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 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]

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]

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).

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]

S. Ashihara, J. Nishina, T. Shimuraa, and K. Kuroda, “Soliton compression of femtosecond pulses in quadratic media,” J. Opt. Soc. Am. B 19, 2505–2510 (2002).

[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]

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]

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]

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]

P. Loza-Alvarez, D. T. Reid, P. Faller, M. Ebrahimzadeh, and W. Sibbett, “Simultaneous second-harmonic generation and femtosecond-pulse compression in aperiodically poled KTiOPO4 with a RbTiOAsO4-based optical parametric oscillator,” J. Opt. Soc. Am. B 16, 1553–1560 (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]

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]

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]

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]

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]

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).

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]

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]

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]

S. Ashihara, J. Nishina, T. Shimuraa, and K. Kuroda, “Soliton compression of femtosecond pulses in quadratic media,” J. Opt. Soc. Am. B 19, 2505–2510 (2002).

[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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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).

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]

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]

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).

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]

S. Ashihara, J. Nishina, T. Shimuraa, and K. Kuroda, “Soliton compression of femtosecond pulses in quadratic media,” J. Opt. Soc. Am. B 19, 2505–2510 (2002).

[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]

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]

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 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 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 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.

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).

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]

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]

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]

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]

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]

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]

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]

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. 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]

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]

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]

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]

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. 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).

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]

P. Loza-Alvarez, D. T. Reid, P. Faller, M. Ebrahimzadeh, and W. Sibbett, “Simultaneous second-harmonic generation and femtosecond-pulse compression in aperiodically poled KTiOPO4 with a RbTiOAsO4-based optical parametric oscillator,” J. Opt. Soc. Am. B 16, 1553–1560 (1999).

[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]

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]

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]

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]

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).

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).

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]

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]

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]

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]

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

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[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]

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 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]

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[CrossRef]

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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.

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.

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[CrossRef]

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[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).

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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]

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]

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[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]

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).

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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).

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[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]

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[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]

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).

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 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.

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.