrossRef]

Bramati, A.

C. Conti, S. Trillo, P. Di Trapani, J. Kilius, A. Bramati, S. Minardi, W. Chinaglia, and G. Valiulis, “Effective lensing effects in parametric frequency conversion,” J. Opt. Soc. Am. B 19, 852–859 (2002).
[CrossRef]

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities in self-trapping due to parametric frequency conversion,” Phys. Rev. Lett. 87, 183902 (2001).
[CrossRef]

Buryak, A. V.

A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

Canto-Said, E.

Chai, B. H. T.

Chinaglia, W.

C. Conti, S. Trillo, P. Di Trapani, J. Kilius, A. Bramati, S. Minardi, W. Chinaglia, and G. Valiulis, “Effective lensing effects in parametric frequency conversion,” J. Opt. Soc. Am. B 19, 852–859 (2002).
[CrossRef]

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities in self-trapping due to parametric frequency conversion,” Phys. Rev. Lett. 87, 183902 (2001).
[CrossRef]

Conti, C.

C. Conti, S. Trillo, P. Di Trapani, J. Kilius, A. Bramati, S. Minardi, W. Chinaglia, and G. Valiulis, “Effective lensing effects in parametric frequency conversion,” J. Opt. Soc. Am. B 19, 852–859 (2002).
[CrossRef]

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities in self-trapping due to parametric frequency conversion,” Phys. Rev. Lett. 87, 183902 (2001).
[CrossRef]

DeSalvo, R.

Di Trapani, P.

S. Minardi, J. Yu, G. Blasi, A. Varanavičius, G. Valiulis, A. Beržanskis, A. Piskarskas, and P. Di Trapani, “Red solitons: evidence of spatiotemporal instability in χ(2) spatial soliton dynamics,” Phys. Rev. Lett. 91, 123901 (2003).
[CrossRef]

C. Conti, S. Trillo, P. Di Trapani, J. Kilius, A. Bramati, S. Minardi, W. Chinaglia, and G. Valiulis, “Effective lensing effects in parametric frequency conversion,” J. Opt. Soc. Am. B 19, 852–859 (2002).
[CrossRef]

A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities in self-trapping due to parametric frequency conversion,” Phys. Rev. Lett. 87, 183902 (2001).
[CrossRef]

Ebrahimzadeh, M.

Faller, P.

Fang, H.

G. I. Stegeman, R. Schiek, H. Fang, R. Malendevich, L. Jankovic, L. Torner, W. Sohle, and G. Schreiber, “Beam evolution in quadratically nonlinear one-dimensional media: LiNbO3 slab waveguides,” Laser Phys. 13, 137–147 (2003).

French, P. M. W.

Fujioka, N.

Hagan, D. J.

G. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, and E. W. Van Stryland, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28–30 (1992).
[CrossRef]

Jankovic, L.

G. I. Stegeman, R. Schiek, H. Fang, R. Malendevich, L. Jankovic, L. Torner, W. Sohle, and G. Schreiber, “Beam evolution in quadratically nonlinear one-dimensional media: LiNbO3 slab waveguides,” Laser Phys. 13, 137–147 (2003).

Juul Rasmussen, J.

L. Bergé, O. Bang, J. Juul Rasmussen, and V. K. Mezentsev, “Self-focusing and soliton-like structures in material with competing quadratic and cubic nonlinearity,” Phys. Rev. E 55, 3555–3570 (1997).
[CrossRef]

L. Berge, V. K. Mezentsev, J. Juul Rasmussen, and J. Wyller, “Formation of stable solitons in quadratic nonlinear media,” Phys. Rev. A 52, R28–R31 (1995).
[CrossRef]

Kan’an, A. M.

Kean, P. N.

Kilius, J.

C. Conti, S. Trillo, P. Di Trapani, J. Kilius, A. Bramati, S. Minardi, W. Chinaglia, and G. Valiulis, “Effective lensing effects in parametric frequency conversion,” J. Opt. Soc. Am. B 19, 852–859 (2002).
[CrossRef]

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities in self-trapping due to parametric frequency conversion,” Phys. Rev. Lett. 87, 183902 (2001).
[CrossRef]

Komissarova, M. V.

M. V. Komissarova, A. P. Sukhorukov, and V. A. Trofimov, “Self-compression of the fundamental and second-harmonic pulses in media with quadratic and cubic nonlinearities,” Bull. Russ. Acad. Sci. Phys. Suppl. Phys. Vibrat. 57, 189–192 (1993).

Kuroda, K.

Leaird, D. E.

LiKamWa, P.

Liu, X.

Loza-Alvarez, P.

Lysak, T. M.

V. A. Trofimov and T. M. Lysak, “Catastrophic self-focusing of axially symmetric laser beams due to cascading SHG,” Proc. SPIE 7822, 78220E (2011).

T. M. Lysak and V. A. Trofimov, “Achieving high-efficiency second harmonic generation in a sequence of laser pulses with random peak intensity. Part II. Suppression of intensity fluctuations in a quadratic-nonlinearity medium,” Computat. Math. Model. 20, 1–25 (2009).
[CrossRef]

T. M. Lysak and V. A. Trofimov, “Achieving high-efficiency second harmonic generation in a sequence of laser pulses with random peak intensity. Part III. Propagation of pulses in a bulk medium,” Comput. Math. Model. 20, 101–112 (2009).
[CrossRef]

V. A. Trofimov and T. M. Lysak, “Highly efficient SHG of a sequence of laser pulses with a random peak intensity and duration,” Opt. Spectrosc. 107, 399–406 (2009).
[CrossRef]

T. M. Lysak and V. A. Trofimov, “Achieving high-efficiency second harmonic generation in a sequence of laser pulses with random peak intensity. Part I. Efficient generation in optical fibers,” Comput. Math. Model. 19, 333–342 (2008).
[CrossRef]

V. A. Trofimov and T. M. Lysak, “Catastrophic self-focusing of axially symmetric laser beams due to cascading SHG,” in Technical Program of 14th International Conference on Laser Optics (LO-2010) (IOP, 2010), p. 27.

Malendevich, R.

G. I. Stegeman, R. Schiek, H. Fang, R. Malendevich, L. Jankovic, L. Torner, W. Sohle, and G. Schreiber, “Beam evolution in quadratically nonlinear one-dimensional media: LiNbO3 slab waveguides,” Laser Phys. 13, 137–147 (2003).

Mezentsev, V. K.

L. Bergé, O. Bang, J. Juul Rasmussen, and V. K. Mezentsev, “Self-focusing and soliton-like structures in material with competing quadratic and cubic nonlinearity,” Phys. Rev. E 55, 3555–3570 (1997).
[CrossRef]

L. Berge, V. K. Mezentsev, J. Juul Rasmussen, and J. Wyller, “Formation of stable solitons in quadratic nonlinear media,” Phys. Rev. A 52, R28–R31 (1995).
[CrossRef]

Midorikawa, K.

K. Mori, Y. Tamaki, M. Obara, and K. Midorikawa, “Second-harmonic generation of femtosecond high-intensity Ti:sapphire laser pulses,” J. Appl. Phys. 83, 2915–2919 (1998).
[CrossRef]

Miller, A.

Minardi, S.

S. Minardi, J. Yu, G. Blasi, A. Varanavičius, G. Valiulis, A. Beržanskis, A. Piskarskas, and P. Di Trapani, “Red solitons: evidence of spatiotemporal instability in χ(2) spatial soliton dynamics,” Phys. Rev. Lett. 91, 123901 (2003).
[CrossRef]

C. Conti, S. Trillo, P. Di Trapani, J. Kilius, A. Bramati, S. Minardi, W. Chinaglia, and G. Valiulis, “Effective lensing effects in parametric frequency conversion,” J. Opt. Soc. Am. B 19, 852–859 (2002).
[CrossRef]

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities in self-trapping due to parametric frequency conversion,” Phys. Rev. Lett. 87, 183902 (2001).
[CrossRef]

Minkov, B. I.

Mori, K.

K. Mori, Y. Tamaki, M. Obara, and K. Midorikawa, “Second-harmonic generation of femtosecond high-intensity Ti:sapphire laser pulses,” J. Appl. Phys. 83, 2915–2919 (1998).
[CrossRef]

Moses, J.

Nishina, J.

Obara, M.

K. Mori, Y. Tamaki, M. Obara, and K. Midorikawa, “Second-harmonic generation of femtosecond high-intensity Ti:sapphire laser pulses,” J. Appl. Phys. 83, 2915–2919 (1998).
[CrossRef]

Pang, Y.

Piskarskas, A.

S. Minardi, J. Yu, G. Blasi, A. Varanavičius, G. Valiulis, A. Beržanskis, A. Piskarskas, and P. Di Trapani, “Red solitons: evidence of spatiotemporal instability in χ(2) spatial soliton dynamics,” Phys. Rev. Lett. 91, 123901 (2003).
[CrossRef]

Qian, L.

Qian, L. J.

X. Liu, L. J. Qian, and F. W. Wise, “Generation of optical spatiotemporal solitons,” Phys. Rev. Lett. 82, 4631–4634 (1999).
[CrossRef]

L. J. Qian, X. Liu, and F. Wise, “Femtosecond Kerr-lens mode locking with negative nonlinear phase shifts,” Opt. Lett. 24, 166–168 (1999).
[CrossRef]

Reid, D. T.

Rizvi, N. H.

Schiek, R.

G. I. Stegeman, R. Schiek, H. Fang, R. Malendevich, L. Jankovic, L. Torner, W. Sohle, and G. Schreiber, “Beam evolution in quadratically nonlinear one-dimensional media: LiNbO3 slab waveguides,” Laser Phys. 13, 137–147 (2003).

Schreiber, G.

G. I. Stegeman, R. Schiek, H. Fang, R. Malendevich, L. Jankovic, L. Torner, W. Sohle, and G. Schreiber, “Beam evolution in quadratically nonlinear one-dimensional media: LiNbO3 slab waveguides,” Laser Phys. 13, 137–147 (2003).

Sheik-Bahae, M.

Shimura, T.

X. Zeng, S. Ashihara, T. Shimura, and K. Kuroda, “Adiabatic femtosecond pulse compression and control by using quadratic cascading nonlinearity,” Proc. SPIE 6839, 68390B (2007).
[CrossRef]

X. Zeng, S. Ashihara, N. Fujioka, T. Shimura, and K. Kuroda, “Adiabatic compression of quadratic temporal solitons in aperiodic quasi-phase-matching gratings,” Opt. Express 14, 9358–9370 (2006).
[CrossRef]

Shimuraa, T.

Sibbett, W.

Skryabin, D. V.

A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

Sohle, W.

G. I. Stegeman, R. Schiek, H. Fang, R. Malendevich, L. Jankovic, L. Torner, W. Sohle, and G. Schreiber, “Beam evolution in quadratically nonlinear one-dimensional media: LiNbO3 slab waveguides,” Laser Phys. 13, 137–147 (2003).

Spence, D. E.

Stegeman, G.

G. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, and E. W. Van Stryland, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28–30 (1992).
[CrossRef]

Stegeman, G. I.

G. I. Stegeman, R. Schiek, H. Fang, R. Malendevich, L. Jankovic, L. Torner, W. Sohle, and G. Schreiber, “Beam evolution in quadratically nonlinear one-dimensional media: LiNbO3 slab waveguides,” Laser Phys. 13, 137–147 (2003).

Sukhorukov, A. P.

M. V. Komissarova, A. P. Sukhorukov, and V. A. Trofimov, “Self-compression of the fundamental and second-harmonic pulses in media with quadratic and cubic nonlinearities,” Bull. Russ. Acad. Sci. Phys. Suppl. Phys. Vibrat. 57, 189–192 (1993).

Tamaki, Y.

K. Mori, Y. Tamaki, M. Obara, and K. Midorikawa, “Second-harmonic generation of femtosecond high-intensity Ti:sapphire laser pulses,” J. Appl. Phys. 83, 2915–2919 (1998).
[CrossRef]

Tang, D.

G. Xie, D. Zhang, L. Qian, H. Zhu, and D. Tang, “Multi-stage pulse compression by use of cascaded quadratic nonlinearity,” Opt. Commun. 273, 207–213 (2007).
[CrossRef]

Taylor, J. R.

Torner, L.

G. I. Stegeman, R. Schiek, H. Fang, R. Malendevich, L. Jankovic, L. Torner, W. Sohle, and G. Schreiber, “Beam evolution in quadratically nonlinear one-dimensional media: LiNbO3 slab waveguides,” Laser Phys. 13, 137–147 (2003).

G. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

Trillo, S.

A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

C. Conti, S. Trillo, P. Di Trapani, J. Kilius, A. Bramati, S. Minardi, W. Chinaglia, and G. Valiulis, “Effective lensing effects in parametric frequency conversion,” J. Opt. Soc. Am. B 19, 852–859 (2002).
[CrossRef]

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities in self-trapping due to parametric frequency conversion,” Phys. Rev. Lett. 87, 183902 (2001).
[CrossRef]

Trofimov, V. A.

V. A. Trofimov and T. M. Lysak, “Catastrophic self-focusing of axially symmetric laser beams due to cascading SHG,” Proc. SPIE 7822, 78220E (2011).

V. A. Trofimov and T. M. Lysak, “Highly efficient SHG of a sequence of laser pulses with a random peak intensity and duration,” Opt. Spectrosc. 107, 399–406 (2009).
[CrossRef]

T. M. Lysak and V. A. Trofimov, “Achieving high-efficiency second harmonic generation in a sequence of laser pulses with random peak intensity. Part III. Propagation of pulses in a bulk medium,” Comput. Math. Model. 20, 101–112 (2009).
[CrossRef]

T. M. Lysak and V. A. Trofimov, “Achieving high-efficiency second harmonic generation in a sequence of laser pulses with random peak intensity. Part II. Suppression of intensity fluctuations in a quadratic-nonlinearity medium,” Computat. Math. Model. 20, 1–25 (2009).
[CrossRef]

T. M. Lysak and V. A. Trofimov, “Achieving high-efficiency second harmonic generation in a sequence of laser pulses with random peak intensity. Part I. Efficient generation in optical fibers,” Comput. Math. Model. 19, 333–342 (2008).
[CrossRef]

V. A. Trofimov and V. V. Trofimov, “High effective SHG of femtosecond pulse with ring profile of beam in bulk medium with cubic nonlinear response,” Proc. SPIE 6610, 66100R (2007).
[CrossRef]

V. A. Trofimov and V. V. Trofimov, “On compression of femtosecond pulses with basic and doubled frequencies,” Proc. SPIE 6165, 616502 (2006).
[CrossRef]

M. V. Komissarova, A. P. Sukhorukov, and V. A. Trofimov, “Self-compression of the fundamental and second-harmonic pulses in media with quadratic and cubic nonlinearities,” Bull. Russ. Acad. Sci. Phys. Suppl. Phys. Vibrat. 57, 189–192 (1993).

V. A. Trofimov and V. V. Trofimov, “Formation of intensive pulses with super short duration under the cascading SHG in bulk medium,” in Proceedings of the 8th International Conference on Laser and Fiber-Optical Networks Modeling (FNM’06) (IEEE, 2006), pp. 403–406.

V. A. Trofimov and T. M. Lysak, “Catastrophic self-focusing of axially symmetric laser beams due to cascading SHG,” in Technical Program of 14th International Conference on Laser Optics (LO-2010) (IOP, 2010), p. 27.

Trofimov, V. V.

V. A. Trofimov and V. V. Trofimov, “High effective SHG of femtosecond pulse with ring profile of beam in bulk medium with cubic nonlinear response,” Proc. SPIE 6610, 66100R (2007).
[CrossRef]

V. A. Trofimov and V. V. Trofimov, “On compression of femtosecond pulses with basic and doubled frequencies,” Proc. SPIE 6165, 616502 (2006).
[CrossRef]

V. A. Trofimov and V. V. Trofimov, “Formation of intensive pulses with super short duration under the cascading SHG in bulk medium,” in Proceedings of the 8th International Conference on Laser and Fiber-Optical Networks Modeling (FNM’06) (IEEE, 2006), pp. 403–406.

Valiulis, G.

S. Minardi, J. Yu, G. Blasi, A. Varanavičius, G. Valiulis, A. Beržanskis, A. Piskarskas, and P. Di Trapani, “Red solitons: evidence of spatiotemporal instability in χ(2) spatial soliton dynamics,” Phys. Rev. Lett. 91, 123901 (2003).
[CrossRef]

C. Conti, S. Trillo, P. Di Trapani, J. Kilius, A. Bramati, S. Minardi, W. Chinaglia, and G. Valiulis, “Effective lensing effects in parametric frequency conversion,” J. Opt. Soc. Am. B 19, 852–859 (2002).
[CrossRef]

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities in self-trapping due to parametric frequency conversion,” Phys. Rev. Lett. 87, 183902 (2001).
[CrossRef]

Van Stryland, E. W.

Varanavicius, A.

S. Minardi, J. Yu, G. Blasi, A. Varanavičius, G. Valiulis, A. Beržanskis, A. Piskarskas, and P. Di Trapani, “Red solitons: evidence of spatiotemporal instability in χ(2) spatial soliton dynamics,” Phys. Rev. Lett. 91, 123901 (2003).
[CrossRef]

Walker, L. A.

Weiner, A. M.

Wise, F.

Wise, F. W.

Wyller, J.

L. Berge, V. K. Mezentsev, J. Juul Rasmussen, and J. Wyller, “Formation of stable solitons in quadratic nonlinear media,” Phys. Rev. A 52, R28–R31 (1995).
[CrossRef]

Xie, G.

G. Xie, D. Zhang, L. Qian, H. Zhu, and D. Tang, “Multi-stage pulse compression by use of cascaded quadratic nonlinearity,” Opt. Commun. 273, 207–213 (2007).
[CrossRef]

Yanovsky, V.

Yu, J.

S. Minardi, J. Yu, G. Blasi, A. Varanavičius, G. Valiulis, A. Beržanskis, A. Piskarskas, and P. Di Trapani, “Red solitons: evidence of spatiotemporal instability in χ(2) spatial soliton dynamics,” Phys. Rev. Lett. 91, 123901 (2003).
[CrossRef]

Zeng, X.

X. Zeng, S. Ashihara, T. Shimura, and K. Kuroda, “Adiabatic femtosecond pulse compression and control by using quadratic cascading nonlinearity,” Proc. SPIE 6839, 68390B (2007).
[CrossRef]

X. Zeng, S. Ashihara, N. Fujioka, T. Shimura, and K. Kuroda, “Adiabatic compression of quadratic temporal solitons in aperiodic quasi-phase-matching gratings,” Opt. Express 14, 9358–9370 (2006).
[CrossRef]

Zhang, D.

G. Xie, D. Zhang, L. Qian, H. Zhu, and D. Tang, “Multi-stage pulse compression by use of cascaded quadratic nonlinearity,” Opt. Commun. 273, 207–213 (2007).
[CrossRef]

Zhu, H.

G. Xie, D. Zhang, L. Qian, H. Zhu, and D. Tang, “Multi-stage pulse compression by use of cascaded quadratic nonlinearity,” Opt. Commun. 273, 207–213 (2007).
[CrossRef]

Bull. Russ. Acad. Sci. Phys. Suppl. Phys. Vibrat. (1)

M. V. Komissarova, A. P. Sukhorukov, and V. A. Trofimov, “Self-compression of the fundamental and second-harmonic pulses in media with quadratic and cubic nonlinearities,” Bull. Russ. Acad. Sci. Phys. Suppl. Phys. Vibrat. 57, 189–192 (1993).

Comput. Math. Model. (2)

T. M. Lysak and V. A. Trofimov, “Achieving high-efficiency second harmonic generation in a sequence of laser pulses with random peak intensity. Part I. Efficient generation in optical fibers,” Comput. Math. Model. 19, 333–342 (2008).
[CrossRef]

T. M. Lysak and V. A. Trofimov, “Achieving high-efficiency second harmonic generation in a sequence of laser pulses with random peak intensity. Part III. Propagation of pulses in a bulk medium,” Comput. Math. Model. 20, 101–112 (2009).
[CrossRef]

Computat. Math. Model. (1)

T. M. Lysak and V. A. Trofimov, “Achieving high-efficiency second harmonic generation in a sequence of laser pulses with random peak intensity. Part II. Suppression of intensity fluctuations in a quadratic-nonlinearity medium,” Computat. Math. Model. 20, 1–25 (2009).
[CrossRef]

J. Appl. Phys. (1)

K. Mori, Y. Tamaki, M. Obara, and K. Midorikawa, “Second-harmonic generation of femtosecond high-intensity Ti:sapphire laser pulses,” J. Appl. Phys. 83, 2915–2919 (1998).
[CrossRef]

J. Opt. Soc. Am. B (3)

Laser Phys. (1)

G. I. Stegeman, R. Schiek, H. Fang, R. Malendevich, L. Jankovic, L. Torner, W. Sohle, and G. Schreiber, “Beam evolution in quadratically nonlinear one-dimensional media: LiNbO3 slab waveguides,” Laser Phys. 13, 137–147 (2003).

Opt. Commun. (1)

G. Xie, D. Zhang, L. Qian, H. Zhu, and D. Tang, “Multi-stage pulse compression by use of cascaded quadratic nonlinearity,” Opt. Commun. 273, 207–213 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lett. (12)

M. Bache, O. Bang, J. Moses, and F. W. Wise, “Nonlocal explanation of stationary and nonstationary regimes in cascaded soliton pulse compression,” Opt. Lett. 32, 2490–2492 (2007).
[CrossRef]

X. Liu, L. Qian, and F. Wise, “High-energy pulse compression by use of negative phase shifts produced by the cascade χ(2):χ(2) nonlinearity,” Opt. Lett. 24, 1777–1779 (1999).
[CrossRef]

A. M. Weiner, A. M. Kan’an, and D. E. Leaird, “High-efficiency blue generation by frequency doubling of femtosecond pulses in a thick nonlinear crystal,” Opt. Lett. 23, 1441–1443 (1998).
[CrossRef]

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, and E. W. Van Stryland, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28–30 (1992).
[CrossRef]

K. Beckitt, F. Wise, L. Qian, L. A. Walker, and E. Canto-Said, “Compensation for self-focusing by use of cascade quadratic nonlinearity,” Opt. Lett. 26, 1696–1698 (2001).
[CrossRef]

V. Yanovsky, Y. Pang, F. Wise, and B. I. Minkov, “Generation of 25 fs pulses from a self-mode-locked Cr:forsterite laser with optimized group delay dispersion,” Opt. Lett. 18, 1541–1543 (1993).
[CrossRef]

V. Yanovsky and F. Wise, “Frequency doubling of 100 fs pulses with 50% efficiency by use of a resonant enhancement cavity,” Opt. Lett. 19, 1952–1954 (1994).
[CrossRef]

D. E. Spence, P. N. Kean, and W. Sibbett, “60 fsec pulse generation from a self-mode-locked Ti:sapphire laser,” Opt. Lett. 16, 42–44 (1991).
[CrossRef]

N. H. Rizvi, P. M. W. French, and J. R. Taylor, “50 fs pulse generation from a self-starting cw passively mode-locked Cr:LiSrAlF6 laser,” Opt. Lett. 17, 877–879 (1992).
[CrossRef]

P. LiKamWa, B. H. T. Chai, and A. Miller, “Self-mode-locked Cr3+:LiCaAlF6 laser,” Opt. Lett. 17, 1438–1440 (1992).
[CrossRef]

Y. Pang, V. Yanovsky, F. Wise, and B. I. Minkov, “Self-mode-locked Cr:forsterite laser,” Opt. Lett. 18, 1168–1170 (1993).
[CrossRef]

L. J. Qian, X. Liu, and F. Wise, “Femtosecond Kerr-lens mode locking with negative nonlinear phase shifts,” Opt. Lett. 24, 166–168 (1999).
[CrossRef]

Opt. Quantum Electron. (1)

G. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

Opt. Spectrosc. (1)

V. A. Trofimov and T. M. Lysak, “Highly efficient SHG of a sequence of laser pulses with a random peak intensity and duration,” Opt. Spectrosc. 107, 399–406 (2009).
[CrossRef]

Phys. Rep. (1)

A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

Phys. Rev. A (1)

L. Berge, V. K. Mezentsev, J. Juul Rasmussen, and J. Wyller, “Formation of stable solitons in quadratic nonlinear media,” Phys. Rev. A 52, R28–R31 (1995).
[CrossRef]

Phys. Rev. E (1)

L. Bergé, O. Bang, J. Juul Rasmussen, and V. K. Mezentsev, “Self-focusing and soliton-like structures in material with competing quadratic and cubic nonlinearity,” Phys. Rev. E 55, 3555–3570 (1997).
[CrossRef]

Phys. Rev. Lett. (3)

X. Liu, L. J. Qian, and F. W. Wise, “Generation of optical spatiotemporal solitons,” Phys. Rev. Lett. 82, 4631–4634 (1999).
[CrossRef]

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities in self-trapping due to parametric frequency conversion,” Phys. Rev. Lett. 87, 183902 (2001).
[CrossRef]

S. Minardi, J. Yu, G. Blasi, A. Varanavičius, G. Valiulis, A. Beržanskis, A. Piskarskas, and P. Di Trapani, “Red solitons: evidence of spatiotemporal instability in χ(2) spatial soliton dynamics,” Phys. Rev. Lett. 91, 123901 (2003).
[CrossRef]

Proc. SPIE (4)

X. Zeng, S. Ashihara, T. Shimura, and K. Kuroda, “Adiabatic femtosecond pulse compression and control by using quadratic cascading nonlinearity,” Proc. SPIE 6839, 68390B (2007).
[CrossRef]

V. A. Trofimov and V. V. Trofimov, “On compression of femtosecond pulses with basic and doubled frequencies,” Proc. SPIE 6165, 616502 (2006).
[CrossRef]

V. A. Trofimov and V. V. Trofimov, “High effective SHG of femtosecond pulse with ring profile of beam in bulk medium with cubic nonlinear response,” Proc. SPIE 6610, 66100R (2007).
[CrossRef]

V. A. Trofimov and T. M. Lysak, “Catastrophic self-focusing of axially symmetric laser beams due to cascading SHG,” Proc. SPIE 7822, 78220E (2011).

Other (2)

V. A. Trofimov and V. V. Trofimov, “Formation of intensive pulses with super short duration under the cascading SHG in bulk medium,” in Proceedings of the 8th International Conference on Laser and Fiber-Optical Networks Modeling (FNM’06) (IEEE, 2006), pp. 403–406.

V. A. Trofimov and T. M. Lysak, “Catastrophic self-focusing of axially symmetric laser beams due to cascading SHG,” in Technical Program of 14th International Conference on Laser Optics (LO-2010) (IOP, 2010), p. 27.

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Figures (7)

Fig. 1.
Fig. 1.

Intensity distribution at the section of the first nonlinear focus (z=4.4) (a) and the second nonlinear focus (z=6.66); (b) for γ=8, Δk=100.

Fig. 2.
Fig. 2.

Longitudinal coordinate zmax of the first nonlinear focus appearance (a), intensity of the wave with fundamental frequency at the pulse and beam center (η=r=0) (b), pulse half duration τh (c), beam radius ar1 (d), and efficiency of energy conversion θ (e) in the section of the nonlinear focus formation as a function of wave-vector mismatching for γ=8.

Fig. 3.
Fig. 3.

Longitudinal coordinate zmax of the first nonlinear focus appearance (a), intensity of the wave with fundamental frequency at the pulse and beam center (η=r=0) (b), pulse half duration τh (c), beam radius ar1 (d), and efficiency of energy conversion θ (e) in the section of the nonlinear focus formation as a function of wave-vector mismatching for γ=16.

Fig. 4.
Fig. 4.

Intensity of the fundamental wave at the pulse and beam center (η=0, r=0) (a), half FWHM pulse duration τh (b), beam radius ar2 and ar1 (c), and efficiency of energy conversion θ (d) at the section z=3 of the medium as a function of wave-vector mismatching.

Fig. 5.
Fig. 5.

Evolution of the fundamental wave intensity at the pulse and beam center (η=r=0) (a), (e), beam profiles |A1(z,r,0)|2 at pulse center (η=0) (b), (f) for two sets of random values (a)–(d) and (e)–(f). Dashed lines in (a) and (e) correspond to unperturbed profiles, and values of zpert are denoted in the figures. Beam profile |A1(z,r,0)|2 at pulse center (η=0) in the nonlinear focus (c) and after its propagation in the linear medium at section z=4.8 (d) with (solid line) and without (dashed line) introducing of the filter in the focal plane.

Fig. 6.
Fig. 6.

Evolution of the average maximum intensity of the fundamental wave I¯1, average deviation of maximum intensity ΔI1, maximum and minimum intensities I1,max and I1,min in the series of realization for 2.5% (a), 20% (b), and 40% (c) of maximum relative deviation of the perturbed amplitude from the unperturbed one. Evolution of unperturbed maximum fundamental wave intensity is shown in the figure by a dashed line.

Fig. 7.
Fig. 7.

Unperturbed and perturbed profiles at pulse center (η=0) (dashed and solid lines, correspondingly) of one beam in the array (a), their profiles at the nonlinear focus (b), and evolution of maximum intensity (c) for 40% of maximum relative deviation of the perturbed amplitude from the unperturbed one.

Tables (2)

Tables Icon

Table 1. First Random Set of Perturbation Parameters

Tables Icon

Table 2. Second Random Set of Perturbation Parameters

Equations (11)

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

A1z+iD12A1η2+iDdifΔA1+iγA1*A2eiΔkz=0,A2z+νA2η+iD22A2η2+iDdif2ΔA2+iγA12eiΔkz=0,Δ=1rr(rr),0<zLz,Lt/2<η<Lt/2,0<r<Lr.
z=z/ld,η=t/τ,r=r/a,ld=2k(ω)a2,Δk=(k(2ω)2k(ω))ld,k(mω)=ωn(mω)/c,ν=ld(dk(2ω)/dωdk(ω)/dω)/τ,Ddif=1,γ=ld/lnl,Dm=ld/ldis(mω),ldis(mω)=2τ2d2k(mω)/dω2,lnl=nλ8π2χ(2)A0,A02=8πncI0,I0=E2πa2τQt2Qr2,Qt2=Lt/2Lt/2|A0(t)|2dt,Qr2=0|A0(r)|2rdr,m=1,2.
A1(z=0,η,r)=A10(η,r)=A10A0(η,r)=A10exp((η/τp)mt/2)exp((r/ab))mr/2),A2(z=0,η,r)=0,Lt/2ηLt/2,0rLr.
θ(z)=0LrLt/2Lt/2r|A2(z,η,r)|2dηdr/0LrLt/2Lt/2r|A10(η,r)|2dηdr.
|A1(z,τh,0)|2=|A1(z,0,0)|2/2,
|A1(z,0,ar1)|2=|A1(z,0,0)|2/2
ar22(z)=0LrLt/2Lt/2r3|A1(z,η,r)|2dηdr/0LrLt/2Lt/2|A10A0(η)A0(r)|2rdrdη.
A10(z=zpert,η,r)=A1(z=zpert,η,r)(1+j=1mΔjcos(2πnjr/R+φj)),
A10(z=zfoc,η,r)=A1(z=zfoc,η,r)exp((r/ar,foc)10)
Δmax=κ/maxr|j=1mΔjcos(2πnjr/ar1,pert+φj)|.
I¯1=j=1N|A1|max,j2N,ΔI1=j=1N||A1|max,j2I¯1|N.

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