F. Baronio, A. Barthélémy, S. Carrasco, V. Couderc, C. De Angelis, L. Lefort, Y. Min, P. H Pioger, V. Quiring, L. Torner, and W. Sohler, “Generation of quadratic spatially trapped beams with short pulsed light,” J. Opt. B 6, S182–S189 (2004).

[CrossRef]

F. Ilday, K. Beckwitt, Y. Chen, H. Lim, and F. Wise, “Controllable Raman-like nonlinearities from nonstationary, cascaded quadratic processes,” J. Opt. Soc. Am. B 21, 376–383 (2004).

[CrossRef]

K. Beckwitt, F. Ilday, and F. Wise, “Frequency shifting with local nonlinearity management in nonuniformly poled quadratic nonlinear materials,” Opt. Lett. 29, 763–765 (2004).

[CrossRef]
[PubMed]

J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, T. Tunnermann, R. Iliew, F. Lederer, J. Broeng, G. Vienne, A. Petersson, and C. Jakobsen, “High-power air-clad large-mode-area photonic crystal fiber laser,” Opt. Express 11, 818–823 (2003).

[CrossRef]
[PubMed]

G. Cerullo and S. De Silvestri, “Ultrafast optical parametric amplifiers,” Rev. Sci. Instrum 74, 1–18 (2003).

[CrossRef]

P. Pioger, V. Couderc, L. Lefort, A. Barthelemy, F. Baronio, C. De Angelis, Y. Min, V. Quiring, and W. Sohler, “Spatial trapping of short pulses in Ti-indiffused LiNbO3 waveguides,” Opt. Lett. 27, 2182–2184 (2002).

[CrossRef]

J.P. Torres and L. Torner, “Self-splitting of beams into spatial solitons in planar waveguides made of quadratic nonlinear media,” Opt. Quantum Electron. 29, 757–776 (1997).

[CrossRef]

C. Balslev Clausen, O. Bang, and Yu. S. Kivshar, “Spatial Solitons and Induced Kerr Effects in Quasi-Phase-Matched Quadratic Media,” Phys. Rev. Lett. 78, 4749–4752 (1997).

[CrossRef]

P. Guerreiro, S. Lee, A. Rodrigues, Y. Hu, E. Wright, S. Najafi, J. Mackenzie, and N. Peyghambarian, “Femtosecond pulse propagation near a two-photon transition in a semiconductor quantum-dot waveguide,” Opt. Lett. 21, 659–661 (1996).

[CrossRef]
[PubMed]

A.S. Rodrigues, M. Santagiustina, and E.M. Wright, “Nonlinear pulse propagation in the vicinity of a two-photon resonance,” Phys. Rev. A 52, 3231–3238 (1995).

[CrossRef]
[PubMed]

D. Anderson and M. Lisak, “Nonlinear asymmetric self-phase modulation and self-steepening of pulses in long optical waveguides,” Phys. Rev. A 27, 1393–1398 (1983).

[CrossRef]

D. Grischkowsky, M. Loy, and P. Liao, “Adiabatic following model for two-photon transitions: Nonlinear mixing and pulse propagation,” Phys. Rev. A 12, 2514–2533 (1975).

[CrossRef]

T.K. Gustafson, J.P. Taran, H.A. Haus, J.R. Lifsitz, and P.L. Kelley, “Self-Modulation, Self-Steepening, and Spectral Development of Light in Small-Scale Trapped Filaments,” Phys. Rev. 177, 306–313 (1969).

[CrossRef]

F. De Martini, C.H. Townes, T.K. Gustafson, and P.L. Kelley, “Self-Steepening of Light Pulses,” Phys. Rev. 164, 312–323 (1967).

[CrossRef]

Y. S. Kivshar and G. P. Agrawal, Optical solitons (Academic press, San Diego, 2003).

D. Anderson and M. Lisak, “Nonlinear asymmetric self-phase modulation and self-steepening of pulses in long optical waveguides,” Phys. Rev. A 27, 1393–1398 (1983).

[CrossRef]

C. Balslev Clausen, O. Bang, and Yu. S. Kivshar, “Spatial Solitons and Induced Kerr Effects in Quasi-Phase-Matched Quadratic Media,” Phys. Rev. Lett. 78, 4749–4752 (1997).

[CrossRef]

C. Balslev Clausen, O. Bang, and Yu. S. Kivshar, “Spatial Solitons and Induced Kerr Effects in Quasi-Phase-Matched Quadratic Media,” Phys. Rev. Lett. 78, 4749–4752 (1997).

[CrossRef]

M. Marangoni, C. Manzoni, R. Ramponi, G. Cerullo, F. Baronio, C. De Angelis, and K. Kitamura, “Groupvelocity control by quadratic nonlinear interactions,” Opt. Lett. 31, 534–536 (2006).

[CrossRef]
[PubMed]

F. Baronio, A. Barthélémy, S. Carrasco, V. Couderc, C. De Angelis, L. Lefort, Y. Min, P. H Pioger, V. Quiring, L. Torner, and W. Sohler, “Generation of quadratic spatially trapped beams with short pulsed light,” J. Opt. B 6, S182–S189 (2004).

[CrossRef]

P. Pioger, V. Couderc, L. Lefort, A. Barthelemy, F. Baronio, C. De Angelis, Y. Min, V. Quiring, and W. Sohler, “Spatial trapping of short pulses in Ti-indiffused LiNbO3 waveguides,” Opt. Lett. 27, 2182–2184 (2002).

[CrossRef]

P. Pioger, V. Couderc, L. Lefort, A. Barthelemy, F. Baronio, C. De Angelis, Y. Min, V. Quiring, and W. Sohler, “Spatial trapping of short pulses in Ti-indiffused LiNbO3 waveguides,” Opt. Lett. 27, 2182–2184 (2002).

[CrossRef]

F. Baronio, A. Barthélémy, S. Carrasco, V. Couderc, C. De Angelis, L. Lefort, Y. Min, P. H Pioger, V. Quiring, L. Torner, and W. Sohler, “Generation of quadratic spatially trapped beams with short pulsed light,” J. Opt. B 6, S182–S189 (2004).

[CrossRef]

F. Ilday, K. Beckwitt, Y. Chen, H. Lim, and F. Wise, “Controllable Raman-like nonlinearities from nonstationary, cascaded quadratic processes,” J. Opt. Soc. Am. B 21, 376–383 (2004).

[CrossRef]

K. Beckwitt, F. Ilday, and F. Wise, “Frequency shifting with local nonlinearity management in nonuniformly poled quadratic nonlinear materials,” Opt. Lett. 29, 763–765 (2004).

[CrossRef]
[PubMed]

J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, T. Tunnermann, R. Iliew, F. Lederer, J. Broeng, G. Vienne, A. Petersson, and C. Jakobsen, “High-power air-clad large-mode-area photonic crystal fiber laser,” Opt. Express 11, 818–823 (2003).

[CrossRef]
[PubMed]

F. Baronio, A. Barthélémy, S. Carrasco, V. Couderc, C. De Angelis, L. Lefort, Y. Min, P. H Pioger, V. Quiring, L. Torner, and W. Sohler, “Generation of quadratic spatially trapped beams with short pulsed light,” J. Opt. B 6, S182–S189 (2004).

[CrossRef]

M. Marangoni, C. Manzoni, R. Ramponi, G. Cerullo, F. Baronio, C. De Angelis, and K. Kitamura, “Groupvelocity control by quadratic nonlinear interactions,” Opt. Lett. 31, 534–536 (2006).

[CrossRef]
[PubMed]

G. Cerullo and S. De Silvestri, “Ultrafast optical parametric amplifiers,” Rev. Sci. Instrum 74, 1–18 (2003).

[CrossRef]

F. Baronio, A. Barthélémy, S. Carrasco, V. Couderc, C. De Angelis, L. Lefort, Y. Min, P. H Pioger, V. Quiring, L. Torner, and W. Sohler, “Generation of quadratic spatially trapped beams with short pulsed light,” J. Opt. B 6, S182–S189 (2004).

[CrossRef]

P. Pioger, V. Couderc, L. Lefort, A. Barthelemy, F. Baronio, C. De Angelis, Y. Min, V. Quiring, and W. Sohler, “Spatial trapping of short pulses in Ti-indiffused LiNbO3 waveguides,” Opt. Lett. 27, 2182–2184 (2002).

[CrossRef]

M. Marangoni, C. Manzoni, R. Ramponi, G. Cerullo, F. Baronio, C. De Angelis, and K. Kitamura, “Groupvelocity control by quadratic nonlinear interactions,” Opt. Lett. 31, 534–536 (2006).

[CrossRef]
[PubMed]

F. Baronio, A. Barthélémy, S. Carrasco, V. Couderc, C. De Angelis, L. Lefort, Y. Min, P. H Pioger, V. Quiring, L. Torner, and W. Sohler, “Generation of quadratic spatially trapped beams with short pulsed light,” J. Opt. B 6, S182–S189 (2004).

[CrossRef]

P. Pioger, V. Couderc, L. Lefort, A. Barthelemy, F. Baronio, C. De Angelis, Y. Min, V. Quiring, and W. Sohler, “Spatial trapping of short pulses in Ti-indiffused LiNbO3 waveguides,” Opt. Lett. 27, 2182–2184 (2002).

[CrossRef]

F. De Martini, C.H. Townes, T.K. Gustafson, and P.L. Kelley, “Self-Steepening of Light Pulses,” Phys. Rev. 164, 312–323 (1967).

[CrossRef]

G. Cerullo and S. De Silvestri, “Ultrafast optical parametric amplifiers,” Rev. Sci. Instrum 74, 1–18 (2003).

[CrossRef]

D. Grischkowsky, M. Loy, and P. Liao, “Adiabatic following model for two-photon transitions: Nonlinear mixing and pulse propagation,” Phys. Rev. A 12, 2514–2533 (1975).

[CrossRef]

P. Guerreiro, S. Lee, A. Rodrigues, Y. Hu, E. Wright, S. Najafi, J. Mackenzie, and N. Peyghambarian, “Femtosecond pulse propagation near a two-photon transition in a semiconductor quantum-dot waveguide,” Opt. Lett. 21, 659–661 (1996).

[CrossRef]
[PubMed]

T.K. Gustafson, J.P. Taran, H.A. Haus, J.R. Lifsitz, and P.L. Kelley, “Self-Modulation, Self-Steepening, and Spectral Development of Light in Small-Scale Trapped Filaments,” Phys. Rev. 177, 306–313 (1969).

[CrossRef]

F. De Martini, C.H. Townes, T.K. Gustafson, and P.L. Kelley, “Self-Steepening of Light Pulses,” Phys. Rev. 164, 312–323 (1967).

[CrossRef]

T.K. Gustafson, J.P. Taran, H.A. Haus, J.R. Lifsitz, and P.L. Kelley, “Self-Modulation, Self-Steepening, and Spectral Development of Light in Small-Scale Trapped Filaments,” Phys. Rev. 177, 306–313 (1969).

[CrossRef]

P. Guerreiro, S. Lee, A. Rodrigues, Y. Hu, E. Wright, S. Najafi, J. Mackenzie, and N. Peyghambarian, “Femtosecond pulse propagation near a two-photon transition in a semiconductor quantum-dot waveguide,” Opt. Lett. 21, 659–661 (1996).

[CrossRef]
[PubMed]

K. Beckwitt, F. Ilday, and F. Wise, “Frequency shifting with local nonlinearity management in nonuniformly poled quadratic nonlinear materials,” Opt. Lett. 29, 763–765 (2004).

[CrossRef]
[PubMed]

F. Ilday, K. Beckwitt, Y. Chen, H. Lim, and F. Wise, “Controllable Raman-like nonlinearities from nonstationary, cascaded quadratic processes,” J. Opt. Soc. Am. B 21, 376–383 (2004).

[CrossRef]

J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, T. Tunnermann, R. Iliew, F. Lederer, J. Broeng, G. Vienne, A. Petersson, and C. Jakobsen, “High-power air-clad large-mode-area photonic crystal fiber laser,” Opt. Express 11, 818–823 (2003).

[CrossRef]
[PubMed]

J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, T. Tunnermann, R. Iliew, F. Lederer, J. Broeng, G. Vienne, A. Petersson, and C. Jakobsen, “High-power air-clad large-mode-area photonic crystal fiber laser,” Opt. Express 11, 818–823 (2003).

[CrossRef]
[PubMed]

T.K. Gustafson, J.P. Taran, H.A. Haus, J.R. Lifsitz, and P.L. Kelley, “Self-Modulation, Self-Steepening, and Spectral Development of Light in Small-Scale Trapped Filaments,” Phys. Rev. 177, 306–313 (1969).

[CrossRef]

F. De Martini, C.H. Townes, T.K. Gustafson, and P.L. Kelley, “Self-Steepening of Light Pulses,” Phys. Rev. 164, 312–323 (1967).

[CrossRef]

Y. S. Kivshar and G. P. Agrawal, Optical solitons (Academic press, San Diego, 2003).

C. Balslev Clausen, O. Bang, and Yu. S. Kivshar, “Spatial Solitons and Induced Kerr Effects in Quasi-Phase-Matched Quadratic Media,” Phys. Rev. Lett. 78, 4749–4752 (1997).

[CrossRef]

J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, T. Tunnermann, R. Iliew, F. Lederer, J. Broeng, G. Vienne, A. Petersson, and C. Jakobsen, “High-power air-clad large-mode-area photonic crystal fiber laser,” Opt. Express 11, 818–823 (2003).

[CrossRef]
[PubMed]

P. Guerreiro, S. Lee, A. Rodrigues, Y. Hu, E. Wright, S. Najafi, J. Mackenzie, and N. Peyghambarian, “Femtosecond pulse propagation near a two-photon transition in a semiconductor quantum-dot waveguide,” Opt. Lett. 21, 659–661 (1996).

[CrossRef]
[PubMed]

F. Baronio, A. Barthélémy, S. Carrasco, V. Couderc, C. De Angelis, L. Lefort, Y. Min, P. H Pioger, V. Quiring, L. Torner, and W. Sohler, “Generation of quadratic spatially trapped beams with short pulsed light,” J. Opt. B 6, S182–S189 (2004).

[CrossRef]

P. Pioger, V. Couderc, L. Lefort, A. Barthelemy, F. Baronio, C. De Angelis, Y. Min, V. Quiring, and W. Sohler, “Spatial trapping of short pulses in Ti-indiffused LiNbO3 waveguides,” Opt. Lett. 27, 2182–2184 (2002).

[CrossRef]

D. Grischkowsky, M. Loy, and P. Liao, “Adiabatic following model for two-photon transitions: Nonlinear mixing and pulse propagation,” Phys. Rev. A 12, 2514–2533 (1975).

[CrossRef]

T.K. Gustafson, J.P. Taran, H.A. Haus, J.R. Lifsitz, and P.L. Kelley, “Self-Modulation, Self-Steepening, and Spectral Development of Light in Small-Scale Trapped Filaments,” Phys. Rev. 177, 306–313 (1969).

[CrossRef]

J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, T. Tunnermann, R. Iliew, F. Lederer, J. Broeng, G. Vienne, A. Petersson, and C. Jakobsen, “High-power air-clad large-mode-area photonic crystal fiber laser,” Opt. Express 11, 818–823 (2003).

[CrossRef]
[PubMed]

D. Anderson and M. Lisak, “Nonlinear asymmetric self-phase modulation and self-steepening of pulses in long optical waveguides,” Phys. Rev. A 27, 1393–1398 (1983).

[CrossRef]

D. Grischkowsky, M. Loy, and P. Liao, “Adiabatic following model for two-photon transitions: Nonlinear mixing and pulse propagation,” Phys. Rev. A 12, 2514–2533 (1975).

[CrossRef]

P. Guerreiro, S. Lee, A. Rodrigues, Y. Hu, E. Wright, S. Najafi, J. Mackenzie, and N. Peyghambarian, “Femtosecond pulse propagation near a two-photon transition in a semiconductor quantum-dot waveguide,” Opt. Lett. 21, 659–661 (1996).

[CrossRef]
[PubMed]

F. Baronio, A. Barthélémy, S. Carrasco, V. Couderc, C. De Angelis, L. Lefort, Y. Min, P. H Pioger, V. Quiring, L. Torner, and W. Sohler, “Generation of quadratic spatially trapped beams with short pulsed light,” J. Opt. B 6, S182–S189 (2004).

[CrossRef]

P. Pioger, V. Couderc, L. Lefort, A. Barthelemy, F. Baronio, C. De Angelis, Y. Min, V. Quiring, and W. Sohler, “Spatial trapping of short pulses in Ti-indiffused LiNbO3 waveguides,” Opt. Lett. 27, 2182–2184 (2002).

[CrossRef]

P. Guerreiro, S. Lee, A. Rodrigues, Y. Hu, E. Wright, S. Najafi, J. Mackenzie, and N. Peyghambarian, “Femtosecond pulse propagation near a two-photon transition in a semiconductor quantum-dot waveguide,” Opt. Lett. 21, 659–661 (1996).

[CrossRef]
[PubMed]

J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, T. Tunnermann, R. Iliew, F. Lederer, J. Broeng, G. Vienne, A. Petersson, and C. Jakobsen, “High-power air-clad large-mode-area photonic crystal fiber laser,” Opt. Express 11, 818–823 (2003).

[CrossRef]
[PubMed]

J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, T. Tunnermann, R. Iliew, F. Lederer, J. Broeng, G. Vienne, A. Petersson, and C. Jakobsen, “High-power air-clad large-mode-area photonic crystal fiber laser,” Opt. Express 11, 818–823 (2003).

[CrossRef]
[PubMed]

P. Guerreiro, S. Lee, A. Rodrigues, Y. Hu, E. Wright, S. Najafi, J. Mackenzie, and N. Peyghambarian, “Femtosecond pulse propagation near a two-photon transition in a semiconductor quantum-dot waveguide,” Opt. Lett. 21, 659–661 (1996).

[CrossRef]
[PubMed]

P. Pioger, V. Couderc, L. Lefort, A. Barthelemy, F. Baronio, C. De Angelis, Y. Min, V. Quiring, and W. Sohler, “Spatial trapping of short pulses in Ti-indiffused LiNbO3 waveguides,” Opt. Lett. 27, 2182–2184 (2002).

[CrossRef]

F. Baronio, A. Barthélémy, S. Carrasco, V. Couderc, C. De Angelis, L. Lefort, Y. Min, P. H Pioger, V. Quiring, L. Torner, and W. Sohler, “Generation of quadratic spatially trapped beams with short pulsed light,” J. Opt. B 6, S182–S189 (2004).

[CrossRef]

F. Baronio, A. Barthélémy, S. Carrasco, V. Couderc, C. De Angelis, L. Lefort, Y. Min, P. H Pioger, V. Quiring, L. Torner, and W. Sohler, “Generation of quadratic spatially trapped beams with short pulsed light,” J. Opt. B 6, S182–S189 (2004).

[CrossRef]

P. Pioger, V. Couderc, L. Lefort, A. Barthelemy, F. Baronio, C. De Angelis, Y. Min, V. Quiring, and W. Sohler, “Spatial trapping of short pulses in Ti-indiffused LiNbO3 waveguides,” Opt. Lett. 27, 2182–2184 (2002).

[CrossRef]

P. Guerreiro, S. Lee, A. Rodrigues, Y. Hu, E. Wright, S. Najafi, J. Mackenzie, and N. Peyghambarian, “Femtosecond pulse propagation near a two-photon transition in a semiconductor quantum-dot waveguide,” Opt. Lett. 21, 659–661 (1996).

[CrossRef]
[PubMed]

A.S. Rodrigues, M. Santagiustina, and E.M. Wright, “Nonlinear pulse propagation in the vicinity of a two-photon resonance,” Phys. Rev. A 52, 3231–3238 (1995).

[CrossRef]
[PubMed]

A.S. Rodrigues, M. Santagiustina, and E.M. Wright, “Nonlinear pulse propagation in the vicinity of a two-photon resonance,” Phys. Rev. A 52, 3231–3238 (1995).

[CrossRef]
[PubMed]

J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, T. Tunnermann, R. Iliew, F. Lederer, J. Broeng, G. Vienne, A. Petersson, and C. Jakobsen, “High-power air-clad large-mode-area photonic crystal fiber laser,” Opt. Express 11, 818–823 (2003).

[CrossRef]
[PubMed]

F. Baronio, A. Barthélémy, S. Carrasco, V. Couderc, C. De Angelis, L. Lefort, Y. Min, P. H Pioger, V. Quiring, L. Torner, and W. Sohler, “Generation of quadratic spatially trapped beams with short pulsed light,” J. Opt. B 6, S182–S189 (2004).

[CrossRef]

P. Pioger, V. Couderc, L. Lefort, A. Barthelemy, F. Baronio, C. De Angelis, Y. Min, V. Quiring, and W. Sohler, “Spatial trapping of short pulses in Ti-indiffused LiNbO3 waveguides,” Opt. Lett. 27, 2182–2184 (2002).

[CrossRef]

T.K. Gustafson, J.P. Taran, H.A. Haus, J.R. Lifsitz, and P.L. Kelley, “Self-Modulation, Self-Steepening, and Spectral Development of Light in Small-Scale Trapped Filaments,” Phys. Rev. 177, 306–313 (1969).

[CrossRef]

F. Baronio, A. Barthélémy, S. Carrasco, V. Couderc, C. De Angelis, L. Lefort, Y. Min, P. H Pioger, V. Quiring, L. Torner, and W. Sohler, “Generation of quadratic spatially trapped beams with short pulsed light,” J. Opt. B 6, S182–S189 (2004).

[CrossRef]

J.P. Torres and L. Torner, “Self-splitting of beams into spatial solitons in planar waveguides made of quadratic nonlinear media,” Opt. Quantum Electron. 29, 757–776 (1997).

[CrossRef]

C. Menyuk, R. Schiek, and L. Torner, “Solitary waves due to χ(2): χ(2) cascading,” J. Opt. Soc. Am. B 11, 2434–2443 (1994).

[CrossRef]

J.P. Torres and L. Torner, “Self-splitting of beams into spatial solitons in planar waveguides made of quadratic nonlinear media,” Opt. Quantum Electron. 29, 757–776 (1997).

[CrossRef]

F. De Martini, C.H. Townes, T.K. Gustafson, and P.L. Kelley, “Self-Steepening of Light Pulses,” Phys. Rev. 164, 312–323 (1967).

[CrossRef]

J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, T. Tunnermann, R. Iliew, F. Lederer, J. Broeng, G. Vienne, A. Petersson, and C. Jakobsen, “High-power air-clad large-mode-area photonic crystal fiber laser,” Opt. Express 11, 818–823 (2003).

[CrossRef]
[PubMed]

J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, T. Tunnermann, R. Iliew, F. Lederer, J. Broeng, G. Vienne, A. Petersson, and C. Jakobsen, “High-power air-clad large-mode-area photonic crystal fiber laser,” Opt. Express 11, 818–823 (2003).

[CrossRef]
[PubMed]

K. Beckwitt, F. Ilday, and F. Wise, “Frequency shifting with local nonlinearity management in nonuniformly poled quadratic nonlinear materials,” Opt. Lett. 29, 763–765 (2004).

[CrossRef]
[PubMed]

F. Ilday, K. Beckwitt, Y. Chen, H. Lim, and F. Wise, “Controllable Raman-like nonlinearities from nonstationary, cascaded quadratic processes,” J. Opt. Soc. Am. B 21, 376–383 (2004).

[CrossRef]

P. Guerreiro, S. Lee, A. Rodrigues, Y. Hu, E. Wright, S. Najafi, J. Mackenzie, and N. Peyghambarian, “Femtosecond pulse propagation near a two-photon transition in a semiconductor quantum-dot waveguide,” Opt. Lett. 21, 659–661 (1996).

[CrossRef]
[PubMed]

A.S. Rodrigues, M. Santagiustina, and E.M. Wright, “Nonlinear pulse propagation in the vicinity of a two-photon resonance,” Phys. Rev. A 52, 3231–3238 (1995).

[CrossRef]
[PubMed]

J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, T. Tunnermann, R. Iliew, F. Lederer, J. Broeng, G. Vienne, A. Petersson, and C. Jakobsen, “High-power air-clad large-mode-area photonic crystal fiber laser,” Opt. Express 11, 818–823 (2003).

[CrossRef]
[PubMed]

F. Baronio, A. Barthélémy, S. Carrasco, V. Couderc, C. De Angelis, L. Lefort, Y. Min, P. H Pioger, V. Quiring, L. Torner, and W. Sohler, “Generation of quadratic spatially trapped beams with short pulsed light,” J. Opt. B 6, S182–S189 (2004).

[CrossRef]

F. Ilday, K. Beckwitt, Y. Chen, H. Lim, and F. Wise, “Controllable Raman-like nonlinearities from nonstationary, cascaded quadratic processes,” J. Opt. Soc. Am. B 21, 376–383 (2004).

[CrossRef]

C. Menyuk, R. Schiek, and L. Torner, “Solitary waves due to χ(2): χ(2) cascading,” J. Opt. Soc. Am. B 11, 2434–2443 (1994).

[CrossRef]

J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, T. Tunnermann, R. Iliew, F. Lederer, J. Broeng, G. Vienne, A. Petersson, and C. Jakobsen, “High-power air-clad large-mode-area photonic crystal fiber laser,” Opt. Express 11, 818–823 (2003).

[CrossRef]
[PubMed]

P. Guerreiro, S. Lee, A. Rodrigues, Y. Hu, E. Wright, S. Najafi, J. Mackenzie, and N. Peyghambarian, “Femtosecond pulse propagation near a two-photon transition in a semiconductor quantum-dot waveguide,” Opt. Lett. 21, 659–661 (1996).

[CrossRef]
[PubMed]

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

[CrossRef]
[PubMed]

M. Marangoni, C. Manzoni, R. Ramponi, G. Cerullo, F. Baronio, C. De Angelis, and K. Kitamura, “Groupvelocity control by quadratic nonlinear interactions,” Opt. Lett. 31, 534–536 (2006).

[CrossRef]
[PubMed]

K. Beckwitt, F. Ilday, and F. Wise, “Frequency shifting with local nonlinearity management in nonuniformly poled quadratic nonlinear materials,” Opt. Lett. 29, 763–765 (2004).

[CrossRef]
[PubMed]

P. Pioger, V. Couderc, L. Lefort, A. Barthelemy, F. Baronio, C. De Angelis, Y. Min, V. Quiring, and W. Sohler, “Spatial trapping of short pulses in Ti-indiffused LiNbO3 waveguides,” Opt. Lett. 27, 2182–2184 (2002).

[CrossRef]

J.P. Torres and L. Torner, “Self-splitting of beams into spatial solitons in planar waveguides made of quadratic nonlinear media,” Opt. Quantum Electron. 29, 757–776 (1997).

[CrossRef]

F. De Martini, C.H. Townes, T.K. Gustafson, and P.L. Kelley, “Self-Steepening of Light Pulses,” Phys. Rev. 164, 312–323 (1967).

[CrossRef]

T.K. Gustafson, J.P. Taran, H.A. Haus, J.R. Lifsitz, and P.L. Kelley, “Self-Modulation, Self-Steepening, and Spectral Development of Light in Small-Scale Trapped Filaments,” Phys. Rev. 177, 306–313 (1969).

[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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[CrossRef]

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In literature, the fourth term in Eq. (2) is usually referred as the self-steepening term (see for example Ref. [4–9]).